Modeling Phosphorus in the Environment

Modeling Phosphorus in the Environment Edited by David E. Radcliffe Miguel L. Cabrera © 2007 by Taylor & Francis Grou...

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Modeling Phosphorus in the Environment

Edited by

David E. Radcliffe Miguel L. Cabrera

© 2007 by Taylor & Francis Group, LLC

Cover design: A. Radcliffe, New York City.

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8493-3777-1 (Hardcover) International Standard Book Number-13: 978-0-8493-3777-2 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Modeling phosphorus in the environment / editors, David E. Radcliffe, Miguel L. Cabrera. p. cm. ISBN 0-8493-3777-1 (alk. paper) 1. Phosphorus--Environmental aspects--Mathematical models. 2. Phosphorus cycle (Biogeochemistry)--Mathematical models. I. Radcliffe, David Elliott, 1948- II. Cabrera, Miguel L. III. Title. TD427.P56M63 2006 577’.14--dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com


2006049391

Preface Models of phosphorus (P) transport in the environment are finding many uses today from research on mechanisms to regulatory applications such as the Total Maximum Daily Load and Source Water Assessment and Protection programs and even in the courtroom. Many of the basic approaches to modeling P were developed in the 1980s. Despite other advancements in modeling, such as graphic user interfaces and the use of geographic information system layers and databases for developing input files, the basic approaches to modeling P have changed very little. Our understanding of P processes has advanced, and these new ideas need to be incorporated into the current models. The purpose of this book is to describe the basic approaches to modeling P, how the current models implement these approaches, and ways to improve the current models. In the first section, an introductory chapter sets the background, and it is followed by chapters on the general approaches to modeling runoff and erosion (Chapter 2), P in runoff (Chapter 3), leaching of P (Chapter 4), and stream processes that affect P (Chapter 5). This section ends with a chapter on the important issue of model uncertainty (Chapter 6). The second section describes six state-of-the-science watershed-scale P transport models. We start with two of the most commonly used dynamic semidistributed models, the Soil Water Assessment Tool (Chapter 7) and the Hydrologic Simulation Program-Fortran (Chapter 8). Next are two fully distributed models of intermediate complexity, the Annualized Agricultural Nonpoint Source Pollution (Chapter 9) and the Nonpoint Source Pollution Model for Water, Sediment, and Phosphorus Losses (Chapter 10). The section ends with two lumped models, the Watershed Ecosystem Nutrient Dynamic-Phosphorus (Chapter 11) and the Generalized Watershed Loading Functions model (Chapter 12). The third section discusses phosphorus indices (PIs), which represent one end of the modeling spectrum in that they are field-scale, long-term estimates of the risk of P loss, or in some cases the actual P loss, from the edge of fields. Chapter 13 is a comprehensive look at the PIs developed in each state. Chapter 14 illustrates some of the problems encountered in incorporating PIs into farm-scale manure management software. The incorporation of best management practices into P transport models is a priority, and Section 3 includes a chapter on this topic (Chapter 15). Monitoring data from fields and streams are critical in calibrating and assessing the accuracy of watershed-scale models, and Section 3 concludes with a chapter on data for modeling (Chapter 16). The final section consists of a chapter on suggestions to improve modeling of P (Chapter 17). The idea for this book originated in the Modeling Workgroup of the Organization to Minimize Phosphorus Losses from Agriculture (SERA-17) (http://www.sera17. ext.vt.edu/). Many of the chapter authors are members of SERA-17, but the project has expanded beyond this group and includes a number of outside authors.


Editors David E. Radcliffe has been with the University of Georgia, Athens, since 1983, where he is a professor in the crop and soil sciences department. He teaches an undergraduate and two advanced graduate courses in soil physics and team teaches an introductory course in water resources. He received a B.S. in naval science from the U.S. Naval Academy and an M.S. and Ph.D. in soil physics from the University of Kentucky, Lexington. His research is focused on watershed-scale modeling of phosphorus and sediment transport and modeling of on-site wastewater systems. Dr. Radcliffe has published more than 70 journal articles and book chapters and has been an associate editor and technical editor for the Soil Science Society of America (SSSA) Journal. He has been chair of the Soil Physics Division of the SSSA and is currently a board member and fellow of the SSSA. Miguel L. Cabrera joined the University of Georgia, Athens, in 1990 and is currently a professor in the crop and soil sciences department. He teaches an undergraduate course in soil fertility, a graduate seminar course, and a graduate course in nutrient cycling models. He received a B.S. in agronomy (Ing. Agr.) from Facultad de Agronomia, Universidad de la Republica, in Uruguay, and an M.S. and Ph.D. in agronomy from Kansas State University, Manhattan. His research is focused on nitrogen and phosphorus cycling in soils fertilized with animal manures. Dr. Cabrera has published more than 100 journal articles and book chapters, has served as associate editor for Agronomy Journal, and is currently on the editorial board of Nutrient Cycling in Agroecosystems. He is a fellow of the ASA and SSSA.


Acknowledgments We would like to thank John Sulzycki and Jill Jurgensen with the Taylor & Francis Group for their support and patience. We thank the authors for their hard work in writing and reviewing chapters. Finally, we thank the following outside chapter reviewers: Ms. Carolyn Adams, East National Technology Support Center, USDA NRCS Dr. Wole Akinremi, University of Manitoba Dr. Bruce Beck, University of Georgia Dr. Douglas Beegle, Pennsylvania State University Dr. W. J. Chardon, University of Wageningen Dr. Thomas Daniel, University of Arkansas Dr. Paul Delaune, University of Arkansas Dr. Barnali Dixon, University of South Florida Dr. William Effland, USDA NRCS, Washington, D.C. Dr. Thomas Fisher, University of Maryland Dr. Don Flaten, University of Manitoba Ms. Jennifer Gilbert, University of Delaware Dr. James Hamlett, Pennsylvania State University Dr. Philip Haygarth, University of Sheffield Dr. William Jokela, USDA ARS, Marshfield, WI Dr. Peter Kinnel, Canberra, Australia Dr. Antonio Lo Porto, Water Research Institute, Bari, Italy Dr. John Lory, University of Missouri Dr. Rory Maguire, North Carolina State University Dr. Kyle Mankin, Kansas State University Dr. Anne McFarland, Tarleton State University Mr. Don Meals, Ice.Nine Environmental Consulting, Burlington, VT Dr. Nicolaos Nikolaidis, Technical University of Crete Dr. L. Mark Risse, University of Georgia Mr. Lawrence Schinkel, Alberta Agriculture Dr. J. Thomas Sims, University of Delaware Dr. Puneet Srivastava, Auburn University Dr. Allen Torbert, National Soil Dynamics Laboratory, USDA-ARS Dr. Peter Vadas, Pasture Systems and Watershed Management Research Unit, USDA-ARS Dr. Forbes Walker, University of Tennessee


Contributors J.G. Arnold Grassland, Soil, and Water Research Lab USDA-ARS Temple, Texas Stefanie G. Aschmann USDA NRCS Portland, Oregon Keith Beven Environmental Science/Lancaster Environment Centre Lancaster University Lancaster, UK Ronald L. Bingner National Sedimentation Laboratory USDA-ARS Oxford, Mississippi Faycal Bouraoui European Commission–DG Joint Research Centre Institute for Environment and Sustainability Ispra, Italy Miguel L. Cabrera Crop and Soil Sciences Department University of Georgia Athens, Georgia E. Alan Cassell The Rubenstein School of Environment and Natural Resources University of Vermont Burlington, Vermont


Indrajeet Chaubey Department of Biological and Agricultural Engineering University of Arkansas Fayetteville, Arkansas Theo A. Dillaha Department of Biological Systems Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Bradley Eisenhauer Department of Agronomy Purdue University West Lafayette, Indiana Margaret W. Gitau Biological and Agricultural Engineering University of Arkansas Fayetteville, Arkansas C.H. Green Grassland, Soil, and Water Research Laboratory USDA-ARS Temple, Texas Brian E. Haggard USDA-ARS Biological and Agricultural Engineering Department Crop, Soil, and Environmental Sciences Department University of Arkansas Fayetteville, Arkansas Daren Harmel USDA-ARS Grassland, Soil and Water Research Laboratory Temple, Texas

Philip Hess Department of Agronomy Purdue University West Lafayette, Indiana Brad Joern Department of Agronomy Purdue University West Lafayette, Indiana Robert L. Kort USDA NRCS Colchester, Vermont Zhulu Lin Crop and Soil Sciences Department University of Georgia Athens, Georgia

David E. Radcliffe Crop and Soil Sciences Department University of Georgia Athens, Georgia Elliot M. Schneiderman New York City Department of Environmental Protection Kingston, New York Andrew N. Sharpley Pasture Systems and Watershed Management Research Unit USDA-ARS University Park, Pennsylvania

Malcolm McGechan Environment Division Scottish Agricultural College Bush Estate Penicuik, UK

R. Srinivasan Department of Biological and Agricultural Engineering Texas A&M University College Station, Texas

K.W. Migliaccio Agricultural and Biological Engineering Department University of Florida Tropical Research and Education Center Homestead, Florida

Tamie L. Veith Pasture Systems and Watershed Management Research Unit USDA-ARS University Park, Pennsylvania

Nathan O. Nelson Department of Agronomy Throckmorton Plant Sciences Center Kansas State University Manhattan, Kansas

Jennifer Weld Department of Crop and Soil Sciences The Pennsylvania State University University Park, Pennsylvania

Trevor Page Environmental Science Lancaster Environment Centre Lancaster University Lancaster, UK

Mary Leigh Wolfe Biological Systems Engineering Department Virginia Polytechnic Institute and State University Blacksburg, Virginia

John E. Parsons (Deceased) Department of Biological and Agricultural Engineering North Carolina State University Raleigh, North Carolina


Yongping Yuan National Sedimentation Laboratory USDA-ARS Oxford, Mississippi

Table of Contents Section I Basic Approaches .....................................................................................................1 Chapter 1

Modeling Phosphorus Movement from Agriculture to Surface Waters .................................................................................3

Andrew N. Sharpley Chapter 2

Modeling Runoff and Erosion in Phosphorus Models......................21

Mary Leigh Wolfe Chapter 3

Modeling Phosphorus in Runoff: Basic Approaches ........................65

Miguel L. Cabrera Chapter 4

Basic Approaches to Modeling Phosphorus Leaching......................81

Nathan O. Nelson and John E. Parsons Chapter 5

Phosphorus Transport in Streams: Processes and Modeling Considerations ..................................................................................105

Brian E. Haggard and Andrew N. Sharpley Chapter 6

Uncertainty Estimation in Phosphorus Models ...............................131

Keith Beven, Trevor Page, and Malcolm McGechan Section II Models ...................................................................................................................161 Chapter 7

Phosphorus Modeling in Soil and Water Assessment Tool (SWAT) Model .................................................................................163

Indrajeet Chaubey, K.W. Migliaccio, C.H. Green, J.G. Arnold, and R. Srinivasan Chapter 8

Modeling Phosphorus with Hydrologic Simulation Program-Fortran ...............................................................................189

David E. Radcliffe and Zhulu Lin


Chapter 9

Phosphorus Modeling in the Annualized Agricultural Nonpoint Source Pollution (AnnAGNPS) Model ...........................215

Yongping Yuan, Ronald L. Bingner, and Indrajeet Chaubey Chapter 10 ANSWERS-2000: A Nonpoint Source Pollution Model for Water, Sediment, and Phosphorus Losses .................................241 Faycal Bouraoui and Theo A. Dillaha Chapter 11 Watershed Ecosystem Nutrient Dynamics–Phosphorus (WEND-P Models) ..........................................................................261 Robert L. Kort, E. Alan Cassell, and Stefanie G. Aschmann Chapter 12 Modeling Phosphorus with the Generalized Watershed Loading Functions (GWLF) Model...............................277 Elliot M. Schneiderman Section III Phosphorus Indices, Best Management Practices, and Calibration Data...........................................................................................299 Chapter 13 Phosphorus Indices ..........................................................................301 Jennifer Weld and Andrew N. Sharpley Chapter 14 Challenges to Using and Implementing Phosphorus Indices in Nutrient Management Planning: an MMP Perspective ..............333 Philip Hess, Bradley Eisenhauer, and Brad Joern Chapter 15 Quantifying the Effects of Phosphorus Control Best Management Practices .....................................................................351 Margaret W. Gitau and Tamie L. Veith Chapter 16 Small Watershed Data Collection to Support Phosphorus Modeling ......................................................................383 Daren Harmel and Brian E. Haggard Section IV Modeling in the Future........................................................................................403 Chapter 17 Suggestions to Improve Modeling of Phosphorus ..........................405 David E. Radcliffe and Miguel L. Cabrera


Section I Basic Approaches


1

Modeling Phosphorus Movement from Agriculture to Surface Waters Andrew N. Sharpley U.S. Department of Agriculture-Agricultural Research Service, University Park, PA

CONTENTS 1.1 Introduction.......................................................................................................3 1.2 Types of Models ...............................................................................................4 1.2.1 Process–Based Models..........................................................................5 1.2.2 Export Coefficient Models ....................................................................5 1.2.3 Statistical or Empirical Models ............................................................6 1.3 How Models Simulate P Transport ..................................................................6 1.3.1 Dissolved P............................................................................................6 1.3.2 Particulate P...........................................................................................8 1.4 Fertilizer and Manure Management ...............................................................10 1.5 Spatial Data Requirements for Modeling.......................................................11 1.6 Defining Future Best Management Practices.................................................12 1.7 How Models Simulate Fluvial Processes and Impact of P in Surface Waters....................................................................................12 1.7.1 Fluvial Processes .................................................................................12 1.7.2 Surface Water Impacts ........................................................................14 1.8 Summary .........................................................................................................14 References................................................................................................................15

1.1 INTRODUCTION Phosphorus (P), an essential nutrient for crop and animal production, can accelerate freshwater eutrophication, which is the most ubiquitous water quality impairment in the U.S., with agriculture a major contributor of P (Sharpley 2000; U.S. Geological Survey 1999). Environmental concerns from harmful algal bloom outbreaks

3


4


(Burkholder and Glasgow 1997) and regulatory pressure to reduce P loadings to surface waters via implementation of Total Maximum Daily Loads (TMDLs) (U.S. Environmental Protection Agency 2000) have increased the urgency for information on the impacts of agricultural management, specifically conservation practices and best management practices (BMPs) on P loss. Because of the time and expense involved in assessing P loss, models are often a more efficient and feasible means of evaluating management alternatives. In their most comprehensive form, models can integrate information over a watershed scale to identify BMPs and critical source areas where BMPs are most likely to affect watershed-scale P losses. A common limitation to model application is the lack of detailed parameterization data on soil physical, chemical, and biological properties as well as on crop and tillage details. Thus, existing databases are increasingly being linked to nonpoint source models, often via geographical information systems (GIS). Generally, key input data for nutrient transport models involve land use, soil texture, topography, and management practices. Once these data are in digital form, GIS techniques can be used to combine them with experimental or model results to extrapolate other properties needed for model application. This introduction chapter previews the general principles of how models represent soil P release and transport, effects of mineral fertilizer and manure management on P loss, spatial resolution, and channel processes that translate edge-of-field losses to water body inputs. Future modeling efforts needed to address these issues are presented.

1.2 TYPES OF MODELS Models that simulate the runoff and water quality from watersheds can be categorized in several ways, but for purposes of this brief review they are segregated into three groups: 1. Process-based models: Models that explicitly simulate watershed processes, albeit usually conceptually. These models typically involve the numerical solution of a set of governing differential and algebraic equations that are a mathematical representation of processes such as rainfall runoff; infiltration leaching; P application method, rate, and timing; land management; and fate and chemical transformation of added P in soil. 2. Export coefficient models: Models that rely on land-use categorization — sometimes through a linkage to a GIS evaluation — coupled with export coefficients or event mean concentrations (EMCs), loosely categorized as spreadsheet approaches, although highly sophisticated in many cases. These models rarely, if ever, involve solution of a differential equation and almost always rely on simple, empirical formulations, such as the use of a runoff coefficient for generation of runoff from rainfall. 3. Statistical or empirical models: Models that involve regression or other techniques, which relate water-quality measures to various characteristics of the watershed. These models range from purely heuristic regression equations (e.g., Driver and Tasker 1990) to relatively sophisticated


Modeling Phosphorus Movement from Agriculture to Surface Waters

5

derived-distribution approaches for prediction of the frequency distribution of loadings and concentrations (e.g., DiToro and Small 1984; Driscoll et al. 1989). All of the model types have their drawbacks related to availability of required data, scaling up from pedon input parameters, for example, to a watershed scale, and quantifying system functionality. For more detailed information on the approaches used in models described in the sections following and in other models, reviews are given as separate chapters in this publication.

1.2.1 PROCESS–BASED MODELS The Agricultural Nonpoint Source (AGNPS) Pollution model (Young et al. 1989, 1995) was originally developed to provide estimates of runoff water quality from watersheds of up to 20,000 hectares and to quantify the effects of BMPs targeted to specific areas. To make model output more meaningful to decision makers, such as conservationists and farmers, AGNPS, which ran on a storm or flow event basis, was recently superseded by an annualized version, Annualized AGNPS (AnnAGNPS) (Bingner et al. 2001; Croshley and Theurer 1998). The model operates on a cell basis that makes it possible to analyze spatially discrete management units (fields) within a watershed, thereby enabling identification of individual fields that may serve as critical source areas of nutrient export. AnnAGNPS is described in Chapter 9 of this book. The Soil and Water Assessment Tool (SWAT) was developed to assess the impact of land management on water quality in watersheds and large river basins (Arnold et al. 1998). The model runs on a continuous time step and is currently being utilized in a variety of large-scale studies to estimate the off-site impacts of climate and management on water use and nonpoint source loadings. SWAT is described in Chapter 7 of this book. Other process-based nutrient transport models include, but are not limited to Areal Nonpoint Source Watershed Environment Response Simulation 2000 (ANSWERS-2000) (Beasley et al. 1985; Bouraoui and Dillaha 1996), the Guelph Model for Evaluating the Effects of Agricultural Management Systems on Erosion and Sedimentation (GAMES) (Cook et al.. 1985), Hydrologic Simulation ProgramFortran (HSPF) (Johanson et al. 1984), Agricultural Runoff Model (ARM) (Donigian et al. 1977), Erosion Productivity Impact Calculator (EPIC) (Sharpley and Williams 1990), Groundwater Loading Effects of Agricultural Management Systems (GLEAMS) (Leonard et al. 1987), Watershed Ecosystem Nutrient DynamicsPhosphorus (WEND-P) (Cassell et al. 1998), and CENTURY (Parton et al. 1993). HSPF, ANSWERS-2000, and WEND-P are described in Chapters 8, 10, and 11, respectively.

1.2.2 EXPORT COEFFICIENT MODELS Export coefficient models have also been widely used to predict P loading of receiving water bodies (Beaulac and Reckhow 1982; Hanrahan et al. 2001;


6


Johnes et al. 1996). Export coefficients define P loss from a particular source or land use in a watershed and are usually derived from actual field measured losses of P or from EMC values, if runoff volumes are known (Johnes 1996; Johnes and Heathwaite 1997). Both export coefficients and EMCs fit easily into spreadsheet formats for watershed loading estimates. An advantage of EMCs is that they may be coupled with any hydrologic simulation model to produce loads. Export coefficient models calculate watershed export of P as the sum of individual loads from each source in the watershed. This approach accounts for the complexity of land-use systems, spatial distribution of data from various sources (point and nonpoint), and permits scaling up from plot to watersheds. As export coefficients are empirical, these types of models are as accurate as input data, as are process-based models (Hanrahan et al. 2001). Coefficients derived from short-term monitoring of small drainage areas, however, can contribute to predictive variability (Lathrop et al. 1998). The Generalized Watersheds Loading Functions (GWLF) model (Haith and Shoemaker, 1987) is an example of an export coefficient model and is described in Chapter 12.

1.2.3 STATISTICAL

OR

EMPIRICAL MODELS

Statistical models are empirical. Although they are derived from observations, the relationship described must have a basis in our underlying understanding of processes if we are to have faith in the predictive capabilities of the model (National Research Council 2000). Furthermore, extrapolation from empirical data is known to be fraught with danger. For example, scaling problems can occur when one extrapolates the results of scaled experiments to full-sized natural systems. One must, of course, always remain cognizant of the fact that system function may be scale dependent. Thus, these models are most judiciously used in the range of observational situations used to derive the model. Statistical or empirical models are most useful when they are based on first principles. The ability to describe system functions in terms of mathematical equations often gives the impression that the underlying principles are fully understood, as might be the situation in basic physics. Unfortunately, empirical coefficients introduced into these equations often hide the degree of uncertainty concerning these principles. This publication does not include reviews of any statistical models per se, but many P indices include statistical relationships and might be considered a type of statistical model. P indices are described in Chapter 13.

1.3 HOW MODELS SIMULATE P TRANSPORT 1.3.1 DISSOLVED P Most nonpoint source models simulate dissolved P transport in overland flow as a function of the extractability of P in the surface 5 cm of soil [e.g., Chemicals, Runoff and Erosion from Agricultural Management Systems (CREAMS), AGNPS]. This can be represented by Dissolved P = Extraction Coefficient × Available soil P × Overland flow volume (1.1)



7

2000 a. Overland flow 1500

Dissolved P (µg L-1)

1000

500

y = 1.98x + 79 R2 = 0.78

0 1000 b. Subsurface flow from lysimeters 750

500

250

0 0

y = 0.93x + 60 R2 = 0.79 200

400

600

800

Mehlich-3 extractable soil P (mg kg-1)

FIGURE 1.1 Relationship between the concentration of dissolved P in overland (a) and subsurface flow (b) from 30-cm-deep lysimeters and the Mehlich-3 extractable soil P concentration of surface soil (0 to 5 cm) from a central Pennsylvania watershed. (Adapted from R.W. McDowell and A.N. Sharpley, J. Environ. Qual. 30, 508–520, 2001; and A.N. Sharpley, P.J.A. Kleinman, R.J. Wright, T.C. Daniel, B. Joern, R. Parry, and T. Sobecki, in International Conference on Agricultural Effects in Ground and Surface Waters, J. Steenvooreden (Ed.), Wageningen, The Netherlands, International Association of Hydrologic Sciences.)

where dissolved P is orthophosphate loss in overland flow (kg ha−1), available soil P is the amount of P in a unit depth of surface soil — usually 5 cm — (Sharpley 1985b) as estimated by recommended soil test P methods (STP) (kg ha−1 5 cm−1), and extraction coefficient is the fraction of STP that can be released to overland flow for a given flow event volume (cm). Extraction coefficients can be determined as the slope of the linear regression of STP and overland flow dissolved P (Figure 1.1a). A similar relationship holds for subsurface flow P and surface STP, although the slope of the relationship (0.93) is almost half that for overland flow (slope of 1.98) (Figure 1.1b). The dependence of dissolved P transport in subsurface flow as well as overland flow suggests the importance of preferential flow pathways, such as earthworm burrows and old root channels, in the downward movement of P through the soil profile (Kleinman et al. 2003; McDowell and Sharpley 2001a; Sims et al. 1998).


8


Extraction coefficient

20

15

Native grass / pasture No till Reduced till Conventional till

10

0.30

y = 1.25x R2 = 0.90

5

0 0.001

0.01

0.1

1 -1

10

-1

Erosion (tonnes ha yr ) Decreasing soil cover FIGURE 1.2 Extraction coefficient — the slope of the relationship between soil test P and dissolved P in overland flow — as a function of erosion to represent soil vegetative cover for sites in Arkansas, Oklahoma, New York, and Pennsylvania. (Data adapted from D.H. Pote, T.C. Daniel, D.J. Nichols, A.N. Sharpley, P.A. Moore, Jr., D.M. Miller, and D.R. Edwards, J. Environ. Qual. 28, 170–175, 1999; McDowell and A.N. Sharpley, J. Environ. Qual. 30, 508–520, 2001; and A.N. Sharpley and S.J. Smith, Soil Tillage Res. 30, 33–38, 1994.)

Most models use a constant extraction coefficient value, assuming that STP extractability is similar among soils. A re-analysis of data published by McDowell and Sharpley (2001a), Pote et al. (1999), and Sharpley and Smith (1994) relating STP and overland flow dissolved P revealed a range of extraction coefficient values (Figure 1.2). Extraction coefficients were much greater for cropped (8 to 17) than grassed watersheds (1 to 4). Using erosion as a surrogate for land cover, extraction coefficients increased with greater erosion or decreased soil cover (Figure 1.2). Although erosion is influenced by other factors such as slope and soil structure, the sites used in this example were similar in slope (~4%). A larger soil P extraction coefficient represents a greater release of P as overland flow dissolved P per unit STP increases. This can be attributed to a lower degree of interaction between surface soil and overland flow with a protective grass cover than for a cropped situation, where the soil is more exposed to overland flow. Other factors that influence P release among soils are the dominant forms of P in soil, texture, aggregate diffusion, degree of interaction between soil and water, organic matter content, vegetative soil cover, and P sorption capacities.

1.3.2 PARTICULATE P As the sources of particulate P in overland flow and stream flow include eroding surface soil, stream banks, and channel beds, processes determining erosion also



9

control particulate P transport. In general, eroded particulate material is enriched with P compared to source surface soil, due to the preferential transport of finer (i.e., clay size), more sorptive soil and organic particles of greater P content than coarser inorganic particles (i.e., sand size). Sharpley (1985a) found that the plant available P content of sediment in overland flow was on average three times greater — or more enriched — than that of source soil and 1.5 times greater for total, inorganic, and organic P. The degree of P enrichment is expressed as a P enrichment ratio (PER), that is, the P concentration of sediment discharged divided by that of source soil. In assembling enrichment ratio information for the CREAMS model, Menzel (1980) concluded that for particulate P, a logarithmic relationship as in Equation 1.2 seemed to hold for a wide range of soil vegetative conditions. Ln (PER) = 2.00 – 0.16 Ln (Sediment discharge)

(1.2)

where sediment discharge is in kg ha−1. Most nonpoint source models adopted this approach to predicting particulate P transport in overland flow. This relationship is based on the well-documented increase in particulate P loss with increasing erosion (Figure 1.3). Based on the total P concentrations of source soils for each of the watersheds represented in Figure 1.3, PER decreases with an increase in erosion. As erosion increases, there is less particle-size sorting by overland flow, relatively less clay-size particles are transported, and P enrichment thus decreases.

7.5

10 8 6

5.0 4

2.5

0 0.001

2

0.01

0.1

1

10

P enrichment ratio

Particulate P (kg ha-1)

Particulate P P enrichment ratio

1 100

Erosion (tonnes ha-1)

FIGURE 1.3 Particulate P loss and enrichment ratio of eroded sediment as a function of erosion in overland flow from watersheds in El Reno, Oklahoma. (Adapted from A.N. Sharpley, S.J. Smith, J.R. Williams, O.R. Jones, and G.A. Coleman, J. Environ. Qual. 20, 239–244, 1991; and S.J. Smith, A.N. Sharpley, J.W. Naney, W.A. Berg, and O.R. Jones, J. Environ. Qual. 20, 244–249, 1991.)


10


Once an appropriate PER is obtained from sediment discharge, particulate P loss can be calculated as Particulate P = Total soil P × Sediment concentration × PER × Overland flow volume

(1.3)

where particulate P is the loss in overland flow (kg ha−1), total soil P is the amount in a unit depth of surface soil (usually kg ha−1 5 cm−1), sediment concentration is g sediment L−1 overland flow, and PER is calculated from Equation 1.2, for a given flow event volume (cm).

1.4 FERTILIZER AND MANURE MANAGEMENT Fertilizer and manure management, as it affects P availability to overland flow over the near term, can profoundly affect prediction of P transport in overland flow. Although soil P represents a source of P enrichment in overland flow, the application of fertilizer and manure to soil — including type, method, timing, and rate of P application — can temporarily overwhelm relationships derived between STP and P in overland flow (Sharpley and Tunney 2000). As such, accounting for fertilizer and manure management in P models is essential to their accuracy under certain conditions. However, most models do not directly address the effect of applied P, either as fertilizer or manure, on P transport in overland flow. Rather, added P is incorporated into the soil P pool, and the extraction coefficient is adjusted. Thus, P transport in overland flow as affected by the amount, type, method, and time after applying P is, in general, poorly represented and predicted. Mineral fertilizer and manure represent concentrated sources of soluble P that can greatly increase dissolved P losses in overland flow. Consequently, the concentration of soluble P in these sources may provide effective predictions depending on the solubility of the P source, method of application, rate of application, and timing of application relative to the overland flow event (Figure 1.4) (Kleinman et al. 2002). Surface application of manure and mineral fertilizer concentrates P at the extreme soil surface where it is vulnerable to removal by overland flow (Eghball and Gilley 1999; McDowell and Sharpley 2001b; Sharpley et al. 1984). Although injection, knifing, and immediate incorporation of manure and fertilizer may decrease P losses, cultivation may increase site vulnerability to particulate P loss due to greater erosion potential (Andraski et al. 1985; Romkens et al. 1973). Modifying the effect of P source and application method on P concentrations in overland flow is the timing of application relative to when an overland flow event occurs (Sharpley 1997; Westerman and Overcash 1980). Immediately following application of a P source, the potential for P loss peaks and then declines over time, as applied P increasingly interacts with the soil and is converted from soluble to increasingly recalcitrant forms (Edwards and Daniel 1993). As a result, fertilizer and manure management effects on overland flow P are predictable.


Dissolved P in overland flow (µg L-1)


11

6000 Poultry manure Swine slurry

4000 Dairy compost

Poultry litter

Dairy manure

2000

Poultry compost 0 0

2

4

6

8 -1

Water extractable manure P (g kg )

FIGURE 1.4 Relationship between water extractable manure P and the dissolved P in overland flow one week after manure or mineral fertilizer was broadcast (100 kg total P ha−1) on a Hagerstown silt loam soil (7 cm hr−1 rainfall for 30 min). (Adapted from P.J.A. Kleinman, A.N. Sharpley, B.G. Moyer, and G.F. Elwinger, J. Environ. Qual. 31, 2026–2033, 2002.)

1.5 SPATIAL DATA REQUIREMENTS FOR MODELING Models that assess nonpoint sources of P loss from agricultural lands rely on spatial data as input. Land use, soil properties, and topographic data that include stream locations and watershed boundaries are commonly required inputs. However, with an expansion in the geographical scale at which watershed processes are to be modeled, there is a great increase in the size of associated spatial databases. Data and parameter requirements also increase rapidly as models become more mechanistic to better represent physical and chemical processes and spatial interactions involved in P loss. The complexity of managing these large databases in support of a watershed model can limit the degree of spatial resolution of existing models. Spatial parameters are frequently lumped so that units having similar soil, land use, and topographic characteristics respond the same to driving variables, such as those used to simulate runoff generation. However, spatially lumped parameters can pose a problem when responses from lumped units cannot distinguish between relative spatial locations of individual units, which can be critical in determining P export from a watershed to a water body. To overcome the spatial data limitations thus far identified, a nested modeling approach is recommended. Field and farm scale models that incorporate the knowledge of P source and transport processes involved in P loss can be supported with highly detailed spatial databases that are already available in some areas or could be easily developed in others. Results and generalizations from these models could be aggregated to represent sub-basins in a simpler, less mechanistic model that requires lower spatial resolution. Similarly, results from sub-basin models could be further aggregated to represent whole watersheds of several hundreds of square kilometers in size. Beyond that scale and with enough knowledge of processes operating in individual subwatersheds,


12


the principles of mapping could be invoked to derive generalizations about large watersheds that span multiple physiographic regions, such as the Chesapeake Bay Watershed and Mississippi River Basin. Map units of the Major Land Resource Areas (MLRAs) of the U.S. are defined on the basis of topography, soils, and land use and, therefore, are ideally suited for extrapolating detailed studies of whole watersheds to the broader area of the MLRA map unit.

1.6 DEFINING FUTURE BEST MANAGEMENT PRACTICES The implementation of P control measures has often been carried out with insufficient knowledge as to the suitability of these practices for P control. A large number of BMPs exist; their suitability likely varies depending on the particular situation. Given that BMP impacts are largely site specific (Baker and Johnson 1983; Deere and Company 1995; U.S. Environmental Protection Agency 1993), defining future BMPs for P control depends a great deal on being able to establish the effectiveness of these BMPs under the variety of field conditions that are constantly encountered. Several factors complicate BMP assessment in a field situation: site variability, lack of controlled replication, and length of study time needed. In turning to models, we try to overcome some of these complications. Though models greatly simplify the natural system, they also provide a means of carrying out complex BMP evaluations. Nonetheless, the large amounts of data that have accumulated over the years can be extremely useful in working on a modeling approach to BMP evaluation (see Chapter 15 on BMPs in this book; Gitau et al. 2001). An initial step in modeling BMP-induced reduction in P loss is the characterization of the BMPs of concern with regard to their mechanisms of operation, such as source (i.e., soil P; type, rate, and form of P applied) and transport (i.e., runoff, erosion) factors controlling P loss. This characterization would enable identification of source and transport mechanisms impacted by particular BMPs and, thus, the determination of model changes that would be necessary to fully represent the BMPs (Gitau et al. 2001).

1.7 HOW MODELS SIMULATE FLUVIAL PROCESSES AND IMPACT OF P IN SURFACE WATERS In-channel processes modify the potential for agriculture to impact a downstream freshwater body. As surface water impacts drive activities such as TMDL development, understanding the role of in-channel or fluvial processes on P transport and the impact of transported P on downstream water bodies is necessary to link upstream changes in agricultural management with downstream water quality impacts.

1.7.1 FLUVIAL PROCESSES If simulating the influence of landscape processes on P transport seems complex, simulating fluvial processes that influence the form and amount of edge-of-field P



13

entering downstream water bodies is even more challenging. Basically, fluvial transport involves a complex and dynamic interaction of hydrologic, physical, chemical, and biological processes. As stream flow varies from base to storm flow, a greater cross-sectional area of channel sediments interacts with water, the course of some streams may even meander, and time of interaction between water and sediment or biotic material decreases. Fluvial erosion of gullies, ditches, and stream banks generally contributes subsoil material, which usually has a low P content and high P sorption capacity, which can function as a sink for P within the fluvial system (Baldwin et al. 2002; Sharpley et al. 1996). Fluvial P chemistry is dominated by the uptake and release of P by sediment, the direct and extent of which is a function of streamwater-dissolved P, sediment P (i.e., equilibrium P concentration), stream water pH, P released from dead biota, hydrolysis of organic P species, and changes in sediment crystallinity and oxidation and reduction. Biological uptake of P can decrease dissolved P, whereas bacteria can mediate a sizeable proportion — 30 to 40% — of sedimentary P uptake and release (Khoshmanesh et al. 1999; McDowell and Sharpley 2003). Biologically controlled P release during the decomposition of organic matter in sediments can be an important source of dissolved P at times of high temperature and low flow in areas with organic-rich sediments, such as streams draining forested areas. The effects of all these processes on fluvial P transport varies greatly, reflecting seasonal cycles, management of streamside land, sediment P forms, size of flow event, and streambed geology. Much information can be found on the influence of fluvial sediments on streamwater P. For example, McDowell et al. (2002) examined the processes controlling sediment P release to the Winooski River, Vermont, the largest tributary to Lake Champlain. Iron-oxide strip P (algal-available P) of the river sediments adjacent to agricultural land (3.6 mg kg−1) was significantly greater (p < .05) than that of sediments adjacent to forested land (2.4 mg kg−1). Notably, impoundment (731 mg kg−1) and reservoir sediments (803 mg kg−1) had greater total P concentrations than did river sediments (462 mg kg−1). This was attributed to more fines (< 63 µm) in impoundments and reservoirs (64%) than in river sediments (33%). Consequently, impoundment and reservoir sediments had lower abilities to release P to solution in the short term, thereby acting as P sinks. The results of this research clearly demonstrate that fluvial hydraulics has a strong influence on the properties of sediment within river systems. The input and delivery of fine sediments enriched with P was influenced by adjacent land use. The fluvial sediment, particularly at the outflow of the river into Lake Champlain for example, represents a store of P, which has a long-term potential to release a large amount of P to overlying waters. In the short term, however, river flow and physical properties of the sediments will influence the amount of sediment P leaving the watershed in the Winooski River, Vermont. Thus, modeling of inchannel or fluvial processes must account for variability in flow, local sources of P, and sediment properties, particularly near the point of impact. Because of these complexities, fluvial processes and changes in P forms and loads are not currently simulated or are simulated in a simple manner in most watershed models (Hanrahan et al. 2001).


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1.7.2 SURFACE WATER IMPACTS Intuitively, biological responses are different among water bodies, with variations in geographic location, climate, water residence times, and surface area and depth of water body. For example, the Cannonsville Reservoir — which is part of the New York City water supply system — flushes in a matter of months, whereas Cayuga Lake — the longest Fingerlake in New York State — has a mean water residence time of about 12 years. Also, the Chesapeake Bay has a completely different set of critical biological indicators in comparison with the Gulf of Mexico (National Research Council 2000). In fact, the ratio of watershed drainage area and Bay water volume (2410 km2 km−3) is nearly an order of magnitude greater than any other lake or bay in the world; next is the Gulf of Finland (380 km2 km−3). As a result, simulation as well as management of the biological response within the Chesapeake Bay presents unique challenges because of the relatively large area for nutrient source inputs that must be considered. Although P loss in overland flow, the related effects of agricultural management, and how nutrients cycle within a water body can be simulated, it is still difficult to relate P loss as a function of watershed management to the biological response of a receiving water body. Because of the scales involved, connectivity, and dominant processes in terrestrial and aquatic systems, watershed and water-body response models have tended to develop independently. Summer et al. (1990) attempted to link watershed (i.e., AGNPS) and lake process (i.e., FARM POND) models. However, a lack of adequate water monitoring data, such as chemistry and flow rate, limits rigorous testing of their ability to simulate a lake’s response to changes in agricultural management and climate.

1.8 SUMMARY This brief introduction has presented background information on processes controlling P transport in overland and subsurface flow from agricultural landscapes and how nonpoint source models attempt to simulate P loss. New information on soil and site dependency of extraction coefficients relating STP and overland flow dissolved P and the use of enrichment ratios to estimate particulate P transport should be incorporated into these models. Also, incorporation of new formulations describing the release and transport of inorganic and organic P from manure in overland and subsurface flow will improve model predictions of P loss following land application of manures. However, much information on the fate and transport of P in agricultural landscapes and on the effectiveness of various BMPs to minimize this loss through source or transport controls is already available. Mechanisms are being developed to apply this information through innovative database management and integration with existing models to better use existing data rather than to reinvent the wheel. Many complex models are available and are gaining greater acceptance with managers and planners, as computers become more powerful and less expensive and as people become more comfortable using them. However, because models yield clear numerical results with which to gauge progress, they have a strong appeal to policymakers and managers — an appeal that can sometimes bring false confidence and misconceptions (Boesch et al. 2001). Though all models are wrong, some are useful. It is of critical importance that modelers clearly define what the model is useful



15

for and what it is not designed to do. Likewise, users must decide what they want to accomplish with a model. For example, one must consider the scale (i.e., field, watershed, or basin), time (i.e., flow event, annual, or multiyear), and level of accuracy (i.e., 0.1 or 10 kg ha−1 year−1) that needs to be simulated, as well as the amount of parameterization data available. Thus, a key to useful simulation of P loss is selection of the appropriate model and data to run it. If, for instance, one needs to identify areas in a watershed at greater risk for P loss to target remedial BMPs, then site-vulnerability tools such as the P index are available (Gburek et al. 2000; Lemunyon and Gilbert 1993). On the other hand, most P indices are not designed to quantify P loss as are many nonpoint source models described earlier in this discussion. Even so, it is clear that a great deal of uncertainty can exist in model computations. Uncertainty arises in connection with an imperfect representation of the physics, chemistry, and biology of the real world, caused by numerical approximations, inaccurate parameter estimates and data input, and errors in measurements of the state variables being computed. Whenever possible, this uncertainty should be represented in the model output (e.g., as a mean plus standard deviation) or as confidence limits on the output of a time series of concentrations or flows. The tendency described earlier for decision makers to believe models because of their presumed deterministic nature and exact form of output must be tempered by responsible use of the models by engineers and scientists such that model computations or predictions are not oversold or given more weight than they deserve. Above all, model users should determine that the model computations are reasonable in the sense of providing output that is physically realistic and based on input parameters within accepted ranges. Model uncertainty is addressed in Chapter 6 of this book. The role of modeling will be more and more important over the next decade in making management and policy decisions related to conservation programs and water-quality enhancement and enforcement. Also, the availability of water monitoring data is increasing in response to water quality concerns in the U.S. and other parts of the world and is providing new opportunities to develop, to calibrate, and to test watershed models. Monitoring data for models is discussed in Chapter 16 of this book. As we move forward, however, an interdisciplinary approach is needed that involves hydrologists, soil scientists, engineers, economists, animal scientists, and, possibly, rural sociologists. With the knowledge that many and varied working models exist, our efforts should be directed to improving or adapting existing models rather than reinventing or developing new models, except where major limitations have been clearly defined. Finally, and most importantly, it is essential that the most appropriate model be carefully selected to meet a user’s needs in terms of level of predictive accuracy needed, input data available, and scale of simulation being considered — both time and space.

REFERENCES Andraski, B.J., D.H. Mueller, and T.C. Daniel. 1985. Phosphorus losses in runoff as affected by tillage. Soil Sci. Soc. Am. J. 49:1523–1527. Arnold, J.G., R. Srinivasa, R.S. Muttiah, and J.R. Williams. 1998. Large area hydrologic modeling and assessment part 1: model development. J. Am. Water Resour. Assoc. 34:73–89.


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Baker, J.L. and H.P. Johnson. 1983. Evaluating the effectiveness of BMPs from field studies. Pp. 281–304 in Agricultural Management and Water Quality, F.W. Schaller and G.W. Bailey (Eds.). Ames: Iowa State University Press. Baldwin, D.S., A.M. Mitchell, and J.M. Olley. 2002. Pollutant-sediment interactions: sorption, reactivity and transport of phosphorus. Pp. 265–280 in Agriculture, Hydrology and Water Quality, P.M. Haygarth and S.C. Jarvis (Eds.). Oxford: CABI International. Beasley, D.B., E.J. Monke, E.R. Miller, and L.F. Huggins. 1985. Using simulation to assess the impacts of conservation tillage on movement of sediment and phosphorus into Lake Erie. J. Soil Water Conserv. 40:233–237. Beaulac, M.N. and K.H. Reckhow. 1982. An examination of land use — nutrient export relationships. Water Res. Bull. 18:1013–1023. Bingner, R.L., F.D. Theurer, R.G. Cronshey, and R.W. Darden. 2001. AGNPS 2001 Web Site. http://www.ars.usda.gov/Research/docs.htm?docid=5199. Boesch, D.F., R.B. Brinsfield, and R.E. Magnien. 2001. Chesapeake Bay eutrophication: scientific understanding, ecosystem restoration, and challenges for agriculture. J. Environ. Qual. 30:303–320. Bouraoui, F. and T.A. Dillaha. 1996. ANSWERS-2000: Runoff and sediment transport model. J. Environ. Eng. 122(6):493–502. Burkholder, J.A. and H.B. Glasgow, Jr. 1997. Pfiesteria piscicidia and other Pfiesteriadinoflagellates behaviors, impacts, and environmental controls. Limnol. Oceanogr. 42:1052–1075. Cassell, E.A., J.M. Dorioz, R.L. Kort, J.P. Hoffmann, D.W. Meals, D. Kirschtel, and D.C. Braun., 1998. Modeling phosphorus dynamics in ecosystems: mass balance and dynamic simulation approaches. J. Environ. Qual. 27:293–298. Cook, D.J., W.T. Dickinson, and R.P. Rudra. 1985. GAMES — the Guelph model for evaluating the effects of agricultural management systems in erosion and sedimentation: User’s manual. Technical Report 126-71, School of Engineering, University of Guelph, Ontario. Croshley, R.G and F.G. Theurer. 1998. AnnAGNPS nonpoint pollutant loading model. Proceedings of the First Federal Interagency Hydrologic Modeling Conference, April 19–23, Las Vegas, NV. Deere and Company. 1995. Managing nonpoint source pollution in agriculture. Technical Report 272. 61265. Moline, IL: Deere and Company Technical Center. DiToro, D.M. and M.J. Small. 1984. Probability model of stream quality due to runoff. J. Environ. Eng. 110:607–628. Donigian, A.S., Jr., D.C. Beyerlein, H.H. Davis, Jr., and N.H. Crawford. 1977. Agricultural Runoff Management (ARM) Model Version II: Refinement and testing. U.S. Environmental Protection Agency, EPA 600/3-77-098, Environmental Research Lab, Athens, GA. Driscoll, E.D., P.E. Shelley, and E.W. Strecker. 1989. Pollutant Loadings and Impacts from Highway Stormwater Runoff: Design Procedure. Mclean, VA: Office of Engineering and Highway Operations R&D, Federal Highway Administration. Driver, N.E. and G.D. Tasker. 1990. Techniques for Estimation of Storm-Runoff Loads, Volumes, and Selected Constituent Concentrations in Urban Watersheds in the United States. Reston, VA: U.S. Geological Survey. Edwards, D.R. and T.C. Daniel. 1993. Drying interval effects on runoff from fescue plots receiving swine manure. Trans. Am. Soc. Agric. Eng. 36:1673–1678. Eghball, B. and J.E. Gilley. 1999. Phosphorus and nitrogen in runoff following beef cattle manure or compost application. J. Environ. Qual. 28:1201–1210.



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Gburek, W.J., A.N. Sharpley, A.L. Heathwaite, and G.J. Folmar. 2000. Phosphorus management at the watershed scale: a modification of the phosphorus index. J. Environ. Qual. 29:130–144. Gitau, M.W., E. Schneiderman, W.J. Gburek, and A.R. Jarrett. 2001. An evaluation of best management practices installed in the Cannonsville Reservoir Watershed, New York. Proceedings of the 9th National Non-point Source Monitoring Workshop, August 27–30, Indianapolis, IN. Haith, D.A. and L.L. Shoemaker. 1987. Generalized watershed loading functions for stream flow nutrients. Water Res. Bull. 23(3):471–478. Hanrahan, G., M. Gledhill, W.A. House, and P.J. Worsfold. 2001. Phosphorus loading in the Frome catchment, UK: seasonal refinement on the coefficient modeling approach. J. Environ. Qual. 30:1738–1746. Johanson, R.C., J.C. Imhoff, J.L. Little, and A.S. Donigian. 1984. Hydrological Simulation Program-Fortran (HSPF): user’s manual. U.S. Environmental Protection Agency, EPA-600/3-84-066, Athens, GA. Johnes, P.J. 1996. Evaluation and management of the impact of land use changes on the nitrogen and phosphorus load delivered to surface waters: The export coefficient modeling approach. J. Hydrol. 183:323–349. Johnes, P.J. and A.L. Heathwaite. 1997. Modelling the impact of land use change on water quality in agricultural catchments. Hydrol. Proc. 11:269–286. Johnes, P.J., B. Moss, and G. Phillips. 1996. The determination of total nitrogen and total phosphorus concentrations in freshwaters from land use, stock headage and population data: testing of a model for use in conservation and water quality management. Freshwater Biol. 36:451–473. Khoshmanesh, A., B.T. Hart, A. Duncan, and R. Beckett. 1999. Biotic uptake and release of phosphorus by a wetland sediment. Environ. Technol. 29:85–91. Kleinman, P.J.A., B.A. Needelman, A.N. Sharpley, and R.W. McDowell. 2003. Using soil phosphorus profile data to assess phosphorus leaching potential in manured soils. Soil Sci. Soc. Am. J. 67:215–224. Kleinman, P.J.A., A.N. Sharpley, B.G. Moyer, and G.F. Elwinger. 2002. Effect of mineral and manure phosphorus sources on runoff phosphorus. J. Environ. Qual. 31:2026–2033. Krogstad, T. and Ø. Løvstad. 1989. Erosion, phosphorus and phytoplankton response in rivers of southeastern Norway. Hydrobiologia 183:33–41. Lathrop, R.C., S.R. Carpenter, C.A. Stow, P.A. Soranno, and J.C. Panuska. 1998. Phosphorus loading reductions needed to control blue-green algal blooms in Lake Mendota. Can. J. Fish. Aquat. Sci. 55:1169–1178. Lemunyon, J.L. and R.G. Gilbert. 1993. The concept and need for a phosphorus assessment tool. J. Prod. Agric. 6:483–496. Leonard, R.A., W.G. Knisel, and D.A. Still. 1987. GLEAMS: groundwater loading effects of agricultural management systems. Trans. Am Soc. Agric. Eng. 30:1403–1418. McDowell, R.W. and A.N. Sharpley. 2001a. Approximating phosphorus release from soils to surface runoff and subsurface drainage. J. Environ. Qual. 30:508–520. McDowell, R.W. and A.N. Sharpley. 2001b. Phosphorus losses in subsurface flow before and after manure application to intensively farmed land. Sci. Tot. Environ. 278:113–125. McDowell, R.W. and A.N. Sharpley. 2003. Phosphorus uptake and release from stream sediments. J. Environ. Qual. 32: 937–948. McDowell, R.W., A. Sharpley, and A.T. Chalmers. 2002. Chemical characterisation of fluvial sediment: the Winooski River, Vermont. Ecol. Eng. 18:447–487.


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Menzel, R.G. 1980. Enrichment ratios for water quality modeling. Pp. 486–492 in CREAMS — A Field Scale Model for Chemicals, Runoff and Erosion from Agricultural Management Systems, vol. 3, W. Knisel (Ed.). Supporting Documentation, U.S. Department of Agriculture, Conservation Research Report 26, U.S. Government Printing Office, Washington, D.C. National Research Council. 2000. Clean Coastal Waters: Understanding and Reducing the Effects of Nutrient Pollution. Washington, D.C.: National Academy Press. Parton, W.J., J.M.O. Scurlack, D.S. Ojima, T.G. Gilmanov, R.J. Scoles, D.S. Schimal, T. Kirchner, J.C. Menaut, T. Seastedt, E. Garcia Moya, A. Kamnalrut, and J.L. Kinyamario. 1993. Observations and modeling of biomass and soil organic matter dynamics for the grasslands biome world-wide. Global Biochem. Cycles 7:785–809. Pote, D.H., T.C. Daniel, D.J. Nichols, A.N. Sharpley, P.A. Moore, Jr., D.M. Miller, and D.R. Edwards. 1999. Relationship between phosphorus levels in three Ultisols and phosphorus concentrations in runoff. J. Environ. Qual. 28:170–175. Romkens, M.J.M., D.W. Nelson, and J.V. Mannering. 1973. Nitrogen and phosphorus composition of surface runoff as affected by tillage method. J. Environ. Qual. 2: 292–295. Sharpley, A.N. 1985a. The selective erosion of plant nutrients in runoff. Soil Sci. Soc. Am. J. 49:1527–1534. Sharpley, A.N. 1985b. Depth of surface soil-runoff interaction as affected by rainfall, soil slope, and management. Soil Sci. Soc. Am. J. 49:1010–1015. Sharpley, A.N. 1997. Rainfall frequency and nitrogen and phosphorus in runoff from soil amended with poultry litter. J. Environ. Qual. 26:1127–1132. Sharpley, A.N. (Ed.). 2000. Agriculture and Phosphorus Management: The Chesapeake Bay. Boca Raton, FL: CRC Press. Sharpley, A.N., P.J.A. Kleinman, R.J. Wright, T.C. Daniel, B. Joern, R. Parry, and T. Sobecki. 2000. The National Phosphorus Project: interfacing agricultural and environmental phosphorus management in the U.S. Pp. 156–165 in International Conference on Agricultural Effects in Ground and Surface Waters, J. Steenvooreden (Ed.). Wageningen, The Netherlands: International Association of Hydrologic Sciences. Sharpley, A.N. and S.J. Smith. 1994. Wheat tillage and water quality in the Southern Plains. Soil Tillage Res. 30:33–38. Sharpley, A.N., S.J. Smith, B.A. Stewart, and A.C. Mathers. 1984. Forms of phosphorus in soil receiving cattle feedlot waste. J. Environ. Qual. 13:211–215. Sharpley, A.N., S.J. Smith, J.R. Williams, O.R. Jones, and G.A. Coleman. 1991. Water quality impacts associated with sorghum culture in the Southern Plains. J. Environ. Qual. 20:239–244. Sharpley, A.N., S.J. Smith, J.A. Zollweg, and G.A. Coleman. 1996. Gully treatment and water quality in the Southern Plains. J. Soil Water Conserv. 51:512–517. Sharpley, A.N. and H. Tunney. 2000. Phosphorus research strategies to meet agricultural and environmental challenges of the 21st century. J. Environ Qual. 29:176–181. Sharpley, A.N. and J.R. Williams (Eds.). 1990. EPIC-Erosion/Productivity Impact Calculator: I — model documentation. U.S. Department of Agriculture Tech. Bull. 1768. Sims J.T., R.R. Simard, and B.C. Joern. 1998. Phosphorus losses on agricultural drainage: Historical perspectives and current research. J. Environ. Qual. 27:277–293. Smith, S. J., A.N. Sharpley, J.W. Naney, W.A. Berg, and O.R. Jones. 1991. Water quality impacts associated with wheat culture in the Southern Plains. J. Environ. Qual. 20:244–249. Summer, R.M., C.V. Alonso, and R.A. Young. 1990. Modeling linked watershed and lake processes for water quality management decisions. J. Environ. Qual. 19:421–427.



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U.S. Environmental Protection Agency. 1993. Guidance specifying management measures for sources of non-point pollution in coastal waters. EPA-840-B93-100c, U.S. Government Printing Office, Washington, D.C. U.S. Environmental Protection Agency. 2000. The Total Maximum Daily Load (TMDL) program. EPA 841-F-00-009, Office of Water (4503F), U.S. Government Printing Office, Washington, D.C. Available at http://www.epa.gov/owow/tmdl/overviewfs.html. U.S. Geological Survey. 1999. The quality of our nation’s waters: nutrients and pesticides. U.S. Geological Survey Circular 1225, Information Services, Denver, CO. Available at http://www.usgs.gov. Westerman, P.W. and M.R. Overcash. 1980. Short-term attenuation of runoff pollution potential for land-applied swine and poultry manure. Pp. 289–292 in Livestock waste — A renewable resource. Proceedings of the 4th International Symposium on Livestock Wastes, April, Amarillo, TX. Young, R.A., C.A. Onstad, and D.D. Bosch. 1995. AGNPS: An agricultural nonpoint source model. Pp. 1001–1020 in Computer Models of Watershed Hydrology, V.P. Singh (Ed.). Highlands Ranch, CO: Water Resources Publication. Young, R.A., C.A. Onstad, D.D. Bosch, and W.P. Anderson. 1989. AGNPS: A nonpoint-source pollution model for evaluating agricultural watersheds. J. Soil Water Conserv. 44:168–173.


2

Modeling Runoff and Erosion in Phosphorus Models Mary Leigh Wolfe Virginia Polytechnic Institute and State University, Blacksburg, VA

CONTENTS 2.1 2.2

Introduction ....................................................................................................22 Modeling Runoff............................................................................................22 2.2.1 Runoff Volume ...................................................................................22 2.2.1.1 Curve Number Method.......................................................23 2.2.1.2 Curve Number Method Implementation ............................25 2.2.1.3 Infiltration-Based Approaches ............................................29 2.2.2 Hydrograph Development ..................................................................32 2.2.2.1 Kinematic Flow Routing ....................................................33 2.2.2.2 SCS Unit Hydrograph ........................................................34 2.2.2.3 Hydrograph Development Implementation ........................35 2.2.3 Streamflow, or Channel, Routing....................................................... 36 2.2.3.1 Hydrologic, or Storage, Routing ........................................37 2.2.3.2 Muskingum Routing Method .............................................37 2.2.3.3 Streamflow, or Channel, Routing Implementation .....................................................39 2.2.4 Peak Rate of Runoff ..........................................................................40 2.2.4.1 Rational Formula ................................................................40 2.2.4.2 SCS TR-55 Method ............................................................41 2.2.4.3 Peak Runoff Rate Implementation .....................................41 2.3 Modeling Erosion and Sediment Yield..........................................................44 2.3.1 USLE-Based Approaches...................................................................45 2.3.2 USLE-Based Approach Implementation ...........................................48 2.3.3 Process-Based Approaches ................................................................49 2.3.4 Process-Based Approach Implementation .........................................52 2.3.5 Channel Erosion.................................................................................53 2.3.6 Channel Erosion Implementation ......................................................54 2.4 Summary ........................................................................................................56 References................................................................................................................60 21


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2.1 INTRODUCTION Runoff and erosion are the overland processes that transport phosphorus. The processes and equations describing the processes have been described in many references. The purpose of this chapter is to present the common approaches used for modeling runoff and erosion processes in models that simulate phosphorus transport and to illustrate similarities and differences in implementation among selected phosphorus models. Implementation of the processes varies among the phosphorus models, depending on model characteristics such as spatial representation of the drainage area (e.g., lumped or distributed), spatial scale (e.g., field or watershed), purpose of the model (e.g., event prediction or average annual predictions for management), computational time step (e.g., daily vs. shorter time steps during rainfall or runoff events), and land uses and conditions represented (e.g., agricultural, urban, forested land uses, frozen soils). Examples of implementation from the following models are included in the chapter: Annualized Agricultural Nonpoint Source (AnnAGNPS) (Cronshey and Theurer 1998), Areal Nonpoint Source Watershed Environment Response Simulation 2000 (ANSWERS-2000) (Bouraoui 1994), Erosion Productivity Impact Calculator (EPIC) (Sharpley and Williams 1990), Groundwater Loading Effects of Agricultural Management Systems (GLEAMS) (Knisel 1993; Leonard et al. 1987), Hydrologic Simulation Program-Fortran (HSPF) (Bicknell et al. 2001), and Soil and Water Assessment Tool (SWAT) (Neitsch et al. 2002). Unless otherwise noted, the information about the models is from the sources cited in this paragraph. Because of the variety of equations and variability in how they are implemented in different models, a mixture of units is used in this chapter. Generally, units are expressed as length, mass, time (L, M, T, respectively) or in both International System of Units (SI) and English units for empirical equations or as used in the cited models.

2.2 MODELING RUNOFF Runoff is a complex, variable process, influenced by many factors such as soil characteristics, land cover, and topography. Runoff calculations typically include estimating runoff volume, peak runoff rate, and hydrographs, or the time distribution of runoff. For some phosphorus models, peak runoff rate is computed only for use in erosion calculations. For example, in GLEAMS the peak rate is used in the erosion component for calculating the characteristic discharge rate, sediment transport capacity, and shear stress in a concentrated flow. Common approaches used in phosphorus models for estimating runoff volume, hydrographs, and peak discharge are described in the following sections.

2.2.1 RUNOFF VOLUME Runoff volume, often termed rainfall excess, is the total amount of rainfall minus infiltration and interception. Two general approaches are used to model runoff volume in phosphorus transport models: (1) the curve number (CN) method and (2) infiltration methods. The CN method directly calculates runoff volume, whereas the infiltration methods calculate infiltration first and then estimate runoff as the difference between rainfall and infiltration. Some phosphorus models include both CN


Modeling Runoff and Erosion in Phosphorus Models

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and infiltration methods. The CN method is usually used when daily rainfall values are available; infiltration methods require hourly — or other intervals shorter than daily — rainfall values. 2.2.1.1 Curve Number Method The most common method used to estimate runoff volume in phosphorus models is the U.S. Department of Agriculture (USDA) Soil Conservation Service (SCS) (now Natural Resources Conservation Service, NRCS) runoff approach. The CN method correlates runoff with rainfall, antecedent moisture condition (AMC), soil type, and vegetative cover and cultural practices. Runoff volume is computed using the following relationships (SCS 1972): Q= S=

25, 400 − 254 , CN

( P − 0.2 S )2 P + 0.8 S

S in mm or

S=

(2.1) 1000 − 10 , S in in. CN

(2.2)

where Q is direct storm runoff volume (mm or in.), P is storm rainfall depth (mm or in.), S is the retention parameter or maximum potential difference between rainfall and runoff at the time the storm begins (mm or in.), and CN is the runoff curve number, which represents runoff potential of a surface based on land use, soil type, management, and hydrologic condition. Rainfall depth, P, must be greater than 0.2S (referred to as the initial abstraction, Ia) for the equation to be applicable. Values of CN have been tabulated (Table 2.1) by hydrologic soil group for AMC II, or average conditions. The CN ranges from 1 to 100, with runoff potential increasing with increasing CN. Required information to determine a CN value from the table includes the hydrologic soil group (defined in Table 2.2), the vegetal and cultural practices of the site, and the AMC (defined in Table 2.3). The CN obtained from Table 2.1 for AMC II can be converted to AMC I (dry) or III (wet) using the values in Table 2.3. Curve numbers can be determined from rainfall-runoff data for a particular site. Investigations have been conducted to determine CN values for conditions not included in Table 2.1 or similar tables. Examples include exposed fractured rock surfaces (Rasmussen and Evans 1993), animal manure application sites (Edwards and Daniel 1993), and dryland wheat–sorghum–fallow crop rotation in the semi-arid western Great Plains (Hauser and Jones 1991). The CN approach is widely used for estimating runoff volume. Because the CN is defined in terms of land use treatments, hydrologic condition, AMC, and soil type, the approach can be applied to ungaged watersheds. Errors in selecting CN values can result from misclassifying land cover, treatment, hydrologic conditions, or soil type (Bondelid et al. 1982). The magnitude of the error depends on both the size of the area misclassified and the type of misclassification. In a sensitivity analysis of runoff estimates to errors in CN estimates, Bondelid et al. (1982) found that effects of variations in CN decrease as design rainfall depth increases and confirmed Hawkins’s (1975) conclusion that errors in CN estimates are especially critical near the threshold of runoff.


24


TABLE 2.1 Runoff Curve Numbers for Hydrologic Soil-Cover Complexes Land Use Description/Treatment/Hydrologic Condition Residential:a Average lot size (ha) 0.05 or less 0.10 0.13 0.20 0.40

Hydrologic Soil Group A

B

C

D

77 61 57 54 51

85 75 72 70 68

90 83 81 80 79

92 87 86 85 84

98

98

98

98

98 76 72

98 85 82

98 89 87

98 91 89

Commercial and business areas (85% impervious)

89

92

94

95

Industrial districts (72% impervious)

81

88

91

93

39 49

61 69

74 79

80 84

—

77

86

91

94

Average % imperviousb 65 38 30 25 20

Paved parking lots, roofs, driveways, etc.c Street and roads: Paved with curbs and storm sewersc Gravel Dirt

Open spaces, lawns, parks, golf courses, cemeteries, etc. Good condition: grass cover on 75% or more of the area Fair condition: grass cover on 50 to 75% of the area Fallow

Straight row

Row crops

Straight row Straight row Contoured Contoured Contoured and terraced Contoured and terraced

Poor Good Poor Good Poor Good

72 67 70 65 66 62

81 78 79 75 74 71

88 85 84 82 80 78

91 89 88 86 82 81

Small grain

Straight row


65 63 63 61 61 59

76 75 74 73 72 70

84 83 82 81 79 78

88 87 85 84 82 81

Contoured Contoured and terraced

(continued)



25

TABLE 2.1 (CONTINUED) Runoff Curve Numbers for Hydrologic Soil-Cover Complexes Land Use Description/Treatment/Hydrologic Condition Close–seeded legumesd or rotation meadow

Hydrologic Soil Group

Straight row Straight row Contoured Contoured Contoured and terraced Contoured and terraced


66 58 64 55 63 51

77 72 75 69 73 67

85 81 83 78 80 76

89 85 85 83 83 80

Contoured Contoured Contoured

Poor Fair Good Poor Fair Good

68 49 39 47 25 6

79 69 61 67 59 35

86 79 74 81 75 70

89 84 80 88 83 79

Meadow

Good

30

58

71

78

Woods or forest land

Poor Fair Good

45 36 25

66 60 55

77 73 70

83 79 77

—

59

74

82

86

Pasture or range

Farmsteads Note: Antecedent moisture condition II and Ia = 0.2S. a

Curve numbers are computed assuming the runoff from the house and driveway is directed toward the street with a minimum of roof water directed to lawns where additional infiltration could occur. b

The remaining pervious areas (lawn) are considered to be in good pasture condition for these curve numbers. c

In some warmer climates of the country a curve number of 95 may be used.

d

Close-drilled or broadcast.

Source: SCS. 1972. Hydrology, Section 4: National Engineering Handbook, U.S. Soil Conservation Service, Washington, D.C., Government Printing Office. With permission.

2.2.1.2 Curve Number Method Implementation The curve number method is used in several phosphorus models to compute runoff volume. The most common implementation (e.g., AnnAGNPS, GLEAMS, EPIC, SWAT) includes a modification of the CN to account for daily changes in soil moisture content (Williams et al. 1990). Typically, the models require the user to input a value for CN2, the curve number for average conditions, or AMC II. Then,


26


TABLE 2.2 Hydrologic Soil Group Descriptions and Antecedent Rainfall Conditions for Use with SCS Curve Number Method Soil Group A B

C

D

Description Lowest Runoff Potential. Includes deep sands with very little silt and clay, also deep, rapidly permeable loess. Moderately Low Runoff Potential. Mostly sandy soils less deep than A, and loess less deep or less aggregated than A, but the group as a whole has above-average infiltration after thorough wetting. Moderately High Runoff Potential. Comprises shallow soils and soils containing considerable clay and colloids, though less than those of group D. The group has below-average infiltration after presaturation. Highest Runoff Potential. Includes mostly clays of high swelling percent, but the group also includes some shallow soils with nearly impermeable subhorizons near the surface. 5-Day Antecedent Rainfall (mm)

Condition

General Description

I

Optimum soil condition from about lower plastic limit to wilting point Average value for annual floods Heavy rainfall or light rainfall and low temperatures within 5 days prior to the given storm

II III

Dormant Season

Growing Season

< 6.4

< 35.6

6.4 to 27.9 > 27.9

35.6 to 53.3 > 53.3

Source: SCS. 1972. Hydrology, Section 4: National Engineering Handbook, U.S. Soil Conservation Service, Washington, D.C., Government Printing Office. With permission.

curve numbers corresponding to AMC I (dry), CN1, and AMC III (wet), CN3, are computed as a function of CN2. The retention parameter, S, also changes due to fluctuations in soil moisture content. For example, the same relationship is used in EPIC and SWAT, with the soil water content expressed differently:     FFC SW S = S1 1 − in EPIC or S = Smax 1 − in SWAT [ w1 − w2 ( FFC )]  ( w1 − w2 SW )   FFC + e   SW + e  (2.3) where S1 (L) and Smax (L) is the value of S associated with CN1 (computed with Equation 2.2), FFC is the fraction of field capacity, SW is the soil water content (L3/L3), and w1 and w2 are shape parameters. FFC is computed in EPIC as FFC =


SW − WP FC − WP

(2.4)


27

TABLE 2.3 Conversion Factors for Converting Runoff Curve Numbers Factor to Convert Curve Number for Condition II to

Curve Number for Condition II

Condition I

Condition III

0.40 0.45 0.50 0.55 0.62 0.67 0.73 0.79 0.87 1.00

2.22 1.85 1.67 1.50 1.40 1.30 1.21 1.14 1.07 1.00

10 20 30 40 50 60 70 80 90 100

Note: AMC II to AMC I and III (Ia = 0.2S). Source: SCS. 1972. Hydrology, Section 4: National Engineering Handbook, U.S. Soil Conservation Service, Washington, D.C., Government Printing Office. With permission.

where SW is the soil water content in the root zone, WP is the wilting point water content (corresponds to 1500 kPa matric potential for many soils) (L3/L3), and FC is the field capacity water content (corresponds to 33 kPa matric potential for many soils) (L3/L3). In EPIC, values for w1 and w2 are obtained by simultaneous solution of Equation 2.3 with the assumptions that S = S2 when FFC = 0.5 and S = S3 when FFC = 1.0. In SWAT, w1 and w2 are determined by solving Equation 2.3 with the following assumptions: S = S1 when SW = WP, S = S3 when SW = FC, and the soil has a CN of 99 (S = 2.54) when completely saturated. The soil water content can be taken as being uniformly distributed through the root zone or top meter or some other depth of soil, or a nonuniform distribution of soil water can be considered. If more of the soil water is at the surface than deeper in the profile, the potential for runoff is greater. Some of the phosphorus models keep track of soil moisture by layer, so they have the potential to include the soil water distribution in their runoff calculations. For example, because EPIC estimates water content of each soil layer daily, the effect of depth distribution on runoff is expressed by using a depth-weighted FFC value in Equation 2.3:

FFC = *


∑iM=1 FFCi ∑

(

Zi − Zi −1 Zi

M Zi − Zi −1 i =1 Zi

),

Zi ≤ 1.0 m

(2.5)

28


where FFC* is the depth-weighted FFC value for use in Equation 2.3, Z is the depth (m) to the bottom of soil layer i, and M is the number of soil layers. Equation 2.5 reduces the influence of lower layers because FFCi is divided by Zi and gives proper weight to thick layers relative to thin layers because FFC is multiplied by the layer thickness. GLEAMS also computes a depth-weighted retention parameter:  S = S1 1.0 − 

N





 ∑ W  SM UL    i

i

i =1

(2.6)

i

where Wi is the weighting factor, SMi is the water content in soil layer i (L), and ULi is the upper limit of water storage in layer i (L). The weighting factors decrease with depth according to the equation:  D   −4.16 Di−1  −4.16  i   Wi = 1.016 e  RD  − e  RD      

(2.7)

where Di is the depth to the bottom of layer i (L) and RD is the root zone depth (L). The sum of the weighting factors equals one. Assuming that the CN2 value in Table 2.1 (SCS 1972) is appropriate for a 5% slope, Williams et al. (1990) developed an equation to adjust that value for other slopes: 1 CN 2 s = (CN 3 − CN 2 )[1 − 2e −13.86 s ] + CN 2 3

(2.8)

where CN2s is the handbook CN2 value adjusted for slope and s is the average slope of the watershed (L/L). This adjustment is included in EPIC but not in SWAT. EPIC also accounts for uncertainty in the retention parameter, or CN, by generating the final curve number estimate from a triangular distribution. The mean of the distribution is the best estimate of CN based on using Equations 2.2 through 2.5, and 2.8 and an equation to adjust S for frozen ground. The extremes of the distribution are ±5 curve numbers from the mean. Another example of a modification in implementation of the CN method is seen in GLEAMS. In the U.S., soils are grouped by series name, and a hydrologic soil group is assigned to each series. However, a series name can include different soil textures, which would have different runoff potentials but would still be in the same hydrologic soil group. The developers of GLEAMS expanded Table 2.1 to give a range of curve numbers for each combination in the table to allow users to distinguish between similar soils within a series (Table 2.4). For example, CN2 for row crops with straight rows in good hydrologic condition could be 78 for a Cecil sandy loam and 82 for a Cecil clay loam. Care must be taken in utilization of the CN method in different scale models. The CN method was developed based on data from small watersheds, so it should



29

TABLE 2.4 Excerpt of Expanded Curve Number Table for GLEAMS Model Land Use Treatment or Practice

Hydrologic Condition

SR SR SR + CT SR + CT CNT CNT


Hydrologic Soil Group A Row Crops 65 72 77 60 67 73 66 71 75 57 64 70 64 70 75 59 65 70

B

78 74 76 71 76 71

81 78 79 75 79 75

C

85 82 83 79 81 79

86 83 84 80 82 80

87 85 86 82 84 82

D

88 87 87 83 86 84

90 88 88 84 87 85

91 89 89 85 88 86

92 90 90 86 89 87

Note: SR = straight row; CT = conservation tillage; CNT = contoured. Source: Knisel, W.G., GLEAMS: Groundwater Loading Effects of Agricultural Management Systems, Version 2.10, University of Georgia, Coastal Plain Experiment Station, Biological and Agricultural Engineering Department, Publication 5, p. 130, 1993. With permission.

not be applied to a whole watershed larger than that. A larger watershed is subject to spatial variability in rainfall amounts and increased transmission losses due to increased flow path lengths, changing the CN value from that of a smaller watershed. For example, Simanton et al. (1996) found that the optimum curve number — to match measured runoff values — decreased with increasing drainage area for 18 semi-arid watersheds in southeastern Arizona. Some phosphorus models divide large watersheds into subwatersheds or other smaller hydrologic response units. It is reasonable to apply the CN to the smaller response units and then to determine how the runoff from the individual units contributes to streamflow, through routing or other methods, as described in the following sections (2.2.3).

2.2.1.3 Infiltration-Based Approaches Infiltration is defined as the entry of water from the surface into the soil profile. From a ponded surface or a rainfall situation, infiltration rate decreases over time and asymptotically approaches a final infiltration rate. The final infiltration rate is approximately equal to the saturated hydraulic conductivity, Ks, of the soil. The amount and rate of infiltration depend on infiltration capacity of the soil and the availability of water to infiltrate. Infiltration capacity is influenced by soil properties, soil texture, initial soil moisture content, surface conditions, and availability of water to be infiltrated, i.e., precipitation or ponded water. Rainfall intensity affects infiltration rate. If the infiltration capacity of the soil is exceeded by the rainfall intensity (L/T), then water will pond on the soil surface, and the infiltration rate will equal the infiltration capacity. If the rainfall rate is less than the saturated hydraulic


30


conductivity of the soil, the infiltration rate will equal the rainfall rate, and ponding will not occur. A number of infiltration equations have been developed, ranging from solving the Richards (1931) equation to empirical equations. The Richards equation, the generalized equation for flow in porous media, is a partial differential equation derived from conservation of mass and Darcy’s equation describing flux. To simulate infiltration, the Richards equation is solved subject to appropriate boundary and initial conditions. Empirical infiltration equations typically include coefficients or exponents to represent soil properties and to generate the relationship of decreasing infiltration rate with time. Some infiltration equations that have been used in phosphorus models include the Holtan (1961) equation, which was used in the original ANSWERS event-based model (Beasley et al. 1982); the Philip (1957) equation, which is the basis of the infiltration calculations in HSPF; and the Green and Ampt (1911) equation. 2.2.1.3.1 Green and Ampt Approach Description In phosphorus models that include infiltration simulation (e.g., ANSWERS-2000, SWAT), the Green and Ampt (1911) equation as modified by Mein and Larson (1973) is the most common approach used to estimate infiltration. This approach is physically based, and its parameters can be determined from readily available soil and vegetal cover information. The approach has been tested for a variety of conditions and has successfully simulated the effects of different management practices on infiltration. The original Green and Ampt (1911) equation was derived using Darcy’s law for infiltration from a ponded surface into a deep, homogeneous soil profile with uniform initial water content. Water is assumed to enter the soil as slug flow resulting in a sharply defined wetting front that separates a zone that has been wetted from an unwetted zone. Infiltration rate is expressed as  MS av  f = Ks  1 + F  

(2.9)

where f is infiltration rate (L/T), Ks is saturated hydraulic conductivity (L/T), M is the difference between final and initial moisture content (the difference in moisture content across the wetting front) (L3/L3), Sav is average wetting front suction (L), and F is cumulative infiltration (L). Substituting f = dF dt into Equation 2.9 and integrating with F = 0 at time (t) = 0 yields  F  K s t = F − S av M ln  1 + MS av  

(2.10)

Mein and Larson (1973) extended the Green and Ampt equation to rainfall conditions by first determining cumulative infiltration at the time of surface ponding: Fp =


S av M R −1 Ks

(2.11)


31

where Fp is cumulative infiltration at time of ponding (L) and R is rainfall rate (L/T). Before ponding occurs, the infiltration rate is equal to the rainfall rate. After ponding occurs, the infiltration rate is a function of the infiltration capacity of the soil. The Green-Ampt-Mein-Larson (GAML) model for infiltration rate is a two-stage model with f = R for t ≤ tp, and f is computed with Equation 2.9 after ponding. If R < Ks, surface ponding will not occur, providing the profile is deep and homogeneous as was assumed in the derivation of the equations and f = R. By recognizing that f = dF/dt and accounting for the preponding stage, Mein and Larson (1971) developed an equation for cumulative infiltration over time:  F  K s (t − t p + t ′p ) = F − MSav ln 1 +  MS  av 

(2.12)

where t′p is the equivalent time (T) to infiltrate Fp under initially ponded conditions. Since Equation 2.12 is implicit in F, it might be desirable to increment F and to solve directly for time, t, and then for f from Equation 2.9. A number of studies have been conducted related to estimating the values of the GAML parameters Ks, M, and Sav. Skaggs and Khaleel (1982) reported that Bouwer (1966) and Bouwer and Asce (1969) showed that the hydraulic conductivity parameter should be less than the saturated value because of entrapped air. When measured values are not available, Bouwer (1966) suggested that an effective hydraulic conductivity of 0.5 Ks be used in place of Ks. Other adjustments to Ks have also been recommended to account for the impact of surface conditions on infiltration, resulting in the concept of an effective hydraulic conductivity, Ke. Similarly, it has been suggested that the final moisture content included in the determination of M be something less than saturation due to air entrapment in the field. The most difficult Green-Ampt parameter to estimate is the suction term, presented as effective suction at the wetting front by Green and Ampt and then as average suction at the wetting front by Mein and Larson. One accepted estimation method (Mein and Larson 1973) is using the unsaturated hydraulic conductivity as a weighting factor and defining Sav as 1

∫

Sav = ψ dKr

(2.13a)

0

where ψ is the soil water suction (negative of the matric potential) (L) and Kr is the relative hydraulic conductivity = K(ψ)/Ks. Neuman (1976) obtained a theoretical expression for Sav, similar to Equation 2.13a, by relating it to the physical characteristics of the soil: ψi

Sav =

∫ K dψ r

0


(2.13b)

32


where ψi is the suction at the initial water content. Morel-Seytoux and Khanji (1974) found that for most cases the value of Sav given by Equation 2.13a or 2.13b is a reasonable approximation for an effective matric drive, which is dependent on the relative conductivities of both air and water (Skaggs and Khaleel 1982). Because Equation 2.13 requires the K(ψ) relationship, researchers have developed predictive equations for K(ψ) or Sav , and Ke as well, based on readily available soil characteristics (e.g., Brakensiek and Rawls 1983; Rawls and Brakensiek 1986; Rawls et al. 1989). 2.2.1.3.2 Green-Ampt Approach Implementation The Green-Ampt approach is implemented in several phosphorus models. In ANSWERS-2000, Equation 2.10 is solved using Newton’s iteration technique to determine cumulative infiltration depth, F. The infiltration rate is then computed using Equation 2.9. ANSWERS-2000 replaces Ks with Ke, which is computed as the weighted sum of Ke under canopy cover and Ke for the area outside the canopy. The values are computed as functions of soil parameters, (i.e., Ks, effective porosity, bulk density, residual soil water, sand, silt, and clay fractions) and vegetation parameters (i.e., percent area outside the canopy, percent bare area under canopy, percent canopy area) using equations primarily from Rawls et al. (1989). The available porosity, M, is computed as the difference between porosity corrected for rocks and the antecedent soil moisture content. Sav is computed using an empirical equation developed by Rawls and Brakensiek (1985), in which Sav is a function of total porosity, sand fraction, and clay fraction. For implementation in the SWAT model, Equation 2.10 applied at time (t – ∆t) was subtracted from Equation 2.10 applied at time t to yield the following expression for F at time t:  F + S av M  Ft = Ft −1 + K s ∆t + S av M ln  t   Ft −1 + S av M 

(2.14)

SWAT uses a successive substitution technique to solve Equation 2.14. For each time step, SWAT calculates the amount of water entering the soil. The water that does not infiltrate into the soil becomes surface runoff. SWAT uses effective hydraulic conductivity, Ke, in place of Ks; Ke is computed as a function of Ks and CN, thus incorporating land-cover impacts into the hydraulic conductivity value (Nearing et al. 1996). Similar to ANSWERS-2000, SWAT uses the expression developed by Rawls and Brakensiek (1985) to calculate Sav .

2.2.2 HYDROGRAPH DEVELOPMENT A hydrograph is the relationship between flow rate and time. In some phosphorus models, only the runoff hydrograph as it enters a receiving stream is computed. In others, the spatial variability of the hydrograph along the slope is simulated as well. Some phosphorus models do not directly compute a hydrograph; instead, all of the runoff is assumed to reach the receiving water in a certain time frame or the runoff is lagged in some way to determine when it arrives at the receiving water.



33

Runoff, or overland flow, can be visualized as sheet-type flow — as opposed to channel flow — with small depths of flow and slow velocities (less than 0.3 m/sec). Considerable volumes of water can move through overland flow. Overland flow is spatially varied and usually unsteady and nonuniform — that is, the velocity and flow depth vary in both time and space. Input (rainfall) to the flow is distributed over the flow surface. Methods for determining hydrographs range from direct calculations of the basic hydrograph descriptors — peak flow, time to peak, and base time — to overland flow routing, which yields the relationship of runoff rate with space and time. Examples of the methods used in some phosphorus models are described in the following sections. 2.2.2.1 Kinematic Flow Routing The theoretical hydrodynamic equations attributed to St. Venant are based on the fundamental laws of conservation of mass (continuity) and conservation of momentum applied to a control volume or fixed section of channel with the assumptions of one-dimensional flow, a straight channel, and a gradual slope (Huggins and Burney 1982). With these assumptions, a uniform velocity distribution and a hydrostatic pressure distribution can be assumed, resulting in quasi-linear partial differential equations. Because these equations are not typically implemented in phosphorus models, they are not given here. Detailed derivations of continuity and momentum equations as they apply to unsteady, nonuniform flow can be found in Strelkoff (1969). Lighthill and Whitham (1955), cited by Huggins and Burney (1982), proposed that the dynamic terms in the momentum equation had negligible influence for cases in which backwater effects were absent. Neglecting these terms yields a quasi-steady approach, known as the kinematic wave approximation. The kinematic approximation is composed of the continuity equation ∂y ∂q =I− f + ∂t ∂x

(2.15)

and a flow (depth-discharge) equation of the general form q = α ym

(2.16)

where y is local depth of flow (L), q is discharge per unit width (L3/T/L), I is lateral inflow per unit length and width of the flow plane (L3/T/L2), f is lateral outflow per unit length and width of the flow plane (L3/T/L2), t is time (T), x is the flow direction axis (L), and α and m are parameters. The flow equation can be one describing laminar or turbulent channel flow, with the overland flow plane represented by a wide channel. Overton (1972) analyzed 200 hydrographs for relatively long, impermeable planes and found that flow was turbulent or transitional. Foster et al. (1968) concluded that both Manning’s and Darcy-Weisbach flow equations were satisfactory for describing overland flow on short erodible slopes.


34


The most commonly used flow equation for overland flow is Manning’s equation, which can be written for overland flow as q=

1 5/ 3 1/ 2 y S n

(2.17)

where q is discharge (m3/s/m of width), n is the roughness coefficient, y is flow depth (m), and S is the slope of energy gradeline, usually taken as surface slope (m/m). Values of Manning’s n factor vary from 0.02 for smooth pavement to 0.40 for average grass cover. Manning’s n values are tabulated in a variety of sources (e.g., Linsley et al. 1988; Novotny and Olem 1994). Woolhiser and Liggett (1967) developed an accuracy parameter to assess the effect of neglecting dynamic terms in the momentum equation: k=

So L HF 2

(2.18)

where k is a dimensionless parameter, So is the bed slope (L/L), L is the length of bed slope (L), H is the equilibrium flow depth at the outlet (L), and F is the equilibrium Froude number for flow at the outlet (dimensionless). For values of k greater than 10, very little advantage in accuracy is gained by using the momentum equation in place of a depth–discharge relationship. Since k is usually much greater than 10 in virtually all overland flow conditions, the kinematic wave equations generally provide an adequate representation of the overland flow hydrograph (Huggins and Burney 1982). 2.2.2.2 SCS Unit Hydrograph The SCS unit hydrograph method generates a triangular-shaped hydrograph. The relationship among the time parameters of the hydrograph is described as D D + TL = + 0.6T c (2.19) 2 2 where Tp is time to peak (T), D is duration of excess rainfall (T), TL is lag, or mean travel time (T), and Tc is the time of concentration (T), or travel time from the most hydraulically remote point in the watershed to the watershed outlet. Lag time (h) is computed as Tp =

0.7

0.8

TL=L

 1000  − 9   CN  4407( Sg )0.5

(2.20)

where L is the maximum length of flow (m), CN is the runoff curve number, and Sg is the average watershed gradient (m/m). The peak discharge is a function of amount of runoff computed with Equation 2.1: q p = qu AQ


(2.21)


35

where qp is peak runoff rate (m3/s), qu is unit peak flow rate (m3/s per ha/mm of runoff), Q is the runoff volume (mm), and A is watershed area (ha). Unit peak flow rate, qu, can be obtained from charts (e.g., SCS 1986) or computed from Haan et al. (1994): log(qu ) = C0 + C1 log tc + C2 (log tc )2

(2.22)

where the Cs are from a table as a function of Ia/P, with Ia generally taken as 0.2 S, with S computed from Equation 2.2. 2.2.2.3 Hydrograph Development Implementation Phosphorus models use different methods to develop runoff hydrographs or route overland flow. For example, ANSWERS-2000 uses kinematic routing, HSPF includes a flow equation with an empirical relationship, SWAT computes a runoff lag time for delivery to channels, and AnnAGNPS applies the SCS unit hydrograph. ANSWERS-2000 applies the kinematic wave equations to route overland flow with an explicit, backward difference solution of the continuity equation combined with Manning’s stage-discharge equation. The hydraulic radius in Manning’s equation is assumed equal to the average detention depth in the cell — ANSWERS-2000 represents a watershed as a grid of cells. Detention depth is calculated as the total volume of surface water in a cell minus the retention volume divided by the area of the cell. This implies that the entire specified retention volume of an element must be filled before any water becomes available for surface detention and runoff. ANSWERS-2000 uses a surface detention model developed by Huggins and Monke (1966) to describe the surface storage potential of a surface as a function of the water depth on the soil surface. Each cell acts as an overland flow plane with a userspecified slope steepness and direction. Flow is routed from one cell to another until it enters a channel element, which then routes the runoff to the watershed outlet. In HSPF, overland flow is treated as a turbulent flow process. It is simulated using the Chezy-Manning equation and an empirical expression that relates outflow depth to detention storage. The rate of overland flow discharge is determined by the equations 1.67    3  Sd     O = ∆tCr  Sd 1.0 + 0.6     ,  Se       

(

O = ∆tSr 1.6 S d

)

1.67

,

for Sd < Se

for Sd ≥ Se

(2.23a)

(2.23b)

where O is surface outflow (in./interval), ∆t is the length of the time interval, Cr is the routing variable = 1020 s /nL , Sd is the mean surface detention storage over the time interval (in.), Se is the equilibrium surface detention storage (in.) for current


36


supply rate, s is slope of the overland flow plane (ft/ft), n is Manning’s roughness coefficient, and L is length of the overland flow plane (ft). Equation 2.23a applies when the overland flow rate is increasing, whereas Equation 2.23b applies when the overland flow rate is at equilibrium or receding. SWAT determines when overland flow reaches a channel based on the time of concentration for the overland flow area. If tc is less than one day, SWAT adds the runoff generated on that day to the channel on that day. If tc is greater than one day, only a portion of the surface runoff will reach the main channel on the day it is generated. SWAT incorporates a surface runoff storage feature to lag a portion of the surface runoff release to the main channel. After surface runoff is calculated, the amount of surface runoff released to the main channel is calculated as

Qsurf = (Qsurf ′ + Qstor, i −1

) (1 − e

 − surlag    t c  

)

(2.24)

where Qsurf is the amount of surface runoff discharged to the main channel on a given day (mm), Q′surf is the amount of surface runoff generated on a given day (mm), Qstor, i-1 is the surface runoff stored or lagged from the previous day (mm), surlag is the surface runoff lag coefficient, and tc is the time of concentration for the sub-basin (h). The expression [1 − exp(-surlag/tc)] in Equation 2.24 represents the fraction of the total available water that will be allowed to enter the reach on any one day. For a given tc, as surlag decreases more water is held in storage. The delay in release of surface runoff smooths the streamflow hydrograph simulated in the reach.

2.2.3 STREAMFLOW,

OR

CHANNEL, ROUTING

Many phosphorus models include channel processes in addition to upland processes. Routing streamflow entails computing the effect of channel storage on the shape and movement of a hydrograph, or flood wave. When a flood wave advances into a reach segment, inflow exceeds outflow and a wedge of storage is produced. As the flood wave recedes, outflow exceeds inflow in the reach segment, and a negative wedge is produced. In addition to the wedge storage, the reach segment contains a prism of storage formed by a volume of constant cross-section along the reach length. Streamflow routing involves relationships among inflow, outflow, and storage in each reach or segment of the stream. The continuity equation for unsteady flow relating inflow, outflow, and storage in a reach is

I −O =

dS dt

(2.25)

where I is inflow (L3/T), O is outflow (L3/T), S is storage (L3), and t is time (T). Flow routing procedures typically assume that the average of flows at the beginning



37

and end of a short time period ∆t (routing period) equals the average flow during the period. Expressing Equation 2.25 for a finite time interval yields I1 + I 2 O + O2 ∆t − 1 ∆t = S2 − S1 2 2

(2.26)

where the subscripts 1 and 2 refer to the beginning and end of the time period, respectively. The routing period should be selected to be sufficiently short to ensure that this assumption is not seriously violated. If ∆t is too long (> travel time through reach), the wave crest could pass through the reach during the routing period. Generally, ∆t is 1/2 to 1/3 the travel time through the reach. Most storage routing methods are based on Equation 2.26, which includes two unknowns: the storage and outflow at the end of the time interval. A second relationship is required to determine the unknowns. Different methods define the second relationship in different ways. 2.2.3.1 Hydrologic, or Storage, Routing Hydrologic, or storage, routing is the simplest form of routing and is based on the continuity equation (Equation 2.26) (Haan et al. 1994). The storage in a channel reach depends on the channel geometry and depth of flow. The flow rate can be related to the depth or cross-sectional area of flow, assuming steady, uniform flow using Manning’s equation for each cross-section: q=

1 2 /3 1 /2 R S A n

(2.27)

where q is the flow rate (m3/s); R is the hydraulic radius (m), which is equal to the cross-sectional area of flow divided by the wetted perimeter; S is the slope of the channel (m/m); and A is the cross-sectional area of flow (m2). Manning’s equation was previously presented for overland flow (Equation 2.17), in which an overland flow plane is assumed to be a very wide, shallow channel — which leads to R being approximated by y — and discharge is computed per unit width. A simple method for computing the storage in a reach is to multiply the length of the reach by the average cross-sectional area of the reach at a given flow rate. Flow routed down the channel as the outflow from one reach becomes the inflow to the next reach. Additional inflows from overland flow, tributaries, and ground water can be added to the inflow or outflow of each reach as well. 2.2.3.2 Muskingum Routing Method The Muskingum flow routing method is described in many references. The following description is adapted from Linsley et al. (1988). The Muskingum routing method models the storage volume in a channel length as a combination of wedge and prism storages. As defined by Manning’s equation,


38


the cross-sectional area of flow is assumed to be directly proportional to the discharge for a given reach segment. The Muskingum flow routing method is based on the continuity equation (Equation 2.25). The second relationship between storage and outflow is based on the following expression for storage in a reach of a stream: S=

b [ XI m / n + (1 − X )O m / n ] a

(2.28)

where a and n are constants from the mean stage–discharge relation for the reach, q = ayn, and b and m are constants from the mean stage–storage relation for the reach, S = bym. In a uniform rectangular channel, storage would vary with the first power of stage (m = 1), and discharge would vary as the 5/3 power of stage (Manning’s formula). In a natural channel with overbank floodplains, the exponent n may approach or become less than unity. The constant X expresses the relative importance of inflow and outflow in determining storage. For a simple reservoir, X = 0 (storage has no effect), whereas if inflow and outflow were equally effective, X would be 0.5. For most streams, X is between 0 and 0.3, with a mean value near 0.2. The Muskingum method assumes that m/n = 1 and lets b/a = K, yielding S = K[XI + (1 – X)O]

(2.29)

The constant K, known as the storage constant, is the ratio of storage to discharge and has the dimension of time. It is approximately equal to the travel time through the reach and in the absence of better data is sometimes estimated in this way. If flow data on previous floods are available, K and X are determined by plotting S vs. [XI + (1 – X)O] for various values of X. The best value of X is that which causes the data to plot most nearly as a single-valued curve. The Muskingum method assumes that this curve is a straight line with slope K. The units of K depend on the units of flow and storage. Substituting Equation 2.29 for S in Equation 2.26 and collecting like terms yields O2 = c0I2 + c1I1 + c2O1

(2.30)

KX − 0.5 ∆t K − KX + 0.5 ∆t

(2.30a)

where c0 = − c1 =

KX + 0.5 ∆t K − KX + 0.5 ∆t

(2.30b)

c2 =

K − KX − 0.5 ∆t K − KX + 0.5 ∆t

(2.30c)

c0 + c1 + c2 = 1


(2.30d)


39

The routing period ∆t is in the same units as K. With K, X, and ∆t established, the values of c0, c1, and c2 can be computed. The routing operation then consists of solving Equation 2.30 with the O2 of one routing period becoming the O1 of the succeeding period. To maintain numerical stability and to avoid the computation of negative outflows, the following condition must be met: 2 KX < ∆t < 2 K (1 − X )

(2.31)

2.2.3.3 Streamflow, or Channel, Routing Implementation The SWAT model utilizes either the variable storage routing method developed by Williams (1969) and used in the hydrologic model (HYMO) (Williams and Hann 1973) and routing outputs to outlets (ROTO) (Arnold et al. 1995) models or the Muskingum method. The variable storage-routing method is based on the continuity equation. Travel time is computed by dividing the volume of water in the channel by the flow rate. Substituting the relationship for travel time into the continuity equation (Equation 2.26) and simplifying yields the expression for outflow from the reach segment:  2 ∆t   I1 + I 2  O2 =  + S1     2T T + ∆t   2 

(2.32)

where T T is travel time. In the implementation of the Muskingum routing procedure in SWAT, the value for the weighting factor, X, is input by the user. As just noted, for most streams X is between 0 and 0.3 with a mean value near 0.2. The user can use this information or site-specific knowledge to assign a value for X. The value for K, the storage time constant, is estimated as K = coef1K bnkfull + coef2 K 0.1bnkfull

(2.33)

where K is the storage time constant for the reach segment, coef1 and coef2 are weighting coefficients input by the user, Kbnkfull is the storage time constant calculated for the reach segment with bankfull flows, and K0.1bnkfull is the storage time constant calculated for the reach segment with one tenth of the bankfull flows. An equation developed by Cunge (1969) is used to calculate Kbnkfull and K0.1bnkfull. Routing in HSPF is also based on the continuity equation. The second relationship is based on the assumption that outflows are functions of volume or time, or a combination of the two. If the outflow is a function of volume, the user defines the depth-surface area-volume-discharge relationship in an input table (an FTABLE in HSPF terms). This is one of four optional methods for computing overland flow. Another method is a simple power function method. Some phosphorus models also include transmission, or leaching, losses from channels during periods when a stream receives no groundwater contributions.


40


For example, SWAT uses Lane’s method described in Chapter 19 of the SCS Hydrology Handbook (SCS 1983) to estimate transmission losses from intermittent or ephemeral channels. Water losses from the channel are a function of effective hydraulic conductivity of the channel alluvium, flow travel time, wetted perimeter, and channel length. Both volume and peak rate are adjusted when transmission losses occur in tributary channels.

2.2.4 PEAK RATE

OF

RUNOFF

2.2.4.1 Rational Formula The rational method is the most common method used for peak flow estimation in practice. The method is presented in many references. The following description is based on Haan et al. (1994). The rational equation is q p = CiA

(2.34)

where qp is the peak rate of runoff (cfs), C is a dimensionless runoff coefficient, i is the rainfall intensity (in./h) for a duration equal to the time of concentration, tc, and A is the drainage area (ac). To be dimensionally correct, a conversion factor of 1.008 should be included to convert acre-inches per hour to cubic feet per second; however, this factor is generally neglected. Time of concentration, tc, is defined as the travel time from the most hydraulically remote point in the watershed to the watershed outlet and is typically computed as a function of the length of flow and the slope of the watershed. The basic concept of the rational equation is as follows. If a steady rainfall occurs on a watershed, the runoff rate will increase until the entire watershed is contributing runoff. If a rainfall of duration less than tc occurs, the entire basin will not be contributing, so the resulting runoff rate will be less than from a rainfall with a duration equal to tc. If a rainfall of duration greater than tc occurs, the relationship between average rainfall intensity and duration for a given frequency shows that the average intensity will be less than if the duration was equal to tc. Thus, it is reasoned that a rainfall of duration tc produces the maximum flow rate. The rational equation is based on several assumptions: The rainfall occurs uniformly over the drainage area. The peak rate of runoff can be reflected by the rainfall intensity averaged over a time period equal to the time of concentration for the drainage area. The frequency of runoff is the same as the frequency of the rainfall used in the equation. The runoff coefficient, C, is the most difficult factor to accurately determine since it represents the impact of many factors — such as interception, infiltration, surface detention, and antecedent moisture conditions — on the peak runoff. Various tables



41

of C values are available in many sources. Some provide ranges of values for different conditions such as land use, rainfall intensity, and soil texture. Others provide single values for combinations of factors. Haan et al. (1994) note that in spite of the recognized shortcomings of the rational method, it continues to be widely used because of its simplicity, entrenchment in practice, coverage in texts, and lack of a comparable alternative. 2.2.4.2 SCS TR-55 Method SCS (1986) presented the Graphical method for computing peak discharge from rural and urban areas. The Graphical method was developed from hydrograph analyses using TR-20, “Computer Program for Project Formulation — Hydrology” (SCS 1983). In the Graphical method, the peak discharge equation is computed as qp = qu AQFp

(2.35)

where qp is the peak discharge (cfs), qu is the unit peak discharge (cfs/mi2/in. runoff), A is the drainage area (mi2), Q is the runoff (in.), and Fp is a pond and swamp adjustment factor. The unit peak discharge, qu, is a function of tc and Ia/P, the ratio of initial abstraction to rainfall amount. SCS (1986) provided tables and figures for determining qu based on known tc, CN, and P. Q is computed from the curve number equation, Equation 2.1, based on a 24-h P with a return period of the peak flow. Fp is based on the percentage of ponds and swampy areas, assumed to be distributed throughout the watershed. The value of Fp ranges from 1.0 for 0% pond and swamp areas to 0.72 for 5% pond and swamp areas. 2.2.4.3 Peak Runoff Rate Implementation Some phosphorus models do not include calculations of peak runoff rate. In some models, peak discharge can be determined from overland flow routing. In other models, peak runoff rate is computed for use in erosion calculations but not in hydrologic calculations. EPIC and SWAT compute peak runoff rate using a modified rational formula, whereas AnnAGNPS computes peak discharge similar to the TR-55 method, and GLEAMS uses a different empirical relationship. In EPIC and SWAT, the peak runoff rate is predicted based on a modification of the rational formula, with different units used in the two models:

qp =

αQA 360tc

in EPIC

qp =

α t QArea c

3.6tc

in SWAT

(2.36)

where qp is peak runoff (m3/s), α is a dimensionless parameter expressing the proportion of total rainfall that occurs during tc, Q is runoff volume (mm), A is drainage area (ha), tc is time of concentration (h), α tc is the fraction of daily rainfall


42


that occurs during tc, Area is drainage area (km2), and 360 and 3.6 are unit conversions. Equation 2.36 results from relationships for C and i, described in the following paragraphs, substituted into Equation 2.34 with changes in units. The runoff coefficient, C, is calculated for each storm as the ratio of the runoff volume and the amount of rainfall. The runoff volume is computed in the model, and rainfall is an input to the model. This modification eliminates the need to estimate C from published tables. The rainfall intensity, i, is determined as the average rainfall rate during the time of concentration. An analysis of rainfall data collected by Hershfield (1961) for different durations and frequencies showed that the amount of rain falling during the time of concentration, Rtc, was proportional to the amount of rain falling during the 24-h period, or Rtc = α tc R24 , where αtc is the fraction of daily rainfall that occurs during the time of concentration. For short-duration storms, all or most of the rain will fall during the time of concentration, causing αtc to approach its upper limit of 1.0. The minimum value of αtc would be seen in storms of uniform intensity (i24 = i). Thus, αtc falls in the range tc/24 ≤ α tc ≤ 1.0. When the value of α tc is assigned based on only daily rainfall and simulated runoff, there is considerable uncertainty. Thus, in EPIC α is generated from a gamma function with the base ranging from tc/24 to 1.0. SWAT estimates αtc as a function of the fraction of daily rain falling in the half hour of highest intensity rainfall:

α tc = 1 − e[ 2tc ln(1−α 0.5 )]

(2.37)

where α0.5 is the fraction of daily rain falling in the half hour of highest-intensity rainfall. If subdaily precipitation data are used in the model, SWAT calculates the maximum half hour rainfall fraction directly from the precipitation data. If daily precipitation data are used, SWAT generates a value for α0.5 from a triangular distribution, which requires four inputs: (1) average monthly half hour rainfall fraction, (2) maximum value for half hour rainfall fraction allowed in month, (3) minimum value for half hour rainfall fraction allowed in month, and (4) a random number between 0.0 and 1.0. The time of concentration is computed in EPIC and SWAT as the sum of surface and channel flow times. The time of concentration for channel flow is computed as the average channel flow length for the watershed divided by the average channel velocity. Average channel flow length is estimated as Lc = ( L )( Lca )

(2.38)

where L is the channel length from the most distant point to the watershed outlet (km) and Lca is the distance along the channel to the watershed centroid (km). Average velocity is estimated using Manning’s equation, assuming a trapezoidal channel with 2:1 side slopes and a 10:1 bottom width-to-depth ratio. Further,



43

assuming that Lca = 0.5 L and that the average flow rate is about 6.35 mm/h and is a function of the square root of drainage area yields the final equation for the time of concentration for channel flow, tcc: tcc =

1.1Ln 0.75 A0.125σ 0.375

(2.39)

where n is Manning’s roughness coefficient and σ is the average channel slope (m/m). A similar approach is used to estimate time of concentration for surface flow, tcs, assuming that tcs is the surface slope length divided by the surface flow velocity. Manning’s equation was applied to a strip 1 m wide and the average flow rate was assumed to be 6.35 mm/h. The resulting equation for estimating tcs in hours is tcs =

(λ n)0.6 18 S 0.3

(2.40)

where λ is the surface slope length (m) and S is the land surface slope (m/m). Williams et al. (1990) noted that although some of the assumptions used in developing the equations for tcc and tcs may appear liberal, they generally give satisfactory results from small homogeneous watersheds. The authors also stated that since the equations are based on hydraulic considerations, they are more reliable than purely empirical equations. For implementation in AnnAGNPS, the TR-55 Graphical method was extended to apply to drainage areas with tc greater than 10 h and to Ia/P ratios from 0 to 1. The equation is implemented in AnnAGNPS as  a + ctc + etc2  q p = 2.77777778 ⋅ 10 −3 P24 Da  3  2  1 + btc + dtc + ftc 

(2.41)

where qp is peak discharge (m3/s), P24 is 24-h effective rainfall (mm), Da is drainage area (ha), tc is time of concentration (h), and a, b, c, d, e, and f are regression coefficients for a given Ia/P and rainfall distribution type. The regression coefficients eliminate the need for look-up tables in the program. In GLEAMS, peak flow rate for daily runoff is computed with an empirical relationship: q p = 200( DA)0.7 S 0.159Q 0.917 DA0.0166 ( LW )−0.187

(2.42)

where qp is the peak runoff rate (ft3/s), DA is the drainage area (mi2), S is the hydraulic slope (ft/mi), Q is the daily runoff volume (in.), and LW is the length-to-width ratio of the watershed. The hydraulic slope of a field is defined as the slope of the longest flow path. The longest flow path is the flow line from the most remote point on the


44


field (drainage) boundary to the outlet of the field. This length and difference in elevation from the most remote point to the outlet are the same as those used in estimating a time of concentration of a drainage area. As the length-to-width ratio increases, the peak rate of runoff decreases — that is, runoff is attenuated, and the runoff peak occurs later in the runoff period.

2.3 MODELING EROSION AND SEDIMENT YIELD Erosion can be divided into three processes: detachment, transport, and deposition. Detachment is the dislodging of soil particles (sediment) by raindrop impact or runoff over the soil surface. Detachment occurs when the erosive forces of raindrop impact or flowing water exceed the soil’s resistance to detachment or when the kinetic energy of water exceeds the shear strength (cohesiveness) of the soil. After particles are detached, they are available for transport. Transport is movement of sediment from its original location (source area) to downslope locations. Some transport is caused by splash resulting from the impact of raindrops. The transport capacity of the flowing water is a function of the kinetic energy of the water and sediment characteristics — particle size, density, and shape. Raindrops impacting shallow flow will enhance the transport capacity of runoff. The third process, deposition or sedimentation, refers to the settling of sediment particles out of the flowing water. The transport capacity of flowing water varies for different particle types. Deposition occurs when the sediment load of a given particle type exceeds its corresponding transport capacity. Transport capacity varies as the velocity of the flowing water varies due to changes in surface conditions, such as vegetative cover, slope steepness, and, in the case of shallow rain-impacted flow, raindrop size, velocity, and frequency. Sediment is typically deposited on the toe of slopes and on flood plains. Because phosphorus is adsorbed more to finer soil particles than to coarser particles, the distribution of sediment particle sizes is also important. Because deposition of sands occurs first, followed by large aggregates and then small aggregates, the distribution of particles in the sediment leaving a field or entering a water body is usually different than the residual soil in the field. This increase in the proportion of fine soil particles is referred to as enrichment. One measure is the enrichment ratio; that is, the ratio of the specific surface area of the sediment to the specific surface area of the residual soil. The term sheet erosion describes removal of soil in thin layers from sloping land. Very little soil might move in this manner because water does not typically flow as a sheet down a slope, except on slopes with low gradients. Often, a flow pattern of small well-defined channels, or rills, forms, and erosion occurs in the rills and the areas between the rills, commonly termed rill and interrill erosion. Rills are generally 3 to 300 mm in depth. Through interrill erosion, soil is moved by raindrop splash and overland flow to rills. Flowing water in rills detaches soil particles from the rills and transports sediment originating in both rills and interrill areas. Rill erosion is a function of soil critical shear stress; cover conditions; soil slope; and surface runoff depth, velocity, and energy. Gully erosion is an advanced form of rill



45

erosion. Gullies can be described as rills, or channels, that are greater than 300 mm in depth and that cannot be removed by ordinary tillage operations. Erosion also occurs in stream channels. Soil can be removed from stream banks (undercut banks) or the bed. Channel erosion is similar to rill and gully erosion except it occurs in perennial streams (continuously flowing) as opposed to rill and gully erosion, which are ephemeral in nature. Approaches used in phosphorus models to simulate upland erosion and sediment yield can be classified into two general categories: approaches based on the Universal Soil Loss Equation (USLE) and process-based approaches. Some of the newer, more physically based erosion modeling approaches such as Water Erosion Prediction Project (WEPP) (Laflen et al. 1997) are not described here because such detailed modeling is generally not included in phosphorus models.

2.3.1 USLE-BASED APPROACHES The USLE was developed by Wischmeier and Smith (1965, 1978) to predict longterm average annual erosion (rill and interrill combined) for conservation planning — that is, for determining appropriate combinations of cropping systems and management practices for specific fields to meet soil conservation goals. Site-specific characteristics represented in the equation include soil type, rainfall patterns, topography, and cropping and management practices. The USLE does not predict deposition or sediment yield and does not predict gully or channel erosion. The USLE (Wischmeier and Smith, 1978) is expressed as A = RKLSCP

(2.43)

where A is soil loss per unit area (M/L2/T), R is the rainfall and runoff factor (EI units/T, where T is usually annual), K is the soil erodibility factor (M/L2/EI unit from the unit plot), L is the slope length factor (dimensionless), S is the slope steepness factor (dimensionless), C is the cover and management factor (dimensionless), and P is the support practice factor (dimensionless). The numerical value for R in the soil loss equation must quantify the raindrop impact effect and must also provide relative information on the amount and rate of runoff likely to be associated with the rain (Wischmeier and Smith 1978). The rainfall erosion index derived by Wischmeier (1959) was selected as best in meeting those requirements. Values for average annual R were presented on a map of the U.S. (Wischmeier and Smith 1978). Further discussion of the R factor by Wischmeier and Smith (1978) explained the concept of the EI rainstorm parameter. EI for a given rainstorm is defined as the product of total storm energy (E) and the maximum 30-min intensity (I30), where E is in hundreds of ft-tons per acre and I30 is in in./h. The sum of the storm EI values for a given period is a numerical measure of the erosive potential of the rainfall within that period. The average annual total of the storm EI values in a particular locality is the rainfall erosion index for that locality. Because of apparent cyclical patterns in rainfall data, the published rainfall erosion index values were generally based on station rainfall records exceeding 20 years.


46


The soil loss equation and factor evaluation charts were initially developed in terms of English units commonly used in the U.S., with A being computed in tons/ac/yr; R in 100 ft-tons/acre × in./h, defined as a Wischmeier English EI unit (Foster 1982); and K in tons/ac × EI. Wischmeier and Smith (1978) noted that because the factor definitions are interdependent, direct conversion of acres, tons, inches, and feet to metric units would be awkward and undesirable; converting the computed A value is more desirable. The factors L, S, C, and P were derived based on a unit plot concept. The unit plot is 72.6 ft long with a uniform 9% slope in clean-tilled continuous fallow condition with straight-row farming up and down the slope. The values of the L, S, C, and P factors are ratios of soil loss for the field and management system of interest to a field with the unit plot conditions. Thus, the USLE computes erosion for a unit plot as RK and then adjusts that value by multiplying by LSCP to account for the difference in erosion between the unit plot and the area of interest. Values for R, K, L, S, C, and P are available in Wischmeier and Smith (1978) as well as in other references. Values for those factors have been developed through field experiments and other analyses. Generally in phosphorus modeling, sediment yield is the quantity of interest as opposed to the average annual soil erosion or movement within a field or site. Estimates of sediment yield based on the USLE are often computed by multiplying the USLE soil erosion value by a sediment delivery ratio or by the ratio of sediment yield to gross erosion. Sediment delivery ratios lump together all the transport and deposition processes that occur in a field or watershed into a single value. Sediment delivery ratios are typically determined using empirical functions of watershed characteristics such as slope length and drainage area. Such sediment delivery ratios should be used with caution because sediment delivery depends on additional factors such as runoff amount and peak runoff (Williams 1975); upslope erosion, unless no deposition occurs (Kinnell 2004b); and sediment characteristics (Walling 1983). The Revised USLE (RUSLE) (Renard et al. 1991, 1997) was developed to update the USLE based on more recent data as well as a new evaluation of the original USLE. RUSLE is essentially the same as the USLE, with some differences in the estimation of some factor values. The R factor is the same except that RUSLE includes updated values for the western U.S. and accounts for the reduction in erosion due to ponding on flat slopes. RUSLE includes seasonal variation of K, whereas the USLE K is assumed constant through the year. The S factor in RUSLE is significantly modified from the original USLE as a result of extensively reevaluating the original database, adding factors for short slope lengths, and providing new values for thawing soils (McCool et al. 1987). The L factor was developed by McCool et al. (1989) from the original USLE database, augmented with theoretical considerations. The factor is computed in the same way, but the exponent in the relationship used in RUSLE is a function not only of slope steepness, as in the USLE, but also of the ratio of rill-to-interrill erosion for the soil. The USLE C factor is a lumped factor to account for above-ground, surface, and below-surface effects. RUSLE uses a subfactor approach in which subfactors accounting for prior land use, canopy cover, surface cover, surface roughness, and soil moisture are multiplied to yield the C



47

factor. These subfactors depend on cropping and management and can be expressed as a function of residue cover, canopy cover, canopy height, surface roughness, below-ground root mass and residue, prior cropping, and time. RUSLE also uses a subfactor approach for the P factor. Subfactors account for contouring, strip cropping, and terracing. Use of subfactors allows a more detailed evaluation of factors affecting P, particularly when considering a combination of practices. Also, it allows a correction for the impact of large storms on contouring. Three major limitations of the USLE restrict its application in many modeling analyses (Foster 1982). First, the USLE is not intended for estimating soil loss from single storm events. Second, it is an erosion equation and does not estimate deposition. Third, it does not estimate gully or channel erosion. Several modifications of the USLE have been developed to address these limitations. Williams (1975) replaced the USLE R factor with runoff variables in developing the Modified USLE (MUSLE) to compute sediment yield: Y = 11.8(Q*q p )0.56 KLSCP

(2.44)

where Y is the sediment yield (t/ha), Q * is the runoff volume (m3), and qp is the peak runoff rate (m3/s). Williams (1975) concluded that runoff variables increased the prediction accuracy, eliminated the need for a delivery ratio, which was used in the USLE to estimate sediment yield, and enabled the equation to give single-storm estimates of sediment yield. Foster et al. (1973) modified the USLE to include both rainfall and runoff terms (Onstad and Foster 1975):

(

)

A = 0.5 Rst + 15Qq1p/ 3 KLSCP

(2.45)

where A is soil loss for a storm (tons/ac), Rst is the storm rainfall factor (EI units), Q is the runoff volume (in.), and q*p is the peak runoff rate (in./h). The objective of the modification was to better account for the contributions of interrill and rill erosion than the original USLE by using terms more directly targeted at these two forms of erosion. The coefficients were evaluated assuming that under certain conditions detachment by rainfall and runoff is about evenly divided. Equations like 2.44 and 2.45 that specify the USLE or the RUSLE variables K, C, and P when the R factor is not based on EI, the product of total storm energy and the maximum 30-min intensity, are not sound (Kinnell 2004a). K is, by definition, the average annual soil loss per unit of R. If the basis of R is changed, then values of K that differ from those used in the USLE and RUSLE must be used. Also, since runoff is not explicitly considered in determining the R factor in the USLE and RUSLE, variations in runoff associated with variations in vegetation, crop management, and support practices are incorporated implicitly in the USLE and RUSLE C and P factors. Consequently, the USLE and RUSLE C and P factors can only be used if runoff for the unit plot condition is used in determining R.


48


The USLE and RUSLE overpredict small soil loss and underpredict high soil loss (Risse et al. 1993). The failure of the EI index to explicitly consider runoff as a factor in determining the erosivity of individual rainfall events is a major factor in generating this overprediction–underprediction problem. Kinnell and Risse (1998) showed that combining the EI index with the runoff ratio markedly improved the accuracy of the prediction of erosion if event runoff amount was determined accurately.

2.3.2 USLE-BASED APPROACH IMPLEMENTATION EPIC contains three equations to simulate rainfall and runoff erosion: the USLE, the MUSLE (Williams 1975), and the Onstad-Foster modification of the USLE (Onstad and Foster 1975). The model user specifies which equation interacts with other EPIC components. As indicated previously, the three equations are identical except for their energy components. In EPIC, a coarse fragment factor, which is a function of the percent rock in the first soil layer, has been added to each equation as a multiplicative factor. Erosion is calculated in SWAT using MUSLE with the coarse fragment factor. SWAT also provides USLE estimates of erosion for comparison purposes. The USLE estimates are not used for any calculations in SWAT. Delivery of sediment to the main channel from overland flow is lagged in SWAT for large drainage areas with a time of concentration greater than one day, similar to the lag of runoff (Equation 2.24). After the sediment load in surface runoff is calculated, the amount of sediment released to the main channel is calculated as  − surlag       sed = (sed ′ + sed stor,i −1 ) 1 − e  tc      

(2.46)

where sed is the amount of sediment discharged to the main channel on a given day (metric tons), sed′ is the amount of sediment load generated on a given day (metric tons), sedstor,i-1 is the sediment stored or lagged from the previous day (metric tons), surlag is the surface runoff lag coefficient, and tc is the time of concentration (h). The expression [1 − exp(-surlag/tc)] in Equation 2.46 represents the fraction of the total available sediment that will be allowed to enter the reach on any one day. The sheet and rill erosion model in AnnAGNPS is based on RUSLE. Factor values are determined for each cell; AnnAGNPS represents a watershed as a grid of cells. The C factor is assigned an annual value for non-cropland and a series of 24 values, each representing an increment of 15 or more days, for each year in the operation management schedule for cropland. The P factor is assigned an annual value for non-cropland and a series of annual values for cropland, one value for each year in the operation management schedule. EI values are expressed for the watershed as 24 values, each representing an increment of 15 or more days, for the calendar year. The delivery ratio for each cell to its receiving reach is computed by particle-size classes, proportioned to the respective fall velocities of the classes. AnnAGNPS also computes gully erosion. The runoff from the cell that drains through the gully is based on the ratio of the gully drainage area to the cell drainage area. The mass of sediment is determined from gully runoff and a power equation using



49

a user-supplied coefficient and exponent for the equation (Merkel et al. 1988). The sediment from the gully is added to the appropriate stream reach.

2.3.3 PROCESS-BASED APPROACHES Process-based approaches represent detachment, transport, and deposition separately, in contrast to the USLE, which computes an overall erosion rate. Rill and interrill erosion are often calculated separately. Channel erosion is represented as a separate process. The main concept for modeling upland erosion is that sediment load is controlled by either the amount of sediment made available for transport through detachment or the transport capacity of the flowing water. Deposition occurs when sediment load exceeds transport capacity. Detachment by flow can occur when transport capacity exceeds sediment load. A detachment capacity can be defined based on the local conditions, but the actual detachment rate depends on the degree to which the transport capacity is filled. Conservation of mass of sediment provides a framework for the interrelationship among detachment, transport, and deposition. Bennett (1974) presented the conservation of mass (continuity) equation for sediment, including dispersion of sediment while it is suspended in flow. The form of the equation normally used in dynamic upland erosion models omits dispersion because it is normally negligible (Foster 1982): ∂qs ∂(cy) + ρs = Dr + Dl ∂x ∂t

(2.47)

where qs is the sediment load per unit width (M/L/T), x is distance along the slope (L), ρs is mass density of the sediment particles (M/L3), c is concentration of the sediment in the flow (volume of sediment/volume of flow, L3/L3), y is flow depth (L), t is time (T), Dr is rill erosion rate (M/L2/T), and Dl is delivery rate of sediment from interrill areas (M/L2/T). The term ∂qs /∂x is the build-up or loss of the sediment load with distance; ρs ∂(cy)/∂t is the storage rate of sediment with the flow depth; and Dr and Dl are contributions of sediment from lateral inflow. Dr and Dl are the net result of detachment and transport by rainfall and runoff. To solve the continuity equation for sediment, relationships are needed for Dr , Dl, and shear stress. A number of relationships have been proposed to describe the various processes. Some of those relationships are summarized in the following paragraphs. The next section provides examples of the relationships used for the various erosion processes in phosphorus models. Relationships have been proposed that relate detachment by rainfall, which is important in interrill erosion, to both rainfall and soil characteristics. Many investigators have found that the amount of soil detached by rainfall is directly related to rainfall intensity. Total rainfall mass, or kinetic energy at impact, also has been found to influence rainfall erosivity. A number of soil characteristics have been identified as influencing rainfall detachment (e.g., moisture content, organic matter, pH, structure, bulk density, amount of air-filled pore space, degree of aggregation, particle


50


size, percentage of clay). The influence of overland flow on detachment by rainfall has been included in some relationships. Transport by rainfall, or splash, is a function of slope steepness, amount of rain, rainfall intensity, soil properties, microtopography, and wind velocity. Though this form of transport is often negligible and not included in most models, relationships have been proposed to describe transport by rainfall as a function of rainfall and soil properties. Detachment by overland flow is a function of the shear stress, or tractive force, on the soil boundary. Shear stress is defined by the surface slope and the velocity and depth of flow (Kilinc and Richardson 1973). Relationships have been proposed that express detachment by runoff as a function of variables such as flow rate, velocity, slope, shear stress, critical shear stress, and soil erodibility. Transport by runoff is a function of flow rate, depth, and velocity, rainfall effects, soil depth, and slope steepness. Transport capacity also depends on sediment characteristics, such as particle size and density. Though differences exist between the hydraulics of shallow flows in upland areas and deeper channel flows, important similarities can be identified between streamflow and shallow flow concentrated in small channels. Researchers have investigated the applicability of sediment transport equations for streamflow to transport by overland flow. Alonso et al. (1981) evaluated nine sediment transport equations with respect to field and laboratory data. They concluded that although no equation satisfactorily represented the entire spectrum of sediment and flow characteristics, three of the tested equations could give satisfactory estimates of transport capacity over different subsets of the data range. The Yalin (1963) equation can be used to compute sediment transport capacities for overland flows and to predict transport rates of light materials in streamflows. The Yang (1973) equation best estimated streamflow transport capacity in the range of fine to coarse sands, whereas the Laursen (1958) equation predicted reasonably for small streamflows carrying very fine sands and silts. Foster and Meyer (1972) also chose the Yalin equation for determining transport capacity of overland flow because of the equation’s theoretical soundness for shallow flow. The Yalin equation assumes that sediment motion begins when the lift force of flow exceeds a critical lift force (Foster and Meyer 1972). Once a soil particle is entrained in flowing water, the drag force of the flow carries the particle downstream until the particle weight forces it out of the flow and back to the ground surface or channel bed. Observations of the erosion process on natural soils during simulated rainstorms indicated that a large fraction of the transported soil moves by saltation and by a rolling fashion along the bottom of the small-flow channels. Such soil is detached and transported in the form of aggregates having larger diameters but lower densities than primary particles (Moldenhauer and Koswara 1968). When the flow slows, these aggregates readily deposit. These observations indicate that once aggregates are detached from cohesive agricultural soils, their transport is very similar to that of noncohesive grains, the type of particles for which the Yalin equation was developed. Foster and Meyer (1972) also cited the simplicity of the equation and its excellent fit to observed data as reasons for selecting it. The Yalin equation requires only two common flow parameters: hydraulic radius and slope of the energy-grade line. The



51

transportability of a soil is described by particle density, particle diameter, and the critical lift force, which is given by the extended Shields’ diagram (Mantz 1977). Foster and Meyer (1972) presented the Yalin equation as  1  Ws = 0.635δ 1 − ln(1 + σ )  Sg ρw dV* g  σ 

(2.48)

where

σ = Aδ δ=

(2.48a)

Y − 1 (if Y < YCR, δ = 0) YCR

A = 2.45( Sg )−0.4 (YCR )0.5 Y=

V*2 ( Sg − 1) gd

V = ( gRS f)1/ 2

(2.48b)

(2.48c)

(2.48d)

(2.48e)

where Ws is transport capacity (M/L/T), Sg is particle specific gravity (dimensionless), ρw is mass density of the fluid (M/L3), d is particle diameter (L), V* is shear velocity (L/T), g is acceleration of gravity (L/T2), δ is the dimensionless excess tractive force, YCR is critical lift force given by the Shields’ diagram, R is hydraulic radius, and Sf is slope of the energy-grade line. In the derivation of the equation, the constant 0.635 is the only empirically derived factor other than the critical lift force from the Shields’ diagram. The Yalin equation was developed for particles of uniform size. Foster and Meyer (1972) modified the equation to predict transport rates of mixtures. The basis of the Yalin derivation was that the sediment transport rate is equal to the number of particles in transport over a unit area times the weight and velocity of each particle. To modify the equation, a mixture of sizes was assumed to reduce the number, but not the velocity, of particles of a given size in transport. Yalin assumed the number of particles in transport to be proportional to δ. For a mixture, the number of particles of a given size i was assumed to be proportional to δi. Then the number of transported particles of size i in a mixture was δ  ( N e )i = N i  i  T

(2.49)

where Ni is the number of particles transported in sediment of uniform size i for a δi and T = ∑in=1 δ i where n is the number of size groups.


52


As derived by Yalin, the left side of Equation 2.48 is proportional to the number of particles in transport. If the left side of Equation 2.48 is equal to P, the nondimensional transport is then ( Pe )i =

Piδ i T

(2.50)

where (Pe)i is the effective P for particle size i in a mixture and Pi is P calculated for uniform material of size i. The actual transport rate, Wsi, of each particle size in a mixture is then expressed as Wsi = ( Pe )i Sg ρw gdV*

(2.51)

2.3.4 PROCESS-BASED APPROACH IMPLEMENTATION Some models, including GLEAMS, HSPF, and ANSWERS-2000, use a processbased approach to model erosion. Specifically, they consider detachment, transport, and deposition processes discretely. The GLEAMS model uses the same equations as the CREAMS model with only slight modifications. The following description of the GLEAMS erosion equations is from Foster et al. (1980). Detachment is computed as q  DI = 0.210 EI (s + 0.014) KCP  p   Vu   x  DR = 37983mVu q1p/ 3   72.6 

m −1

(2.52)

 qp  s 2 KCP    Vu 

(2.53)

where DI is interrill detachment rate (lb/ft2/sec), DR is rill detachment capacity rate (lb/ft2/sec), EI is Wischmeier’s rainfall erosivity (energy × 30-min intensity), x is length of the overland flow element (ft), s is sine of the slope angle, m is slope length exponent, K is USLE soil erodibility factor [(tons/ac)(ac/100 ft-tons)(h/in.)], C is USLE cover management factor, qp is peak runoff rate (ft/sec), and Vu is runoff volume (ft). Equations 2.52 and 2.53 were derived from the equation of continuity for sediment transport (Bennett 1974), incorporating expressions to describe rill and interrill erosion (Foster et al. 1977). The sum of Equation 2.52 and 2.53 defines the sediment load. Sediment transport by overland flow is computed in GLEAMS using the Yalin equation for multiple particle classes — sand, silt, clay, and small and large aggregates––with sizes estimated internally after Foster et al. (1985). HSPF includes calculations of detachment by rainfall and runoff, transport, and deposition. Soil detachment by rainfall is computed as  RAIN  DET = ∆t (1.0 − CR)( SMPF )( KRER)   ∆t 


JRER

(2.54)


53

where DET is sediment detached from the soil matrix by rainfall (tons/ac/interval), ∆t is time interval (h), CR is the fraction of the land covered by snow and other cover, SMPF is the supporting management practice factor based on the USLE P factor, KRER is a detachment coefficient dependent on soil properties, RAIN is rainfall intensity (in./interval), and JRER is a detachment exponent dependent on soil properties. When simulating the washoff of detached sediment, the transport capacity of the overland flow is estimated and compared to the amount of detached sediment available. HSPF includes two options for these calculations. One option is identical to the method used in the Agricultural Runoff Management (ARM) model (Donigian and Crawford 1976b; Donigian et al. 1977) and Nonpoint Source (NPS) model (Donigian and Crawford 1976a), which are both predecessors to HSPF that include some dimensionally nonhomogeneous equations designed for 15- and 5-min intervals. The second option is dimensionally homogeneous and generally less dependent on the time step. In the second option, the transport capacity is calculated as  SURO  STCAP = ∆t ( KSER)   ∆t 

JSER

(2.55)

where STCAP is the capacity for removing detached sediment (tons/ac/interval), KSER is a coefficient for transport of detached sediment, SURO is surface outflow of water (in./interval), and JSER is an exponent for transport of detached sediment. The amount of washoff of detached sediment, WSSD (tons/ac/interval), is equal to the detached sediment storage when STCAP exceeds the amount of sediment in storage. When STCAP is less than the amount of detached sediment in storage, the situation is transport limiting, so WSSD is equal to STCAP. In addition, detachment and transport of soil particles from the soil matrix by flowing water is computed as  SURO  SCRSD = ∆t ( KGER)   ∆t 

JGER

(2.56)

where SCRSD is scour of matrix soil (tons/ac/interval), KGER is a coefficient for scour of the matrix soil, and JGER is an exponent for scour of the matrix soil. The sum of the two fluxes, WSSD and SCRSD, represents the total sediment outflow from the land segment.

2.3.5 CHANNEL EROSION Detachment (or scour), transport, and deposition in channels are functions of flow, channel, and sediment characteristics. Incoming flow and sediment affect channel erosion. If the incoming sediment load exceeds the flow’s transport capacity, deposition occurs. If incoming sediment load is less than the transport capacity, erosion can occur. In channels where deposition occurred previously during periods of excessive upland erosion, sediment yield might continue at a high rate after upland sediment yield is reduced because the previously deposited sediment is susceptible


54


to being eroded. Often in modeling, however, the previously deposited sediment is assumed to have the same critical shear stress as the channel soil. Similar to upland erosion, channel erosion simulation methods are often based on the continuity equation for sediment. Transport capacity can be represented by several different sediment transport equations for channels. Detachment is often based on shear stress exerted by the flowing water as compared to the critical shear stress required to detach soil from the stream bed or bank.

2.3.6 CHANNEL EROSION IMPLEMENTATION HSPF simulates transport, deposition, and scour of sediment separately for noncohesive (sand) particles and for cohesive (silt and clay) particles. Erosion and deposition of sand is affected by the transport capacity of the flow. If the amount of sand being transported is less than the transport capacity, then sand will be scoured from the bed. Scour occurs until the actual sand load becomes equal to the carrying capacity of the flow or until the available bed sand is all scoured. Conversely, deposition occurs if the sand load exceeds the transport capacity. The user selects one of three methods to compute transport capacity of the flow for sand: the Toffaleti’s method, the Colby method, or a user-provided power function of velocity. In Toffaleti’s method, the stream is divided into four zones: bed, lower, middle, and upper, which extends to the surface. The sand particle concentration is computed by a power relation for each of the three upper zones. The velocity profile is represented by a power relation. Transport capacity is then computed for each zone based on the concentration and velocity. The total sand transport capacity is the sum of the transport capacity for the four zones. Colby’s method computes transport capacity using empirical relationships based on the median bed sediment diameter, average stream velocity, hydraulic radius, fine sediment load concentration, and water temperature. The deposition and scour of cohesive sediment fractions (silt and clay) in HSPF is dependent on the shear stress exerted on the bed surface. Whenever shear stress is less than the user-supplied critical shear stress for deposition, deposition occurs. Whenever shear stress is greater than critical shear stress for scour, scouring of cohesive bed sediments occurs. Shear stress is calculated as a function of the slope and hydraulic radius of the reach. The concentration of suspended sediment lost to deposition (DEPCONC) during a simulation interval is  −W   τ    AVDEPM  1− τ     CD  DEPCONC = CONC 1 − e    

(2.57)

where CONC is the concentration of suspended sediment at the start of the interval (mg/L), W is the settling velocity for the sediment fraction (m/interval), AVDEPM is the average depth of water in the reach (m), τ is shear stress (lb/ft2 or kg/m2), and τCD is critical shear stress for deposition. The rate of resuspension, or scour, of cohesive sediments from the bed is derived from a modified form of Partheniades’s (1962)



55

equation. The concentration of suspended sediment added to suspension by scour during a simulation interval (SCRCONC) is

SCRCONC =

 τ  M 1000  − 1 AVDEPM  τ CS 

(2.58)

where M is the erodibility coefficient (kg/m2), 1000 is a conversion factor, and τ CS is the critical shear stress for scour (lb/ft2 or kg/m2). The user must supply values for M and τ CS for each fraction of cohesive sediment that is modeled. If the amount of scour calculated is greater than available storage in the bed, the bed scour is set equal to the bed storage, and the bed storage is set equal to zero. Since the value specified for τ CS should be greater than that for τ CD, only one process (deposition or scour) occurs during each simulation interval. In SWAT, sediment transport in the channel is a function of two simultaneous processes: deposition and degradation. SWAT has the capability to compute deposition and degradation using the same channel dimensions for the entire simulation, or SWAT can simulate downcutting and widening of the stream channel and can update channel dimensions throughout the simulation. Previous versions of SWAT used stream power, defined as the product of water density, flow rate, and water surface slope by Bagnold (1977), to estimate deposition and degradation in the channel (Arnold et al. 1995). In SWAT2000, the equations have been simplified, and the maximum amount of sediment that can be transported from a reach segment is a function of the peak channel velocity. Available stream power is used to reentrain loose and deposited material until all of the material is removed. Excess stream power causes bed degradation, which is adjusted for stream bed erodibility and cover. The maximum amount of sediment that can be transported from a reach segment is spexp concsed ,ch,mx = csp vch , pk

(2.59)

where concsed,ch,mx is the maximum concentration of sediment that can be transported by the water (ton/m3 or kg/L), csp is a coefficient defined by the user, vch,pk is the peak channel velocity (m/s), and spexp is an exponent defined by the user. The exponent, spexp, normally varies between 1.0 and 2.0 and was set at 1.5 in the original Bagnold stream power equation (Arnold et al. 1995). The maximum concentration of sediment calculated with Equation 2.59 is compared to the concentration of sediment in the reach at the beginning of the time step, concsed,ch,i. If concsed,ch,i > concsed,ch,mx, deposition is the dominant process in the reach segment, and the net amount of sediment deposited is calculated as the difference between the two concentrations multiplied by the volume of water in the reach segment. If concsed,ch,i < concsed,ch,mx, degradation is the dominant process in the reach segment. Sediment routing in a reach is accomplished in AnnAGNPS using a unit-width, steady-state, uniform, spatially varied sediment discharge model, with a modified Einstein deposition equation and the Bagnold suspended sediment formula for the


56


transport capacity by particle size class. The sediment transport capacity for each particle size (Theurer and Cronshey 1998) is qsc =

kτ vw2 vf

(2.60)

where k is transport capacity factor (nondimensional) with values provided for each of five particle types, τ is bed shear stress (mg/m2), vw is flow velocity (m/s), and vf is particle fall velocity (m/s). Channel erosion occurs if the transport capacity exceeds the incoming sediment load to the reach and sediment is available to be eroded from the channel bed or bank. Channel erosion in GLEAMS simulates erosion in terrace channels, diversions, major flow concentrations where topography has caused overland flow to converge, grass waterways, row middle or graded rows, tail ditches, and other similar channels (Foster et al. 1980). The channel element does not describe gully or large streamchannel erosion. With the exception that shear stress and detachment by flow are estimated differently, the same concepts and equations are used in both the channel and overland flow elements. As with the overland flow element, changes in the controlling variables along the channel are allowed. Thus, a channel with a decreasing slope or a change in cover can be analyzed. Detachment by flow is calculated as D = Kch (1.35τ − τ cr )1.05

(2.61)

where D is detachment capacity (lb/ft 2 /s), K ch is an erodibility factor [lb/ft2/s)(ft2/lb)1.05], τ is average shear of the flow in the channel (lb/ft2), and τcr is a critical shear stress (lb/ft2) below which erosion is negligible. Shear stress is assumed to be triangularly distributed in time during the runoff event to estimate the time that shear stress is greater than the critical shear stress, during which shear stress is assumed constant and equal to peak shear stress for the storm. Erosion can proceed to a nonerodible layer, and then the channel widens and the erosion rate decreases.

2.4 SUMMARY Runoff and erosion are important transport mechanisms for phosphorus. Runoff transports dissolved forms of phosphorus, whereas erosion transports sedimentadsorbed phosphorus. Runoff and erosion processes are simulated in different ways in different phosphorus models. Table 2.5 summarizes the approaches used in some models. The most common approach for estimating runoff volume is the SCS curve number method in which runoff is correlated with rainfall, soil type, land cover, hydrologic condition, and antecedent soil-moisture content. This method is applicable to small watersheds and estimates the total storm runoff from total storm rainfall, ignoring rainfall intensity. A second approach for estimating runoff volume is to


Runoff Model

Volume

Hydrograph

Erosion Peak Rate

Channel Flow Routing

Upland

AnnAGNPS

Curve number modified for soil moisture content

SCS unit hydrograph

Similar to TR-55

Daily to watershed outlet

Based on RUSLE; Ephemeral Gully Erosion Model

ANSWERS2000

Green-Ampt infiltration equation

Kinematic routing with Manning’s equation

Implicit with routing

Kinematic routing with Manning’s equation

Empirical detachment equations

EPIC


NI

Modified rational formula

NI

GLEAMS


NI

Empirical relationship

NI

USLE, MUSLE, Onstad-Foster modification of USLE Empirical interrill and rill detachment equations

Sediment Transport Delivery ratio based on Hydrogeomorphic USLE (HUSLE) (Theurer and Clarke 1991) Yalin equation extended by Mantz (1977)

NI

Yalin equation

Channel Modified Einstein equation for sediment transport; Bagnold suspended sediment formula for transport capacity Based on unit stream power and critical shear theory used in the WEPP model (Alberts et al. 1995) NI


TABLE 2.5 Representation of Runoff and Erosion Processes and Quantities in Selected Field- and Watershed-Scale Models

NI

(continued)

57


58

TABLE 2.5 (CONTINUED) Representation of Runoff and Erosion Processes and Quantities in Selected Field- and Watershed-Scale Models Runoff

Erosion

Volume

Hydrograph

HSPF

Empircal equations based on soil water storage

Chezy-Manning flow equation with an empirical relationship

Outflow depth related to detention storage

SWAT

Curve number modified for soil moisture content; Green-Ampt infiltration equation

Runoff lag time based on time of concentration

Modified rational formula

WEND-P

Regional water quantity budget

NI

Peak Rate

NI

Channel Flow Routing Continuity equation plus outflow as function of volume or time or simple power function Variable storage routing or Muskingum routing plus transmission losses from channels NI

Note: NI = not included; WEND-P = Watershed Ecosystem Nutrient Dynamics-Phosphorus.


Upland Empirical relationship for rainfall–runoff detachment

Sediment Transport Empirical relationship

Channel Transport, deposition, and scour for noncohesive and cohesive sediments

MUSLE + USLE for comparison purposes

NI

Deposition, degradation

Assigned erosion rate

NI

NI


Model


59

determine infiltration using the Green-Ampt or other infiltration equation and then to subtract infiltration from rainfall to determine the amount of runoff. The runoff hydrograph can then be determined empirically or through kinematic routing of the runoff over the land surface. The runoff from overland flow can then be routed through the channel to the watershed outlet in a watershed-scale model. Erosion models can be broadly categorized as USLE- and process-based approaches. The USLE computes average annual soil erosion as a function of soil properties, slope steepness and length, cover management practices, and supporting, or conservation, practices. The USLE estimates gross erosion, or soil movement, rather than sediment yield since it does not estimate deposition. A process-based model estimates detachment and sediment transport separately and considers their interaction to determine deposition. Many of the current process-based erosion prediction methods used in phosphorus models utilize the K, C, and P factors from the USLE. This is often inappropriate because those factor values are interdependent and were determined using a particular representation of rainfall–runoff energy (i.e., the USLE R factor). The phosphorus models often use a different representation of rainfall–runoff energy; thus, the USLE K, C, and P values are inappropriate. Appropriate representations of runoff and erosion quantities and rates to include in phosphorus fate and transport models depend on the purpose of the model, as well as on the spatial and temporal scales of the model. The purpose of such models is usually either to determine the relative impact of different management practices on phosphorus fate — often termed management models — or to predict the absolute values of phosphorus fate and transport. The use of the CN approach for runoff volume estimation and the USLE or its modifications for erosion prediction can be adequate in management models. Those approaches have been shown in many instances to accurately predict the relative impacts of different land-management practices and site characteristics. Problems arise when those same approaches are implemented when the goal is absolute prediction. For runoff prediction, the CN approach was developed for small watersheds. It is not appropriate to apply it in a spatially lumped model to a large watershed. It can be appropriate to apply it in a distributed model where the CN and resulting runoff are determined for small land areas independently. The USLE does not represent sediment deposition or sediment yield. The sediment delivery ratio used in conjunction with the USLE has limitations because variation of the ratio with factors such as flow conditions, erosion amount, and sediment characteristics is not included in commonly used sediment delivery ratio estimations. Limitations of some other USLE-based equations were described previously. Models designed for absolute prediction should use process-based representations. Infiltration-based approaches have the potential to give more accurate predictions of runoff than the curve number approach. At this time, only limited use has been made of process-based erosion models such as WEPP (Laflen et al. 1997) in models of phosphorus fate and transport. Utilization of such process-based models to simulate soil erosion processes provides the opportunity to improve the absolute prediction of phosphorus fate and transport.


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REFERENCES Alberts, E.E., M.A. Nearing, M.A. Weltz, L.M. Risse, F.B. Pierson, X.C. Zhang, J.M. Laflen, and J.R. Simanton. 1995. Chapter 7. Soil component. Pp. 7.1–7.47 in USDA-Water Erosion Prediction Project: Hillslope Profile and Watershed Model Documentation, D.C. Flanagan and M.A. Nearing (Eds.). NSERL Report 10, USDA-ARS National Soil Erosion Research Laboratory, West Lafayette, IN. Alonso, C.V., W.H. Neibling, and G.R. Foster. 1981. Estimating sediment transport capacity in watershed modeling. Trans. ASAE 24(5):1211–1220, 1226. Arnold, J.G., J.R. Williams, and D.R. Maidment. 1995. Continuous-time water and sedimentrouting model for large basins. J. Hydraul. Eng. 121:171–183. Bagnold, R.A. 1977. Bedload transport in natural rivers. Water Resour. Res. 13:303–312. Beasley, D.B., L.F. Huggins, and E.J. Monke. 1982. ANSWERS: a model for watershed planning. Trans. ASAE 23(4): 938–944. Bennett, J.P. 1974. Concepts of mathematical modeling of sediment yield. Water Resour. Res. 10(3): 485–492. Bicknell, B.R., J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobes, and A.S. Donigian, Jr., 2001. Hydrological Simulation Program-Fortran: HSPF Version 12 User’s Manual. Athens, GA: U.S. Environmental Protection Agency National Exposure Research Laboratory. Bondelid, T.R., R.H. McCuen, and T.J. Jackson. 1982. Sensitivity of SCS models to curve number variation. Water Res. Bull. 18(1):111–116. Bouraoui, F. 1994. Development of a continuous, physically-based, distributed parameter, nonpoint source model. Ph.D. dissertation Virginia Polytechnic Institute and State University, Blacksburg. Bouwer, H. 1966. Rapid field measurement of air-entry value and hydraulic conductivity of soil as significant parameters in flow system analysis. Water Resour. Res. 2:729–738. Bouwer, H. and M. Asce. 1969. Infiltration of water into nonuniform soil. J. Irrig. Drain. Div., ASCE 95(4):451–462. Brakensiek, D.L. and W.J. Rawls. 1983. Agricultural management effects on soil water processes part II: Green-Ampt parameters for crusting soils. Trans. ASAE. 26(6):1751–1757. Cronshey, R.G. and F.G. Theurer. 1998. AnnAGNPS nonpoint pollutant loading model. Paper presented at the First Federal Interagency Hydrologic Modeling Conference, April 19–23, Las Vegas, NV. Cunge, J.A. 1969. On the subject of a flood propagation method (Muskingum method). J. Hydraul. Res. 7(2):205–230. Donigian, A.S., Jr., D.C. Beyerlein, H.H. Davis, Jr., and N.H. Crawford. 1977. Agricultural Runoff Management (ARM) model version II: refinement and testing. U.S. Environmental Protection Agency, EPA 600/3-77-098, Environmental Research Laboratory, Athens, GA. Donigian, A.S., Jr. and N.H. Crawford. 1976a. Modeling pesticides and nutrients on agricultural lands. U.S. Environmental Protection Agency, EPA 600/2-7-76-043, Environmental Research Laboratory, Athens, GA. Donigian, A.S., Jr., and N.H. Crawford. 1976b. Modeling nonpoint pollution from the land surface. U.S. Environmental Protection Agency, EPA 600/3-76-083, Environmental Research Laboratory, Athens, GA. Edwards, D.R. and T.C. Daniel. 1993. Abstractions and runoff from fescue plots receiving poultry litter and swine manure. Trans. ASAE 36(2):405–411. Foster, G.R. 1982. Modeling the erosion process. Pp. 295–380 in Hydrologic Modeling of Small Watersheds, C.T. Haan, H.P. Johnson, and D.L. Brakensiek (Eds.). St. Joseph, MI: American Society of Agricultural Engineers.



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Foster, G.R., L.F. Huggins, and L.D. Meyer. 1968. Simulation of overland flow on short field plots. Water Resour. Res. 4:1179. Foster, G.R., L.J. Lane, J.D. Nowlin, J.M. Laflen, and R.A. Young. 1980. A model to estimate sediment yield from field sized areas: Development of model. Pp. 36–64 in CREAMS — A Field Scale Model for Chemicals, Runoff, and Erosion from Agricultural Management Systems, Volume 1: Model Documentation. USDA-SEA Conservation Report 26. Foster, G.R. and L.D. Meyer. 1972. Transport of soil particles by shallow flow. Trans. ASAE 15(1):99–102. Foster, G.R., L.D. Meyer, and C.A. Onstad. 1973. Erosion equation derived from modeling principles. American Society of Agricultural Engineers Paper 73-2550. St. Joseph, MI: American Society of Agricultural Engineers. Foster, G.R., L.D. Meyer, and C.A. Onstad. 1977. A runoff erosivity factor and variable slope length exponents for soil loss estimates. Trans. ASAE 20(4):683–687. Foster, G.R., R.A. Young, and W.H. Neibling. 1985. Sediment composition for nonpoint source pollution analyses. Trans. ASAE 28(1):133–139, 146. Green, W.H. and G.A. Ampt. 1911. Studies on soil physics — 1 — the flow of air and water through soils. J. Agric. Sci. 4:11–24. Haan, C.T., B.J. Barfield, and J.C. Hayes. 1994. Design Hydrology and Sedimentology for Small Catchments. San Diego, CA: Academic Press. Hauser, V.L. and O.R. Jones. 1991. Runoff curve numbers for the Southern High Plains. Trans. ASAE 34(1):142–148. Hawkins, R.H. 1975. The importance of accurate curve numbers in the estimation of storm runoff. Water Res. Bull. 11(5):887–891. Hershfield, D.M. 1961. Rainfall frequency atlas of the United States for durations from 30 minutes to 24 hours and return periods from 1 to 100 years. U.S. Department of Commerce Technology. Paper 40. Holtan, H.N. 1961. A concept for infiltration estimates in watershed engineering. USDA-ARS Bull. 41–51. Huggins, L.F. and J.R. Burney. 1982. Surface runoff, storage, and routing. Pp. 167–225 in Hydrologic Modeling of Small Watersheds, C.T. Haan, H.P. Johnson, and D.L. Brakensiek (Eds.). St. Joseph, MI: American Society of Agricultural Engineers. Huggins, L.F. and E.J. Monke. 1966. The mathematical simulation of the hydrology of small watersheds. Technical Report 1, Water Resources Research Center, Purdue University, West Lafayette, IN. Kilinc, M. and E.V. Richardson. 1973. Mechanics of soil erosion from overland flow generated by simulated rainfall. Hydrology Paper 3, Colorado State University, Fort Collins. Kinnell, P.I.A. 2004a. Letter to the editor: the mathematical integrity of some USLE variants. Soil Sci. Soc. Amer. J. 68:336–337. Kinnell, P.I.A. 2004b. Sediment delivery ratios: a misaligned approach to determining sediment delivery from hillslopes. Hydrol. Proc. 18:3191–3194. Kinnell, P.I.A. and L.M. Risse. 1998. USLE-M: empirical modelling rainfall erosion through runoff and sediment concentration. Soil Sci. Soc. Amer. J. 62:1667–1672. Knisel, W.G., Ed. 1993. GLEAMS: Groundwater Loading Effects of Agricultural Management Systems, version 2.10. University of Georgia, Publication 5, Coastal Plain Experiment Station, Biological and Agricultural Engineering Department, Athens, GA. Laflen, J.M., W.J. Elliot, D.C. Flanagan, C.R. Meyer, and M.A. Nearing. 1997. WEPPpredicting water erosion using a process-based model. J. Soil Water Conserv. 52(2): 96–102. Laursen, E. 1958. The total sediment load of streams. J. Hydraul. Div. 84(1):1–36.


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Leonard, R.A., W.G. Knisel, and D.A. Still. 1987. GLEAMS: Groundwater Loading Effects of Agricultural Management Systems. Trans. ASAE 30(5):1403–1418. Lighthill, M.J. and G.B. Whitham. 1955. On kinematic waves 1. Proc. Royal Soc., London, Ser. A, Mathematics and Physical Sciences (1934–1990). 229 (1178):281–316. Linsley, R.K., M.A. Kohler, and J.L.H. Paulhus. 1988. Hydrology for Engineers. London: McGraw-Hill. Mantz, P.A. 1977. Incipient transport of fine grains and flakes by fluids — extended Shields diagram. J. Hydraul. Div. ASCE 103(HY6):601–615. McCool, D.K., L.C. Brown, G.R. Foster, C.K. Mutchler, and L.D. Meyer. 1987. Revised slope steepness factor for the Universal Soil Loss Equation. Trans. ASAE 30(5):1387–1396. McCool, D.K., L.C. Brown, G.R. Foster, C.K. Mutchler, and L.D. Meyer. 1989. Revised slope length factor for the Universal Soil Loss Equation. Trans. ASAE 32(5):1571–1576. Mein, R.G. and C.L. Larson. 1971. Modeling infiltration component of the rainfall–runoff process. Bulletin 43, Water Resources Research Center, University of Minnesota, Minneapolis, MN. Mein, R.G. and C.L. Larson. 1973. Modeling infiltration during a steady rain. Water Resour. Res. 9(2):384–394. Merkel, W.A., D. Woodword, and C.D. Clarke. 1988. Ephemeral Gully Erosion Model. Pp. 315–323 in Modeling of Agricultural, Forest, and Range Hydrology, St. Joseph, MI: American Society of Agricultural Engineers. Moldenhauer, W.C. and J.C. Koswara. 1968. Effect of initial clod size on characteristics of splash and wash erosion. Soil Sci. Soc. Amer. Proc. 32(6):875–879. Morel-Seytoux, H.J. and J. Khanji. 1974. Derivation of an equation of infiltration. Water Resour. Res. 10(4):795–800. Nearing, M.A., B.Y. Liu, L.M. Risse, and X. Zhang. 1996. Curve number and Green-Ampt effective hydraulic conductivities. Water Res. Bull. 32:125–136. Neitsch, S.L., J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King. 2002. Soil and Water Assessment Tool theoretical documentation version 2000. TWRI Report TR-191, Texas Water Resources Institute, College Station, TX. Neuman, S.P. 1976. Wetting from pressure head in the infiltration model of Green and Ampt. Water Resour. Res. 12(3):564–566. Novotny, V. and H. Olem. 1994. Water Quality: Prevention, Identification, and Management of Diffuse Pollution. New York: Van Nostrand Reinhold. Onstad, C.A. and G.R. Foster. 1975. Erosion modeling on a watershed. Trans. ASAE 18(2):288–292. Overton, D.E. 1972. Kinematic flow on long impermeable planes. Water Res. Bull. 8(6):1198–1204. Partheniades, E. 1962. A study of erosion and deposition of cohesive soils in salt water. Ph.D. thesis, University of California, Berkeley. Philip, J.R. 1957. The theory of infiltration: 1 — the infiltration equation and its solution. Soil Sci. 83:435–448. Rasmussen, T.C. and D.D. Evans. 1993. Water infiltration into exposed fractured rock surfaces. Soil Sci. Soc. Amer. J. 57(2):324–329. Rawls, W.J. and D.L. Brakensiek. 1985. Prediction of soil water properties for hydrologic modeling. Pp. 293–299 in Watershed Management in the 80’s, E.B. Jones and T.J. Ward (Eds). New York: American Society of Civil Engineers. Rawls, W.J. and D.L. Brakensiek. 1986. Comparison between Green-Ampt and curve number runoff predictions. Trans. ASAE 29(6):1597–1599.



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Rawls, W.J., J.J. Stone, and D.L. Brakensiek. 1989. Infiltration. Pp. 4.1–4.12 in Water Erosion Prediction Project: Hillslope Profile Version, L.J. Lane and M.A. Nearing (Eds.). National Soil Erosion Laboratory Report 2, USDA-ARS, West Lafayette, IN. Renard, K.G., G.R. Foster, G.A. Weesies, and J.P. Porter. 1991. RUSLE: Revised universal soil loss equation. J. Soil Water Conserv. 46(1):30–33. Renard, K.G., G.R. Foster, G.A. Weesies, D.K. McCool, and D.C. Yoder. 1997. Predicting soil erosion by water: a guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE). U.S. Department of Agriculture Agricultural Handbook 703, Washington, D.C. Risse, L.M., M.A. Nearing, A.D. Nicks, and J.M. Laflen. 1993. Error assessment in the Universal Soil Loss Equation. Soil Sci. Soc. Amer. J. 57:825–833. Richards, L.A. 1931. Capillary conduction through porous mediums. Physics 1:313–318. Sharpley, A.N. and J.R. Williams (Eds.). 1990. EPIC — Erosion/productivity impact calculator: 1: model documentation. U.S. Department of Agriculture Technical Bulletin 1768, Washington, D.C. Simanton, J.R., R.H. Hawkins, M. Mohseni-Saravi, and K.G. Renard. 1996. Runoff curve number variation with drainage area, Walnut Grove, Arizona. Trans. ASAE 39(4): 1391–1394. Skaggs, R.W. and R. Khaleel. 1982. Infiltration. Pp. 119–166 in Hydrologic Modeling of Small Watersheds, C.T. Haan, H.P. Johnson, and D.L. Brakensiek (Eds.). St. Joseph, MI: American Society of Agricultural Engineers. Soil Conservation Service (SCS). 1972. Hydrology, Section 4: National Engineering Handbook. Washington, D.C.: Government Printing Office. Soil Conservation Service (SCS). 1983. Computer program for project formulation-hydrology. Draft, SCS Technical Release 20, Washington, D.C. Soil Conservation Service (SCS). 1986. Urban hydrology for small watersheds. U.S. Department of Agriculture Technical Release 55, Washington, D.C. Strelkoff, T. 1969. One-dimensional equations of open channel flow. Trans. Hyd. Div. ASCE 95(HY3):861–876. Theurer, F.D. and C.D. Clarke. 1991. Wash load component for sediment yield modeling. Pp. 7-1–7-8 in Proceedings of the Fifth Federal Interagency Sedimentation Conference, Washington, D.C.: Federal Energy Regulatory Commission. Theurer, F.G. and R.G. Cronshey. 1998. AnnAGNPS–reach routing processes. Paper presented at the First Federal Interagency Hydrologic Modeling Conference, April 19–23, Las Vegas, NV. Walling, D.E. 1983. The sediment delivery problem. J. Hydrol. 65:209–237. Williams, J.R. 1969. Flood routing with variable travel time or variable storage coefficients. Trans. ASAE 12(1):100–103. Williams, J.R. 1975. Sediment-yield prediction with universal equation using runoff energy factor. Pp. 224–252 in Present and Prospective Technology for Predicting Sediment Yields and Sources, Publ. ARS. 5-40. U.S. Gov. Print Office, Washington, D.C. Williams, J.R. and R.W. Hann. 1973. HYMO: Problem-oriented language for hydrologic modeling––user’s manual. publ. ARS-S-9, U.S. Department of Agriculture, Washington, D.C. Williams, J.R., C.A. Jones, and P.T. Dyke. 1990. The EPIC model. Pp. 3–92 in EPIC— Erosion/Productivity Impact Calculator: 1: Model Documentation, A.N. Sharpley and J.R. Williams (Eds.). U.S. Department of Agriculture Technical Bulletin 1768, Washington, D.C. Wischmeier, W.H. 1959. A rainfall erosion index for a Universal Soil-Loss Equation. Soil Sci. Soc. Am. Proc. 23:246–249.


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Wischmeier, W.H. and D.D. Smith. 1965. Predicting rainfall erosion losses from cropland east of the Rocky Mountains. U.S. Department of Agriculture Handbook no. 282, Washington, D.C. Wischmeier, W.H. and D.D. Smith. 1978. Predicting rainfall erosion losses — a guide to conservation planning. Agriculture Handbook 537 U.S. Department of Agriculture Science and Education Administration, Washington, D.C. Woolhiser, D.A. and J.A. Liggett. 1967. Unsteady one-dimensional flow over a plane — the rising hydrograph. Water Resour. Res. 3(3):753–771. Yalin, M.S. 1963. An expression for bed load transportation. J. Hydraul. Div. ASCE 89(HY3):221–250. Yang, C.T. 1973. Incipient motion and sediment transport. J. Hydraul. Div. ASCE 99(HY10):1679–1704.


3

Modeling Phosphorus in Runoff: Basic Approaches Miguel L. Cabrera University of Georgia, Athens, GA

CONTENTS 3.1 Modeling Dissolved Inorganic Phosphorus....................................................66 3.1.1 Dissolved Inorganic Phosphorus Derived from Soil ..........................66 3.1.1.1 Model Based on Laboratory-Derived Relationships............66 3.1.1.2 Model Based on Field-Derived Relationships .....................69 3.1.2 Dissolved Inorganic P Derived from Surface-Applied Manures........73 3.1.2.1 Model Based on Laboratory-Derived Relationships............73 3.1.2.2 Model Based on Field-Derived Relationships .....................75 3.2 Modeling Particulate Inorganic P in Surface Runoff.....................................75 3.3 Summary and Conclusions .............................................................................77 References................................................................................................................77

The potential impact of phosphorus (P) in accelerating eutrophication of surface waters has made evident the need for simulation models to estimate P concentrations in surface runoff and P exports from watersheds. Although much progress has been made with P simulation models, there are still difficulties in obtaining accurate estimates of runoff P. Some of these difficulties are caused in part by incomplete modeling of the mechanisms involved, as well as a lag in the incorporation of recent scientific results into models. A complete model of runoff P should include all important P fractions present in surface runoff. In general, P in runoff is divided into dissolved P and particulate P based on fraction size. Dissolved P is associated with fractions < 0.45-µm, whereas particulate P is associated with fractions > 0.45-µm. Dissolved and particulate P can contain organic and inorganic forms, both of which can contribute to eutrophication of surface waters. However, whereas inorganic P is immediately available to algae (Nürnberg and Peters 1984), organic P has to be mineralized before it can be utilized. Because of this immediate availability of inorganic P, most models of P in surface runoff have concentrated on modeling inorganic P. This chapter reviews basic approaches used to model dissolved inorganic P and particulate inorganic P in surface runoff and highlights current additional needs. Some of the approaches described here are used in current P simulation models such Agricultural Nonpoint Source 65


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(AGNPS), Areal Nonpoint Source Watershed Environment Response Simulation 2000 (ANSWERS-2000), Erosion Productivity Impact Calculator (EPIC), Hydrologic Simulation Program-Fortran (HSPF), and Soil and Water Assessment Tool (SWAT).

3.1 MODELING DISSOLVED INORGANIC PHOSPHORUS Two main sources of dissolved inorganic P in runoff are P present in the soil and P present in surface-applied animal manures. Approaches used for each of these sources will be presented separately.

3.1.1 DISSOLVED INORGANIC PHOSPHORUS DERIVED

FROM

SOIL

Models for dissolved inorganic P derived from the soil have used two main approaches: one using laboratory-derived relationships and one using field-derived relationships. The underlying assumption in both approaches is that soils have a pool of P from which runoff water can desorb P. 3.1.1.1 Model Based on Laboratory-Derived Relationships This model of dissolved P in runoff is based on studies dealing with the kinetics of P desorption-from-soil. Sharpley et al. (1981a) used the following equation to estimate the amount of dissolved inorganic P desorbed from soil: P desorbed (mg kg−1) = K Po Tα Wβ

(3.1)

where K, α, and β are parameters, Po is desorbable P (mg kg−1), T is extraction time (min), and W is the water-to-soil extraction ratio (cm3 g−1). According to Sharpley et al. (1981a), Equation 3.1 can be derived by assuming that P desorption is controlled by nonlinear diffusion. These authors developed parameters for Equation 3.1 by treating four soils with different amounts of P — 0, 47.5, 95, and 190 µg P g−1 soil — incubating them at 25°C for 3 days, and then shaking duplicate samples with distilled water at a water-to-soil ratio of 10:1, 40:1, 100:1, 200:1, 400:1, and 1000:1 for 5 to 180 min. The water extracts were then analyzed for inorganic P using Murphy and Riley’s (1962) method. It should be noted that in addition to measuring inorganic P, this method may include a small fraction of organic P. Because of that, the P determined with this method is usually called dissolved reactive P (DRP). Parameter Po in Equation 3.1 represents the pool of desorbable P present in the soil and was estimated following the 3-day incubation with two sequential 1-h extractions with water at a water-to-soil ratio of 40:1 (Sharpley et al. 1981a). Parameter α was estimated by plotting for each soil P amendment and water-to-soil ratio, the log(P desorbed) vs. the log(T ), and fitting a straight line. The following derivation shows the rationale for such a procedure. For a given soil and water-to-soil ratio W, Equation 3.1 can be simplified by taking decimal logarithms on both sides to yield log (P desorbed) = log (K) + log ( Po) + β log (W) + α log (T )


(3.2)

Modeling Phosphorus in Runoff: Basic Approaches

67

In Equation 3.2, the sum of log (K) + log (Po) + β log (W) represents the intercept of the straight line fitting log (P desorbed) vs. log (T), whereas α represents the slope of the line. Sharpley et al. (1981a) found that for a given soil α was fairly constant across P amendments and extracting ratios. Parameter β was estimated by plotting for each soil, P amendment, and shaking time the log (P desorbed) vs. the log (W) and fitting a straight line. The following derivation shows the rationale for such a procedure. For a given soil and given shaking time T, Equation 3.1 can be simplified by taking decimal logarithms on both sides as follows: log (P desorbed) = log (K) + log (Po) + α log (T ) + β log (W)

(3.3)

In Equation 3.3, the sum log (K) + log (Po) + α log (T ) represents the intercept of the straight line fitting log (P desorbed) vs. log (W), whereas β represents the slope of the line. Sharpley et al. (1981a) found that β was fairly constant across soils, P amendments, and extracting times. Finally, parameter K in Equation 3.1 was determined by plotting for each soil, W, and T the amount of P desorbed vs. desorbable P (Po) and fitting a straight line to the data. For a given soil, W, and T, the slope of the line is given by Slope = K Tα Wβ

(3.4)

Thus, K can be calculated as follows: K = Slope/(Tα Wβ)

(3.5)

Sharpley et al. (1981a) found that for a given soil, the values of K at different shaking times and water-to-soil ratios were fairly similar. Because the aforementioned procedure for the determination of α, β, and K is time consuming, Sharpley (1983) explored the possibility of estimating these parameters from soil properties and found that the following equations could be used to obtain reasonable estimates of α, β, and K for 78 soils from the continental U.S. and Puerto Rico.

α = 0.815 (percent clay/percent organic C)−0.540

R = 0.89

(3.6)

β = 0.141 (percent clay/percent organic C)0.429

R = 0.84

(3.7)

KB = 0.630 (percent clay/percent organic C)−0.698

R = 0.82

(3.8)

KL = 1.422 (percent clay/percent organic C)−0.829

R = 0.95

(3.9)

where KB represents the value for K when desorbable P (Po) is measured by the Bray-1 soil test method (Bray and Kurtz 1945) and KL represents the value for K when desorbable P is measured by isotopic dilution (Sharpley 1983).


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Vadas and Sims (2002) developed the following equations to estimate α, β, and K for 23 sandy soils from Delaware. They measured desorbable P (Po) with iron (Fe)-oxide impregnated filter strips.

α = 0.024 (Feox /organic C)−0.346 R = 0.86

(3.10)

β = 0.107 (Feox + Alox)0.251

R = 0.72

(3.11)

K = 2.168 (Feox + Alox)−0.773

R = 0.85

(3.12)

where Feox and Alox are acid ammonium oxalate-extractable Fe and aluminum (Al) (mmol kg−1), and organic C is expressed in mmol kg−1. Vadas and Sims (2002) used this approach because determining α, β, and K from clay content, as proposed by Sharpley (1983), might not be accurate for sandy soils with little clay where P chemistry is controlled mainly by Fe and Al oxides. Equation 3.1 estimates P desorbed from soil in terms of mg kg−1 soil. Thus, to estimate the concentration of dissolved inorganic P in surface runoff in mg P L−1 it is necessary to know the amount of soil that interacts with surface runoff as well as the volume of surface runoff. The amount of soil that interacts with runoff can be calculated from the effective depth of interaction (EDI) and the bulk density of the soil under consideration. Therefore, Sharpley et al. (1981b) proposed the following model to estimate dissolved inorganic P in runoff: DIP = (K Po EDI Db Tα Wβ)/V

(3.13)

where DIP is dissolved inorganic P in runoff (mg L−1), Po is desorbable P measured by Bray-1 P (mg P kg−1), EDI is the effective depth of interaction (mm), Db is the soil bulk density (g cm−3), K, α, and β are constants, T is time of contact (min), W is the water-to-soil ratio during runoff (cm3 g−1), and V is the runoff volume per unit area (mm). Parameters EDI and Db are needed to calculate the amount of soil from which P is released, which in turn is used to estimate W. To obtain estimates for EDI, Sharpley (1985a) carried out rainfall simulation experiments with soil packed in boxes that received different amounts of straw (0.5, 1.25, 2.5, 3.75, and 5 mg ha−1) and were positioned at slopes of 2, 4, 6, 8, 12, and 20%. Constants K, α, and β were calculated from the percent of clay and the percent of organic C of the soil, and DIP was measured in the runoff. Because all the terms of Equation 3.13, with the exception of EDI, were known for each treatment, Equation 3.13 was then solved for EDI to obtain estimates for this parameter. Sharpley (1985a) found that EDI increased with slope rainfall intensity, and rate of wheat straw and that EDI could be estimated from the following equation: ln EDI = i + 0.576 ln(soil loss; kg ha−1)

(3.14)

i = –3.13 + 0.071 soil aggregation

(3.15)



69

where soil aggregation is the proportion of particles less than 2 µm in dispersed soil divided by the proportion of particles less than 2 µm in undispersed soil. Although the concepts on which Equations 3.13, 3.14, and 3.15 are based appear valid, these equations have not been used in current simulation models. Thus, further investigation is needed on the development and use of this approach to simulate DIP in runoff. Vadas et al. (2002) used Equations 3.10 through 3.15 to estimate DIP concentrations in surface runoff from coastal plain soils and found that the approach overestimated DIP values by a factor of about 20. They suggested that the source of the overestimation may have been the presence of sediment in runoff, which would have caused resorption of the dissolved P initially released from the soil. Consequently, they developed a correction factor of the form: corrected P (mg L−1) = estimated P (mg L−1)/error

(3.16)

error = 2.68 × ln(sediment yield, kg ha−1) + 4.94

(3.17)

where

Vadas et al. (2002) suggested incorporating this approach into Field Hydrologic and Nutrient Transport Model (FHANTM) 2.0, a model developed to simulate fieldscale water and P movement in the watershed of Lake Okeechobee in Florida (Fraisse and Campbell 1997). 3.1.1.2 Model Based on Field-Derived Relationships The model based on field-derived relationships uses the following equation to estimate the concentration of dissolved inorganic P in runoff: DIP = Po/Kd

(3.18)

where DIP is the dissolved inorganic P in runoff (mg P L−1), Po is desorbable P (mg P kg−1), and Kd is P partitioning coefficient (L kg−1). The partitioning coefficient, Kd, is generally obtained from rainfall simulation studies by determining the slope of a straight line fitted to a plot of flow-weighted concentration of inorganic P in runoff vs. desorbable P in soil, Po. The reciprocal of the slope is Kd. The amount of desorbable P in soil to be used in this equation has been measured by several procedures, including Mehlich-3 P, Bray-1 P, water-extractable P, and soil P sorption saturation (Vadas et al. 2005a). Values of Kd obtained by Vadas et al. (2005a) were 345 to 500 L kg−1 for Mehlich-3 P or Bray-1 P, 63 to 89 L kg−1 for water-extractable P, and 39 L kg−1 for soil P sorption saturation. The approach described in Equation 3.18 is similar to the one used in the EPIC model, except that the desorbable P pool in EPIC is called labile P and was defined by Sharpley et al. (1984) as the P extracted from soil by a loose anion exchange resin saturated with bicarbonate ions. Because values of anion exchange resin P in soil are not as available as values of P extracted by common soil test P extractants, Sharpley et al. (1984) developed equations to estimate labile P from values of Olsen


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TABLE 3.1 Equations to Estimate Labile P from Common Soil Test P Extractants Equation

Independent Variable Range

R2

Labile P = 0.55 Bray-1 P + 6.1 Labile P = 1.09 Olsen P + 3.2 Labile P = 0.10 Mehlich-1 P + 10.2

Calcareous Soilsa 1 to 77 3 to 38 3 to 338

0.83 0.74 0.51


Slightly Weathered Soilsb 4 to 79 3 to 42 3 to 215

0.79 0.77 0.39


Highly Weathered Soilsc 3 to 222 2 to 50 2 to 147

0.76 0.61 0.84

Labile P = 0.84 Bray-1P + 20.6 Labile P = 0.61 Olsen P + 0.84 Labile P = 0.97 Mehlich-3 P + 19.7

Continental U.S. Soilsd 1 to 221 1 to 131 2 to 226

0.51 0.96 0.62

Note: All variables are expressed in mg P kg−1. a b c d

n n n n

= = = =

20. 35. 23. 24.

Sources: R.G. Myers, A.N. Sharpley, S.J. Thien, and G.M. Pierzynski, Soil Sci. Soc. Am. J. 69, 511–521, 2005; and A.N. Sharpley, C.A. Jones, C. Gray, and C.V. Cole, Soil Sci. Soc. Am. J. 48, 805–809, 1984. With permission.

P, Bray-1 P, and Mehlich-1 P. Table 3.1 shows these equations for 78 soils from the continental U.S. and Puerto Rico, which were divided into calcareous (n = 20), slightly weathered (n = 35), and highly weathered (n = 23) soils. In recent work, Myers et al. (2005) suggested a standardized method for extraction of labile P with anion exchange resin membrane strips saturated with bicarbonate ions. In the proposed method, 1 g of soil is placed into a 125-mL wide-mouth bottle with 80 mL of deionized water and is shaken for 24 h with three anion exchange resin strips (each 2.08 × 4.15 cm, BDH 551642S), followed by P elution and determination. Myers et al. (2005) also presented equations relating labile P to Bray1 P, Olsen P, and Mehlich-3 P for 24 soils from the continental U.S. (Table 3.1). These equations are useful to initialize the labile P pool in the EPIC model (Jones et al. 1984) as well as in other models that use the same approach, such as AGNPS, ANSWERS-2000, HSPF, and SWAT (Figure 3.1).



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TABLE 3.2 Equations to Estimate the Phosphorus Availability Index (PAI) from Soil Characteristics Equation to Estimate Parameter PAI

Range of Independent Variables

Calcareous Soilsa PAI = –0.0061 CaCO3 (%) + 0.58 R2 = 0.71

CaCO3: 0.5 to 54

Slightly Weathered Soilsb BS: 40 to 100 PAI = 0.0043 BS(%) + 0.0034 labile Labile P: 4 to 53 P (mg/kg) + 0.11 pH – 0.70 pH: 5.2 to 8.3 R2 = 0.75 Highly Weathered Soilsc PAI = –0.047 ln(CL,%) + 0.0045 labile CL: 0.4 to 76 P(mg/kg) – 0.053 OC(%) + 0.39 Labile P: 3 to 43 R2 = 0.78 OC: 0.4 to 3.8 Notes: CaCO3 = calcium carbonate; BS = base saturation; CL = clay; OC = organic carbon. a b c

n = 20. n = 35. n = 23.

Source: A.M. Sharpley, C.A. Jones, C. Gray, and C.V. Cole, Soil Sci. Soc. Am. J. 48, 805–809, 1984. With permission.

Fresh Organic P

Fertilizer P

Stable Organic P

Labile P

Stable Inorganic P

Active Inorganic P

FIGURE 3.1 Flow diagram for phosphorus model in EPIC.


Runoff P

72


In addition to being directly involved in the estimation of runoff P, the labile P pool in EPIC and similar models is also important because it is used in the initialization of the active inorganic P pool, as described by the following equation: active inorganic P = labile P × (1 – PAI)/PAI

(3.19)

where active inorganic P is mg P (kg soil) −1, labile P is mg P (kg soil) −1, and PAI is the phosphorus availability index (unitless). Parameter PAI is determined by measuring labile P at the end of a six-month incubation of soil samples that receive different amounts of P fertilizer at the start of the incubation. The slope of the graph of labile P vs. P fertilizer added (g labile P/g P fertilizer added) is the value of PAI. Because the determination of this parameter is time consuming, Sharpley et al. (1984) developed equations to estimate it from soil characteristics, as shown in Table 3.2. In addition to being used in the initialization of the active inorganic P pool, parameter PAI is also used to calculate the rate of transfer between labile P and active inorganic P, as follows: P transfer = 0.1 {labile P – [active P × PAI/(1 – PAI)]}

(3.20)

Vadas et al. (2006) found that replacing the 0.1 P sorption rate factor in Equation 3.20 with a dynamic one provided more accurate estimates of labile P in nine soils from the eastern U.S. Incorporation of this dynamic P sorption factor in EPIC and other models would be expected to improve the estimation of short-term runoff P from soils receiving incorporated applications of P fertilizer, particularly in the case of soils with large clay contents. Parameter PAI is also used to define the rate constant of P transfer (Kas) between the active inorganic P pool and the stable inorganic P pool (Figure 3.1), as shown here: rate of transfer = Kas (4 × inorganic active P – inorganic stable P)

(3.21)

where Kas = exp( –1.77 PAI – 7.05). The active inorganic P pool is in turn used to initialize the inorganic stable P pool: inorganic stable P = 4 × inorganic active P

(3.22)

where both pools are expressed in mg P kg−1. The active inorganic P and the stable inorganic P pools are important in runoff P estimation because they can affect the labile P pool, which is directly involved in soluble P in runoff, as indicated before. Another pool that may have an important influence on the labile P pool is the stable organic P pool, but values for organic P are not commonly found in soil databases. Thus, Sharpley et al. (1984) developed a regression equation to estimate organic P from total nitrogen (N) in soil: organic P (mg kg−1) = 44.4 + 1130 total N (%) R2 = 0.64


(3.23)


73

One of the drawbacks of the EPIC P model (and other models that use the EPIC routine) is that fertilizer P added in inorganic or organic (manure) form is assumed to be incorporated into the soil, even when the fertilizer is surface applied as in the case of pastures. Consequently, the added P is assumed to move rapidly into the labile P pool and subsequently into the active inorganic P and stable inorganic P pools (Figure 3.1). As a result, the EPIC model tends to underestimate the amount of soluble P in runoff derived from surface applications of manure to grasslands (Pierson et al. 2001). The addition of a surface pool to hold surface-applied fertilizer or manure would likely improve simulations of runoff P from grasslands by the EPIC-based models.

3.1.2 DISSOLVED INORGANIC P DERIVED MANURES

FROM

SURFACE-APPLIED

Models for dissolved inorganic P desorbed from manures have also used two approaches: one that uses laboratory-derived relationships and one that uses fieldderived relationships. 3.1.2.1 Model Based on Laboratory-Derived Relationships This model is based on the assumption that manures have a pool of water-extractable P from which runoff water can solubilize P. Vadas et al. (2004) used manure extraction data from Dou et al. (2000, 2002) and Kleinman et al. (2002b), as well as runoff P data from Kleinman et al. (2002a) and Kleinman and Sharpley (2003), to develop the following model for dissolved inorganic P (DIP) in runoff from surface-applied dairy slurry, poultry manure, and swine slurry. Dairy Slurry: DIP (mg P L−1) = [(0.024W0.27) × (extractable P) × (runoff/rainfall) × 0.35]/W (3.24) Poultry Manure: DIP (mg P L−1) = [(0.003W + 0.32) × (extractable P) × (runoff/rainfall)]/W

(3.25)

Swine Slurry: DIP (mg P L−1) = [(0.004W + 0.23) × (extractable P) × (runoff/rainfall) × 0.60]/W (3.26) In Equations 3.24, 3.25, and 3.26, W is the water-to-manure ratio (L kg−1 dry manure), extractable P (mg P kg−1 dry manure) is inorganic P extracted by shaking manure with deionized water at a water-to-manure ratio of 250 (cm3 g−1 dry) for 60 min, and runoff/rainfall is the ratio of runoff volume over rainfall volume. The equations for slurries include a reduction factor (0.35 for dairy and 0.60 for swine) that represents P infiltrated into the soil in the free-draining water present in the slurries. The assumption is that P that infiltrates into the soil is not exposed to


74


surface runoff. This infiltration factor is used to calculate runoff P in the first runoff event only; it is not used in subsequent events. Vadas et al. (2004) found that these equations yielded good estimates of DIP concentration in runoff from soil boxes where manures had been surface applied and subjected to simulated rainfall. In further work, Vadas et al. (2005b) collected more manure extraction data, combined the poultry and swine data into one equation, made all extraction equations nonlinear, and updated all equations, as follows. Dairy Slurry: DIP (mg P L−1) = [1.2W/(W + 73.1)] × (extractable P) × 0.4 × (runoff/rainfall)/W

(3.27)

Poultry and Swine Manure: DIP (mg P L−1) = [2.2W/(W + 300.1)] × (extractable P) × 0.4 × (runoff/rainfall)/W

(3.28)

The 0.4 factor in Equation 3.27 and 3.28 is only used for slurries and only for the first runoff after manure application. In the same work, Vadas et al. (2005b) proposed replacing the runoff/rainfall factor with a P distribution factor, which is the fraction of manure-extractable inorganic P released by rain transported in surface runoff. Calculation of the P distribution factor requires knowledge of rainfall rate as well as times for start and stop of runoff with respect to start of rainfall. The concept behind the P distribution factor is that the amount of rain causing release of manure P to runoff is that which occurs between the start and stop of runoff. In contrast, the rain that occurs between the start of rainfall and the start of runoff causes release of manure P that is leached into the soil instead of being carried off by runoff. Vadas et al. (2005b) showed that the P distribution factor allowed better estimations of DIP in runoff from soil boxes and field plots than the use of the runoff/ rainfall factor. They also observed good relationships between the runoff/rainfall factor and the P distribution factor and between the runoff/rainfall factor and the percent of error in estimation of DIP by using runoff/rainfall instead of the P distribution factor. P distribution factor = 0.95 (runoff/rainfall)0.255

R2 = 0.59***

(3.29)

% error = 0.88 (runoff/rainfall)−0.68

R2 = 0.72***

(3.30)

where *** indicates significance at the 0.001 probability levels. Vadas et al. (2005b) proposed that Equation 3.29 or 3.30 could be used to estimate either the P distribution factor or correct DIP estimations obtained by using the runoff/rainfall factor. The advantage of using the runoff/rainfall factor over the P distribution factor in simulation models is that the data to calculate runoff/rainfall are usually computed in runoff simulation models, whereas data to estimate the P distribution factor are not available in simulation models that use daily time steps. Vadas (personal communication, 2006) has recently developed a manure and P runoff model that incorporates these concepts to simulate manure on the surface and transformation with time so that DIP in runoff can be estimated on an event basis. © 2007 by Taylor & Francis Group, LLC


75

It should be pointed out that Equations 3.27 and 3.28 estimate only dissolved inorganic P in runoff. Vadas et al. (2004) found that equations containing the first two terms of Equation 3.24, 3.25, and 3.26 could also be used to estimate release of organic P from manures, but this approach has not been tested for estimating organic P in runoff. Thus, additional work is needed to simulate dissolved organic P in runoff, which may be significant, especially if the pH of manure drops after application to a field. Work by Tasistro et al. (2004) showed that the pH of poultry litter that was surface applied to a tall fescue and Bermuda grass pasture dropped from 8.5 to 6.5 within 30 days after application. The same study also showed that decreasing the pH of poultry litter increased the amount of water-soluble organic P released. Thus, additional research on the release of organic P to runoff is needed to further improve P models. The model recently developed by Vadas et al. (personal communication, 2006) includes dissolved organic P in runoff. 3.1.2.2 Model Based on Field-Derived Relationships Models based on field-derived relationships estimate dissolved inorganic P concentration in runoff from the rate of manure application or from the rate of soluble P applied with the manure. For example, DeLaune et al. (2004a) presented data on dissolved inorganic P concentration as a function of broiler litter application rate for the first three runoff events after application. In subsequent work, DeLaune et al. (2004b) developed a linear relationship between dissolved inorganic P concentration in runoff and soluble inorganic P applied: DIP (mg P L−1) = 2.40 + 1.49 soluble P applied (kg ha−1)

(3.31)

A similar relationship is used in the Georgia phosphorus index to estimate inorganic P in runoff, which is then multiplied by runoff volume to estimate total P loss (Cabrera et al. 2002). DeLaune et al. (2004a) also developed an equation to estimate total P loss in runoff from pastures as a function of the rate of soluble P applied: DIP (kg P ha−1) = 1.79 + 0.44 soluble P applied (kg ha−1)

(3.32)

A potential problem with this approach is that it ignores transformations of manure P after application. Recent work shows that water-extractable P in manure increases after application (McGrath et al. 2005; Tasistro et al. 2004).

3.2 MODELING PARTICULATE INORGANIC P IN SURFACE RUNOFF Sharpley and Smith (1992) conducted research to estimate bioavailable particulate P (BPP), which includes particulate inorganic P as well as other bioavailable P sources that are attached to soil particles > 0.45 µm. They estimated BPP with the following equation: BPP (mg P L−1) = soil BP (mg kg−1) × sediment in runoff (g L−1) × ER


(3.33)

76


where ER is the enrichment ratio, which represents the P concentration in eroded sediments divided by the P concentration in the surface soil, and soil BP is the bioavailable P in the soil estimated by extracting the soil with 0.1 M sodium hydroxide (NaOH) at a solution-to-soil ratio of 500 to 1 for 17 h. The value of ER can be estimated from soil loss as follows: ln(ER) = 1.21 – 0.16 ln(Soil loss; kg ha−1)

(3.34)

A similar approach to that described in Equation 3.33 is used in the EPIC model. Sharpley (1985b) presented different equations for estimating ER for different soil pools as used in EPIC. To visualize the effects of desorbable soil P and soil loss on total bioavailable P (DRP + BPP), Equations 3.13 and 3.33 were used to estimate the concentration of total bioavailable P in a 35-mm runoff event from a soil with 10% clay, 1% organic C, and a bulk density of 1.35 g cm−3. The results presented in Figure 3.2 clearly show that when yearly soil losses are small (< 0.5 Mg ha−1 yr−1), total bioavailable P in runoff is below 1000 µg P L−1, even at soil test P levels as great as 250 mg P kg−1. As soil test P levels and soil losses increase, the concentration of total bioavailable P increases to values as great as 4000 µg P L−1. It should be noted that these results are for Bray-1 P and may be different for other soil tests. Sharpley and Smith (1992) used Equation 3.13 and 3.33 to estimate bioavailable P in surface runoff from native grasslands and cropped fields and compared estimated values to measured values. They found that the model tended to underestimate

Particulate + Soluble P (µg P L-1)

4000

3000

2000

1000

250 200 Bra 150 y-1 P ( m 100 50 gP k g -1 )

5

Soil

10

15

20 -1

ha (Mg Loss

25 -1 yr )

FIGURE 3.2 Concentration of particulate + soluble P in a 35-mm runoff event from a hypothetical soil as affected by soil test P (Bray-1) and yearly soil loss (no application of manure).



77

TABLE 3.3 Method Used by Different Models for Calculating Inorganic P in Runoff Model AnnAGNPS ANSWERS-2000 GWLF HSPF SWAT WEND-P

Method of Calculating Inorganic P in Runoff Based on EPIC model Based on EPIC model Requires input on runoff P concentration for each land use Similar to EPIC Based on EPIC model Proportional to soil P content

Notes: AnnAGNPS = Annualized Agricultural Nonpoint Source; ANSWERS = Areal Non-Point Source Watershed Environment Response Simulation; GWLF = Generalized Watershed Loading Functions; HSPF = Hydrologic Simulation Program-Fortran; SWAT = Soil and Water Assessment Tool; WEND-P = Watershed Ecosystem Nutrient Dynamics-Phosphorus.

bioavailable P in runoff from native grasslands and no-till fields and suggested this underestimation may have resulted from an inadequate modeling of the release of P from vegetation.

3.3 SUMMARY AND CONCLUSIONS Current approaches to modeling P in runoff consider dissolved and particulate inorganic P derived from soil as well as dissolved inorganic P derived from surfaceapplied manures (Table 3.3). Some approaches are based on laboratory data, whereas others are based on field data. Further work is needed to improve these models and to include dissolved and particulate organic P derived from soil and surface-applied manures. Additional work is also needed to model the release of P from vegetation.

REFERENCES Bray, R.H. and L.T. Kurtz. 1945. Determination of total, organic, and available forms of phosphorus in soil. Soil Sci. 59:39–45. Cabrera, M.L., D.H. Franklin, G.H. Harris, V.H. Jones, H.A. Kuykendall, D.E. Radcliffe, L.M. Risse, and C.C. Truman. 2002. The Georgia phosphorus index. Cooperative Extension Service, Publications Distribution Center, University of Georgia, Athens. DeLaune, P.B., P.A. Moore, Jr., D.K. Carman, A.N. Sharpley, B.E. Haggard, and T.C. Daniel. 2004a. Development of a phosphorus index for pastures fertilized with poultry litter — factors affecting phosphorus runoff. J. Environ. Qual. 33:2183–2191. DeLaune, P.B., P.A. Moore, Jr., D.K. Carman, A.N. Sharpley, B.E. Haggard, and T.C. Daniel. 2004b. Evaluation of the phosphorus source component in the phosphorus index for pastures. J. Environ. Qual. 33:2192-2200.


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Dou, Z., J.D. Toth, D.T. Galligan, C.F. Ramberg, Jr., and J.D. Ferguson. 2000. Laboratory procedures for characterizing manure phosphorus. J. Environ. Qual. 29:508–514. Dou, Z., K.F. Knowlton, R.A. Kohn, Z. Wu, L.D. Satter, G. Zhang, J.D. Toth, and J.D. Ferguson. 2002. Phosphorus characteristics of dairy feces affected by diets. J. Environ. Qual. 31:2058–2065. Fraisse, C.W. and K.L. Campbell. 1997. FHANTM: Field hydrologic and nutrient transport model: version 2.0. Agriculture Biology Engineering Department, Institute of Food and Agriculture Science, University of Florida, Gainesville. Jones, C.A., C.V. Cole, A.N. Sharpley, and J.R. Williams. 1984. A simplified soil and plant phosphorus model. I. Documentation. Soil Sci. Soc. Am. J. 48:800–805. Kleinman, P.J.A. and A.N. Sharpley. 2003. Effect of broadcast manure on runoff phosphorus concentrations over successive rainfall events. J. Environ. Qual. 32:1072–1081. Kleinman, P.J.A., A.N. Sharpley, B.G. Moyer, and G.F. Elwinger. 2002a. Effect of mineral and manure phosphorus sources on runoff phosphorus. J. Environ. Qual. 31:2026–2033. Kleinman, P.J.A, A.N. Sharpley, A.M. Wolf, D.B. Beegle, and P.A. Moore, Jr. 2002b. Measuring water-extractable phosphorus in manure as an indicator of phosphorus in runoff. Soil Sci. Soc. Am. J. 66:2009–2015. McGrath, J.M., J.T. Sims, R.O. Maguire, W.W. Saylor, C.R. Angel, and B.L. Turner. 2005. Broiler litter diet modification and litter storage: impacts on phosphorus in litters, soils, and runoff. J. Environ. Qual. 34:1896–1909. Murphy, J. and J.P. Riley. 1962. A modified single solution method for the determination of phosphate in natural waters. Anal. Chim. Acta 27:31–36. Myers, R.G., A.N. Sharpley, S.J. Thien, and G.M. Pierzynski. 2005. Ion-sink phosphorus extraction methods applied on 24 soils from the continental USA. Soil Sci. Soc. Am. J. 69:511–521. Nürnberg, G. and R.H. Peters. 1984. Biological availability of soluble reactive phosphorus in anoxic and oxic freshwaters. Can. J. Fish. Aquat. Sci. 41:757–765. Pierson, S.T., M.L. Cabrera, G.K. Evanylo, P.D. Shroeder, D.E. Radcliffe, H.A. Kuykendall, V.W. Benson, J.R. Williams, C.S. Hoveland, and M.A. McCann. 2001. Phosphorus losses from grasslands fertilized with broiler litter: EPIC simulations. J. Environ. Qual. 30:1790–1795. Sharpley, A.N. 1983. Effect of soil properties on the kinetics of phosphorus desorption. Soil Sci. Soc. Am. J. 47:462–467. Sharpley, A.N. 1985a. Depth of surface soil-runoff interaction as affected by rainfall, soil slope, and management. Soil Sci. Soc. Am. J. 49:1010–1015. Sharpley, A.N. 1985b. The selective erosion of plant nutrients in runoff. Soil Sci. Soc. Am. J. 49:1527–1534. Sharpley, A.N., L.R. Ahuja, M. Yamamoto, and R.G. Menzel. 1981a. The kinetics of phosphorus desorption from soil. Soil Sci. Soc. Am. J. 45:493–496. Sharpley, A.N., L.R. Ahuja, M. Yamamoto, and R.G. Menzel. 1981b. The release of soil phosphorus in runoff in relation to the kinetics of desorption. J. Environ. Qual. 10:386–391. Sharpley, A.N., C.A. Jones, C. Gray, and C.V. Cole. 1984. A simplified soil and plant phosphorus model. II: prediction of labile, organic, and sorbed phosphorus. Soil Sci. Soc. Am. J. 48:805–809. Sharpley, A.N. and S.J. Smith. 1992. Prediction of bioavailable phosphorus loss in agricultural runoff. J. Environ. Qual. 21:32–37. Tasistro, A., M.L. Cabrera, and D.E. Kissel. 2004. Water soluble phosphorus released by poultry litter: effect of extraction pH and time after application. Nutr. Cycl. Agroecosys. 68:223–234.



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Vadas, P.A. and J.T. Sims. 2002. Predicting phosphorus desorption from mid-Atlantic coastal plain soils. Soil Sci. Soc. Am. J. 66:623–631. Vadas., P.A., J.T. Sims, A.B. Leytem, and C.J. Penn. 2002. Modifying FHANTM 2.0 to estimate phosphorus concentrations in runoff from mid-Atlantic coastal plain soils. Soil Sci. Soc. Am. J. 66:1974–1980. Vadas, P.A., P.J.A. Kleinman, and A.N. Sharpley. 2004. A simple method to predict dissolved phosphorus in runoff from surface-applied manures. J. Environ. Qual. 33:749–756. Vadas, P.A., P.J.A. Kleinman, A.N. Sharpley, and B.L. Turner. 2005a. Relating soil phosphorus to dissolved phosphorus in runoff: a single extraction coefficient for water quality modeling. J. Environ. Qual. 34:572–580. Vadas, P.A., B.E. Haggard, and W.J. Gburek. 2005b. Predicting dissolved phosphorus in runoff from manured field plots. J. Environ. Qual. 34:1347–1353. Vadas, P.A. 2006. A new model for surface application of animal manure and manure phosphorus transformation and loss in runoff. (Personal communication). Vadas, P.A., T. Krogstad, and A.N. Sharpley. 2006. Modeling phosphorus transfer between labile and nonlabile P pools: updating the EPIC model. Soil Sci. Soc. Am. J. (In press).


4

Basic Approaches to Modeling Phosphorus Leaching Nathan O. Nelson Kansas State University, Manhattan, KS

John E. Parsons* North Carolina State University, Raleigh, NC

CONTENTS 4.1 Introduction.....................................................................................................81 4.2 Functional Definition of P Leaching ..............................................................83 4.3 Model Components Affecting P Leaching.....................................................83 4.3.1 Hydrology............................................................................................83 4.3.1.1 Vertical Flow ........................................................................83 4.3.1.2 Nonequilibrium and Preferential Flow ................................86 4.3.1.3 Lateral Flow .........................................................................89 4.3.2 Phosphorus Chemistry ........................................................................90 4.3.2.1 Inorganic P Leaching ...........................................................90 4.3.2.2 Dissolved Organic P Leaching ............................................96 4.3.2.3 Preferential and Subsurface Particulate P Transport...........96 4.4 Model Evaluation............................................................................................97 4.5 Conclusions.....................................................................................................98 References................................................................................................................99

4.1 INTRODUCTION Leaching is an active process in the phosphorus (P) cycle, thereby affecting P transport in agroecosystems. Although subsurface P transport is not the predominant loss pathway in most regions (Hansen et al. 2002; Lemunyon and Daniel 2002; Osborne and Kovacic 1993; Peterjohn and Corell 1984), there is increasing evidence of vertical P movement in soils when P applications exceed crop P removal over extended periods of time. For example, many studies have documented elevated subsoil P concentrations * Deceased

81


82


resulting from repeated waste applications (King et al. 1990; Maguire et al. 2000; Mozaffari and Sims 1994; Nelson et al. 2005; Novak et al. 2002; Sharpley et al. 1984a). Leaching processes affect P distribution within the soil, removing P from surface horizons where it would be available for crop uptake or loss through runoff and erosion. In soils with low P sorption capacities, leaching can potentially remove more P from the root zone than crop uptake (Nelson et al. 2005). P can also be lost to surface waters through leaching and subsurface transport in soils where P loading exceeds crop P removal (resulting in a high soil test P), P sorption capacities are low (sandy or organic soils), and subsurface transport is expedited by artificial drainage systems. Sims et al. (1998) reviewed past research and found evidence indicating that subsurface P losses from tile-drained lands can be an environmentally significant component of the total P exported from agricultural watersheds, where 4 of 21 studies had tile drainage P concentrations > 0.3 mg L−1. Culley and Bolton (1983) estimated that tile drainage contributed 25% of total P and 50% of dissolved P exported from a 51-km2 watershed in Ontario, Canada. An adequate description of P leaching is an important component of modeling the fate and transport of P in the environment. As with other model processes, an adequate model for describing P leaching is dependent on the characteristics of the agroecosystem being modeled and the modeling objectives. Because most soils have strong P sorption characteristics, P has historically been considered immobile within soils; therefore, most watershed- and field-scale models tend to underestimate vertical and subsurface P transport. However, accurately representing P leaching processes is important in long-term simulations with excessive P applications (e.g., with animal waste). In these cases, underestimation of P leaching can result in unrealistically high estimates of P accumulation in surface soils, potentially overestimating P loss through erosion and overland flow (Knisel 1993; Stone et al. 2001). It is important to consider subsurface pathways in artificially drained soils because subsurface drainage can be an order of magnitude greater than surface runoff; therefore, relatively low P concentrations in subsurface drainage can produce greater P losses than from surface runoff (Deal et al. 1986). Excessive accumulation of P in soils buffers soil solution P concentrations to changes in management. Therefore, P leaching losses from artificially drained soils can continue for many years after initial detection of increased P concentrations in drainage waters, despite changes in management practices (Breeuwsma and Silva 1992; Schoumans and Groenendijk 2000). Unremediable circumstances could eventually result if traditional models, which focus on P loss through surface pathways and underestimate P leaching losses, are used to decide issues with long-term consequences, such as siting of confined animal feeding operations. Computer models, with accurate P leaching subroutines, are therefore a primary tool in the prevention of P leaching losses from tile-drained soils and the protection of ecologically sensitive water bodies in regions dominated by sandy soils, such as the eastern U.S. coastal plain. The objective of this chapter is to develop a framework for evaluating a model with respect to its capabilities to describe, in part or entirety, P transport from field to surface waters through leaching processes and subsurface flow pathways.


Basic Approaches to Modeling Phosphorus Leaching

83

4.2 FUNCTIONAL DEFINITION OF P LEACHING A complete description of P leaching processes requires continuity and conservation of mass to describe P movement from the soil surface through the profile with eventual delivery to surface water — through tile drainage or interflow — or deep ground water. Because this is a complex process, mostly occurring on a time scale of decades or more, P leaching is often either ignored or simplified as one of the following partial descriptions: Vertical movement of P past a given depth, such as the bottom of a specific soil layer: surface horizon, root zone, or soil pedon Delivery of P to surface water through subsurface flow by means of a user-supplied or management-dependent P concentration in interflow and tile drainage Furthermore, a single model may use both partial descriptions but may lack the continuity and conservation of mass linking them in an actual setting.

4.3 MODEL COMPONENTS AFFECTING P LEACHING Incorporating complete or partial descriptions of P leaching into a simulation model requires coupling models that describe system hydrology and P transformations (Figure 4.1). Although a watershed model may handle hydrology separately from P transformations, the methods used to describe the hydrology will affect the output from the P reaction/transport submodel. For example, simplifications in model hydrology may preclude more complex descriptions of P transformation and transport since some of the water fluxes and content distributions may not be simulated.

4.3.1 HYDROLOGY A wide range of techniques is used for modeling water movement through soils with a correspondingly wide range of complexities. This chapter is not meant to be a complete review of these techniques but rather a brief review of the techniques as they affect the model capabilities to simulate P leaching, with a focus on methods employed by models described in subsequent chapters. Modeling the complete leaching process requires, at minimum, a hydrological model with two-dimensional water flow. In the unsaturated soil, lateral water fluxes can be assumed to be negligible and vertical flow dominates; however, lateral flow in the saturated portion of the soil is necessary for describing flow to surface waters. 4.3.1.1 Vertical Flow The one-dimensional Richards equation offers the most complete description of vertical water movement in soils and is C (h)


∂h ∂  ∂h  ∂K (h) =  K (h)  − ∂z ∂t ∂z  ∂z 

(4.1)

84


adsorption

Adsorbed P desorption precipitation

Mineral P Soil Surface Vertical Flow Interflow

dissolution

Solution P 2-

HPO4 H2PO4 Organic P

Soil P Transformations immobilization

Organic P mineralization

Soil Surface

Vertical Flow

Stream

Tile Drainage Base Flow

Drain Tile

FIGURE 4.1 General soil P transformations and subsurface transport pathways in crosssectional views of naturally drained and artificially drained landscapes.

where h is the matric potential (cm), K(h) is the unsaturated hydraulic conductivity (cm h−1) expressed as a function of matric potential, z is the depth (cm), t is time (h), and C(h) is the capacitance function or d/dh (cm3 cm−3 cm−1) where θ is the volumetric water content (cm3 cm−3). This is referred to as the h-based formulation and is more easily applied in situations with the presence of a water table. The Richards equation is frequently used for modeling water flow in laboratory column leaching studies (Porro et al. 1993), occasionally used in field-scale water quality models such as SWATRE and Root Zone Water Quality Model (RZWQM) (Jacques et al. 2002; Johnsen et al. 1995) but is seldom used for watershed-scale models. The Richards equation allows simulation of unsaturated water flow and typically uses relatively small temporal and spatial increments, thus facilitating the use of the advection-dispersion equation (ADE), also known as the advectiondispersion-reactive equation or convection-dispersion equation (Leij and van Genuchten 2002; Parsons 1999; Wierenga 1995). Drawbacks to the Richards equation are that (1) boundary conditions can be difficult to define especially for continuous models; (2) it requires computationally intensive numerical solutions that tend to be susceptible to numerical instabilities and may not converge to a solution; and (3) generally it requires labor-intensive inputs to describe the relationship among soil moisture tension, water content, and hydraulic conductivity. These drawbacks, combined with the high spatial variability of soil properties, prohibit routine implementation of the Richards equation at field and watershed scales. However, inputs may be adequately estimated from soil texture alone (Starks et al. 2003), potentially removing the requirement for intensive soil characterization. A much simpler approach for estimating percolation uses a simplified field capacity-water balance (FCWB) method — also referred to as the cascade method, or plate theory method — in which soil water in excess of a measured or userdefined field capacity flows to the underlying soil horizon (Diekkruger et al. 1995;



85

Wegehenkel 2000). The general equation for determining percolation by the field capacity method is Perc = (SWC – FC) * β if SWC > FC, Perc = 0

if SWC ≤ FC,

(4.2) (4.3)

where Perc is the percolation (cm), SWC is the soil water content of the layer (cm), FC is the field capacity of the layer (cm), and β is a coefficient that determines the fraction of soil water excess (SWC – FC) that can drain during a time step, usually a function of saturated hydraulic conductivity. The simplifications of the FCWB method greatly reduce the computational complexity and the required inputs compared to the Richards equation. Although the FCWB method requires fewer soil parameters than the Richards equation, field capacity is a somewhat arbitrarily defined soil property. Field capacity is generally defined as the content of water, on a mass or volume basis, remaining in a soil two or three days after having been wetted with water and after free drainage is negligible (Soil Science Society of America 1997). Field capacity is often determined as the water content at –33 kPa soil water potential, but soil water potential at field capacity can be as high as – 4 kPa (Wierenga 1995). Furthermore, field capacity is affected by soil structure, texture, layering, and antecedent moisture (Hillel 1982). Field capacity can also change throughout the year (Romano and Santini 2002) and should not be viewed as an intrinsic soil property (de Jong and Bootsma 1996). The FCWB method only considers water flow at water contents in excess of field capacity, neglecting any water redistribution at lower water contents. This results in a few relatively large percolation events rather than continuous drainage predicted with models employing the Richards equation (Diekkruger et al. 1995). Using a FCWB method will generally preclude the use of the advection-dispersion equation because large spatial and temporal increments are usually used with FCWB methods. Large spatial and temporal increments can result in numerical instability in solutions to the advection-dispersion equation, especially for longer simulations and when solutes undergo sorption and precipitation reactions (Leij and van Genuchten 2002). Although models employing the FCWB method may not be able to account for the effects of diffusion and dispersion on P transport, multiple soil layers (e.g., soil horizons) tend to reduce the overall effect of hydrodynamic dispersion on solute transport (Porro et al. 1993), and the coefficient of hydrodynamic dispersion is not a sensitive parameter in P leaching models (Notodarmojo et al. 1991). In situations with shallow water tables, such as those requiring artificial drainage, the field-capacity concept does not apply. The free vertical drainage assumption for determining the field capacity is violated since the vertical drainage rate is confined by the presence of a water table. As the unsaturated soil reaches hydraulic equilibrium, the water contents tend to be determined by the water table and not field capacity. Modeling approaches such as those in DRAINMOD (Skaggs 1978) employ a drained-to-equilibrium profile and allow the water table fluctuations to govern vertical water fluxes in the unsaturated zone.


86


Several studies have compared results from hydrology models employing the onedimensional Richards equation to those using various FCWB methods (de Jong and Bootsma 1996; Diekkruger et al. 1995; Eitzinger et al. 2004; Wegehenkel 2000). The use of small spatial increments in FCWB models increases the accuracy of predictions. Simplified FCWB methods, using small spatial increments (< 10 cm), are capable of predicting average soil water contents and long-term percolation amounts with accuracy similar to models using the one-dimensional Richards equation. However, models employing the FCWB method tend to use large spatial increments (> 10 cm); therefore, they tend to overpredict percolation volumes and predict percolation in only a few relatively large events. Despite its drawbacks, the FCWB method is a very common method of predicting percolation in field- and watershed-scale models (Table 4.1). 4.3.1.2 Nonequilibrium and Preferential Flow The terms nonequilibrium flow and preferential flow are used to describe the rapid transport of water and solutes through certain soil channels (e.g., cracks, root channels, macropores) while bypassing a fraction of the soil matrix (Hendricks and Flury 2001). Because preferential flow transports solutes through large pores, bypassing the soil matrix, breakthrough of conservative tracers in structured soils occurs sooner than would be expected based on the advection-dispersion equation (Gerke and Kohne 2004). Furthermore, solute transport through preferential flow reduces soil–solute interaction, a particularly important factor when considering adsorbed solutes such as P. Various approaches for modeling preferential flow in soils were reviewed by Simunek et al. (2003) and included single-porosity, dual-porosity, and dual-permeability models. Single-porosity models are the simplest of the three approaches, where the Richards equation is used with one additional parameter to represent nonequilibrium water contents in the soil. The advantage of the single-porosity model is that it only requires one additional parameter; however, the model results are independent of the antecedent moisture content. Dual-porosity models divide the soil into two regions: fractures, which have mobile water; and the soil matrix, which has immobile water. Although the soil matrix will not conduct water in a dualporosity model, it can exchange and retain water. Dual-permeability models divide the soil into two flow regimes: one representing the fractures and the other representing the matrix, both of which conduct water. Simunek et al. (2003) and Hendricks and Flury (2001) provide a comprehensive explanation of the aforementioned models. The major drawback of dual-porosity and dual-permeability models is the large number of parameters needed for their implementation. For example, dual-permeability models may require as many as 16 parameters to describe water flux (Gerke and van Genuchten 1993), compared to six parameters generally required to solve the Richards equation and only three parameters to solve the FCWB model. Dualpermeability models not only require a large number of parameters, but there is also little guidance on how to obtain these parameters (Simunek et al. 2003). Despite the large number of soil parameters required, dual-porosity models have been implemented for water and solute transport at the field scale. Gerke and Kohne (2004) developed a dual-permeability model that described bromide transport in a tiledrained field. Their model showed substantial improvement over model simulations


Vertical Flow

Model

Preferential Flow

Tile Drainage

AnnAGNPS

FCWB with two soil layersa,b

NI

Hooghoudt equationa

ANSWERS-2000

FCWB single layer profileb,c

NI

GWLF

FCWBe

HSPF

Empirical equationg

SWAT

FCWB with 10 soil layersh,i

EPIC

FCWB with 14 soil layersj

Interflow

Base Flow

Darcy’s equationa

NI

Constant drainage rated

Empirical equationd

NI

NI

NI

Empirical equatione,f

Empirical equationf

NI

NI

Empirical equationg

Empirical equationg

Kinematic storage model based on field capacity concepth

Based on a steady state groundwater recharge equation assuming a linear relationship to changes in water table heighth

Empirical equation based on field capacity conceptj

NI

Bypass- or crack-flow, intended for use with high shrink/swell soils (Vertisols), not intended for use in other soils8

NI

Empirical equation based on field capacity concepth

NI


TABLE 4.1 Hydrological Classification of Selected Field- and Watershed-Scale Models

(continued)

87


88

TABLE 4.1 (CONTINUED) Hydrological Classification of Selected Field- and Watershed-Scale Models Vertical Flow

Preferential Flow

GLEAMS

FCWB with 12 soil layersk

NI

RZWQM

Green-Ampt infiltration and Richards equation for redistributionm

Model

Dual-porosity model with Richards equation for matrix and gravitational flow in fracturesn

Tile Drainage Hooghoudt equation with GLEAMSWTl Richards equation with source/sink component linked to the Hooghoudt equation m

Interflow

Base Flow

NI

NI

NI

NI

a

R.L. Bingner and F.D. Theurer, 2005, AnnAGNPS technical processes: documentation version 3.2, http://www.ars.usda.gov/Research/docs.htm?docid=5199. D.K. Borah and M. Bera, 2003, Trans. ASAE 46, 1553–1566. c F. Bouraoui, 1994, Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg. d ANSWERS user’s manual. e D.A. Haith and L.L. Shoemaker, 1987, Water Resour. Bull. 23, 471–478. f K.Y. Lee, T.R. Fisher, and E. Rochell-Newall, 2001, Biogeochem. 56, 311–348. g B.R. Bicknell, J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobes, and A.S. Donigian, Jr., 2001, Hydrological Simulation Program-FORTRAN (HSPF): user’s manual for release 12, U.S. Environmental Protection Agency National Exposure Research Laboratory, Athens, GA, in cooperation with U.S. Geological Survey, Water Resources Division, Reston, VA. h S.L. Neitsch, J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King, 2002a, Soil and water assessment tool theoretical documentation: version 2000, GSWRL Report 0201, BRC Report 02-05, TWRI Report TR-191, College Station, TX. i S.L. Neitsch, J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King, 2002b, Soil and water assessment tool user’s manual version 2000, GSWRL Report 02-02, BRC Report 02-06, TWRI Report TR-192, College Station, TX. j J.R. Williams, 1995, Pp. 909–1000 in Computer Models of Watershed Hydrology, V.J. Singh (Ed.), Highlands Ranch, CO: Water Resources Publications. k W.G. Knisel and J.R. Williams, 1995, Pp. 1069–1114 in Computer Models of Watershed Hydrology, V. J. Singh (Ed.), Highlands Ranch, CO: Water Resources Publications. l M.R. Reyes, R.L. Bengtson, and J.L. Fouss, 1994, Trans. ASAE 37, 1115–1120. m K.E. Johnsen, H.H. Liu, J.H. Dane, L.R. Ahuja, and S.R. Workman, 1995, Trans. ASAE 38, 75–83. n J. Simunek, N.J. Jarvis, M.Th. van Genuchten, and A. Gardenas, 2003, J. Hydrol. 272, 14–35. b



Note: AnnAGNPS = Annualized Agricultural Non-Point Source; ANSWERS = Areal Non-Point Source Watershed Environment Response Simulation; BRC = Blackland Research Center; EPIC = Erosion Productivity Impact Calculator; FCWB = field capacity-water balance; GLEAMS = Groundwater Loading Effects of Agricultural Management Systems; WT = Water Table; GSWRL = Grassland, Soil and Water Research Laboratory; GWLF = Generalized Watershed Loading Functions; HSPF = Hydrologic Simulation ProgramFortran; NI = Not Included; RZWQM = Root Zone Water Quality Model; SWAT = Soil and Water Assessment Tool; TWRI = Texas Water Resources Institute.


89

employing the equilibrium-based Richards equation. RZWQM, a field-scale model employing a dual-porosity hydrologic model (Table 4.1), was used to model the transport of metribuzin, a pesticide that adsorbs to soil, through structured soils (Malone et al. 2004). Predicted metribuzin losses from RZWQM were in close agreement with observed values, whereas Groundwater Loading Effects of Agricultural Management Systems (GLEAMS) simulations produced a ten-fold underprediction of metribuzin losses. The MACRO model, employing a dual-porosity hydrologic model, has been used to model preferential P transport through macropores following slurry spreading (McGechan 2002a) and from grazing cattle (McGechan 2003). 4.3.1.3 Lateral Flow Lateral flow within field- and watershed-scale models can generally be categorized as tile drainage, interflow, or base flow (Figure 4.1); however, many models may interchange terminology for these processes. A complete P model would have allowances for P transport by each pathway. Tile drainage refers to interception of shallow groundwater with an artificial drainage system, which then transports the water directly to a surface ditch or canal. Tile drainage systems expedite the flow of shallow ground water to surface water and greatly decrease solution–soil interaction. Hooghoudt’s equation is often used to quantify the amount of drainage flux: q=

8 Kd e m + 4 Km 2 L2

(4.4)

where q is the drainage rate (cm h−1), K is the lateral saturated conductivity (cm h−1), de is the effective depth to the impermeable layer (cm), m is the water table height above the drain at the midpoint between drains (cm), and L is the drain spacing (cm) (van der Ploeg et al. 1999). The depth from the drains to the impermeable layer is often adjusted to account for the convergence of the flow lines near the drains. The adjusted depth, de, corrects the flow for this and depends on the size and spacing of the drains (van der Ploeg et al. 1999). Models described in the following chapters simulate tile drain flow in a variety of ways, including the Richards equation linked with the Hooghoudt equation using a source/sink term, the FCWB linked with the Hooghoudt equation, and empirical methods (Table 4.1). Interflow refers to lateral flow below and near the soil surface (Figure 4.1), usually during periods of saturation resulting from a perched water table. Interflow returns to streams within minutes to hours of rainfall events (Haygarth and Sharpley 2000). Interflow modeling techniques include the kinematic storage model, Darcy’s equation based on the lateral gradient from the source area to the exit to the stream, and empirical methods (Table 4.1). Base flow is background, low-magnitude flow arising from groundwater discharge to the stream. Travel time for base flow is on the order of days to months (Preedy et al. 1999). Soil and Water Assessment Tool (SWAT) determines base flow with a steady-state lateral groundwater recharge equation using a form of Hooghoudt’s equation (Neitsch et al. 2002b), whereas Hydrologic Simulation Program-Fortran


90


(HSPF) and Generalized Watershed Loading Functions (GWLF) determine base flow with empirical equations (Bicknell et al. 2001; Lee et al. 2001).

4.3.2 PHOSPHORUS CHEMISTRY Subsurface P transport is the product of water flux and P concentration; therefore, modeling the leaching process requires a description of P transformations within the soil combined with one of the aforementioned hydrologic models (Figure 4.1). Total P concentration in soil water includes inorganic and organic forms of dissolved and particulate P (Heathwaite and Dils 2000; Toor et al. 2003; Turner and Haygarth 2000). Because of the complexities of the organic P cycle and vertical particulate P transport, many models only consider dissolved inorganic P in the leaching process. 4.3.2.1 Inorganic P Leaching Inorganic P reacts with a variety of solutes and mineral surfaces in the soil system. Phosphorus is generally thought to precipitate as calcium (Ca) phosphates in alkaline to neutral soils or aluminum (Al) and iron (Fe) phosphates in more acidic soils but can also precipitate as magnesium (Mg) or manganese (Mn) phosphates depending on soil solution characteristics. Phosphorus is also strongly adsorbed to mineral surfaces. Phosphate adsorption can be simplified into two processes: (1) a fast, reversible reaction of P adsorption to surface sites; and (2) a slow, more irreversible reaction of P diffusion followed by precipitation (van der Zee and van Riemsdijk 1988). The combination of adsorption or desorption and precipitation or dissolution reactions control inorganic P concentrations in soil solution. Sorption and precipitation reactions are affected by organic and inorganic solutes and solution pH; therefore, complete descriptions of the transformations require modeling the dynamics of solution pH and chemical speciation of the solution. Grant and Heaney (1997) modeled the P leaching process for one-dimensional flow in small soil columns with the advection-dispersion equation using a ligand exchange model to represent adsorption or desorption reactions and a comprehensive solution speciation model for determining precipitation or dissolution reactions. Advantages of this approach are that all model inputs are determined independently of the model and model parameters are not soil dependent. However, the model required extensive information on soil chemical composition and supercomputer facilities to iteratively solve numerically intensive algorithms at fine spatial and temporal scales (ranging from 2.5 to 10 mm depth with time steps of 2 to 60 min). Because of these drawbacks, the authors concluded that this approach was not feasible for routine use. The processes of adsorption or desorption and precipitation or dissolution are difficult to separate in macroscale observations and are often collectively described by relating solid-phase (sorbed) P to dissolved P with a variety of nonlinear equations (McGechan 2002b; McGechan and Lewis 2002). Two of the more common equations are the Freundlich and Langmuir equations. The general form of the Freundlich equation is Q = kF Cb


(4.5)


91

Sorbed P (mg kg-1)

250 200 150 100 Data Langmuir Freundlich

50 0 0.0

5.0

10.0

15.0

-1

Solution P (mg L ) FIGURE 4.2 Freundlich and Langmuir equations fit to P adsorption data for a Norfolk sandy loam A horizon (Fine-loamy, kaolinitic, thermic typic kandiudults). Coefficients for Equations 4.5 and 4.6 are as follows: kF = 104, b = 0.309, Qmax = 194, and kL = 1.45. (N.O. Nelson, 2001, unpublished data.)

where Q is the quantity of P sorbed in mg kg−1, C is the concentration of P in solution in mg L−1, and kF (mg1−b Lb kg−1) and b (unitless) are fitting coefficients. The Freundlich equation produces very good fits to experimental data (Figure 4.2), but the fitting parameters do not correspond with the theoretical models of surface adsorption. An alternate approach is the Langmuir equation: Q = Qmax [kLC/(1 + kLC)]

(4.6)

where Qmax is the maximum amount of P adsorbed to the soil (mg kg−1) assuming monolayer coverage, kL is a constant related to the binding energy of P (L mg−1), and other parameters are as previously defined. The Langmuir equation has the advantage of describing a theoretical adsorption maximum, which can be useful in regulatory arenas, but it does not always provide a good fit to experimental data (Figure 4.2). Freundlich and Langmuir equations have been incorporated into several field-scale models that describe P leaching. For example, Enfield et al. (1981) developed a sitespecific field-scale P leaching model that used the Langmuir equation with a simplified precipitation model. The Agricultural Nutrient Model (ANIMO), a field-scale model developed in the Netherlands, also uses a Langmuir equation to determine solution P concentrations (Groenendijk and Kroes 1999). HSPF has the option of using either a linear kinetic relationship or a Freundlich equation to determine solution P concentration (Table 4.2) but includes a retardation factor to correct for consistent overpredictions of P leaching (Bicknell et al. 2001). However, there are several drawbacks to using the


92

TABLE 4.2 Basic Approaches to Modeling Subsurface P Transport and Transformation in Selected Field- and Watershed-Scale Models

Model GWLFa,b

HSPFc

Method of Determining Soil Water P Concentration

Model Parameters and Associated Soil Properties Affecting Soil Water P Concentration

User input User input

Vertical Interflow Base flow

NI User defined User defined

NI User-defined concentration User-defined concentration

Vertical

Dissolved inorganic

Inorganic P is partitioned between solid and solution phases with either a linear or Freundlich equation depending on user settings. A retardation factor reduces solution P mobility.

Adsorption and desorption constants (user input) Freundlich coefficient and exponent (user input) Permanently fixed P (user input) Retardation factor (user input)

Interflow

Dissolved inorganic

Retardation factor (user input)

Base flow

Same as for interflow

Solution P concentration is determined from soil profile. P reactions are not simulated. A retardation factor reduces P mobility. Same as for interflow

Vertical

Dissolved inorganic (only from top 1 cm)

kd (user input) PSP (user input)

Tile drainage Preferential flow Interflow Base flow

NI NI NI Dissolved inorganic

Labile P is partitioned between solid and solution phase with a linear relationship (Equation 4.8) NI NI NI User-defined P concentration


NI

Same as for interflow

NI NI NI User input


SWATd,e,i

Pathway

P Forms Subject to Transport

Vertical

Dissolved inorganic

Labile P is partitioned between solid and solution phase with a linear relationship (Equation 4.8)

Tile drainage (GLEAMS)

Dissolved inorganic and particulate inorganic with PARTLEh

Labile P is partitioned between solid and solution phase with a linear relationship (Equation 4.8). Surface labile P concentration determines P concentration for particulate P transport

kd (function of % clay) PSP (function of % CaCO3, % clay, base saturation, and pH depending on soil weathering) kd (function of % clay) PSP (function of % CaCO3, % clay, base saturation, and pH depending on soil weathering) Sediment concentration in drain tiles (user input)

Notes: AnnAGNPS, ANSWERS-2000, and RZWQM were not included because the current model versions do not consider P leaching or subsurface P transport. Only pathways included in the model are listed; see Table 4.1 for additional details on pathways. NI = not included; PARTLE = particulate. a

D.A. Haith and L.L. Shoemaker, 1987, Water Resour. Bull. 23, 471–478. K.Y. Lee, T.R. Fisher, and E. Rochell-Newall, 2001, Biogeochem. 56, 311–348. c B.R. Bicknell, J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobes, and A.S. Donigian, Jr., 2001, Hydrological Simulation Program-FORTRAN (HSPF): user’s manual for release 12, U.S. Environmental Protection Agency National Exposure Research Laboratory, Athens, GA, in cooperation with U.S. Geological Survey, Water Resources Division, Reston, VA. d S.L. Neitsch, J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King, 2002a, Soil and Water Assessment Tool theoretical documentation: version 2000, GSWRL Report 02-01, BRC Report 02-05, TWRI Report TR-191, College Station, TX. e S.L. Neitsch, J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King, 2002b, Soil and Water Assessment Tool user’s manual version 2000, GSWRL Report 02- 02, BRC Report 02-06, TWRI Report TR-192, College Station, TX. f W.G. Knisel, 1993, GLEAMS Groundwater Loading Effects of Agricultural Management Systems, version 2.10, Department Publication 5, Biological and Agricultural Engineering Department, University of Georgia Coastal Plain Experiment Station, Tifton. g Jimmy Williams, personal communication, December 22, 2005. h A. Shirmohammadi, B. Ulen, L.F. Bergstrom, and W.G. Knisel, 1998, Trans. ASAE 41, 353–360. i SWAT P subroutines are currently undergoing revision. The revised model will include P leaching throughout the entire soil profile (similar to EPIC) and will include dissolved P transport in tile drainage and interflow. Colleen Green, personal communication, December 21, 2005. b


GLEAMSf/ EPICg

93


94


Freundlich and Langmuir equations in field- and watershed-scale models. First, determination of parameters for Equation 4.5 and 4.6 requires time- and labor-intensive laboratory procedures. Second, because soil chemical and physical properties affect P adsorption, model parameters are soil specific. Since the previously mentioned slow, near irreversible adsorption process occurs simultaneously with the fast adsorption process, the subsequent desorption is incomplete, and desorption curves rarely follow the adsorption curve (McGechan and Lewis 2002); therefore, model parameters for desorption are different than for adsorption. As a result of the aforementioned challenges, field- and watershed-scale models commonly use the simplified P cycle model developed by Jones et al. (1984) and Sharpley et al. (1984b) as the basis for describing P transformations (see Chapter 3). For example, various forms of this simplified model are used by Erosion Productivity Impact Calculator (EPIC) (Williams 1995), GLEAMS (Knisel 1993, Table 2), SWAT (Neitsch et al. 2002b, Table 4.2), Annualized Agricultural Nonpoint Source (AnnAGNPS) (Bingner and Theurer 2005), and Areal Nonpoint Source Watershed Environment Response Simulation 2000 (ANSWERS-2000) (Bouraoui 1994). In this model, soil P is represented in two organic P pools — fresh organic P and stable organic P — and three inorganic P pools — labile P, active P, and stable P. Labile P is the plant-available portion, analogous to anion-exchange extractable P, and it is in fast equilibrium with active P, which is in turn in a slow equilibrium with stable P. This is designed to represent two phase-P adsorption: fast, reversible P adsorption (labile P to active P), and slow, near irreversible adsorption (active P to stable P). At equilibrium, the stable P pool is four times the size of the active P pool (regardless of soil properties), and the size of the labile P pool is proportional to the active P pool according to the following equation: Plabile = Pactive (PAI/(1 – PAI))

(4.7)

where PAI is the phosphorus availability index. The PAI is conceptually defined as the fraction of applied fertilizer that remains labile after a six-month incubation with multiple wetting and drying cycles (Jones et al. 1984). The PAI is a function of soil properties and can be estimated with a series of soil-dependent empirical relationships. Although PAI was originally a function of several soil properties, including the size of the labile P pool (Sharpley et al. 1984b), it is often represented as a constant rather than changing with increasing P additions (Knisel 1993; Neitsch et al. 2002b; Williams 1995). Although the original model proposed by Sharpley et al. (1984b) did not estimate solution phase P, labile P is commonly partitioned between solid phase and solution phase according to kd = Qlabile /C

(4.8)

where Qlabile is the concentration of labile P on the solid phase (mg kg−1), C is the concentration of P in the solution phase (mg L−1), and kd is a partitioning coefficient (L kg−1) that either is a user-defined constant or is estimated as a function of clay content (Knisel 1993; Neitsch et al. 2002b; Williams 1995).



95

Sorbed P (mg kg-1)

400

Data

300

200

Langmuir Isotherm GLEAMS - 15 d GLEAMS - 50 d

100

GLEAMS - equilibrium 0 0.0

0.5

1.0

1.5

2.0

-1

Solution P (mg L )

FIGURE 4.3 Relationship between solution and sorbed P concentrations for a Norfolk sandy loam A horizon as predicted with GLEAMS P subroutines at 15 and 50 days following P application and the predicted equilibrium P concentration compared to Langmuir adsorption isotherm and adsorption data from Figure 4.2.

By simplifying the P cycle and by using empirical relationships, inorganic P transformations can be modeled with inputs based on readily available soil characteristics (i.e., total P, soil test P, soil texture, and organic matter content). However, these simplifications contain noteworthy drawbacks. The relationship between C and Qlabile is linear with slope of 1/kd (Equation 4.8). Furthermore, the relationship between labile P and active P is linear (Equation 4.7), as is the relationship between the active and stable P pools. The end result of this combination of equations is a linear relationship between adsorbed P and solution P concentration, as opposed to the nonlinear relationship typical of P adsorption isotherms (Figure 4.3). Although this relationship may be suitable at low soil P concentrations, it can potentially underpredict the solution P concentrations at higher soil P concentrations, thereby underpredicting P leaching. Because of this drawback, Knisel (1993) cautioned against using the GLEAMS model for simulations involving excess P applications. Furthermore, Stone et al. (2001) observed inaccurate predictions of soil P accumulation arising from these simplifications. This is an extremely important point to consider because this modeling approach will produce the greatest errors in scenarios where accurate prediction of P losses is of greatest interest and concern — that is, long-term applications of animal waste or biosolids. Further simplifying the prediction of subsurface P transport, models based on export coefficients determine P concentration in tile drainage, lateral flow, or base flow as a function of land-use characteristics (Table 4.2). Although this approach is simple, the results are highly dependent on the accuracy of the input data and tend not to extrapolate well to other sites. Some process-based models use this method


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to simulate P loading to streams from base flow or tile flow (Neitsch et al. 2002a); however, this may lack continuity with modeling routines depicting P leaching in the soil profile. Recent interest in determining P leaching losses may lead to alternative methods for modeling P leaching. Simplified forms of the adsorption relationships have been made with relationships between quantity and intensity (Q/I), which relate a quantity of adsorbed P (e.g, soil test P concentration) to its intensity (e.g, concentration in solution) (Beauchemin et al. 1996; Koopmans et al. 2002). Several studies have found good linear correlations for Q/I relationships for different soil types (Andraski and Bundy 2003; Pautler and Sims 2000; Sharpley 1995). However, other authors have found split-line graphs more appropriate, which describe the Q/I relationship with two straight lines with significantly different slopes meeting at a change point (Heckrath et al. 1995; Hesketh and Brookes 2000; Koopmans et al. 2002). Q/I relationships based on soil test P can vary significantly between soils as a result of different sorption properties (Andraski and Bundy 2003). To correct for soil differences, Q/I relationships can be normalized based on soil properties that affect adsorption, such as extractable Fe and Al (Maguire and Sims 2002; Nair et al. 2004; Nelson et al. 2005). Q/I relationships utilize more easily accessible soil properties as compared to the standard adsorption isotherm equations, which may make them more adaptable to large-scale models employing limited data. For example, a Q/I relationship is used in the North Carolina Phosphorus Loss Assessment Tool to determine P concentrations in tile drain flow (Osmond et al. 2003). Other studies have found methods of estimating Langmuir adsorption parameters from simple soil extractions (Koopmans et al. 2002; van der Zee et al. 1988), which may allow for increased use of the Langmuir equation in field- and watershed-scale models. 4.3.2.2 Dissolved Organic P Leaching Although dissolved organic P can represent up to 88% of the total P in leachate (Chardon et al. 1997; Toor et al. 2003), relatively few field- and watershed-scale models consider organic P leaching. The ANIMO model allows dissolved organic P from animal waste applications to leach based on a linear adsorption function (Groenendijk and Kroes 1999), but no account is taken for dissolved organic P from other sources. More complex models have been developed but have not been incorporated into commonly available field- and watershed-scale models (Qualls 2000). 4.3.2.3 Preferential and Subsurface Particulate P Transport Preferential flow can transport dissolved or particulate P from the soil surface vertically through macropores, thereby greatly reducing P interaction with the soil matrix. Preferential P transport through macropores has been identified as a primary transport mechanism in well-structured soils (Akhtar et al. 2003; Kleinman et al. 2005). Preferential P transport has also been used to explain correlations between P spikes in drain water and manure applications (van Es et al. 2004) and correlations between surface soil P concentrations and P concentrations in underlying tile drain water (Heckrath et al. 1995). Vertical movement of particulate and colloidal P



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through preferential flow pathways can result in significant contributions to P leaching. For example, particulate P transport in macropore water and tile drain water can represent from 20 to over 70% of total P transported (Heathwaite and Dils 2000; Turner and Haygarth 2000). Modeling these processes requires separation of macropore flow from matrix flow, determination of particle detachment, and determination of particle filtering (Jarvis et al. 1999). Furthermore, soil properties of the macropore walls may be very different from the bulk soil matrix due to clay and organic matter coatings. Therefore, accurately coupling the already complex dual-porosity solute transport models poses a very large challenge (Simunek et al. 2003). Due to these complexities, preferential and vertical particulate P transport is generally not included in field- and watershedscale models; however, some attempts have been made. Shirmohammadi et al. (1998) developed a simplified model that determined particulate P leaching with average annual drain-tile sediment concentrations (user input) and simulated drainage and soil P concentrations from GLEAMS. The MACRO model (Jarvis 1994; Larsson and Jarvis 1999) has been used on a few occasions to model preferential P transport (McGechan 2002a, 2003). McGechan et al. (2002) also found reasonable agreement between measured and modeled particulate P losses using the MACRO model.

4.4 MODEL EVALUATION As previously stated, the characteristics of an adequate model for P leaching are dependent on the characteristics of the agroecosystem being modeled and the modeling objectives. A detailed description of vertical P leaching, including the nonlinear P adsorption isotherm, is important for long-term simulations when P applications exceed crop removal — as with many animal-waste applications. Special attention should be paid to model descriptions of P leaching in soils with low P sorption capacities, such as sandy soils with low iron-oxide concentrations. Accurate representation of vertical P leaching in these scenarios will help avoid unrealistic predictions of P accumulation in the surface horizon, which would lead to equally unrealistic predictions of excessive P transport in surface runoff and with sediment. Continuity between vertical and horizontal P transport is particularly important when modeling systems with high soil P concentrations and artificial drainage systems. Furthermore, it would be particularly important to use a model describing preferential P leaching when simulating P transport in well-structured soils with artificial drainage systems, regardless of the soils’ P sorption capacities. Accurate representation of vertical and horizontal P transport in these situations will improve predictions of subsurface P losses and P export from these potentially high-risk watersheds. Continuity between vertical P leaching and P transport in interflow and base flow will only be important in specific situations where soil, agronomic, and hydrologic evaluations indicate that these will be relatively significant P loss pathways. Underestimation of P leaching will most likely not be a problem where P leaching is not expected, such as typical agricultural systems where P applications do not exceed agronomic recommendations. Furthermore, overall effects of P leaching will generally have a negligible impact on soil P distribution for short-term


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simulations (< 3 to 5 years, depending on soil and management characteristics), regardless of P applications. Model evaluation with respect to P leaching begins by identifying the P transport pathways simulated and the corresponding modeling techniques (Table 4.1). The forms of P — dissolved and particulate, inorganic and organic — transported within each pathway must also be identified. The following characteristics should be identified for each P form and transport pathway: • • •

Method used for determining P concentrations Necessary model parameters affecting soil solution P concentration Method of determining model parameters

This initial evaluation process was completed for selected models as shown in Table 4.1 and Table 4.2. Further site-specific model evaluation must include fieldscale validation. The degree of validation required must be determined by the model user with due attention to site characteristics and modeling objectives. At a minimum, the predicted soil P distribution should be verified by comparison with measured soil P concentrations in similarly managed soils, especially when simulating long-term waste applications. More detailed model validation should be performed when simulating P losses from artificially drained agricultural systems, such as comparison of predicted and observed P concentrations in subsurface drainage water. More extensive model validation would include comparison of predicted and observed P fractions in soils and water, such as sediment-bound P, particulate and organic P, and dissolved P.

4.5 CONCLUSIONS Model evaluation with respect to phosphorus leaching should consider the hydrologic pathways simulated by the model and the P transformations simulated within each of the identified pathways, as illustrated in Table 4.1 and Table 4.2, for selected fieldand watershed-scale models. The majority of these models use a simplified fieldcapacity water-balance approach for simulating vertical water flux and various other approaches for tile-drainage, interflow, and base-flow simulation. Only four of the evaluated models simulated P leaching processes, none of which contained complete continuity and conservation of mass in describing P transformations and transport from the soil surface to surface water via tile drainage, interflow, and base flow. This further emphasizes the importance of model evaluation with respect to P leaching, especially for long-term simulations involving excess P applications. Land-management decisions, particularly those in watersheds with sandy soils or artificially drained soils, that are based on predictions from models with inaccurate representations of P leaching could result in future problems of unremediable long-term P leaching. A review of the literature on vadose zone modeling reveals a disconnect between the sophisticated laboratory-scale models reported in the literature and the simplified model techniques present in the widely available watershed-scale models. This disconnect arises from a few factors. First, there is great difficulty in scaling up the column or detailed soil profile models to watershed scales. Second,



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many watershed-scale models are a conglomeration of previously developed field- and profile-scale models. Although great progress has been made in improving computer interfaces, data input, and watershed characterization used in these models, very little effort as of yet has been focused on updating the nutrient models to correspond with advances in scientific understanding and data availability, changes in typical agricultural management practices, and greater demands of modeling objectives. Therefore, it is the model user’s responsibility to determine model suitability with respect to their modeling objectives and the characteristics of the agroecosystem of interest.

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Eitzinger, J., M. Trnka, J. Hosch, Z. Zalud, and M. Dbrovsky. 2004. Comparison of CERES, WOFOST, and SWAP models in simulating soil water content during growing season under different soil conditions. Ecol. Model. 171:223–246. Enfield, C.G., T. Phan, and D.M. Walters. 1981. Kinetic model for phosphate transport and transformation in calcareous soils. II: laboratory and field transport. Soil Sci. Soc. Am. J. 45:1064–1070. Gerke, H.H. and J.M. Kohne. 2004. Dual-permeability modeling of preferential bromide leaching from a tile-drained glacial till agricultural field. J. Hydrol. 289:239–257. Gerke, H.H. and M.T. van Genuchten. 1993. A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Wat. Resour. Res. 29:305–319. Grant, R.F. and D.J. Heaney. 1997. Inorganic phosphorus transformation and transport in soils: mathematical modeling in ecosystems. Soil Sci. Soc. Am. J. 61:752–764. Groenendijk, P. and J.G. Kroes. 1999. Modelling the nitrogen and phosphorus leaching to groundwater and surface water with ANIMO 3.5. Report 144, Winand Staring Centre, Wageningen, the Netherlands. Available at http://www.alterra.wur.nl/NL/Producten/ Modellen/. Haith, D.A. and L.L. Shoemaker. 1987. Generalized watershed loading functions for stream flow nutrients. Water Resour. Bull. 23:471–478. Hansen, N.C., T.C. Daniel, A.N. Sharpley, and J.L. Lemunyon. 2002. The fate and transport of phosphorus in agricultural systems. J. Soil Water Conserv. 57:408–417. Haygarth, P.M. and A.N. Sharpley. 2000. Terminology for phosphorus transfer. J. Environ. Qual. 29:10–15. Heathwaite, A.L. and R.M. Dils. 2000. Characterizing phosphorus loss in surface and subsurface hydrological pathways. Sci. Total Environ. 251–252:523–538. Heckrath, G., P.C. Brookes, P.R. Poulton, and K.W.T. Goulding. 1995. Phosphorus leaching from soils containing different phosphorus concentrations in the Broadbalk experiment. J. Environ. Qual. 24:904–910. Hendricks, J.M.H. and M. Flury. 2001. Uniform and preferential flow, mechanisms in the vadose Zone. Pp. 149–187 in Conceptual Models of Flow and Transport in the Fractured Vadose Zone, National Research Council (Ed.). Washington, D.C.: National Academy Press. Hesketh, N. and P.C. Brookes. 2000. Development of an indicator for risk of phosphorus leaching. J. Environ. Qual. 29:105–110. Hillel, D. 1982. Introduction to Soil Physics. San Diego, CA: Academic Press. Jacques, D., J. Simunek, A. Timmerman, and J. Feyen. 2002. Calibration of Richards and convection-dispersion equations to field-scale water flow and solute transport under rainfall conditions. J. Hydrol. 259:15–31. Jarvis, N.J. 1994. The MACRO model (version 3.1): technical description and sample simulations. Reports and Dissertations 19, Department of Soil Science, Swedish University of Agricultural Sciences, Uppsala, Sweden, p. 51. Jarvis, N.J., K.G. Villholth, and B. Ulen. 1999. Modelling particle mobilization and leaching in macroporous soil. Eur. J. Soil Sci. 50:621–632. Johnsen, K.E., H.H. Liu, J.H. Dane, L.R. Ahuja, and S.R. Workman. 1995. Simulating fluctuating water tables and tile drainage with a modified root zone water quality model and a new model WAFLOWM. Trans. ASAE 38:75–83. Jones, C.A., C.V. Cole, A.N. Sharpley, and J.R. Williams. 1984. A simplified soil and plant phosphorus model. I: documentation. Soil Sci. Soc. Am. J. 48:800–805. King, L.D., J.C. Burns, and P.W. Westerman. 1990. Long-term swine lagoon effluent applications on Coastal Bermuda grass. II: effect of nutrient accumulation in soil. J. Environ. Qual. 19:756–760.



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Kleinman, P.J.A., M.S. Srinivasan, A.N. Sharpley, and W.J. Gburek. 2005. Phosphorus leaching through intact soil columns before and after poultry manure application. Soil Sci. 170:153–166. Knisel, W.G. 1993. GLEAMS Groundwater Loading Effects of Agricultural Management Systems, version 2.10. Department Publication 5, Biological and Agricultural Engineering Department, University of Georgia Coastal Plain Experiment Station, Tifton. Knisel, W.G. and J.R. Williams. 1995. Hydrology components of CREAMS and GLEAMS models. Pp. 1069–1114 in Computer Models of Watershed Hydrology, V.J. Singh (Ed.). Highlands Ranch, CO: Water Resources Publications. Koopmans, G.F., R.W. McDowell, W.J. Chardon, O. Oenema, and J. Dolfing. 2002. Soil phosphorus quantity–intensity relationships to predict increased soil phosphorus loss to overland and subsurface flow. Chemosphere 48:679–687. Larsson, M.H. and N.J. Jarvis. 1999. Evaluation of a dual-porosity model to predict fieldscale solute transport in a macroporous soil. J. Hydrol. 215:153–171. Lee, K.Y., T.R. Fisher, and E. Rochell-Newall. 2001. Modeling the hydrochemistry of the Choptank River basin using GWLF and Arc/Info. 2: model validation and application. Biogeochem. 56:311–348. Leij, F.J. and M.Th. van Genuchten. 2002. Solute transport. Pp. 189–248 in Soil Physics Companion, A.W. Warrick (Ed.). Boca Raton, FL: CRC Press. Lemunyon, J.L. and T.C. Daniel. 2002 Quantifying phosphorus losses from the agricultural system. J. Soil Water Conserv. 57:399–401. Maguire, R.O. and J.T. Sims. 2002. Measuring agronomic and environmental soil phosphorus saturation and predicting phosphorus leaching with Mehlich 3. Soil Sci. Soc. Am. J. 66:2033–2039. Maguire, R.O., J.T. Sims, and F.C. Coale. 2000. Phosphorus solubility in biosolids-amended farm soils in the mid-Atlantic region of the USA. J. Environ. Qual. 29:1225–1233. Malone, R.W., L. Ma, R.D. Wauchope, L.R. Ahuja, K.W. Rojas, Q. Ma, R. Warner, and M. Byers. 2004. Modeling hydrology, metribuzin degradation, and metribuzin transport in macroporous tilled and no-till silt loam soil using RZWQM. Pest Manage. Sci. 60:253–266. McGechan, M.B. 2002a. Effects of timing of slurry spreading on leaching of soluble and particulate inorganic phosphorus explored using the MACRO model. Biosyst. Eng. 83:237–252. McGechan, M.B. 2002b. Sorption of phosphorus by soil, part 2: measurement methods, results and model parameter values. Biosyst. Eng. 82:115–130. McGechan, M.B. 2003. Modelling phosphorus leaching to watercourses from extended autumn grazing by cattle. Grass Forage Sci. 58:151–159. McGechan, M.B. and D.R. Lewis. 2002. Sorption of phosphorus by soil, part 1: principles, equations and models. Biosyst. Eng. 82:1–24. McGechan, M.B., N.J. Jarvis, P.S. Hooda, and A.J.A. Vinten. 2002. Parameterization of the MACRO model to represent leaching of colloidally attached inorganic phosphorus following slurry spreading. Soil Use Manage. 18:61–67. Mozaffari, M. and J.T. Sims. 1994. Phosphorus availability and sorption in an Atlantic coastal plain watershed dominated by animal-based agriculture. Soil Sci. 157:97–107. Nair, V.D., K.M. Portier, D.A. Graetz, and M.L. Walker. 2004. An environmental threshold for degree of phosphorus saturation in sandy soils. J. Environ. Qual. 33:107–113. Neitsch, S.L., J.G. Arnold, J.R. Kiniry, R. Srinivasan, and J.R. Williams. 2002a. Soil and Water Assessment Tool user’s manual version 2000. GSWRL Report 02-02, BRC Report 02-06, TWRI Report TR-192, College Station, TX.


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Phosphorus Transport in Streams: Processes and Modeling Considerations Brian E. Haggard University of Arkansas, Fayetteville, AR

Andrew N. Sharpley U.S. Department of Agriculture-Agricultural Research Service, University Park, PA

CONTENTS 5.1 Introduction...................................................................................................105 5.2 Abiotic and Biotic Processes........................................................................106 5.3 Phosphorus Spiraling ....................................................................................109 5.3.1 Determining Phosphorus Spiraling...................................................109 5.3.2 Stream Properties and Phosphorus Spiraling ...................................113 5.4 Algal and Microbial Processes .....................................................................114 5.5 Stream Sediments and Phosphorus ..............................................................115 5.5.1 Sediment Source Effects...................................................................115 5.5.2 Sediment and Equilibrium Phosphorus Concentrations...................117 5.6 Impact of Stream Processes on Eutrophication ...........................................120 5.7 Modeling Phosphorus Transport in Stream Channels..................................122 5.8 Conclusions...................................................................................................124 References..............................................................................................................125

5.1 INTRODUCTION Modeling of phosphorus (P) transport from the landscape to aquatic systems represents a number of complex processes, including rainfall–runoff patterns, manure and fertilizer application, soil–water–P interactions, and crop and forage growth. Numerous processbased models are available to accomplish this task, and many of these models are discussed in other chapters of this book. These models integrate large amounts of 105


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information to simulate catchment-scale P transport from the landscape. They have been reasonably successful in predicting catchment-scale to edge-of-field losses of P and how nutrient and land management affects these losses. However, a major gap in predicting the response of receiving water bodies is the simulation of fluvial processes occurring during P transport from landscape (edge of field) to receiving waters. Although much research relates land management to edge-of-field P losses, little data are available on the fate and transport of this P once in fluvial systems, though this can affect the amount ultimately entering a water body (McDowell et al. 2004). Most importantly, tributaries can act as sinks and sources of P and can influence the effectiveness of watershed best management practices (BMPs) and the response time of impacted water bodies to land remediation (Meals 1992). The modeling of P transport through streams must account for variability in flow, P sources, and in-channel processes (Hanrahan et al. 2001); however, the complexity and spatial variability of these instream processes limit the ability of catchment-scale models to simulate P transport in streams (Sharpley et al. 2002). A complex array of physical, abiotic, and biotic processes occurs within the channel and hyporheic zone of streams, and these complex processes, as well as land-use impacts, influence both P concentrations and loads during downstream transport. Furthermore, these channel processes can greatly influence the shortand long-term impact of P inputs on the degree of eutrophic response of receiving waters. The proportion of P transported during storm and base-flow conditions varies with catchment P sources and the importance of stream-channel and riparian processes. Though long-term (e.g., annual) inputs and outputs of P to streams may be similar, short-term (e.g., daily and monthly) transport of P from effluent discharges, drainage fields, and other upstream sources may be heavily buffered by streamchannel processes. Streams that have been enriched with P will often act as shortterm transient storage zones, releasing dissolved P back into the water column when aqueous concentrations are low (Ekka et al. 2006; Haggard et al. 2005). The release of P from sediment to overlying waters can delay or even mask P loss reductions from catchment-based BMPs (Meals 1992; National Research Council 2000). Despite the importance of these in-stream processes, stream effects on discrete and edge-of-field P inputs are not adequately simulated in many process-based models of catchment P transport. This chapter describes the important fluvial processes that influence the form and amount of P transported in streams and approaches to model P transfer from the landscape downstream.

5.2 ABIOTIC AND BIOTIC PROCESSES Aquatic systems — in particular stream reaches and networks — may alter the timing, magnitude, and bioavailability of P transport from the landscape further downstream (Meyer et al. 1988; Sonzogni et al. 1982). Several processes — such as sediment sorption and desorption — occur that may influence P transport through aquatic systems (Froelich 1988; Klotz 1988; Taylor and Kunishi 1971), precipitation and dissolution (Fox 1989; House and Donaldson 1986), microbial and algal uptake (Elwood et al. 1981; Hill 1982), and riparian floodplain and wetland retention (Kronvang et al. 1999; Mitsch 1992; Novak et al. 2004). Many of the abiotic processes are influenced or mediated by biota; for example, coprecipitation of


Phosphorus Transport in Streams: Processes and Modeling Considerations

107

dissolved P with calcite may be biologically mediated during active photosynthesis (Neal 2001). Furthermore, sediment-associated biotia (i.e., microbial organisms) often account for large fractions of P uptake during sediment–P sorption experiments (Haggard et al. 1999). For instance, several studies have found that aquatic biota accounted for 30 to 40% of P uptake and release in wetland and stream sediments (Khoshmanesh et al. 1999; McDowell 2003; McDowell and Sharpley 2003). In contrast, other work has suggested that the microbial community associated with stream sediments played only a small role in P sorption and buffering capacity (Klotz 1988; Meyer 1979). Clearly, the temporary storage of P from these in-channel processes does alter the transport characteristics of P from different landscape positions through streams to a given outlet within a catchment. The importance of these in-channel processes varies with discharge regimes in individual streams, where these abiotic and biotic processes are most likely to be most important during relatively low- or base-flow conditions. Several studies have shown that P retention occurred in stream reaches during low- or base-flow conditions (Dorioz et al. 1998; Hill 1982; House and Warwick 1998). Under these flow conditions P may be temporarily retained within a stream channel, but increasing discharge during episodic storm events may resuspend phosphorus and transport particulate phosphorus (PP) further downstream. The resuspension of sediments might also influence dissolved P concentrations in the water column of streams during these higher flow events (House et al. 1995; Koski-Vähälä and Hartikainen 2001). A large fraction of the P load transported downstream may be resuspended from bottom sediments (Svendsen et al. 1995). In contrast, McDowell et al. (2001) observed the opposite trend of dissolved P retention by channel sediments during storm flow and release during base flow. Reflecting the dynamic nature and site specificity of in-channel processes, catchment hydrology, and sources of sediment and P, McDowell et al. (2001) described the mechanisms controlling P release from soil and stream sediments in relation to storm and base flow at four flumes along the channel of a 40 ha, second-order agricultural catchment (Figure 5.1). Base-flow dissolved P concentrations (average of 1997 to 2004) were greater at the catchment outflow (0.042 mg L−1 at flume 1) than at the uppermost flume (0.025 mg L−1 at flume 4), whereas the inverse occurred during storm flow (0.304 mg L−1 at flume 4 and 0.128 mg L−1 at flume 1). Similar trends in total P concentration were observed. However, it is questionable whether short-term pulses in dissolved P have much ecological impact in streams (Humphrey and Stevenson 1992). During storm flow, in-channel decreases in P concentration were indicative of dilution of P originating from a critical source area above the uppermost flume (flume 4), where an area of high soil P intersected an area of high erosion and overland flow potential (Figure 5.1). During base flow, the increase in P concentrations downstream was clearly controlled by channel sediments, such that the P sorption maximum of the uppermost flume (flume 4) sediment (532 mg kg−1) was far greater than the outlet flume (flume 1) sediment (227 mg kg−1). Paralleling these trends, the sediment equilibrium phosphorus concentration (EPC0) of sediment at flume 1 was greater than at flume 4 (0.034 to 0.004 mg L−1). Sediment EPC0 trends were highly correlated to base flow dissolved P concentrations (0.025 mg L−1 at flume 4 and 0.042 mg L−1 at flume 1).


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Stream and flume location Watershed boundary 1

Field boundaries

2 3 4

> 100 mg kg–1 Mehlich-3 soil P

High erosion, > 6 Mg ha–1 yr–1

Stream sediment P sorption max.

0.3

400 0.2 200 0.1

0

0

0.05 Baseflow dissolved P (mg L–1)

P sorption maximum of stream sediment (mg L–1)

600 Stormflow dissolved P

0.04 Baseflow dissolved P

0.04

0.03

EPC0

0.03 0.02 0.02 0.01

0.01 0

EPC0 of stream sediment (mg L–1)

Stormflow dissolved P (mg L–1)

0.4

0 Flume 4

Flume 3

Flume 2

Flume 1

FIGURE 5.1 The distribution of Mehlich-3 soil P (>100 mg kg−1), erosion (>6 mg ha−1 yr−1), and mean dissolved P concentration in storm and base flow (mean of 1997 to 2004) and P sorption–desorption properties of channel sediment at four flumes in FD-36, Pennsylvania. (Adapted from R.W. McDowell, A.N. Sharpley, and G. Folmar, J. Environ. Qual. 30, 1587–1595, 2001. With permission.)



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In general, P concentrations and loads increase with increasing discharge, especially during storm events (see, e.g., Green and Haggard 2001; Novak et al. 2003). Phosphorus concentrations and other sediment-bound constituents often display hysteresis in streams, where the chemograph increases rapidly and peaks on the rising limb of the storm-event hydrograph (Richards et al. 2001; Thomas 1988). Thus, P concentrations are often greater on the rising limb when compared with concentrations measured at a similar discharge on the falling limb of the storm-event hydrograph (Sharpley et al. 1976). Although P concentrations are typically greater during this flow regime, the importance of in-stream P retention is minimized because of sediment resuspension and scouring within the channel. Many streams export a very large fraction — greater than 80% — of P loads during episodic storm events (Green and Haggard 2001; Pionke et al. 1996; Richards et al. 2001), whereas Novak et al. (2003) observed that greater than half of dissolved P export occurred during base-flow conditions. A single large storm event may often transport a large portion of the annual P load in many streams. Though stream reaches may show significant P retention during base-flow conditions, P inputs would typically equal outputs on large time scales, such as annual export. However, P deposition on riparian floodplains may be a significant P sink during storm events and stream-bank overflow (Kronvang et al. 1999).

5.3 PHOSPHORUS SPIRALING As P enters streams from discrete and diffuse sources, P cycles from the dissolved inorganic form to the particulate form (abiotic and biotic) and back into the dissolved inorganic form many times while being transported downstream. The number of cycles that may occur within a given stream reach depends on the spiraling length, which is the distance traveled when completing a cycle (Newbold et al. 1981; Stream Solute Workshop 1990). The spiraling length is composed of two basic parts: P uptake length and P turnover length (Stream Solute Workshop 1990). The uptake length, Sw , is the average distance dissolved inorganic P, PO4, travels downstream before it is removed from the water column through various abiotic and biotic process that occur within a stream channel (Newbold et al. 1981). The turnover length, Sp, is the distance traveled in various particulate forms before P is returned to the water column in the dissolved inorganic form (Newbold 1992). The movement of P through a stream reach is tightly coupled with the downstream transport of water, and each P cycle begins downstream from the next, producing a spiral through the stream ecosystem. The use of the spiraling concept and short-term solute injections have been increasingly used to estimate P retention efficiency in streams.

5.3.1 DETERMINING PHOSPHORUS SPIRALING Stream Solute Workshop (1990), Newbold (1992), and Webster and Ehrman (1996) provide valuable guidance on solute dynamics in streams and the experimental methods to estimate P uptake length. Short-term solute injections of P and a conservative (hydrologic) tracer are used to estimate P uptake length in a stream reach where PO4 concentrations downstream from the injection point typically exhibit an exponential decline (Figure 5.2). The solute injection should be at a constant rate


110


Dissolved P concentration (mg L–1)

0.025

0.020

0.015

0.010 Solute injection Background

0.005

0.000

0

20

40

60

80

100

0

20

40

60

80

100

40 60 80 Distance from first sampling site downstream of injection point (m)

100

Fraction of dissolved P remaining in the water column

1.0

0.8

0.6

0.4

0.2

0.0

Natural logarithm of the fraction remaining in the water column

0.0

–0.2

–0.4

Slope = –0.006 m–1 Sw = 167 m

–0.6

–0.8

–1.0

0

20

FIGURE 5.2 Dissolved P concentrations in background water samples and water samples collected during a solute injection experiment on September 2, 1999, at Willow Branch, Oklahoma, with a graphical display of P uptake length calculations. (Adapted from B.E. Haggard and D.E. Storm, J. Freshwater Ecol. 18, 557–565, 2003. With permission.)



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and should last long enough for the hydrologic tracer, such as chlorine (Cl), to reach a steady concentration at the most downstream end of the stream reach; conductivity might be used to measure when the steady state is reached downstream. Multiple water samples are collected from sites at increasing distances downstream from the injection point, and P concentrations resulting from the injection are corrected for background concentrations at each site and then for losses due to dilution using a hydrologic tracer (see, e.g., Martí and Sabater 1996). The proportion of P remaining in the water column is used in a negative exponential relation to estimate the P uptake rate per unit distance coefficient, k: Px = Poexp(–kx)

(5.1)

ln(Px /Po) = –kx

(5.2)

where Px is the dissolved P concentration (mg L–1 ) at a distance x downstream corrected for dilution and background concentration, Po is the dissolved P concentration (mg L−1 ) corrected for background concentration at the first site downstream from the injection point, and k is the P uptake rate per unit distance coefficient (m−1) or slope of the linear relationship in Equation 5.2. The P uptake length, Sw (m) is the inverse of the P uptake rate per unit distance coefficient (1/k). Phosphorus uptake length has been measured using radiotracers 32PO4 and 33PO4 (see, e.g., Mulholland et al. 1985, 1990; Newbold et al. 1981, 1983) and stable PO4 additions (see, e.g., Butturini and Sabater 1998; Davis and Minshall 1999; Haggard et al. 2001b; Macrae et al. 2003; Martí and Sabater 1996; Mulholland et al. 1990; Niyogi et al. 2004; Valett et al. 2002). Phosphorus uptake length generally constitutes greater than 90% of the spiraling length in rather pristine streams (Mulholland et al. 1990; Newbold et al. 1983), and uptake length has been used as an indicator of stream P retention efficiency. The calculation of P turnover length, Sp, requires the use of radiotracers and cannot be accomplished with typical short-term solute injections using stable PO4. Because the downstream transport of added PO4 is influenced by stream water velocity, P uptake length, Sw , is often strongly correlated to stream discharge or water velocity (see, e.g., Butturini and Sabater 1998; Haggard et al. 2001b; Niyogi et al. 2004). Davis and Minshall (1999) suggested that the mass transfer coefficient, vf, should be used to compare the retention efficiency of different stream reaches and streams; this parameter would help identify underlying abiotic and biotic processes influencing P retention. The mass transfer coefficient, vf (m s−1), is the vertical velocity at which dissolved P is removed from the water column by abiotic and biotic processes occurring within the stream channel (Stream Solute Workshop 1990); the mass transfer coefficient is the P uptake velocity within a stream reach. The mass transfer coefficient is a function of the uptake length, average water depth and average water velocity as vf = hu/Sw = Q/(Sww)


(5.3)

112


where h is the average water depth (m), u is the average water velocity (m s−1), Q is the stream discharge (m3 s−1), and w is the average stream width (m). Thus, the mass transfer coefficient reduces the variability observed in P retention associated with stream-water velocity and depth (see, e.g., Davis and Minshall 1999). Doyle et al. (2003) developed the following equation to examine the influence of in-stream processes (i.e., vf) and hydrogeomorphology (i.e., h and u) on P retention: Px = Poexp(–Lvf /uh)

(5.4)

where L is the reach length (m). Equation 5.4 is based on mathematical substitution in the preceding equations in this chapter. This approach allowed Doyle et al. (2003) to determine whether a stream reach would be retentive of dissolved P and whether changes in channel form and uptake processes would alter dissolved P retention. Hydrogeomorphology (i.e., h and u) will vary spatially along the longitudinal downstream gradient and temporally with changes in channel form and discharge of a stream (Doyle et al. 2003). The P uptake rate per unit area, U (mg m−2 s−1) may also be calculated as U = (PbQ)/(Sww) = vf Pb

(5.5)

where Pb is the average background P concentration (mg L−1) measured before the short-term solute injection. Phosphorus uptake rates are the product of the mass transfer coefficient and ambient dissolved P concentrations, and uptake rates will increase with increases in ambient concentrations. Uptake rates may increase linearly with ambient concentrations until a threshold concentration is achieved where abiotic and biotic processes are saturated (Haggard et al. 2005; Niyogi et al. 2004). The aforementioned citations would provide the range of P uptake lengths, velocities, and rates. However, the greatest variability would generally be observed in P uptake length and the least amount in P uptake rates. Short-term solute additions, such as those used to estimate these parameters, measure gross nutrient uptake and assume that the injection duration is short enough to avoid regeneration, that uptake processes are not saturated by the level of enrichment, and that the change in concentration through a reach follows an exponential decay (Webster and Erhman 1996). Several studies have shown that P uptake length measured using stable P additions increases as the level of enrichment increases (i.e., ∆PO4↑) (Haggard and Storm 2003; Hart et al. 1992; Mulholland et al. 1990); the uptake velocity and rate would decrease with increasing levels of enrichment from short-term additions. Despite some constraints in short-term solute injections, this methodology provides an extremely valuable means incorporating both abiotic and biotic processes to evaluate whole-reach measures of P uptake processes within the stream channel. Recently, these parameters have been measured in stream reaches where a natural longitudinal gradient in dissolved P exists (Haggard et al. 2001a, 2005; Martí et al. 2004; Merseburger et al. 2005). Within this context and experimental situation, net uptake length, Sw-net, net uptake velocity, vf-net, and net uptake rate, Unet, have become the usual terminology. The parameters measure the net retention efficiency because the upstream P sources are continuous (e.g., effluent discharges or other point



113

sources) and because dissolved P would be retained from and released into the water column continuously by abiotic and biotic processes. Reported net uptake lengths, Sw-net, and rates, Unet, are an order of magnitude greater than uptake lengths, Sw , and rates, U, measured in less disturbed stream ecosystems, whereas net uptake velocities, vf-net, are one to two orders of magnitude less than uptake velocities, vf, (Haggard et al. 2005; Merseburger et al. 2005). These experimental data might be useful in modeling P retention and release through a stream reach where a significant effluent discharge or other point source exists.

5.3.2 STREAM PROPERTIES

AND

PHOSPHORUS SPIRALING

The concept of P spiraling, or the distance traveled downstream by one P molecule as it completes one cycle of uptake and transformations from dissolved to organic forms and back into flow, reveals significant information about the degree to which P changes during transport in rivers (Elwood et al. 1983). Lengths of P spiraling vary from 1 to 1000 m as a function of flow regime, season, bedrock geology, and sediment characteristics (Melack 1995; Munn and Meyer 1990). Similarly, interaction of ground water with stream flow within the hyporheic zone can cause increases or decreases in P concentrations depending on stream-bed upwelling or infiltration of P-rich stream flow. The first definitive measurement of P spiraling length was reported for a firstorder woodland stream in Tennessee using 32PO4 as the tracer. The P spiraling length was 190 m, 165 m of which was in the water, whereas the remainder was in fine particulate organic matter. Other North American workers found that spiraling length ranged from 23 m in November to 99 m in August when the concentration of coarse particulate material was less and P was moving largely in dissolved form (Mulholland et al. 1985). However, during storms the distance traveled by P in particulate material can increase by one or two orders of magnitude above typical uptake lengths (Melack 1995). Differences in geology can have a profound effect on P spiraling length. Munn and Meyer (1990) found that a stream with granite bedrock had a spiraling length of 85 m, whereas in a stream with P-rich volcanic bedrock the spiraling length was 687 m. Factors influencing the P retention and spiraling are notoriously variable along a stream reach. For example, where in-stream geomorphic processes cause size sorting or where sediments are enriched with P due to local contributions of P-rich overland flow, sediments can represent a significant source of P to stream flow, even when inputs from runoff have ceased. Edge-of-field riparian management not only impacts overland flow P removal but also has a strong influence on stream P spiraling (Cooper et al. 1987; Hearne and Howard-Williams 1988). Fencing off pastures from grazing allows palatable aquatic macrophytes to flourish and decreases P spiraling length, whereas riparian afforestation can shade out periphyton and macrophytes, thus increasing spiral length. The placement of riparian afforestation within a catchment is therefore expected to have a major influence on downstream surface water quality. Quinn et al. (1993) reported that forested (Pinus radiata) riparian areas at the headwaters of grassland-dominated catchments in New Zealand adversely influenced downstream P water quality: total phosphorus (TP) concentrations from


114


grazed and riparian forested catchments of 0.488 and 1.195 mg L−1, respectively. This was attributed to a lack of ground cover within the riparian zone. Quinn et al. (1993) suggested that tree planting should be sufficiently sparse to allow development of vegetative ground cover. Fennessy and Cronk (1997) concluded that buffer strips should be located along headwater reaches where most catchment water originates and that storing water high in the catchment decreases downstream erosion. In addition, streams and riparian areas in headwaters tend to be narrower than downstream channels, taking less land out of production while maximizing nutrient retention and removal compared to the targeting of larger channels downstream (Fennessy and Cronk 1997).

5.4 ALGAL AND MICROBIAL PROCESSES The rate at which algae and other microbial organisms take up and release dissolved P in the water column represents an important component of P retention within stream reaches, especially during base-flow conditions. A Michaelis–Menton relationship is often used to describe dissolved P uptake as a function of dissolved P concentrations, where P uptake becomes saturated as dissolved P concentrations increase. Several studies have shown that algal and microbial P uptake can become saturated at relatively low dissolved P concentrations ( 0.01 mg PO4–P L−1) (Bothwell 1985; Mulholland et al. 1990), and this aspect of biotic uptake represents a constraint in typical solute-injection experiments using stable PO4 additions. The level of P enrichment required to measure differences in dissolved P concentrations between sequential monitoring sites downstream from the injection point often exceeds the concentration where algal and microbial uptake would typically be saturated. Furthermore, typical streams draining agricultural catchments would have dissolved P concentrations that are much greater than 0.01 mg L−1 (see, e.g., Haggard et al. 2001b; Macrae et al. 2003; McDowell et al. 2001; Smith et al. 2005), and effluent dominated streams would have dissolved P concentrations that are one to several orders of magnitude greater than 0.01 mg L−1 (see, e.g., Ekka et al. 2006; Haggard et al. 2005; Martí et al. 2004; Merseberger et al. 2005). It is likely that saturation will influence algal and microbial uptake kinetics in most agricultural and urban catchments where catchment-scale P transport is being simulated by process-based models. Though cellular uptake and growth rates are generally saturated at low concentrations, maximum biomass accrual in streams often occurs at somewhat greater concentrations (0.015 to 0.050 mg PO4–P L−1) (Bothwell 1989; Horner et al. 1983; Popova et al. 2006). This range of dissolved P concentrations might be more typical of streams draining agricultural catchments, and therefore algal and microbial uptake likely still plays a significant role in dissolved P retention through stream reaches. However, the importance of algal and microbial P uptake will vary spatially and temporally with dissolved P concentrations in streams and with the uptake kinetics of the algal and microbial community. Dissolved P uptake rates of algae will vary with light, water velocity, temperature, grazing, and time following disturbances within the stream channel (see, e.g., Dodds 2003; Horner and Welch 1981; Mulholland et al. 1994).



115

To determine the importance of algal and microbial uptake within individual streams, some relatively simple experiments could be performed to quantify P limitation and potential uptake rates. Phosphorus limitation of algae in streams is about as likely to occur as nitrogen (N) limitation (Francoeur 2001), although P limitation in streams may be more widespread in some agricultural catchments because of the mobility of nitrate (NO3). Several citations exist in the literature that describe P limitation experimental protocols using nutrient diffusing substrata (see, e.g., Allen and Hershey 1996; Matlock et al. 1998; Stanley et al. 1990); these experiments are usually relatively short in duration (i.e., approximately 10 to 14 days) and inexpensive when measuring chlorophyll a as the response variable on the treatments. Potential P uptake rates from algae and other microbial organisms in the benthic substrate can be measured using stable PO4 or radio-labeled P; Steinman and Mulholland (1996) provided some guidance on simple experimental procedures to estimate P uptake rates. The use of radio-labeled P in these experiments would allow phosphorus turnover or release rates of the stream algae to be measured as well.

5.5 STREAM SEDIMENTS AND PHOSPHORUS Stream sediments can act as either a P sink or source for dissolved P in the water column, depending on several abiotic and biotic processes that basically influence stream sediment equilibrium P concentration (i.e., EPC0). In streams (i.e., fluvial systems with good hydraulic mixing), the availability of P in benthic sediments may be estimated using EPC0 at zero net sorption or desorption (Froelich 1988; Sharpley et al. 2002). A quasi-equilibrium for dissolved P concentration exists between stream sediments and the water column, where sorption and release rates of dissolved P are virtually equivalent. Stream sediments may have a major influence on dissolved P concentrations and P retention, especially during base-flow conditions (see, e.g., Hart et al. 1992; Hill 1982; House and Warwick 1998; Klotz 1988; McDowell and Sharpley 2003; Meyer 1979). In theory, P will desorb from stream sediments if the water column dissolved P concentration is less than the sediment EPC0, or alternatively, P will sorb to stream sediments if the water-column dissolved P concentration is greater than the sediment EPC0 (Taylor and Kunishi 1971). However, dissolved P concentrations in streams are not solely controlled through sediment sorption and desorption processes, and the relative importance of biotic processes may alter this equilibrium between the water column and stream sediments.

5.5.1 SEDIMENT SOURCE EFFECTS Sediments within the fluvial system are derived either from overland flow or stream bank erosion. Sediments derived from stream banks will largely consist of subsoil that is relatively depleted of P. The proportion of sediment within the fluvial system will depend on the age of the channel network. For example, in areas with recent gully formation (channel rejuvenation), subsoil material will dominate (Olley et al. 1993). Furthermore, P derived from subsoil materials in these systems will be less readily available to be released to water, and the subsoils will likely represent a net


116


sink for P (McDowell and Sharpley 2001). As a result of the erosion of subsoils, which are often dominated by silt-sized particles, the predominant form of P transport in these fluvial systems is PP, whereas in sandy catchments most P is transported in dissolved form (Baldwin et al. 2002). In a much larger catchment, McDowell et al. (2002) examined the processes controlling sediment P release to the Winooski River, Vermont, the largest tributary to Lake Champlain (Figure 5.3). Iron-oxide strip P (algal-available P) of the river

A. Impact of physical transport on P in fluvial sediment 40

0.015 Winooski River watershed Lake Champlain New Hampshire

New York Vermont

EPC0 % sand

20 0.005 10

0.000 Massachusetts

30

0.010

Percent sand

Equilibrium P concentration (mg L–1)

Canada

Before confluence

Tributary

After confluence

0

0 25 50 Kilometers

Land use Urban Agriculture Forest

B. Impact of dairy farm adjacent to river

P release rate (mg kg–1 min–1)

600 Sediments enriched by runoff from dairy farm All other sediments 400

200

0

5

10

15

20

Kilometers

Winnoski River watershed

0

0

20

40

60

80

100

Percent sand

FIGURE 5.3 The impact of land use and physical transport processes in P in fluvial sediments with the Winooski River watershed, Vermont. (Adapted from R.W. McDowell, A.N. Sharpley, and A.T. Chalmers, Ecol. Eng. 18, 477–487, 2002. With permission.)



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sediments adjacent to agricultural land (3.6 mg kg−1) was significantly greater (p < .05) than that of sediments adjacent to forested land (2.4 mg kg−1). This was especially the case in the tributary adjacent to a dairy farm where overland flow was directly contributing to the enrichment of fluvial sediment. Notably, impoundment (731 mg kg−1) and reservoir sediments (803 mg kg−1) had greater TP concentrations than river sediments (462 mg kg−1). This was attributed to more fines (< 63 µm) in impoundments and reservoirs than in river sediments. Furthermore, turbulence at the confluence of two tributaries resulted in the shift of the particle size toward coarser particles. This also increased the release rate of these sediments and their sensitivity to incoming P sources. Consequently, impoundment and reservoir sediments had lower abilities to release P to solution in the short term, thereby acting as sinks for sediments rich in P provided the system was maintained in an aerobic state. However, if sediments, like soils, become anaerobic through oxygen depletion and stratification, P release increases via iron and sulphate reducing bacteria (Boström et al. 1988; Lovley et al. 1991). The results of the research on the Winooski River catchment demonstrate that fluvial hydraulics has a strong influence on the properties of sediment within river systems. The input and delivery of fine sediment enriched with P was influenced by adjacent land use. The fluvial sediment, particularly at the outflow of the river into Lake Champlain, represents a P storage pool, which has long-term potential to release a large amount of P to overlying waters. In the short term, however, river flow and the physical properties of the sediments will influence the amount of sediment P leaving the catchment. Thus, in connecting sediment P loss from the landscape to channel processes, variability in flow, local sources of P, and sediment properties must be taken into account, particularly near the point of impact. Because of these complexities, channel processes and changes in P forms and loads are not currently simulated in many models that estimate P loss from catchments (Hanrahan et al. 2001).

5.5.2 SEDIMENT AND EQUILIBRIUM PHOSPHORUS CONCENTRATIONS The first experiments evaluating sediment and soil EPC0 were conducted over 30 years ago (Taylor and Kunishi 1971), and the PO4 buffer mechanism in streams, wetlands, and estuaries has been intensively investigated since the 1980s (see, e.g., Ekka et al. 2006; Froelich 1988; Haggard et al. 1999; House et al. 1995; Klotz 1988; McDowell et al. 2002; McDowell and Sharpley 2001). The methods to estimate EPC0 are fairly straightforward, where sediments are mixed with solutions containing differing initial PO4 concentrations and then P sorbed (mg P kg−1 dry sediment) is plotted as a function of either initial or final dissolved P concentration (mg P L−1) in the aqueous solution (Figure 5.4) (Froelich 1988; Haggard et al. 2004; Klotz 1988; Taylor and Kunishi 1971). However, several experimental variables can significantly influence the sediment EPC0 determined in the laboratory. These equilibration experiments would be best performed on fresh, wet sediments because drying sediments can alter the P sorption characteristics where sediment has a lesser P buffering capacity (Baldwin 1996). Another important consideration is that the chemical composition of the water used in the extraction does influence the estimation


118


Psorbed = 0.033∗DPfinal – 4.89 R2 = 0.9978 Sediment EPC0 = 0.148 mg L–1

10

8

????

6 Psorbed = 0.005∗DPinitial – 0.71 R2 = 0.9996 Sediment EPC0 = 0.142 mg L–1

4

Final DP concentration Linear regression Initial DP concentration Linear regression

2

0 0.0

0.5

1.0 1.5 Dissolved P concentration (mg L–1)

2.0

2.5

FIGURE 5.4 Graphical display of P sorbed as a function of initial and final dissolved P (DP) concentration during equilibration experiments using filtered stream water spiked with additional P and the linear regression used to estimate sediment EPC0 at Osage Creek, Arkansas. (Adapted from B.E. Haggard, S.A. Ekka, M.D. Matlock, and I. Chaubey, Trans. ASAE 47, 1113–1118, 2004. With permission.)

of sediment EPC0, where an increase in dissolved Ca2+ or ionic strength generally reduces the equilibrium concentration (Klotz 1988). Thus, a solution with a chemical composition similar to the natural water (i.e., filtered stream water) would be best when conducting these laboratory experiments (Erickson et al. 2004; Haggard et al. 2004); however, filtered stream water includes an ambient dissolved P concentration that could be greater than the sediment EPC0. Several investigators use a standard molar solution of calcium chloride (CaCl2) or another salt, and some dilute these salt solutions to match the ambient conductivity measured in the stream water (Popova et al. 2006). Perhaps ancillary measurements of dissolved Ca2+ and other metals associated with P sorption and precipitation should be made in the aqueous solution at the end of these equilibration studies to provide a better understanding of specific mechanisms of P uptake (House and Denison 2000). Even with this potential experimental variability, several studies on sediment EPC0 have provided some interesting insights into abiotic processes affecting P transport through fluvial systems. But the comparisons across some studies are limited by these variations in experimental protocol, suggesting the need to standardize such experiments. In a study of the ability of fluvial sediment P chemistry and location to influence stream P concentrations in an agricultural watershed in central Pennsylvania, McDowell and Sharpley (2001) found that because bed sediments contained more sand-sized material, they could release more P and support a greater dissolved P concentration (EPC0 of 0.043 mg L−1) than bank sediments (EPC0 of 0.020 mg L−1) (Figure 5.5).



119

0.08

Equilibrium P concentration (mg PL–1)

Stream bed sediments Stream bank sediments 0.06

r = 0.60 0.04

0.02

r = 0.63 0.00 25

50

75

100

Percent sand

FIGURE 5.5 Variation in equilibrium P concentration (EPC0) with percent sand in stream bed and bank sediments. (Adapted from R.W. McDowell and A.N. Sharpley, Aquat. Geochem. 7, 255–265, 2001. With permission.)

Clearly, Figure 5.5 shows a strong dependency of EPC0 on sediment texture and the ability of the sediment to sorb or to release P. Further, the research suggested that erosion of bank sediments should contribute less P and may be a sink of P in the stream system compared with resuspension of bed sediment. However, bank sediments may have the potential to be a large source of P in downstream reservoirs or lakes, where increased microbial activity and reducing conditions may solubilize sediment-bound P. Using the indoor fluvarium described by McDowell and Sharpley (2003), it is possible to investigate the effect of flow rate, sediment properties, and dissolved P concentration of flowing water on the quasi-equilibrium established between deposited stream sediment and stream flow. Stream-bed sediments were collected from just above the four flumes in the agricultural watershed, FD-36, detailed in Figure 5.1. The sediments were placed in the fluvarium to a 3-cm depth, and water was recirculated over the sediment at a rate representing the average storm flow during 1997 to 2004. The dissolved P concentration of flowing water was the average measured in surface runoff from a manured field (4.0 mg L−1), which entered the channel directly upstream from flume 4 (Figure 5.1). After 24 hours of continuous flow, the dissolved P concentration in the flume reached a steady state or quasi-equilibrium concentration, which varied with location of collected sediment (Figure 5.6). During the high-flow condition representing a high input of P into the stream channel from runoff, stream sediment acted as a sink for P, which was related to the P sorption maximum of the sediment, as determined from Langmuir isotherms for each sediment



Steady-state dissolved P concentration of flow (mg L–1)

120

1.2

0.3

0.8

0.2

0.4

0.1

High flow 0

0

200

Low flow 400

600

P sorption max (mg kg–1)

0 0

0.1

0.2

0.3

0.4

EPC0 (mg L–1)

FIGURE 5.6 Relationship between steady-state dissolved P concentration and P sorption maximum and equilibrium P concentration (EPC0) stream sediment from an agricultural watershed (FD-36) in central Pennsylvania under high- and low-flow conditions.

sample (Figure 5.6). For low- or base-flow conditions, flowing water in the flume was replaced with water at dissolved P concentration of a 0.025 mg L−1, which was the average base-flow value for the years 1997 to 2004. During low or base flow for a further 24 hours, the stream sediment, then charged with P from the previous flow cycle, acted as a source of P to flowing water. The enrichment of flowing water dissolved P was related to the EPC0 of the sediment (Figure 5.6). It is clear that stream sediment and flow characteristics can influence the concentration of P transport in flowing waters. This will in turn affect the biological response or eutrophic status of receiving waters.

5.6 IMPACT OF STREAM PROCESSES ON EUTROPHICATION The transport of P from discrete and diffuse sources in catchments affects the water quality of streams, rivers, lakes, reservoirs, and estuaries. These water-quality impacts have driven the need to understand and to simulate P transport from the landscape, and the use of process-based models to accomplish these tasks has flourished more recently. However, these landscape process-based models often do not simulate the effect of P inputs in streams related to nuisance algal biomass and accelerated eutrophication. Phosphorus has been identified as the rate-limiting nutrient in the accelerated eutrophication of lakes and reservoirs across the U.S. (Correll 1999; Smith et al. 1999).



121

Benthic chlorophyll a content (mg L–2)

100

10

1

0.1 0.001

0.01 0.1 Dissolved P concentration (mg L–1)

1

FIGURE 5.7 The log-log relation between benthic chlorophyll a content and dissolved P concentration at 16 sites across the Illinois River drainage area in northwestern Arkansas. (B.E. Haggard, unpublished data)

Phosphorus and algal concentrations have been used to determine the trophic state classification of lakes and reservoirs (e.g., Carlson 1977); the strong correlation between P and chlorophyll a concentration (Canfield and Bachman 1981; Dillon and Rigler 1974) was the basis for trophic state classification. However, the correlation between P and algal chlorophyll a concentration in streams is often more variable (Figure 5.7) because of the effects of floods, water velocity, turbidity, grazing, shading, and catchment area (see, e.g., Biggs 1996, 2000; Jones et al. 1984; Lohman and Jones 1999; Winterborn et al. 1992). These factors may also shift the taxonomy of algal species in streams (Carpenter and Waite 2000). The use of stream P concentration to predict chlorophyll a concentration has a higher degree of uncertainty compared to predictions made for lakes and reservoirs. Despite the potential disturbance factors affecting algal biomass in streams, simple statistical models or relations have been used to correlate stream P concentrations with algal biomass indirectly measured using sestonic or benthic chlorophyll a. These models have analyzed algal biomass as a function of dissolved nutrient concentration, total nutrient concentration, flooding frequency (days of biomass accrual), water velocity, and temperature (see, e.g, Biggs 2000; Dodds et al. 1997; Welch et al. 1989, 1992; Winter and Duthie 2000). Often, these relations are improved when mean P concentrations are regressed against either mean or maximum chlorophyll a concentrations (Biggs 2000; Winter and Duthie 2000); this would eliminate seasonal variation and some of the other complicating factors. The relations between stream P and chlorophyll a concentrations are likely catchment or regionally specific, and most often P concentrations explain only a small portion of the variability in benthic or sestonic chlorophyll a (i.e., low R2 of the linear regression).


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Nuisance production of algal biomass represents a management issue for streams: an unacceptable degree of eutrophication. Nuisance algal biomass reduces the beneficial uses of streams. For example, high biomass accrual may impair water withdrawals for irrigation and municipal water supply, large amounts of autochthonous biomass production contribute to oxygen demand and diurnal dissolved oxygen swings, and increased coverage of filamentous algae changes the habitat and food web structure of streams (Biggs 1985). The simple relation described in the preceding paragraph has been used to determine trophic classification schemes for streams, based on the P (and nitrogen) concentration at which nuisance algal biomass occurs. Several studies have suggested that nuisance algal biomass occurs when benthic chlorophyll a content exceeds 100 mg chl-a m−2 (10 µg chl-a cm−2) (Biggs 1996; Horner et al. 1983; Welch et al. 1988), and these observations have been based on the presence of filamentous algae, particularly filamentous green algae Cladophora (Dodds 1991; Horner et al. 1983). Though this chapter and book focus on P, it is important to remember that the relation between nutrients and algae are complex and that nitrogen may be as important or more important in the development of nuisance algal biomass at specific catchments or aquatic systems. Despite this, it must be remembered that a certain degree of eutrophication can be beneficial. For example, fishery management often recommends a higher productivity to maintain an adequate phytoplankton–zooplankton–fish food chain for optimum commercial fish production. The food chain may be manipulated by stocking water with certain fish species in addition to P load reductions in an effort to reduce the incidence of algal blooms and to improve overall water quality (Horppila and Kairesalo 1990). Thus, the level of eutrophication that may be acceptable to a given aquatic system depends largely on its designated beneficial uses.

5.7 MODELING PHOSPHORUS TRANSPORT IN STREAM CHANNELS Table 5.1 shows the models described in this volume and indicates what stream processes, if any, are simulated. The Soil Water Assessment Tool (SWAT) (Neitsch et al. 2000) considers three pools in the water column — algal P, dissolved inorganic P, and dissolved organic P — and the interactions among these pools. The dissolved organic P settles to a benthic P pool, which releases P to the dissolved inorganic P pool through diffusion. Although suspended sediment is modeled in SWAT, the sorption and desorption of P to suspended sediment is not modeled, and SWAT does not simulate resuspension of P that has been moved into the benthic P pool. Migliaccio et al. (2006) suggested that the in-stream processes simulated in SWAT do not enhance its predictive abilities of catchment-scale P loss and often result in only small changes in estimated P loss. The Hydrologic Simulation Program-Fortran (HSPF) model (Bicknell et al. 2001) includes benthic release of dissolved P; adsorption and desorption of dissolved P to suspended sediment in the water column; settling and scouring of adsorbed P; uptake by phytoplankton and benthic algae; and release by zooplankton. However, the HSPF model is considered data intensive and somewhat cumbersome to use when simulating catchment-scale P losses, especially



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TABLE 5.1 Select Process-Based Models and In-Stream Processes Simulated Model

In-Stream Processes Simulated

SWAT

Algal, dissolved inorganic, and dissolved organic P pools in water column; benthic P pool; no interaction between P and suspended sediment Dissolved P and suspended sediment adsorbed P pools in water column, phytoplankton and benthic algae uptake, zooplankton release, scour and deposition of sediment with adsorbed P, sorption and desorption of P with suspended sediment None None None Limited modeling of in-stream processes; lumped into a single stream segment; includes channel erosion and transformation between dissolved and particulate P under low-flow conditions

HSPF

AnnAGNPS ANSWERS-2000 WEND-P GWLF

Notes: These models are discussed in following chapters. GWLF = Generalized Watershed Loading Functions.

when considering fluvial processes. The Annualized Agricultural Nonpoint Source Pollution (AnnAGNPS) model (Bingner and Theurer 2005) does not simulate any in-stream P processes other than transport. This is also the case with the Areal Nonpoint Source Watershed Environmental Response Simulation (ANSWERS) (Beasley et al. 1980) and Watershed Ecosystem Nutrient Dynamics-Phosphorus (WEND-P) models (Cassel et al. 1998). Little process-driven simulation of stream channel effects occurs in terms of dilution, channel sedimentation and erosion, sediment P resuspension, and sediment sorption and release of P, even though these processes can dramatically alter predicted edge-of-field losses prior to watershed export. For example, some models include an in-stream decay rate for P, which in reality can be fluvial-system specific. This in-stream decay rate is conceptually similar to the uptake length, Sw, or net uptake length, Sw-net, of dissolved P that could be measured experimentally in multiple streams draining a catchment. However, the decay rate, Sw or Sw-net, only reflects uptake processes and does not generally consider release of dissolved P from the benthos or the downstream transport of particulate P (i.e., turnover length), which can be significant during episodic runoff events. Furthermore, most catchment-scale models do not account for P resuspension within a stream channel and subsequent transport downstream. This gap or modeling need will be of critical importance as watershed models become an integral part of the Total Maximum Daily Load (TMDL) decision-making process and BMP evaluation.


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The concept of sediment EPC0 might provide a useful mechanism to simulate in-stream processes in these watershed models. Although sediment EPC0 is generally driven by abiotic adsorption and desorption of dissolved P from the aqueous solution to the solid phase, some of the uptake occurring in these short equilibration experiments might be biologically mediated. When sediment uptake and release dominate P retention processes in streams, dissolved P concentrations often exceed typical concentrations where algal and microbial P uptake would be saturated. Thus, sediment EPC0 could be used as a model parameter to simulate the combination of abiotic and biotic processes where dissolved P would be removed from the water column or released to the overlying water until the concentration reaches quasiequilibrium in a given stream reach or segment. Of course, sediment EPC0 would have to be spatially variable with the digital hydrography of watershed models because sediment EPC0 can vary through and between streams (Haggard et al. 1999; Klotz 1988; McDowell et al. 2001; Smith et al. 2005), with the amount of agricultural land in subwatersheds (Popova et al. 2006), and with distance downstream from effluent discharges or other point sources (Haggard et al. 2004; Ekka et al. 2006). The use of sediment EPC0 might provide a physically based method to simulate in-stream processes, but it does not solve the problem of sediment or organic P resuspension from within the channel. Another important shortcoming of most predictions of nonpoint source impacts on the chemical and biological response of receiving water bodies is the lack of linked watershed and water-body response models. There must be a greater linkage of interfacing of these models to translate agricultural management effects on the export of P from watersheds to the point of impact in terms of chemical or biological response of receiving water bodies. Though these linkages are possible and have been accomplished (e.g., Migliaccio et al. 2006, 2007), slight differences in model operation, inputs, and outputs can make this integration difficult.

5.8 CONCLUSIONS It is clear from the information presented in this chapter that many complex and interdependent processes influence the transport and retention of P in streams. Landscape processes are spatially and temporally dependent on climate, land management, topography, and hydrology, as they contribute edge-of-field losses of P. Once in a stream channel, other highly variable fluvial processes influence the amounts, forms, and availability of P as it moves downstream to receiving waters or point of impact. These processes are the variation in stream hydrology and area of bank in contact with water during storm or base flow; the effect of stream dissolved P concentration on whether sediment (bank and bed) act as a source or sink for P; the deposition or resuspension of particulate or sediment-bound P; the influence of abiotic and biotic controls on P uptake and release in the fluvial system; and the additional complexities of whether stream channels are aggrading or degrading. Though modeling landscape processes and export of P from watersheds remains a challenge, as clearly documented in other chapters of this book, simulation of stream or fluvial process and associated P transport is also undoubtedly a challenge that remains to be overcome.



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More reliable and process-driven simulation of fluvial processes to estimate P transfer in stream channels is critical to the accurate prediction of land management or BMP impacts on P inputs to receiving waters and, thus, biological response. Further, the accurate simulation of P transport in streams is even vital to selection of appropriate BMPs or remedial measures that would most effectively bring about an improvement in surface-water quality. For example, if a stream system is acting as an active source of either dissolved or particulate P, such that it contributes a relatively large proportion of P input to surface waters compared to edge-of-field losses, then remedial measures should be targeted to the stream channel. This could include stream bank restoration via fencing or setting aside programs like the Conservation Reserve Enhancement Program to stabilize the stream channel. Finally, it is evident that greater effort must be directed to developing processbased routines to simulate P transport in streams so that nonpoint source models can reliably predict the effect of watershed process and management on the quality and biological response of receiving waters.

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6

Uncertainty Estimation in Phosphorus Models Keith Beven Lancaster University, Lancaster, United Kingdom

Trevor Page Lancaster University, Lancaster, United Kingdom

Malcolm McGechan Scottish Agricultural College, Bush Estate, Penicuik, United Kingdom

CONTENTS 6.1 6.2 6.3 6.4 6.5

Sources of Uncertainty in Modeling P Transport to Stream Channels .......132 Sources of Uncertainty .................................................................................133 Uncertainty Is Not Only Statistics ...............................................................134 Uncertainty Estimation: Formal Bayes Methods .........................................135 Uncertainty Estimation Based on the Equifinality Concept and Formal Rejectionist Methods ................................................................137 6.6 Uncertainty as Part of a Learning Process...................................................140 6.7 An Example Application ..............................................................................142 6.7.1 The MACRO Model .........................................................................142 6.7.2 Study Site and Data ..........................................................................143 6.7.2.1 Drainage Discharge and Phosphorous Concentrations......143 6.7.2.2 Slurry Applications.............................................................144 6.7.3 MACRO Implementation within a Model Rejection Framework ...144 6.7.4 Results and Discussion .....................................................................146 6.7.4.1 Using Initial Rejection Criteria..........................................146 6.7.4.2 Using Relaxed Rejection Criteria ......................................148 6.7.4.3 Simulations for the Period from 1994 to 1995 .................148 6.7.4.4 Simulations and Parameterizations for the Period 1995 to 96...................................................150 6.8 Learning from Rejection: What If All the Models Tried Are Nonbehavioral? ......................................................................................153 6.9 What Are the Implications for P Models? ...................................................155 Acknowledgments..................................................................................................157 References..............................................................................................................157 131


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6.1 SOURCES OF UNCERTAINTY IN MODELING P TRANSPORT TO STREAM CHANNELS The starting point for this contribution is the extensive review of Beck (1987). Summarizing his arguments at the end of the review, he posed the following questions: Are the basic problems of model identification ones primarily of inadequate method or of inadequate forms of data? What opportunities are there for the development of improved, novel methods of model structure identification, particularly regarding exposing the failure of inadequate, constituent model hypotheses? How can an archive of prior hypotheses be appropriately engaged in inferring the form of an improved model structure from diagnosis of the failure of an inadequate model structure? Moreover, in what form should the knowledge of the archive be most usefully represented? What does a lack of identifiability imply for the distortion of a model structure, and what are the consequences of a distorted model structure in terms of generating predictions? Given uncertainty, how can one speculate about the prediction of a “radically different” future? What, in the end, does all this mean for decision making under uncertainty? These questions have been reinforced by the more recent analyses of environmental modeling by Beven (2002a, 2002b, 2004a, 2005, 2006a) and demand an answer to why, nearly two decades later, there are still many model structures and applications that do not consider model identification problems and uncertainties explicitly. The uncertainties exist. They are often ignored. It seems as if the saving grace of the environmental modeler has been model calibration. If a model has at least approximately the right sort of functionality, then there are generally sufficient degrees of freedom to be able to adjust effective values of the parameters to get an acceptable fit to the data and to declare some sort of success in reporting results in scientific articles and reports to decision makers. This obviously does not mean that what is being reported is good science if the calibration allows compensation for errors in model structure as a representation of the processes actually controlling water quality variables, including phosphorus (P) concentrations in different forms. Perhaps we are now reaching a stage where it might be possible to take account of some of the sources of uncertainty in predicting water quality more explicitly, P being a particularly interesting and practically relevant example. It is important to recognize from the outset, however, that this will be difficult: (1) to evaluate model structures as working hypotheses about the functioning of catchment systems independently of errors in the input data used to drive the model and the calibration of effective parameter values; and (2) to estimate effective values of physical and geochemical parameter values a priori by measurement. The struggle to improve water-quality modeling remains as much a struggle against the limitations of current measurement techniques as against the limitations of current model structures.


Uncertainty Estimation in Phosphorus Models

6.2

133

SOURCES OF UNCERTAINTY

The sources of uncertainty in the modeling process are manifold, and, generally speaking, good methodologies have not been developed for assessing the nature and magnitude of uncertainties from different sources. They are thus frequently neglected. For example, some uncertainty exists in the input and boundary condition data used to drive a model. Such uncertainties include measurement errors in assessing the inputs at the measurement scale, together with interpolation errors in space and time to provide the values required at the lumped or distributed element scale of the model. The interpolation error may be made worse by a lack of resolution in the measurements in space and time and by nonstationarity in the processes controlling the inputs. Rainfall is a good example. There are issues about all the measurement techniques available to estimate rainfalls, both at a point using gauges or over an area using radar or microwave techniques. Point ground-level measurements may be sparse in space, whereas the spatial and temporal variability of rainfall intensities may vary markedly between events. Rainfall may show fractal characteristics in space and time, but analyses suggest that there may be nonstationarity in the fractal scaling between events. Thus, interpolation of the measurements to provide the inputs — and an estimate of their uncertainty — at the space and time scales of the model may be difficult. What is clear is that a point measurement of rainfall is, under many circumstances, not a good estimate of the rainfall inputs required by the model. The two variables may, because of time and space variability, actually be related but different variables — they are incommensurate. Yet rainfall data are essential to drive models that will predict the fluxes in hydrological pathways that will control the transport of P. However, the number of nonhypothetical hydrological modeling studies that have attempted to include a treatment of rainfall estimation error is very small indeed. The problem is compounded by other uncertainties. Most particularly for eventbased simulations, errors in the estimation of model initial conditions may be important. Errors may be associated with the model structures used due to the incorrect representation of some processes or the neglect of processes (e.g., preferential flow pathways) that are important in the real system. There may be errors in estimating or calibrating the effective values of parameters in the model that may control the predictions of P mobilization and transport in different pathways. Finally, there may be errors in the observations used to evaluate the model predictions or to calibrate the model parameters. Unfortunately, the possibility of assessing all these different sources of error is limited. In general, only the total model error produced can be assessed by comparing an observation, which is not error-free, with a model-predicted variable produced by a model, which is subject to structural and input errors. Unless some very strong — and usually difficult to justify — assumptions are made about the nature of the sources of error, disaggregating the total model error into its component parts will be impossible. It is an ill-posed problem. The result will be an inevitable ambiguity in model calibrations and error assessment — an ambiguity that also brings with it difficulty in transferring information gained in one application to applications at other sites or different hydrological conditions.


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6.3


UNCERTAINTY IS NOT ONLY STATISTICS

The aim of science, however, is a single true description of reality. The ambiguity arising from uncertainties from these different sources means that this aim is difficult to achieve in applications to places that are all unique in their characteristics and uncertainties. It follows that many descriptions may be compatible with current understanding and available observations, called the equifinality thesis (Beven 1993, 2006a). One way of viewing these multiple descriptions is as different working hypotheses of how a system functions. The concept of the single description may remain a philosophical axiom or theoretical aim but will generally be impossible to achieve in practice in applications to real systems (Beven 2002a, 2002b). This view is actually fundamentally different to a statistical approach to model identification. In both frequentist and Bayesian approaches to statistics, the uncertainty associated with a model prediction is often assumed to be adequately treated as a single lumped additive variable in the form O(X, t) = M(Θ, εθ, I, εI, X, t) + ε(X, t)

(6.1)

where O(X, t) is a measured output variable, such as discharge, at point X and time t; M(Θ, εθ, I, εI, X, t) is the prediction of that variable from the model with parameter set Θ with errors εθ and driven by the input vector I with errors εI; and ε(X, t) is the model error at that point in space and time. Transformations of the variables of Equation 6.1 can also be used where appropriate to constrain the modeling problem to this form. A logarithmic transformation, for example, can be used for an error that is multiplicative —that is, increasing with the magnitude of the model prediction — as a simple way of allowing for heteroscedascticity in the errors with nonconstant variance. Other transformations can also be used to try to stabilize the statistical characteristics of the error series (Box and Cox 1964). Normal statistical inference then aims to identify the parameter set Θ that will be in some sense optimal, normally by minimizing the residual error variance of a model of the model error, which might include its own parameters for bias and autocorrelation terms with the aim of making the residual error independent and identically distributed, even though there may be good physical reasons why errors that have constant statistical characteristics in hydrological and water quality modeling should not be expected (see, e.g., Freer et al. 1996). The additive form of Equation 6.1 allows the full range of statistical estimation techniques, including Bayesian updating, to be used in model calibration. The approach has been widely used in hydrological and water resources applications, including flood forecasting involving data assimilation (e.g., Krzysztofowicz 2002; Young 2001, 2002 and references therein), groundwater modeling, including Bayesian averaging of model structures (e.g., Ye et al. 2004), and rainfall-runoff modeling (e.g. Kavetski et al. 2002; Vrugt et al. 2002, 2003). In principle, the additive error assumption that underlies this form of uncertainty is particularly valuable for two reasons: (1) it allows checking of whether the actual errors conform to the assumptions made about the structural model of the errors; and (2) if this is so, then a true probability of predicting an observation, conditional



135

on the model, can be predicted as the likelihood L(O(X, t) | M(θ, I, X, t)). These advantages, however, may be difficult to justify in many real applications where poorly known input errors are processed through a nonlinear model subject to structural error and equifinality (see Hall 2003; Klir 1994 for reviews of more generalized mathematizations of uncertainty, including discussion of fuzzy set methods and the Dempster-Shafer theory of evidence). One implication of the limitations of the additive error model is that it may actually be quite difficult to estimate the true probability of predicting an observation, given one or more models, except in ideal cases because the model structural error has a complex and nonlinear effect structured in both time and space on the total model error, ε(X, t). This implies that a philosophically different approach to the statistical approach might be worth investigating. In the statistical approach, the error model is generally evaluated as conditioned on finding the best maximum likelihood model. In evaluating models as multiple working hypotheses, it is often more interesting to estimate the likelihood of a model conditioned on some vector of observations such as L(M(θ, εθ , I, εI, X, t) | O(X, t)) and, in particular, to reject those models as unacceptable hypotheses that should have a zero likelihood. This is the basis for the Generalized Likelihood Uncertainty Estimation (GLUE) methodology, first proposed by Beven and Binley (1992). It can be argued that the formal statistical approaches are a special case of the GLUE methodology within which the formal assumptions of a defined error model can be accepted such that the formal likelihood function can be used to weight model predictions. It can also be argued that the GLUE methodology is a special case of formal statistical inference, in which informal likelihood measures replace a formal likelihood function with its rigorous assumptions about the nature of the error model. GLUE can indeed make use of formal likelihood measures if the associated assumptions can be justified. It is perhaps better, however, to consider the two approaches as based on different philosophical frameworks to the uncertainty estimation problem.

6.4 UNCERTAINTY ESTIMATION: FORMAL BAYES METHODS The traditional approach to model calibration in hydrological modeling has been to simplify Equation 6.1 to the form O(X, t) = M(θ, I, X, t) + ε(X, t)

(6.2)

with the aim of minimizing the total error in some way. This assumes that the effect of all sources of error can be subsumed into the total error series as if the model was correct and that the input and boundary condition data and observations were known precisely. Furthermore, if the total error ε(X, t) can be assumed to have a relatively simple form — or can be suitably transformed to a simple form — then a formal statistical likelihood function can be defined, dependent on the assumed error structure. Thus, for an evaluation made for observations at a single site for total model errors that


136


can be assumed to have zero mean, constant variance, independence in time, and a Gaussian distribution, the likelihood function takes the form  1 L (ε | M (θ , I , X , t )) = (2πσ 2 )− T / 2 exp  − 2  2σ 

T

∑ε t =1

2 t

   

(6.3)

where εt = O(X, t) − M(θ, I, X, t) at time t, T is the total number of time steps, and σ 2 is the residual error variance. For total model errors that can be assumed to have a constant bias, constant variance, autcorrelation in time, and a Gaussian distribution, the likelihood function takes the form L (ε | M (θ , I , X , t )) = (2πσ 2 )− T / 2 (1 − α 2 )1/ 2  1 × exp  − 2  2σ 

 (1 − α 2 )(ε1 − µ )2 + 

T

∑ t=2

  [ε t − µ − α (ε t −1 − µ )]2     (6.4)

where µ is the mean residual error (bias) and α is the lag 1 correlation coefficient of the total model residuals in time. More complex error structure assumptions will lead to more complex likelihood functions, with more parameters to be estimated. A significant advantage of this formal statistical approach is that when the assumptions are satisfied, the theory allows the estimation of the probability with which an observation will be predicted, conditional on the model and parameter values, and the probability density functions of the parameter estimates, which under these assumptions will be multivariate normal. As more data are made available, the use of these likelihood functions will also lead to reduced uncertainty in the estimated parameter values, even if the total error variance is not reduced. O’Hagan (2004) suggested that this is the only satisfactory way of addressing the issue of model uncertainty; without proper probability estimate statements about modeling, uncertainty will have no meaning. There is an issue, however, about when probability estimates based on additive, or transformed, error structures are meaningful. From a purely empirical point of view, a test of the actual model residuals ε(X, t) for validity relative to the assumptions made in formulating the likelihood function might be considered sufficient to justify probability statements of uncertainty. From a theoretical point of view, however, there has to be some concern about treating the full sources of error in Equation 6.2 in this type of aggregated form. Model structural errors will, in the general case, be nonlinear, nonstationary, and nonadditive. Input and boundary condition errors, as well as any parameter errors, will also be processed through the model structure in nonlinear, nonstationary, and nonadditive ways. Kennedy and O’Hagan (2001) attempted to address this problem by showing that all sources of error might be represented within a hierarchical Bayesian framework. In particular, where any model structural error is simple in form, it might be possible to estimate this as what they called a “model inadequacy function,” or, more



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recently, “model discrepancy function” (O’Hagan 2004). In principle, this could take any nonlinear form, although the most complex in the cases they considered was a constant bias, which can, in any case, be included as a parameter in Equation 6.4. The aim is to extract as much structural information from the total error series as possible, ideally leaving a Gaussian independent and identically distributed residual error term. The model discrepancy function can then also be used in prediction, under the assumption that the nature of the structural errors in calibration will be similar in prediction. It should be noted, however, that the model discrepancy function is not a direct representation of model structural error. It is a compensatory term for all the unknown sources of error in Equation 6.1, conditional on any particular realization of the model, including specified parameter values and input data. These sources of error could, in principle, be considered explicitly in the Bayesian hierarchy if good information were available as to their nature. This will rarely be the case in hydrological modeling applications, where, for example, rainfall inputs to the system may be poorly known for all events in some catchments and where even the most fundamental equation — the water balance — cannot be closed by measurement (Beven 2001, 2002b). Thus, disaggregation of the different error components will be necessarily poorly posed, and ignoring potential sources of error, including model structural error, may result in an overestimation of the information content of additional data and may lead to an unjustified overconfidence in estimated parameter values (see discussion in Beven and Young 2003). In representing the modeling process by the simplified form of Equation 6.2, the error model is required to compensate for all sources of deficiency.

6.5 UNCERTAINTY ESTIMATION BASED ON THE EQUIFINALITY CONCEPT AND FORMAL REJECTIONIST METHODS The equifinality thesis is the central concept of the GLUE methodology (Beven and Binley 1992; Beven and Freer 2001). The GLUE methodology does not purport to estimate the probability of predicting an observation given the model but rather attempts to evaluate the predicted distribution of a variable that is always conditional on the model or models considered, the ranges of parameter values considered, the evaluation measures used, and the input and output data available to the application for model evaluation. The prediction distributions do not consider the residual error associated with a particular model run explicitly. There is instead an assumption that the error series associated with a model run in calibration will have similar characteristics in prediction — note the similar assumption about model structural error in the formal likelihood approach just described. Thus, in weighting the predictions of multiple models to form the predictive distribution for a variable, there is an implicit weighting of the error series associated with those models, without the need to consider different sources of error explicitly; explicit error models can be handled in this framework by treating them as additional model components (see, e.g., Romanowicz et al. 1998).


138


One of the most interesting features of the GLUE methodology is the complementarity of model equifinality and model rejection. Equifinality accepts that multiple models may be useful in prediction and that any attempt to identify an optimal model might be illusory. But if multiple models are to be considered acceptable or behavioral, it is evident that models can also be rejected (given a likelihood of zero) where they can be shown to be nonbehavioral (given unacceptable simulations of the available observables). Thus, there is always a possibility that all the models tried will be rejected — unlike the statistical approach where it is possible to compensate for model deficiencies by some error structure. However, at this point the limitations of implicit handling of error series in the GLUE methodology become apparent since it is possible that some hypothetical perfect model could be rejected if driven by poor input and boundary condition data or if compared with poor observation data. Thus, there is a need for a more explicit consideration of sources of error in this framework while retaining the possibility of model rejection. A potential methodology has been proposed by Beven (2005, 2006a). Equation 6.1 can be rewritten to reflect more sources of error as O(X, t) + εO(X, t) + εC(∆x, ∆t, X, t) = M(θ, εθ , I, εI, X, t) + εM(θ, εθ, I, εI, X, t) + εr (6.5) The error terms on the left-hand side of Equation 6.5 represent the measurement error, εO(X, t), and the commensurability error between observed and predicted variables, εC(∆x, ∆t, X, t). The model term, M(θ, εθ, I, εI, X, t), will reflect error in input and boundary conditions, model parameters, and model structure. The error term, εM(θ, εθ, I, εI, X, t), can now be interpreted as a compensatory error term for model deficiencies, analogous to the discrepancy function in the Bayesian statistical approach of O’Hagan (2004) but that must also reflect error in input and boundary conditions, model parameters, and model structure. Finally, there may be a random error term, εr . Equation 6.5 has been written in this form to both highlight the importance of observation measurement errors and the commensurability error issue and to reflect the real difficulty of separating input and boundary condition errors, parameter errors, and model structural error in nonlinear cases. There is no general theory available for doing this in nonlinear dynamic cases. One simplification can be made in Equation 6.5: If applied on a model-by-model basis, model parameter error has no real meaning. It is the model structure and set of effective parameter values together that process the nonerror-free input data and determine total model error in space and time. Thus, Equation 6.5 could be rewritten, for any model structure, as O(X, t) + εO(X, t) + εC(∆x, ∆t, X, t) = M(θ, I, εI, X, t) + εM(θ, I, εI, X, t) + εr

(6.6)

and εM(θ, I, εI, X, t) is a model specific error term. The question that then arises within this framework is whether εM(θ, I, εI, X, t) is acceptable in relation to the terms εO(X, t) + εC(∆x, ∆t, X, t). This is equivalent to asking if the following inequality holds: Omin(X, t) < M(θ, I, εI, X, t) < Omax(X, t)


for all O(X, t)

(6.7)


139

where Omin(X, t) and Omax(X, t) are acceptable limits for the prediction of the output variables given εO(X, t) and εC(∆x, ∆t, X, t), which together might be termed an effective observation error. The effective observation error takes account of both real measurement errors and commensurability errors between observed and predicted variables. When defined in this way, the effective observation error needs neither zero mean or constant variance nor to be Gaussian or stationary in the form of its distribution in space or time, particularly where there may be physical constraints on the nature of that error. Note that the commensurability error might be expected to be model implementation dependent in that the difference between observed and predicted variables may depend on model time and space discretisations and measurement scales in relation to expected time and space heterogeneities of the observable quantities. However, it should really be possible to develop a methodology for making prior estimates of both measurement and commensurability errors, since they should be independent of individual model runs. An objective evaluation of each model run using Equation 6.7 should then be possible. If a model does not provide predictions within the specified range, for any O(X, t), then it should be rejected as nonbehavioral. This rejectionist framework, based on the equifinality concept, is analogous to set-theoretic concepts previously used in environmental modeling (by, e.g., Klepper et al. 1991; Osidele et al. 2005; Rose et al. 1991; Spear et al. 1994; van Straten and Keesman 1991). It is also a generalization of the Hornberger-Spear-Young method of Generalized Sensitivity Analysis (Hornberger and Spear 1981; Young 1983), which was also based on a split of a series of Monte Carlo model runs into sets of behavioral and nonbehavioral models. It results in a set of provisionally behavioral models that satisfy all the evaluation criteria as expressed as criteria in the form of Equation 6.7. The approach can also be relativist in taking account of the performance of different models within the set of behavioral models (Beven 2004b, 2005). Within the behavioral range, for all O(X, t), a positive weight could be assigned to the model predictions, M(θ, I, εI, X, t), according to the level of past performance. The simplest possible weighting scheme that need not be symmetric around the observed value, given an observation O(X, t) and the acceptable range [Omin(X, t), Omax(X, t)], is the triangular relative weighting scheme, but other bounded weighting schemes could be used — including truncated Gaussian forms. A core range of observational ambiguity, or equal weighting, could be added if required (Beven 2006a). This methodology gives rise to some interesting possibilities. Within this framework there is no possibility of a representation of model error being allowed to compensate for poor model performance, even for the “optimal model,” unless the acceptability limits are made artificially wide to avoid rejecting all of the models — but this might not generally be considered to be good practice. If no model proves to be behavioral, then it is an indication that there are conceptual, structural, or data errors, though it may still be difficult to decide which is the most important. There is perhaps then more possibility of learning from the modeling process on occasions when it proves necessary to reject all the models tried. However, this type of evaluation requires that consideration also be given to input and boundary condition errors, since, as noted before, even the perfect model


140


might not provide behavioral predictions if it is driven with poor input data error. Thus, the combination of input and boundary data realization — within reasonable bounds — and model structure and parameter set in producing M(θ, I, εI, X, t) should be evaluated against the effective observational error. The result will hopefully still be a set of behavioral models, each associated with some likelihood weight. Any compensation effect between an input realization — and initial and boundary conditions — and model parameter set in achieving success in the calibration period will then be implicitly included in the set of behavioral models. There is also the possibility that the behavioral models defined in this way do not provide predictions that span the complete range of the acceptable error around an observation. The behavioral models might, for example, provide simulations of an observed variable O(X, t) that all lie in the range O(X, t) to Omax(X, t) or even in just a small part of it. They are all still acceptable but are apparently biased. This provides real information about the performance of the model or other sources of error that can be investigated and allowed for specifically at that site in prediction rather than being lost in a statistical representation of model error.

6.6 UNCERTAINTY AS PART OF A LEARNING PROCESS Both Bayesian and equifinality (rejectionist set-theoretic) concepts allow the modeling process to be set up within a learning framework, using data assimilation to update the model each time new data become available. This can be for short-term forecasting with the aim of minimizing forecast uncertainty as conditioned on the new data or in a simulation context with the aim of refining the model representation of the system of interest as new information is received to update the Bayes likelihood function or the weights associated with the set of behavioral models using the Bayes equation, originally proposed by Thomas Bayes in 1724 (see Bernado and Smith 1994; Howson and Urbach 1993). In formal Bayes theory, the posterior likelihood is intended to represent the probability of predicting an observation, given the true model, L(Y |θ) where Y is the observation vector and θ is the parameter vector. Lp (O|θ ) ∝ Lo(θ) L(θ |Y)

(6.8)

where Lp (O|θ) is the posterior probability of predicting observations O given a model with parameter set θ, Lo(θ) is the prior likelihood of parameter set θ, and L(θ |Y) is the likelihood given data Y. However, Bayes’s equation was originally stated in the more general conditioning form for hypotheses, H, given evidence, E, as Lp (H|E) ∝ Lo(H) L(E|H)

(6.9)

or, in the discrete form for k potential hypotheses proposed independently by PierreSimon Laplace in 1820 as Lp (Hk |E) ∝ Lo(Hk) L(E|Hk) / ΣkL(Hk |E)


(6.10)


141

where Lp(Hk |E) is the posterior likelihood for hypothesis Hk given the evidence E; Lo(Hk) is a prior likelihood for Hk; and L(E|Hk) is the likelihood of predicting the evidence E given Hk. Here, the hypotheses of interest are each model of the system, including its parameter values and any other ancillary hypotheses. When this type of Bayes conditioning is first applied, the prior likelihoods can be chosen subjectively based on any available evidence about each model as hypothesis. In later evaluations, which may be as each new piece or set of data becomes available, the posterior for the last updating step becomes the prior for the next updating step. It is therefore important that the errors at each updating step remain consistent with the assumptions that underlie the definition of the likelihood function. The equifinality approach as previously formulated in the extended GLUE methodology is also effectively Bayesian in nature in that each time a new model evaluation is made using Equation 6.10, the distribution of behavioral models and the weights associated with them can be reevaluated as a combination of the prior likelihood weights and the new evaluation for each model. The approach is less formal in that more choices can be made about how to weight different behavioral models and how to combine the weights in successive evaluations. It is easy to include model evaluations based on multiple criteria within the GLUE methodology in this way. Bayes’s equation implies a multiplicative combination but other types of combinations, such as a weighted average of multiple evaluation measures, can be used to provide a likelihood weight for each behavioral model. These choices must, however, be made explicit so that they can be reproduced by others if necessary. The most important part of the learning process is the successive application of Equation 6.7. This defines the set of behavioral models and the rejection of nonbehavioral models. In the case of multicriteria evaluation, this may mean that a model that is successful on one criterion may be rejected on another. This type of learning process will increasingly represent the way models are implemented. The possibility of the routine application of data assimilation within a learning framework raises some interesting questions about the nature of modeling and model evaluation. Effectively, repeated updating and correction of model predictions will allow the data assimilation process to compensate for errors in model inputs and model structure. Model evaluation therefore becomes more difficult. In real-time forecasting, this may not be such a problem. In fact, the desire is for the data assimilation process to compensate for errors in model inputs and model structures if this results in improved forecasts with maximized accuracy and minimized uncertainty. This may not be the case, however, in simulation where such compensation may not be desirable if it leads to a model structure being accepted when it should be rejected. There is, of course, a fundamental difficulty in deconstructing the causes of model error and isolating the model structural error alone (see discussions in Beven 2005, 2006a; Beven and Young 2003; Kavetski et al. 2002). Though we do not want to accept a model structure because of the compensation allowed by data assimilation, equally we would not want to make the error of rejecting a perfectly good model because of errors in the input data. Differentiating between these sources of error may be very difficult, if only because the nature of both input errors and model structural errors may be nonstationary in time.


142


Thus, there is a question as to whether the use of data assimilation can, in a simulation context, reveal deficiencies in either model structures or input data. There is an analogy here with the State Dependent Parameter (SDP) estimation methodology used by Young (2003) and Romanowicz et al. (2004). In the SDP approach, an initial estimate of a linear transfer function model is used within a recursive data assimilation framework to examine how the best estimates of the parameters change over time or with respect to some other variable. This can lead to the identification of the dominant nonlinear modes of behavior of the system based directly on the observations rather than prior conceptual assumptions about the system response.

6.7 AN EXAMPLE APPLICATION The following application of the methodology will illustrate some of the issues that arise in thinking about different potential sources of error in the modeling processes and the relationship between observed and predicted variables. It examines the use of the MACRO-P model in predicting observations of P concentrations in the drainage from slurry application experiments on instrumented grassland plots in Scotland.

6.7.1 THE MACRO MODEL The MACRO model of water flow in structured soils was developed by Jarvis and colleagues (Jarvis 1994). It was adapted for colloid-facilitated transport of contaminants (Jarvis et al. 1999; Villholth et al. 2000), and subsequently the version used here was adapted for P transport (McGechan 2002; McGechan et al. 2001). Only a brief description of the representation of the more important model processes will be given here as background to the model parameters investigated in the study. MACRO is a soil profile model that is divided into a number of vertical layers and is partitioned into micropore (soil matrix) and macropore domains. The boundary between the two domains is described in the model by the air–entry soil–water tension in the Brooks-Corey equation. The two domains function separately and are associated with their own degree of saturation, hydraulic conductivity, and flux. Flow in the micropores is calculated using the Richards (1931) equation. Flow in the macropores is gravity driven at a rate determined by degree of macropore saturation. Simulation of soluble P transport requires a single run of the model where the convection-dispersion equation is solved for each layer at each time step to calculate the P concentration. For simulation of colloid-facilitated P transport, two consecutive model runs are required. In the first run the concentration of colloids is simulated in place of the solute, and in the second run the concentration of P sorbed to sites on the colloids is calculated. This requires the concentrations of colloidal particles and inorganic P, respectively, to be specified. For this application, all colloidal particles were those derived from the slurry applied on specific dates. An alternative option in the model that was not used — to reduce the number of parameters to be considered — was colloid generation by rainfall impact.



143

Sorption of P to the soil matrix is described using the Freundlich isotherm equation s = Kd cn

(6.11)

where s is the sorbed phase concentration in either micropores or macropores, Kd is the Freundlich sorption coefficient, c is the solution concentration, and n is the Freundlich sorption exponent. For sorption to colloids a similar formulation is employed using a sorption coefficient for colloids, Kc, and the Freundlich sorption exponent set to unity. Filtration, which is the physical trapping of particles, in macropores and micropores leading to the irreversible trapping of colloids, is included using the following equations. For macropores, F = fref vref nf v1− nf cθ

(6.12)

where F is the filtration sink term, fref is a reference filter coefficient, nf is an empirical exponent, vref is the pore water velocity at which fref is measured, and θ is the volumetric soil water content for the domain. For micropores, F = fc vc θ

(6.13)

where fc is the micropore filter coefficient.

6.7.2 STUDY SITE

AND

DATA

The study site is located at Crighton Royal Farm, Dumfries, Scotland. The annual average precipitation at the site is 1054 mm (Hooda et al. 1999), and the precipitation for the simulation periods chosen for this study are 755 mm (October 1, 1994 to March 31, 1995) and 624 mm (October 1, 1995 to April 30, 1996). The two 0.5 ha grass field plots are grassland with a silty clay loam soil that showed significant vertical macroporous flow channels (Hooda et al. 1999). The plots were isolated from each other and external areas by a drainage system giving isolation, apart from deep percolation, which is thought to be insignificant on these soils (Hooda et al. 1999; McGechan et al. 1997). 6.7.2.1 Drainage Discharge and Phosphorous Concentrations From each plot the discharge from a main drain was recorded and summed to a weekly total. Flow-proportional sampling was used to obtain an effective P concentration for the period since the previous sample. Different forms of P were analyzed, but only total inorganic P (molybdate-reactive phosphorus, MRP) was used for this study.


144


6.7.2.2 Slurry Applications Slurry applications were made at a rate of approximately 50 m3 ha−1 the following times: February 14, 1994, 23 kg ha−1 total phosphorus (TP), 5000 gm−3 colloid concentration; May 25, 1994, 8.4 kg ha−1 TP, 1825 gm−3 colloid concentration; November 21, 1994, 17 kg ha−1 TP, 3700 gm−3 colloid concentration; May 31, 1995, 12.7 kg ha−1 TP, 2760 gm−3 colloid concentration; July 7, 1995, 4.1 kg ha−1 TP, 900 gm−3 colloid concentration; and January 31, 1996, 23.9 kg ha−1 TP, 5200 gm−3 colloid concentration. For assumptions made in estimating the P and colloid concentrations in slurry, see McGechan (2002).

6.7.3 MACRO IMPLEMENTATION REJECTION FRAMEWORK

WITHIN A

MODEL

MACRO has a large number of parameter values that must be specified before a run is made. Many of the parameters are effective parameters with values that are difficult to specify at the scale of application because of scale and heterogeneity effects. Here the most important parameters based on previous experience of calibrating MACRO have been varied across ranges defined to allow for uncertainty in these effective values (Table 6.1). Lacking knowledge about the nature of the prior distributions and the possible covariation of the parameters, uniform independent distributions have been assumed, noting that the evaluation of the simulations from each parameter set will result in posterior likelihood weights that reflect any interactions among the effective parameter values in achieving an acceptable simulation. For the two periods of interest, as specified previously (1994 to 1995 and 1995 to 1996), 10,000 and 11,500 model simulations were carried out, respectively. At each weekly time step, MACRO’s estimates of discharge and P concentration were compared to the observed data described previously. Use of weekly discharge totals and weekly flow-weighted average concentrations in the model evaluation does add a degree of incommensurability to the model evaluations. This is particularly the case for concentrations that can vary rapidly within hydrological events, particularly at this relatively small scale, meaning that flow-weighted average concentrations may systematically differ from those predicted by the model. For discharge the problem is likely to be less pronounced, as the simulation of weekly discharge will depend less on correct model dynamics and more on longer-term mass balances; this does, however, mean that the evaluations will not provide a strong constraint on the model’s description of the flow pathways. To allow for these problems, effective observation errors were defined in a fuzzy manner by allowing model simulations to be considered acceptable within some range of effective observation error in the GLUE framework as described previously. The errors were taken as ± 40% for flow-weighted P concentrations, −30% and +30 to +300% for discharge. The range +30 to +300% was used for the upper limit of discharge evaluations as very low flows were known to be underestimated by the measurement equipment. For this reason positive errors were estimated on a linear sliding scale of +30% for flows of ≥ 80 mm wk−1 to +300% for flows ≤ 1 mm wk−1. The ranges were implemented as triangular fuzzy distributions (see Figure 6.1).



145

TABLE 6.1 MACRO Parameters Varied within the GLUE Simulations and Ranges Used for Sampling Parameter

Description

Min

Max

Units

Hydrology KSATMIN

Macropore Ksata

37.5 (1) 20.8 (2) 16.7 (3-8) 5 × 10−7 (9)

3750 (1) 2080 (2) 1670 (3-8) 5 × 10−7 (9)

mm hr−1

TPORV

Total porositya

50 (1) 47.4 (2) 43.9 (3-9)

54.8 (1) 52.4 (2) 48.5 (3-9)

% (volume)

MAC_POR

Macroporosity fractiona

2.12 (1) 2.71 (2) 0.972 (3-9)

2.59 (1) 3.31 (2) 1.19 (3-9)

% (volume)

CTEN

Critical soil moisture tension MIC/MAC — determines when macropores flow

8.5 (1-9)

17.5 (1-9)

cm H2O

KTHETA

Hydraulic conductivity at critical soil moisture tension (CTEN)

0.5 (1) 0.36 (2) 0.075 (3-8) 1 × 10−26 (9)

6.0(1) 1.92 (2) 0.4 (3-8) 1 × 10−26 (9)

mm hr−1

THETAINI

Initial soil moisture content

38.0 35.6 29.0 32.2 32.6 32.9 32.9 36.3

55.0 53.5 43.6 48.3 48.9 48.9 49.3 54.4

% (volume)

AREA

Drainage basin area (controls deep percolation)

1.29

1.75

ha

FREUND (n)

Freundlich sorption exponent (soil matrix)

0.8

2.2

—

ZKDPC (Kd)

Freundlich sorption coefficient (soil matrix)

0.1

5

m3g−1

ZKD (Kc)

Freundlich sorption coefficient (colloidal particles)

91(1) 185 (2) 300 (3) 750 (4) 1531 (5) 4500 (6-9)

366 (1) 740 (2) 1400 (3) 6000 (4) 7500 (5) 11000 (6-9)

(m3)n mg1−n kg−1

FILTERMI (fc)

Filter coefficient (micropores)

0

80

m−1

REFILTER (fref)

Reference filter coefficient (macropores)

0

4

m−1

(1) (2-3) (4) (5) (6) (7) (8) (9)

(1) (2-3) (4) (5) (6) (7) (8) (9)

P PROCESS

Note: Values in brackets represent the numbering of the soil layers in the model (layer 1 at the surface). a

Parameters varied within ranges by a multiplicative factor applied to all layers simultaneously.



Fuzzy weighting

146

1

0

5

10 15 20 Discharge (mm wk-1)

25

FIGURE 6.1 Example of triangular fuzzy distribution of observed variable used in model constraint.

In assessing the performance of each simulation, it was accepted as behavioral only if simulated values were within the prescribed range for all time steps. For simulations that met this criterion the fuzzy measures at each time step were combined by addition to generate a weighting coefficient. Simulations where the criterion was not met were given a likelihood weighting of zero, i.e., the simulation, was deemed nonbehavioral and was rejected. Furthermore, for simulations to be deemed behavioral, they had to achieve this criterion for both discharge and concentration information. Only the simulations that satisfied both criteria were used in the calculation of the distribution of simulated P fluxes. It is demonstrated in the following that even these rather relaxed rejection criteria had to be relaxed further to allow some predictability using this model in this application.

6.7.4

RESULTS

AND

DISCUSSION

6.7.4.1 Using Initial Rejection Criteria From the 10,000 and 11,500 model simulations for the periods from 1994 to 1995 and 1995 to 1996, using the stringent concentration fuzzy acceptance criteria (Figure 6.2), there were no behavioral simulations. For discharge-constrained simulations, there was a single behavioral simulation for 1994 to 1995 and no behavioral simulations after both evaluation periods. However, the single behavioral simulation constrained by discharge only could be rejected as it did not satisfactorily describe the P concentration criteria. One possible reason for the model’s poor performance with respect to concentration is P inputs from grazing animals. These inputs were poorly known, both in their timing and their magnitude, and were not included as model inputs. The likely effects of grazing inputs on discharge P concentrations are discussed further below. For discharge, the only data problem known a priori was that for the study period from 1994 to 1995 there was approximately 13 mm more discharge than was observed as rainfall input (767.9 mm and 755 mm, respectively). There was no apparent explanation for this, though it appears that there may be a long history of this in plot experiments subject to the possibility of subsurface inflows from upslope (see Beven 2004c). Furthermore, the problem is likely to be more pronounced, owing to the potential underestimation of low magnitude discharges mentioned previously. The effects of this problem are also discussed in the following.


4500

3500

Obs Min obs 1 Max obs 1 Min obs 2 Max obs 2

1600 1400

MRP (mg l-1)

3000 2500 2000 1500

1200 1000 800 600

1000

400

500

200

0

0 1

3

5

7

9

11

13

15

17

19

21

23

1

2

3

4

5

6

Timestep 140

8

9

250


10

11 12

13

100


200

Discharge (mm wk-1)

120

Discharge (mm wk-1)

7

Timestep

80 60 40


4000

MRP (mg l-1)

1800


150

100

50 20 0

0 1

3

5

7

9

11

13

15

Timestep

17

19

21

23

1

2

3

4

5

6

7

8

9

10 11

12

13

Timestep


147

FIGURE 6.2 Time series of fuzzy ranges for stringent rejection criteria (dashed line) compared to relaxed rejection criteria (solid line) for concentration and discharge. Left-hand plots show 1994 to 1995 data; righthand plots show 1995 to 1996 data.

148


Rejection of all models does not allow utilization of the model for prediction but does force attention on possible problems rather than relying on a statistical representation of model error to compensate for such problems. In this study it does appear as if there are important errors in the inputs to the model, and in the observations with which it is being compared, as well as possible model structural errors. There is, therefore, the possibility of unjustifiably rejecting a model because of errors in the data. Thus, in the case of the grazing inputs and the imbalance in the hydrological fluxes, it is argued that the rejection criteria should be relaxed as the model should not be expected to simulate correctly with incorrect or missing inputs. 6.7.4.2 Using Relaxed Rejection Criteria The relaxation of the rejection criteria was performed in such a manner that only those time steps where rejection of many parameterizations occurred were altered to achieve a reasonable number of simulations for analysis to be performed and for adequate simulation of high-magnitude flux time steps. This approach implicitly allowed the investigation of performance at individual time steps and the assessment of apparent errors in terms of their origins. The relaxed criteria (Figure 6.2) allowed the designation of behavioral parameterizations as given in Table 6.2. Results of these most successful simulations are presented in the following in relation to the original rejection criteria so that deviations are clearly seen. 6.7.4.3 Simulations for the Period from 1994 to 1995 Figure 6.3a shows likelihood-weighted percentiles of simulated discharge compared to the original fuzzy measure ranges. It can be seen that, in general, the observed pattern is simulated well but that there is a systematic underestimation for a number of time steps, having both low and high discharge magnitudes. Conversely, and more importantly for the rejection of parameter sets, the two time steps that were the most poorly simulated (steps 13 and 14) are overestimated by the model. Presented in Figure 6.3b are histograms of simulated discharge for time steps 13 and 14 together with a well-simulated time step 17, where the simulated distribution is encompassed, and approximately centered within, the original range of acceptable error. Figure 6.3c shows the same time steps as Figure 6.3b but compares the cumulative distribution functions (CDF) of the observed and simulated discharges. The deviations of given quantiles between the two CDFs for each time step are plotted as a time series in Figure 6.3d where the pattern of

TABLE 6.2 Behavioral Simulation Numbers as Constrained by the Relaxed Criteria Study Period

Discharge

Concentration

Flux

1994 to 1995 1995 to 1996

4120 3010

691 755

620 536



149

120 95th 50th 5th

Discharge (mm wk-1)

100

(a)

max observed min

80

60

40

20

(c)

Cumulative weighting

(b)

Frequency

0

0

5

1 0.5 0

15 Timestep

500

500 0

10

5

10 15 20 Timestep 13

25

25

5

10

15

20

25

0 1 0.5 0

20 500

5

10 15 20 Timestep 14

5 10 15 20 Discharge (mm wk-1)

25

25

0 1 0.5 0

30

Drainflow quantile deviation (mm)

10

10

20 30 Timestep 17

20

30

5th th 25th 50th 75th 95

20

(d)

25

10 0 -10 -20 -30 -40 -50 0

5

10

Timestep

15

20

25

FIGURE 6.3 (a) Likelihood-weighed percentiles of simulated discharge compared to the stringent fuzzy rejection criteria for the study period from 1994 to 1995 (see legend): note the poor simulation of time steps 13 and 14. (b) Histograms of simulated discharge compared to the stringent (full line) and relaxed (dashed line) fuzzy rejection criteria for time steps 13, 14, and 17. (c) Comparison of cumulative distribution functions for observed stringent distribution (dashed line) and simulated distribution (full line) for time steps 13, 14, and 17. (d) Time series of quantile deviations (see legend): note that positive numbers on the y axis denote an overestimation and vice versa.


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general underprediction can be seen, expressed as negative quantile deviations. The fact that time steps 13 and 14 have low-magnitude observed drainage discharges, and hence may be subject to the problem of low-flow measurement error, does not appear to be significant as there is no strong relationship between underestimation and the magnitude of the discharge, although the use of weekly discharges results in a loss of information regarding the dynamics of individual events. The general underestimation is consistent with the known inconsistency between rainfall inputs and observed discharges for the period. However, the use of fuzzy observations has allowed retention of behavioral parameterizations, but it must be remembered that potential bias may now be incorporated into the likelihood weightings assigned to successful parameter sets if used for prediction purposes, though this can be examined explicitly by looking at the distribution of retained predictions in relation to any of the observed values. A similar evaluation of the P concentration simulations showed an underestimation for most time steps (Figure 6.4a,d). To obtain a useful number of behavioral simulations, the rejection criteria had to be relaxed significantly for the majority of time steps. For example, see Figure 6.2b and time step 3, and Figure 6.4b. There is a strong positive relationship between underestimation and the concentration magnitude, particularly for those time steps not directly associated with the slurry application of October 21, 1994 (time step 6). The underestimation also occurs mainly for time steps with relatively high discharges. This suggests that the underestimation may result from the lack of P inputs derived from grazing but may also be as a result of poor model representation of processes during hydrological events. The relaxation of the constraining ranges allowed satisfactory simulation of time step 6, which is associated with the slurry application (Figure 6.4a), although the distribution of simulated concentrations for this time step shows a general underestimation (Figure 6.4b,c). The behavioral simulations for both discharge and concentration were used to estimate MRP fluxes, where the effects of underestimation of both discharge and concentration result in significant underestimation of MRP fluxes for most of the high magnitude time steps (not shown here). As mentioned previously, there is no information regarding the possible imbalance between rainfall and discharge, and it remains unclear whether or not the concentration inconsistencies can be fully explained by grazing inputs. 6.7.4.4 Simulations and Parameterizations for the Period 1995 to 1996 The discharge quantiles for the period 1995 to 1996 show a random pattern of error compared to the original ranges of effective observation error (Figure 6.5a,d). There is no apparent relationship between underestimation or overestimation and discharge magnitude. Two time steps proved the most problematic to simulate: 5 and 13 (Figure 6.5a through 6.5d). Both were underestimated, even though the model explicitly includes a preferential flow component. Time step 1 was also difficult to simulate well in combination with the underestimated time step 5. To achieve an adequate number of behavioral simulations, the rejection criteria had to be relaxed



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for time step 1 to allow far higher initial flows achieved by the specification of high initial soil moisture content (θinit). Simulation of P concentrations showed a significant underestimation from time steps 1 to 7 and 11 but with more reasonable distributions from time steps 8 to 10 and 12 to 13 (Figure 6.6a and 6.6d). Figure 6.6b and 6.6c show that for the time step associated with the slurry application of January 31, 1996 (time step 8; January 15, 1996 to February 12, 1996), the distribution of simulated concentration is adequate and centered on the observed value. As for the study period from 1994 to 1995, the general underestimation for other time steps may result from the lack of grazing inputs, but similarly a strong relationship exists between the magnitude of weekly discharge and underestimation, excluding the time step associated with the slurry application; the observed relationship is nonlinear with decreasing severity of underestimation with a decrease in weekly discharge. In contrast to the study period from 1994 to 1995, the simulated MRP fluxes, resulting from the likelihood-weighted distributions of behavioral discharges and concentrations, represent the observed pattern well. Some of the earlier time steps are underestimated as a result of the underestimation of concentrations but are relatively unimportant in terms of overall MRP flux for the period.

6.8 LEARNING FROM REJECTION: WHAT IF ALL THE MODELS TRIED ARE NONBEHAVIORAL? As noted at the start of this chapter, it is possible to look at a model of a system as a hypothesis about how that system works. Consideration of multiple model structures and parameter sets is then analogous to considering multiple competing hypotheses about how the system works (Beven 2002b). The possibility of model rejection within the modeling framework outlined in this chapter does lead to the possibility that all the models tried as hypotheses will be rejected, as in the application presented here (see also, e.g., Freer et al. 2002; Page et al. 2006). This contrasts with the statistical approach within which at least the best model found will be retained, as if it were correct, and the remaining error can be represented by an error model. The assumption that the model is correct together with overestimating the information content of the observational data can lead to some strange conclusions, however. Thiemann et al. (2001), for example, applying a Bayesian data assimilation approach in a rainfall-runoff modeling application, showed how the updating at each time step results in a very well-defined set of parameters for the model but is associated with a larger error variance. In addition, each time there is a rainfall event the observations are outside the confidence limits of the error model. In such a case it might have been better to allow for other sources of error, including model structural error, or to allow that even the best model does not give an adequate simulation and should be rejected (see discussion by Beven and Young 2003). But concluding that all the models tried are nonbehavioral also demands a response. One response is to ensure that the model space has been searched sufficiently to be sure that no behavioral models exist. In high-dimensional spaces this may require a very large number of model runs, and in the application reported here


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computing resources limited the number of simulations performed to some 10,000 or so, which might be insufficient to find the best possible simulations in the parameter space searched. Iorgulescu et al. (2005), for example, using a model with 17 parameters carried out 2 billion simulations and accepted only 236. It is also necessary to ensure that the reasons for failure can be properly justified and are not just because of outliers or errors in the measurements or treatment of the input data used to drive the models or the observations with which the models are being compared. Some periods of dubious data, or particular types of model failure, might be identified in this way. This was also an issue in the example application previously reported here, though it has to be recognized that it is always difficult to go back over what was done in a particular experiment when such difficulties are identified. This is clearly, however, one way in which modelers and field experimentalists might usefully interact in discussing why particular problems might have occurred. Much more interaction is needed to develop appropriate parameterizations of process at the scale at which they will be applied (Beven 2006b). The most satisfying response would be to learn from the model rejections to try to improve the model structure. In complex model structures, however, there is clearly no easy way of moving from identifying a lack of functionality resulting in model rejection to a modification to improve that functionality. This is a step requiring creativity from the modeler. The least satisfying response is to relax the criteria of rejection — as was necessary in this example — to allow for the multiple unknown sources of error and to ensure that a sample of behavioral models is retained for use in prediction. However, again, examination of the reasons for model failure might be sufficient to justify such a relaxation. This is a step requiring the modeler to act responsibly.

6.9 WHAT ARE THE IMPLICATIONS FOR P MODELS? In outlining the stages of the modeling process, Beven (2001) distinguished between the perceptual model of the processes governing a flux of interest and the conceptual model of those processes as represented in mathematical form. It is important to recognize that the relationship between the two is complex (see Beven 2002a, 2002b, 2006a, 2006b). In particular the perceptual model can recognize many aspects of the processes that are difficult to represent in mathematical form. The conceptual model used in prediction is therefore a simplification, and often a gross simplification, of the perceptual model. This is certainly true of models of P mobilization and transport to stream channels. The perceptual model will recognize the possibility of complex controls on P mobilization in different forms into different pathways, including spatial and temporal nonstationarities, in a way that the conceptual models described in later chapters of this volume can reproduce only approximately. In the perceptual model, a qualitative description always can be provided of processes that may be missing from some conceptual models, such as the role of macropores and preferential pathways in the soil on P movement, or the role of colloids in controlling time variable surface infiltration rates by blocking some larger flow pathways, or the highly variable depths of overland flow and their interaction with raindrop impacts in mobilizing particulate attached P. The conceptual models must assume


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either that some of these complexities are unimportant in controlling the bulk of P fluxes or that the model parameters can be adjusted to reflect such missing processes implicitly. To rely on the latter, however, means that the effective parameter values required by the model will be different from those that can be assessed by experiment. This is a noncommensurability issue in addition to that posed by differences in model and measurement scales for heterogeneous variables. It is an issue meaning that the effective parameter values required by a model will depend on the model structure such that it may be difficult to take values of parameters reported in the literature and use them satisfactorily in another conceptual model structure. It might be an important issue in the modeling of P fluxes where it is not yet clear that we adequately understand the processes of mobilization and retention of different forms of P under different hydrological conditions. There remains process uncertainty about the retention of P in the soil, solute and sediment mobilization and delivery rates, and the role of more extreme events in conjunction with different antecedent conditions on the annual flux of P in different types of catchments (Beven et al. 2005). This process uncertainty is a reflection of the relatively limited number of expensive field studies, the associated limitations of measurement techniques and logistic difficulties of sampling sufficiently in space and time, and the further problem of extrapolating those field results to other catchments. Models act as extrapolating tools in this respect. They are a means of encapsulating past experience in new applications. However, they can only be uncertain extrapolating tools, and it would now seem to be good practice to at least attempt to assess that uncertainty and to find effective ways of trying to reduce it in applications to specific places in the type of learning process described in this chapter (Beven 2000, 2002a, 2004a). However, the types of parameter and uncertainty estimation methodologies described in this contribution are best suited to systems that are not changing and where conditioning data are available. In that way new data should allow a refinement of the feasible model representations and reduction in the predictive uncertainty or learning from the rejection of models. Many applications of simulation to environmental systems, however, involve questions of past, current, or future change under different scenarios. Data assimilation may be valuable in the analysis of past change. Recursive analysis may reveal the impact of past change in terms of changing effective parameter values or model rejections, if — and this is a real if in the case of most P studies — sufficient data are available to be able to distinguish different hypotheses about the response. It is therefore important to end this section on assessing uncertainties in prediction with an emphasis on the importance of data. Uncertainty estimation should not be the endpoint of a study. It should be a starting point for the more important question of what data can be obtained that will allow that uncertainty to be further constrained or competing hypotheses to be distinguished as part of the learning process for the place and application of interest. This is a question of science that goes beyond the calibration of models and declarations of success in prediction. It also suggests that different types of data will have different value in this scientific process for different places and different types of application. As yet, with very few studies that have investigated the value of different types of data in this context it



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is difficult to provide any guidelines. How far, for example, is it necessary to have long-term solute flux data to assess the long residence time pathways and to differentiate the hypotheses inferred from the analyses of Kirchner et al. (2001)? Is it necessary to have information on large, infrequent events to properly estimate the average fluxes of P from a catchment area? What data could be collected that would allow the identification of critical, but dynamic, source areas for P within a catchment area — and do those critical source areas differ from those for runoff? What data are the most cost effective in constraining uncertainties in P models at the catchment scale? These types of questions can be useful when posed within a learning framework as soon as modelers start to make proper assessments of the uncertainty associated with their predictions.

ACKNOWLEDGMENTS Recent work on the GLUE methodology has been supported by NERC Long Term Grant NER/L/S/2001/00658. Applications to modeling phosphorus transfers to stream channels has been supported by BBSRC grant 89/MAF/12247. The authors are grateful to Nick Jarvis for the use of the MACRO model and all the SAC staff involved in the field data collection at the Crighton Royal site.

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Section II Models


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Phosphorus Modeling in Soil and Water Assessment Tool (SWAT) Model Indrajeet Chaubey University of Arkansas, Fayetteville, AR

K.W. Migliaccio University of Florida Tropical Research and Education Center, Homestead, FL

C.H. Green U.S. Department of Agriculture-Agricultural Research Service, Temple, TX

J.G. Arnold U.S. Department of Agriculture-Agricultural Research Service, Temple, TX

R. Srinivasan Texas A&M University, College Station, TX

CONTENTS 7.1 7.2

SWAT Model Background ...........................................................................164 Phosphorus Modeling in SWAT: Soil Phosphorus Interactions..................167 7.2.1 Initialization of Soil Phosphorus Levels......................................... 168 7.2.2 Mineralization, Decomposition, and Immobilization..................... 170 7.2.3 Inorganic Phosphorus Sorption....................................................... 171 7.2.4 Leaching .......................................................................................... 173 7.2.5 Fertilizer Application ...................................................................... 173 7.2.6 Phosphorus Uptake by Plants ......................................................... 174

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Phosphorus Movement in Surface Runoff.................................................. 7.3.1 Soluble Phosphorus......................................................................... 7.3.2 Organic and Mineral Phosphorus Attached to Sediment in Surface Runoff............................................................................ 7.4 In-Stream Phosphorus Cycle ...................................................................... 7.5 Versions of SWAT....................................................................................... 7.6 SWAT Model Applications ......................................................................... 7.7 Model Limitations....................................................................................... 7.8 SWAT Modifications ................................................................................... 7.9 Conclusions ................................................................................................. References.............................................................................................................

175 176 177 179 182 183 184 185

7.1 SWAT MODEL BACKGROUND The Soil and Water Assessment Tool (SWAT) model was developed by the U.S. Department of Agriculture Agricultural Research Service (USDA-ARS). It is a theoretical model that functions on a continuous time step. Model components include weather, hydrology, erosion and sedimentation, plant growth, nutrients, pesticides, agricultural management, channel routing, and pond and reservoir routing. Agricultural components in the model include crop cycles from planting to harvesting, fertilization, tillage options, and animal production and have the capability to include point source loads (Neitsch et al. 2001a, 2001b). All model calculations are performed on a daily time step. The SWAT model predicts the influence of land-management practices on constituent yields from a watershed. SWAT is the continuation of over 30 years of model development within the USDA-ARS. The Chemicals, Runoff, and Erosion from Agricultural Management Systems (CREAMS), Groundwater Loading Effects of Agricultural Management Systems (GLEAMS), and Erosion Productivity Impact Calculator (EPIC) models (Knisel 1980; Leonard et al. 1987; Williams et al. 1984) have each contributed to the scaling up of past field-scale models to one that includes large river basins. Large-area simulations are possible due to the advances in computer software and hardware, including speed and storage, geographic information science (GIS), and spatial analysis and debugging tool software. SWAT model development primarily emphasizes (1) impacts of watershed management and climatic conditions; (2) flow and water quality loadings and fate; (3) flexibility in how a basin is descretized into smaller geographic areas; and (4) continuous time simulation. SWAT is a public domain model that is actively supported by the USDA-ARS at the Grassland, Soil, and Water Research Laboratory in Temple, Texas. To adequately simulate hydrologic processes using the SWAT model for a basin, the basin is divided into sub-basins through which streams are routed. The subunits of the sub-basins are referred to as hydrologic response units (HRUs), which are a unique combination of soil- and land-use characteristics and are considered to be hydrologically homogeneous. The model calculations are performed on an HRU basis, and flow and water-quality variables are routed by HRUs and sub-basins to the basin outlet. The SWAT model simulates hydrology as a two-component system, comprised of land hydrology and channel hydrology. The land portion of the hydrologic


Phosphorus Modeling in Soil and Water Assessment Tool (SWAT) Model

165

cycle is based on a water mass balance. Soil–water balance is the primary consideration by the model in each HRU, which is represented as (Arnold et al. 1998) (see Figure 7.1): t

SWt = SW0 +

∑ (R − Q − ET − P − QR ) i

i

i

i

i

(7.1)

t =1

where SWt is the soil water content after t days, SW0 is the initial soil water content at the beginning of simulation, i is time in days for the simulation period t, and R, Q, ET, P, and QR, respectively, are the daily precipitation, runoff, evapotranspiration, percolation, and return flow. Water enters the SWAT model’s watershed system boundary predominantly in the form of precipitation. Precipitation inputs for hydrologic calculations can be either measured data or simulated with the weather generator available in the SWAT model. Surface runoff is estimated using the Soil Conservation Service (SCS) curve number (CN) or the Green-Ampt infiltration equation. Percolation is modeled with a layered storage routing technique combined with a crack flow model. Potential evaporation can be calculated using the Hargreaves, Priestly-Taylor, or Penman-Monteith method (Arnold et al. 1998). The water balance of each HRU in the watershed contains four storage volumes: snow, the soil profile (0 to 2 m), the shallow aquifer (2 to 20 m), and the deep aquifer (> 20 m). Loadings of flow, sediment, nutrients, pesticides, and bacteria from the upland areas to the main channel are routed through the stream network of the basin using a process similar to hydrologic model (HYMO) (Williams and Hann 1973). The stream processes modeled by SWAT are shown in Figure 7.2 and include channel sediment routing and nutrient and pesticide routing and transformation. The pond and reservoir routing allows for sediment settling and simplified nutrient and pesticide transformation routines. The command structure for routing runoff and chemicals through a basin is similar to the structure for routing flows through streams and reservoirs. The SWAT watershed model also contains algorithms for simulating erosion from the watershed. Erosion is estimated using the Modified Universal Soil Loss Equation (MUSLE). MUSLE estimates sediment yield from the surface runoff volume, the peak runoff rate, the area of the HRU, the Universal Soil Loss Equation (USLE) soil erodibility factor, the USLE cover and management factor, the USLE support practice factor, the USLE topographic factor, and a coarse fragment factor. After the sediment yield is evaluated using the MUSLE equation, the SWAT model further corrects this value considering snow cover effect and sediment lag in surface runoff. The SWAT model also calculates the contribution of sediment to channel flow from lateral and groundwater sources. Eroded sediment that enters channel flow is simulated in the SWAT model to move downstream by deposition and degradation (Neitsch et al. 2001a). Soil nitrogen (N) is simulated in the SWAT model and is partitioned into five N pools, with two being inorganic (ammonium-N [NH4-N] and nitrate-N [NO3-N]) and three being organic (active, stable, and fresh). The SWAT model simulates movement between N pools, such as mineralization, decomposition and immobilization, nitrification, denitrification, and ammonia volatilization. Other soil N processes such as N fixation by legumes and NO3-N movement in water are also


166

Evaporation and Transpiration

Precipitation

Infiltration/plant uptake/ Soil moisture redistribution

Vadose (unsaturated) Zone Revap from shallow aquifer

Percolation to shallow aquifer

Surface Runoff Lateral Flow

Return Flow

Shallow (unconfined) Aquifer Confining Layer Deep (confined) Aquifer

Flow out of watershed

Recharge to deep aquifer

FIGURE 7.1 Hydrologic cycle representation in the SWAT model. (From S.L. Neitsch et al., Soil and Water Assessment Tool theoretical documentation version 2000, 2001. 2001, available at http://www. brc.tamus.edu/swat/doc.html.With permission.) © 2007 by Taylor & Francis Group, LLC


Root Zone


167

Municipal or Industrial Discharge

Non-Point Discharge

i

rt Pa

ort nsp Tra

Biodegradation and Transformation

Sorption onto sediments rt

o

sp

n Tra cle

d ve ol ss i D

Dilution and Diffusion

Deposition and Resuspension

Deposition and Accumulation

FIGURE 7.2 In-stream processes considered by the SWAT model. (From S.L. Neitsch et al., Soil and Water Assessment Tool theoretical documentation version 2000, 2001. 2001, available at http:// www.brc.tamus.edu/ swat/doc.html.With permission.)

included in the model. All soil N processes are simulated in the SWAT model using relationships described in the model’s theoretical documentation (Neitsch et al. 2001a). Once N enters channel flow, the SWAT model partitions N into four pools: organic N, NH4-N, nitrite-N (NO2-N), and NO3-N. The SWAT model simulates changes in N that result in movement of N between pools. The algorithms used to describe N transformations in channel flow were adapted from the QUAL2E model by SWAT model developers (Neitsch et al. 2001a).

7.2 PHOSPHORUS MODELING IN SWAT: SOIL PHOSPHORUS INTERACTIONS Figure 7.3 illustrates the major components of the phosphorus (P) cycle modeled in SWAT. Phosphorus can be added to the soil matrix in the form of inorganic P fertilizer, organic P fertilizer, and P present in plant residue. Soil P is divided into six pools. Three of the pools are characterized as mineral P, and three are characterized as organic P (Figure 7.4). Crop residue and microbial biomass contribute to the fresh organic P pool, and humic substances contribute to the active and stable organic P pools. Soil inorganic P is divided into solution, active, and stable pools. Despite the labeling in Figure 7.4, it is clear in the text of the SWAT User’s Manual that solution P is actually labile P in conformance with the original EPIC version


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Fertilizer Manures, wastes, and sludge

Manures, wastes, and sludge

mineralization

H2PO4HPO4-2

immobilization

Soil Organic Matter

Adsorbed and fixed Inorganic Fe, Al, a, and clay

FIGURE 7.3 Phosphorus cycle processes modeled by SWAT. (From S.L. Neitsch et al., Soil and Water Assessment Tool theoretical documentation version 2000, 2001. 2001, available at http://www.brc.tamus.edu/swat/doc.html.With permission.)

of the P module as described in Jones et al. (1984), Sharpley et al. (1984), and Chapters 3 and 4 of this volume. Labile P is the P extracted by an anion exchange resin (Sharpley et al. 1984) and therefore represents solution P plus weakly sorbed P. This chapter uses the same notation as in the SWAT User’s Manual (Neitsch et al. 2001a) for the equations, but an indication will be provided parenthetically in the text when solution P is actually labile P. Transformations of soil P among these six pools are regulated by algorithms that represent mineralization, decomposition, and immobilization. The solution (labile) pool is considered to be in rapid equilibrium (days to weeks) with active pools that subsequently are considered to be in slow equilibrium with stable pools.

7.2.1 INITIALIZATION

OF

SOIL PHOSPHORUS LEVELS

Initial amounts of soluble (labile) and organic P contained in humic substances for all soil layers can be either specified by the model user or designated with SWAT model default values. The model initially sets concentration of solution (labile) P in all layers to 5 mg P kg−1 soil for unmanaged land under native vegetation and 25 mg P kg−1 soil for cropland conditions (Neitsch et al. 2001a). © 2007 by Taylor & Francis Group, LLC


Mineral Phosphorus Inorganic P fertilizer Plant uptake

Organic Phosphorus Humic substances Mineralization Organic P fertilizer

Stable

Active

Solution

169

Active

Stable

Residue Plant residue

Fresh

Decay Residue mineralization

FIGURE 7.4 Various pools of P and their interactions in soil matrix. (From S.L. Neitsch et al., Soil and Water Assessment Tool theoretical documentation version 2000, 2001, available at http://www.brc.tamus.edu/swat/doc.html.With permission.)

The active mineral pool P (Pactive_mineral_pool) concentration (mg kg-1) is initialized as  1 − PAI  Pactive_mineral_pool = Psolution    PAI 

(7.2)

where Psolution is the amount of labile P (mg P kg–1) and PAI is the P availability index. PAI is estimated using the method outlined by Sharpley et al. (1984). The stable mineral pool P (Pstable_mineral_pool) concentration (mg P kg–1) is initialized as Pstable_mineral_pool = 4 (Pactive_mineral_pool )

(7.3)

Organic P concentration (Phumic_organic) is calculated assuming an N to P ratio in humic substance of 8 to 1 and is calculated as Phuman_organic = 0.125( N human_organic )

(7.4)

where Nhumic_organic is the concentration of humic organic nitrogen in the soil layer (mg kg−1). Phosphorus in the fresh organic pool is set to 0.03% of the initial amount of residue on the soil surface (kg ha−1). The SWAT model makes all nutrient calculations on a mass basis even though all nutrient levels are input in the model as concentrations. The nutrient concentration (mg kg–1 or ppm) is converted to mass (kg P ha–1) by multiplying it by the depth of the soil layer and soil bulk density and performing appropriate unit conversions.


170


7.2.2 MINERALIZATION, DECOMPOSITION,

AND IMMOBILIZATION

The P mineralization calculations also include immobilization and are based on Jones et al. (1984). The fresh organic P associated with crop residue and microbial biomass and active organic P pool associated with soil humus are two P reservoirs considered by the model for mineralization. Temperature factor (γtemperature) and water factor (γwater) are two parameters regulating the impact of temperature and water availability on P mineralization and decomposition. These factors are calculated as   Tsoil γ temperature = 0.9    Tsoil + exp[9.93 − 0.312 * Tsoil ] 

γ water

(7.5)

SW = FC

where Tsoil is the temperature of the soil layer (°C), SW is water content of the soil layer (mm), and FC is water content of the soil layer at field capacity (mm). Temperature of the soil layers should be above 0°C for mineralization and decomposition to occur. The minimum value of γwater allowed by the model is 0.05. The amount of P present in active and stable organic pools associated with humus is calculated as   organic N active organic Pactive = organic Phumus    organic N active + organic N stable 

(7.6)

  organic N stable organic Pstable = organic Phumus    organic N active + organic N stable 

(7.7)

where organic Pactive is the amount of P in the active organic pool (kg P ha−1), organic Pstable is the amount of P in the stable organic pool (kg P ha−1), organic Phumus is the concentration of humic organic P in the soil layer (kg P ha−1), organic Nactive is the amount of nitrogen in the active organic pool (kg N ha−1), and organic Nstable is the amount of nitrogen in the stable organic pool (kg N ha−1). The amount of P mineralized from the humus active organic pool is calculated as follows and is added to the solution P pool in the soil layer. Pmineral_active = 1.4 (βmineral )(γ temperatureγ water )0.5 (organic Pactive )

(7.8)

where Pmineral_active is the P mineralized from the humus active organic P pool (kg P ha−1), and βmineral is the rate coefficient for mineralization of the humus active organic nutrients.



171

Mineralization and decomposition from the residue fresh organic P pool is calculated as Pmineral = 0.8 (δ ntr )(organic Pfresh )

(7.9)

Pdecay = 0.2 (δ ntr )(organic Pfresh )

(7.10)

where Pmineral is the amount of P mineralized from the fresh organic P pool (kg P ha−1) and added to the solution P pool, Pdecay is the amount of P decomposed from the fresh organic pool (kg P ha−1) and added to the humus organic pool, and δntr is the residue decay rate constant. δntr is calculated as

δ ntr = βresidueγ ntr

(

γ temperatureγ water

)

(7.11)

where βresidue is the rate coefficient for mineralization of the residue fresh organic nutrients and γntr is the nutrient cycling residue composition factor for the soil layer. γntr is calculated as

γ ntr

   ε − 25    exp  − 0.693  C:N   25          ε C:P − 200     = min exp  − 0..693     200        1.0     

(7.12)

where εC:N is the C:N ratio on the residue in the soil layer and εC:P is the C:P ratio on the residue in the soil layer. The C:N ratio of the residue is calculated as

ε C:N =

0.58 rsd organic N fresh + NO3

(7.13)

where rsd is the amount of residue in the soil layer (kg ha−1), 0.58 is the fraction of residue that is carbon, and NO3 is the amount of nitrate in the soil layer (kg N ha−1). The C:P ratio is calculated as

ε C:P =

0.58 rsd organic Pfresh + Psolution

(7.14)

7.2.3 INORGANIC PHOSPHORUS SORPTION The inorganic P pool, originating either from mineralization of organic P or P applied directly as inorganic fertilizer, is simulated considering plant uptake and conversion to active and stable forms of inorganic P (Figure 7.4). The movement of P between


172


the solution (labile) and active mineral pools is estimated using the following equilibrium equations (Neitsch et al. 2001a):

 PAI  Psoluble/active = Psolution − mineral Pactive    1− PAI  if

Psoluble/active

 PAI  Psolution > mineral Pactive    1 − PAI 

  PAI   = 0.1 Psolution − mineral Pactive    1− PAI    if

(7.15)

 PAI  Psolution < mineral Pactive    1 − PAI 

where Psolution/active is the amount of P transferred between the soluble (labile) and active mineral pool (kg/ha), Psolution is the amount of labile P (kg P ha−1), and PAI is P availability index. A positive value of Psolution/active indicates transfer of P from solution to the active mineral pool, and a negative value indicates that P is transferred from the active mineral pool to solution (labile) pool. Phosphorus availability index controls the equilibrium between the solution and active mineral pool and specifies what fraction of fertilizer P is in solution after the rapid reaction period. In estimating slow sorption of P (where sorbed P is the stable pool), SWAT assumes that the stable mineral pool is four times the size of the active mineral pool. The movement of P between the active and stable pools is calculated using the following equations (Neitsch et al. 2001a):

(

Pactive/stable = βeqP 4 mineral Pactive − mineral Pstable

mineral Pstable < 4 mineral Pactive

if Pactive/stable =

( 0.1 β ) ( 4 mineral P eqP

active

if

)

− mineral Pstable

)

(7.16)

mineral Pstable > 4 mineral Pactive

where Pactive/stable is the amount of P transferred between the active and stable mineral pools (kg P ha−1), and βeqP is the slow equilibrium rate constant (0.0006 d−1). A positive value of Pactive/stable indicates transfer of P from the active mineral pool to the stable mineral pool, and a negative value indicates transfer of P from the stable mineral pool to the active mineral pool.



173

7.2.4 LEACHING When plants take up P from the root zone in the soil solution, it creates a concentration gradient in the soil-solution matrix. SWAT considers diffusion — the migration of P ions over small distances (1 to 2 mm) in the soil solution in response to a concentration gradient — to be the primary mechanism of P movement in the soil. Soluble P is simulated by the SWAT model to leach only from the top 10 mm of soil into the first soil layer. The mass of solution P leaching into the first soil layer is calculated as

Pperc =

Psolution,surf wperc,surf 10 ρb depthsurf kd,perc

(7.17)

where Pperc is the amount of P moving from the top 10 mm into the first soil layer (kg P ha−1), Psolution,surf is the amount of labile P in the top 10 mm (kg P ha−1), wperc,surf is the amount of water percolating to the first soil layer from the top 10 mm on a given day (mm), ρb is the soil bulk density of the top 10 mm (mg m−3), depthsurf is the depth of the surface layer, and kd,perc is the P percolation coefficient. The kd,perc is calculated as the ratio of the labile P concentration in the surface 10 mm of soil to the concentration of P in percolate.

7.2.5 FERTILIZER APPLICATION SWAT provides the user with the option to incorporate both inorganic and organic fertilizer application to the land-management file. The amount and type of fertilizer applied, timing of application, and depth distribution of application are the input information needed by the model. The model user is required to define the weight fraction of different forms of nutrients in the fertilizer. To predict the interaction of fertilizer with soil and runoff, the model assumes that the effective depth of interaction of runoff with soil is top 10 mm and runoff transports nutrients that are available only in the top 10 mm of soil. The amount of fertilizer not applied in the top 10 mm of soil is added to the first soil layer (Neitsch et al. 2001a). When applied fertilizer is in the form of organic manure, the model partitions the amount of P added to fresh organic and humus organic pools as follows: organic Pfresh,fert = 0.5( fertorganicP )( fert )

(7.18)

organic Phumus,fert = 0.5( fertorganicP )( fert )

(7.19)

where organic Pfresh,fert is the amount of P in the fresh organic pool added to the soil as a result of fertilizer application (kg P ha−1), fertorganicP is the fraction of organic P in fertilizer, fert is the amount of fertilizer applied to the soil (kg ha−1), and organic Phumus,fert is the amount of P in the humus organic pool added to the soil as a result of fertilizer application.


174


7.2.6 PHOSPHORUS UPTAKE

BY

PLANTS

The model calculates plant P demand (Puptake, kg ha−1) as follows: Puptake = 1.5(biomassP,optimum − biomassp )

(7.20)

where biomassP,optimum is the expected amount of P content in plant biomass at a given plant stage, and biomassP is the actual amount of P content in plant biomass. Because of the difference in depth distribution of root density in the soil profile, P uptake by plants also varies with soil depth. SWAT calculates P uptake from different soil depths as follows: Puptake,z =

  z  1 − exp  − βp  1 − exp(− βp )  zroot    Puptake

(7.21)

where Puptake,z is the potential P uptake by the plant to soil depth z (kg ha−1), Puptake is the potential Puptake (kg ha−1), z is soil depth from the surface (mm), and βp is a distribution parameter for P uptake and can be adjusted by a model user. The P uptake for a soil layer is calculated as a difference between P uptake at the lower and upper boundary of that soil layer. SWAT calculates the actual amount of P removed (Pactual) as Pactual = min  Puptake + Pdemand , Psolution 

(7.22)

where Pdemand is the P uptake demand not met by overlying soil layers (kg P ha−1) and Psolution is the amount of labile P present in the soil (kg P ha−1). The model assumes that plant uptake of P comes from the labile P pool (Figure 7.4). If a sufficient amount of P is not available in the soil for optimum plant growth, plants may experience P stress. The P stress in plants is calculated as Pstress = 1 −

ϕP ϕ P + exp(3.535 − 0.02597ϕ P )

(7.23)

where Pstress is the P stress for a given day and ϕP is a scaling factor for P stress and is calculated as follows:   biomassp ϕ P = 200  − 0.5)   biomassp,opt

(7.24)

where biomassP is the actual P content of plant biomass and biomassP,opt is the optimum P content of plant biomass (kg P ha−1) (Neitsch et al. 2001a).



175

7.3 PHOSPHORUS MOVEMENT IN SURFACE RUNOFF 7.3.1 SOLUBLE PHOSPHORUS The SWAT model simulates the movement of P from the landscape into surface runoff as Psurf =

Psolution,surf Qsurf ρb depthsurf kd,surf

(7.25)

where Psurf is the amount of soluble P transported by surface runoff (kg P ha−1), Psolution,surf is the amount of labile P in the top 10 mm (kg P ha−1), Qsurf is the amount of surface runoff on a given day (mm), and kd,surf is the P soil partitioning coefficient (m3 mg−1) (Neitsch et al. 2001b).

7.3.2 ORGANIC AND MINERAL PHOSPHORUS ATTACHED TO SEDIMENT IN SURFACE RUNOFF SWAT estimates the mass of P transported with sediment to the stream using a loading function developed by McElroy et al. (1976) and Williams and Hann (1978). This function is  sed  sediment Psurf = 0.001(concsedP )   ε P:sed  areaHRU 

(7.26)

where sediment Psurf is the amount of P transported with sediment to the main channel in surface runoff (kg P ha−1), concsedP is the concentration of P attached to sediment in top 10 mm (g P metric ton soil−1), sed is the sediment yield on a given day (metric tons), areaHRU is the HRU area (ha), and εP:sed is the P enrichment ratio. The concsedP is calculated as  mineral Pact,surf + mineral Pstable,surf + organic Phumic,surf + organic Pfrsh,surf  concsedP = 100   ρb (depthsurf )   (7.27) As P is transported with runoff, its concentration in the runoff sediment increases as compared to the soil surface concentration due to relative ease with which smaller sediment particles are eroded and the settling of relatively coarse sediment particles during transport. This process is called P enrichment. The ratio of the concentration of P transported with the sediment to the concentration of P in the soil surface layer is defined as the P enrichment ratio (εP:sed). SWAT calculates εP:sed for each storm event as (Menzel 1980)

ε P:sed = 0.78(concsed,surq )−0.2468


(7.28)

176


where concsed,surq is the concentration of sediment in surface runoff (mg sediment m−3) and is calculated as concsed,surq =

sed 10(areaHRU )(Qsurf )

(7.29)

When the time of concentration of runoff exceeds 1 day, which is typical for many large watersheds, only a portion of the surface runoff and lateral flow reaches the main channel on the day they are generated. A storage feature is used by the model to account for delay of surface runoff and lateral flow release to the main channel. Both dissolved and sediment attached P in the surface and lateral flow experience a lag that is a function of the surface runoff lag coefficient, time of concentration for the HRU, and lateral flow travel time (Neitsch et al. 2001a).

7.4 IN-STREAM PHOSPHORUS CYCLE SWAT model users have an option to include or exclude in-stream processes in SWAT simulations. When the in-stream component is included, the model routes the state variables through additional algorithms that have been adapted from QUAL2E, a steady-state stream water-quality model developed by Brown and Barnwell (1987). These QUAL2E additional algorithms are included to simulate in-stream processes otherwise not considered by SWAT. The differences between the algorithms used in SWAT and QUAL2E are predominantly related to model characteristics of being a dynamic (SWAT) or steadystate model (QUAL2E). The steady-state constituent concentrations are calculated in the QUAL2E model using a mass transport equation that includes advection, dispersion, dilution, constituent reactions and interactions, and source and sink components (Barnwell et al. 1987):

(

)

∂C ∂( AxuC ) dC s ∂C ∂ Ax DL ∂x = − + ∂t Ax ∂x Ax ∂x dt ν

(7.30)

where C is concentration, Ax is the cross-sectional area, DL is the dispersion coefficient, u is mean velocity, s is external sources or sinks, and v is incremental volume. In Equation 7.30, the partial derivative of C with respect to t refers to the local concentration gradient, whereas dC dt −1 refers to constituent changes such as growth and decay. Each QUAL2E constituent concentration is solved using Equation 7.30 with respective constituent parameters. For example, in QUAL2E organic P is calculated as dP1 dt

= α 2 ρ A − β4 P1 − σ 5 P1

(7.31)

where P1 is the concentration of organic P in the water, α2 is the P content of algae, ρ is algal respiration rate, A is algal biomass concentration, β4 is the organic P decay



177

rate, and σ5 is the organic P settling rate. The QUAL2E organic P differential equation and other QUAL2E differential equations are solved using the classical implicit backward difference method (Barnwell et al. 1987). These methods are appropriate for the QUAL2E steady-state model. Integration of QUAL2E equations into the SWAT model required some modification of the equations to accommodate for SWAT model daily continuous simulation. The P cycle simulated in QUAL2E includes minimal sediment interactions. One sink of organic P is governed by the σ5 parameter representing organic P settling, implying the addition of organic P to the stream bed. The additional P-sediment type of interaction in the QUAL2E model is expressed by the σ2 parameter, which describes the benthos source rate for dissolved P. These two parameters, σ2 and σ5, are not mathematically associated with each other. No other sediment-P interactions are accounted for with the given, off-the-shelf QUAL2E model. However, there is potential for modification of the code to include sediment-P interactions such as P adsorption to sediment. A comparison between QUAL2E and SWAT model constituent concentration equations indicated minimal differences between the two. This can be illustrated by comparing the QUAL2E model organic P equation (Equation 7.31) with the SWAT model organic P equation (Equation 7.32). Organic P in SWAT is calculated as ∆orgPstr = (α 2 ρa algae − βP,4 orgPstr − σ 5orgPstr )TT

(7.32)

where ∆orgPstr is the change in organic P concentration, α2 is the fraction of algal biomass that is P, ρa is the local respiration or death rate of algae, algae is the algal biomass concentration at the beginning of the day, βP,4 is the rate constant for mineralization of organic P, orgPstr is the organic P concentration at the beginning of the day, σ5 is the rate coefficient for organic P settling, and TT is the flow travel time in the reach segment for that day (Neitsch et al. 2001a). Hence, the dominant difference between the two is that the SWAT equation includes a dynamic variable TT for variable rates of flow travel time. The SWAT model also allows the user to adjust organic P inputs on a daily basis, which is not available in QUAL2E. This results in the orgPstr variable being dynamic in the SWAT model instead of a steadystate constraint as in QUAL2E.

7.5 VERSIONS OF SWAT SWAT model simulations have provided water-resource managers with a tool to be able to plan and make decisions in evaluating water supplies and nonpoint source pollution impacts in large river basins. Ultimately, SWAT is designed to be a model that (1) is computationally efficient; (2) allows considerable spatial detail; (3) requires readily available inputs; (4) is continuous in time; (5) is capable of simulating landmanagement scenarios; and (6) gives reasonable results. The model is continually evolving to increase simulation accuracy of land-use changes and agricultural management on stream flow and constituent yields. SWAT2000 was enhanced with bacterial transport routines, urban routines, the


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Green-Ampt infiltration equation, an improved weather generator, the ability to read in daily solar radiation, relative humidity, wind speed and potential evapotranspiration (ET), the Muskingum channel routing, and modified dormancy calculations for tropical areas. For the SWAT2000 version, theoretical documentation and a user manual are available with descriptions of the model algorithms, input and output files, and variables (Neitsch et al. 2001a, 2001b). ArcView SWAT (AVSWAT) version 1.0 (Di Luzio et al. 2002) is a GIS-based hydrological system that links the SWAT model and ArcView GIS software. Its main purpose is to enhance the hydrological characterization of a watershed in the assessment of nonpoint and point pollution. The AVSWAT system has user-friendly tools to assist the user in setting up and completing a model simulation (Di Luzio et al. 2004). The main components include a preprocessor, interface, and postprocessor of the SWAT2000 model (Di Luzio et al. 2002). Without exiting the ArcView GIS environment, the user applies tools for the following to occur: watershed delineation, definition and editing of the hydrological and agricultural management inputs, and running and calibration of the model. AVSWAT is organized accordingly: (1) watershed delineation; (2) HRU definition tool; (3) model databases editor; (4) weather stations definition; (5) input parameterization and editor; (6) model run; (7) read and map chart results; and (8) calibration tool. The pertinent GIS data that must be included to describe the watershed are the digital elevation model, the land-use and land-cover map, and the soil map (Di Luzio et al. 2004). SWAT was integrated as a component of the Better Assessment Science Integrating Point and Nonpoint Sources (BASINS) version 3.0, which is a software system developed by the U.S. Environmental Protection Agency Office of Water to meet the requirements of developing Total Maximum Daily Load (TMDL) programs. With over 30 years of USDA modeling experience, the SWAT model has proven successful in the watershed assessments of both agricultural and urban scenario management effects on water quality, rendering it useful for the Clean Water Act’s requirement for the creation of TMDLs that appraise pollution for each listed water system. The latest version, SWAT2003, includes additional improvements. •

•

• • • •

The model contains a bacteria component that includes E. coli and fecal coliform. This component has been tested through a study in Walnut Creek, Iowa. Tile flow has been improved to more adequately simulate the presence of a water table and its draw down due to tile drains. Initially the lower soil levels are saturated, creating a water table. Rather than being based on soil moisture content, flow is a function of the water table above the tile. The presence of potholes has been added; however, additional work must be completed before it can be used. A curve number option based on antecedent weather (i.e., precipitation and climate) was developed rather than solely being based on soil moisture content. An autocalibration and sensitivity analysis option was added to SWAT2003, and progress continues to make this component more efficient and effective. Finally, with the enhancements added to SWAT2003, future support will focus on this version rather than maintaining SWAT2000.



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As natural resource protection, including water quality, maintains its importance, this model will continue to develop and improve according to environmental necessity while aiming to keep the model user-friendly yet adequate to efficiently simulate watershed processes. SWAT has been modified or supplemented or has formed the basis for new model developments for special requirements of various catchments throughout the world. •

•

•

•

• •

Watson et al. (2005) adapted SWAT to improve the Leaf Area Index simulation for the eucalyptus and pine forests common to Australia. The SWAT model is more suited to crops and deciduous vegetation. Extended SWAT (E-SWAT) is a computer program designed by Griensven (2002) that uses a time step of a user-defined fraction of an hour to calculate the rainfall and runoff and an hourly time step to calculate instream river-routing processes. SWAT Giessen (SWAT-G) (Eckhardt et al. 2002), is a river-basin scale model that operates on a daily time step and was designed for usage in low mountain range areas with high proportions of interflow. Sophocleous et al. (1999) linked SWAT with the Modular Groundwater Flow (MODFLOW) model (McDonald and Harbaugh 2003) model to increase the accuracy of groundwater simulations. Lenhart et al. (2002) added an improved sediment concept to SWAT-G. In 1998, Krysanova et al. (1998) based the Soil and Water Integrated Model (SWIM) on SWAT hydrologic components.

7.6 SWAT MODEL APPLICATIONS The SWAT model has been used extensively to evaluate watershed management options. For example, the SWAT model has been implemented to assess alternative management practices that incorporate both point and nonpoint sources (Kirsch et al. 2002; Santhi et al. 2001a, 2001b, 2001c). The SWAT model has also been used to investigate land-use changes such as the conversion of agriculture and forestland into turf grass usage (e.g., golf courses, residential neighborhoods) (King et al. 2001). These SWAT model applications were successful because of sufficient model calibration and validation, which ensured that the model represented the system being considered. Investigators that have included sensitivity analysis consider specific output variables. The parameter having the greatest relative sensitivity for output variables of flow, NO3-N, and TP were identified as the CN parameter (Cotter et al. 2003). Another study, focusing on base-flow predictions, identified several soil and groundwater parameters that influenced their output values (Spruill et al. 2000). A larger contingency of SWAT model developers has documented parameters used in calibration (Table 7.1). SWAT model calibration results are also often reported in model publications (Tables 7.2 and 7.3); however, model calibrations should be considered with respect to their individual modeling objectives. The number of calibration sites included in model calibration is one modeling objective to consider. Although a single site calibration is the most often presented


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TABLE 7.1 Review of Parameters Used in Calibration as a Function of Output Variable Predicted in Published SWAT Model Applications Output Variable

Calibration Parameters

Flow

CANMXd Crop growth routinee Curve numbera,b,c,d,e,f,g,h ESCOc,e,f,h Revap coefficientsb,c,d Soil bulk densitye

Soil propertiesa AWCf,g EPCOc Groundwater parameterse Soil hydraulic conductivitye

ALPHA BFh SURLAGh

Sediment

AMPd,h Channel covere Channel erosione CH_N2d MUSLE parameterse PRF d, h

SLSUBBSNd,h SPCONc,d,h SPEXPc,d USLE_K(1)d,h SLOPEd,h CH_N1d,h

OVNh ROCKh USLE_Ph

TP

ANION_EXCLd ERORGPd Initial soil concc PPERCOc,d,h PSPd SOL_BDd

UBPd,h PHSKDc,d,h AI2h BC4h CMNh

RS5h

TN

CMNe

Initial soil concc

NPERCOc, d

Notes: TP = total phosphorus; TN = total nitrogen. a

J.G. Arnold and P.M. Allen, J. Hydrol. 176, 57, 1996. R. Srinivasan, T.S. Ramanarayanan et al., J. Am. Water Resour. Assoc. 34(1), 91, 1998. c C. Santhi, J.G. Arnold et al., J. Am. Water Resour. Assoc. 37(5), 1169, 2001a. d A.S. Cotter, M.S. thesis, Department of Biological and Agricultural Engineering, University of Arkansas, Fayetteville, 2002. e K. Kirsch, A. Kirsch et al., Trans. ASAE 45(6), 1757, 2002. f J.G. Arnold, R.S. Muttiah et al., J. Hydrol. 227, 21–40, 2000. g J.G. Arnold, R. Srinivasan et al., Water Sci. Technol. 39(3), 121–133, 1999. h K.L. White and I. Chaubey, J. Am. Water Resour. Assoc. 41(5), 1077–1086, 2005. b

application of the SWAT model, multisite calibration is becoming more common (Arnold et al. 1999; Kirsch et al. 2002; Santhi et al. 2001a). The increased frequency of multisite applications is likely due to greater availability of measured data and to improved model sophistication and computing abilities. Another modeling objective that influences model calibration is the number of response variables selected for calibration. The most commonly calibrated watershed response variable in SWAT model publications is stream flow (Arnold and Allen 1996; Manguerra and Engel 1998; Peterson and Hamlett 1998; Sophocleous et al. 1999). However, multivariable calibrations are often conducted when multiple


Reference Arnold and Allen (1996) Arnold and Allen (1999) Arnold et al. (1999)a

Base Flow

Storm Flow

(0.38 to 0.51) (0.62 to 0.98)

(0.79 to 0.94)

Arnold et al. (2000)a Spruill et al. (2000) Santhi et al. (2001b)a Cotter (2002) Hanratty and Stefan (1998) Di Luzio et al. (2002) Tripathi et al. (2003) Srinivasan et al. (1998)a Srinivasan and Arnold (1994) White and Chaubey (2005)a Notes: NS = Nash-Sutcliffe efficiency coefficient. a

Total Flow

Sediment

Phosphorus

Nitrogen

0.80, 0.69 (0.81, 0.87)

0.53 to 0.70 (0.60 to 0.71) 0.66 (0.83) 0.54 0.58, 0.70

–0.08 to 0.59 (0.60 to 0.72)

0.40 to 0.67 (0.50 to 0.82)

–2.36 to 0.29 (0.01 to 0.84)

(0.63 to 0.95) –1.11 to 0.87 (0.23 to 0.96) (0.63) 0.58, 0.89 0.79, 0.83 (0.80, 0.89) 0.76 (0.77) 0.78 0.82 0.98 (0.97) 0.77, 0.84 (0.87, 0.84) 0.86 0.50 to 0.89 (0.41 to 0.91)

0.50 (0.69) 0.59 0.78 0.79 (0.89)

0.23 to 0.76 (0.45 to 0.85)

0.44 (0.54) 0.57, 0.68 0.60


TABLE 7.2 Summary of Monthly Calibrations Performed on SWAT Models with Their Respective Statistic of Measurement of NS (with Respective R2 Shown in Parenthesis)

Multiple calibration sites used in SWAT model calibration.

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TABLE 7.3 Summary of Annual Calibrations Performed on SWAT Models with Their Respective Statistic of Measurement of NS (R2) Reference Arnold et al. (1999)a Arnold et al. (2000)a Kirsch and Kirsch (2001) Kirsch et al. (2002)a

Base Flow

(0.62)

Total Flow –1.11 to 0.87 (0.23 to 0.96) (0.89) 0.76 (0.78) 0.18 to 0.84 (0.28 to 0.98)

Sediment

Phosphorus

0.75 (0.82)

0.07 (0.95)

Note: NS = Nash-Sutcliffe efficiency coefficient. a

Multiple calibration sites used in SWAT model calibration.

response variables are chosen (Cotter et al. 2003; Kirsch et al. 2002; Santhi et al. 2001a; White and Chaubey 2005). The increase in the number of variables in the calibration process requires model developers to designate multi-objective functions that consider multiple variables. When evaluating a multivariable objective function, SWAT model users generally calibrate flow first when performing calibration. This is followed by sediment calibration and then by any nutrient calibrations (Cotter et al. 2003; Grizzetti et al. 2003; Kirsch and Kirsch 2001; Santhi et al. 2001b). Previous investigations have reported different evaluation priorities for nitrogen and P. For example, Santhi et al. (2001b) evaluated nitrogen and P components by first calibrating organic nitrogen and organic P and then calibrating mineral nitrogen and mineral P, whereas Cotter et al. (2003) evaluated nitrate first, followed by total P calibration. The prediction capacity of the SWAT model is fairly simple. The model predicts discrete output variable values for a given time step. However, there is uncertainty associated with this value. To account for a portion of the uncertainty in the SWAT model, stochastic techniques can be used. Cotter (2002) conducted stochastic evaluation for a SWAT model using CN. Stochastic analysis was completed by generating input parameter probability distribution functions (PDFs) and output PDFs followed by an assessment of model performance. Similar stochastic analyses using the CN were explored by Chaubey et al. (2003). However, further investigation into stochastic analyses of SWAT model parameters is needed to provide some measure of uncertainty in model predictions, particularly for parameters that are identified as influencing output variables.

7.7 MODEL LIMITATIONS A major limitation of large-area hydrologic modeling is the spatial detail required to correctly simulate environmental processes. For example, it is difficult to capture the spatial variability associated with precipitation within a watershed. Another limitation is the accuracy of hydrologic response units simulating field variations including conservation practices. SWAT is being altered to account for landscape



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spatial positioning so that conservation practices such as riparian buffers and vegetative filter strips can be adequately simulated. SWAT does not simulate detailed eventbased flood and sediment routing.

7.8 SWAT MODIFICATIONS The SWAT model modifications under consideration are (1) the dynamics of P exchange between the solution and active mineral (organic) pools; (2) the desorption of P from soil to runoff water; (3) the simulation of surface applied manures and the loss of P from surface manures to runoff water; (4) soil cracking; (5) the addition of best management practices that can be correctly simulated such as vegetated filter strips and buffer zones; and (6) the improvement of autocalibration and sensitivity analysis components. The factors are addressed further in the following. •

•

•

•

SWAT assumes equilibrium between P in solution and in the active mineral pools. SWAT is being modified to slow the availability of P from the solution to the active mineral pool while transfer from the active mineral to the solution pool is instantaneous. This is potentially important when a runoff event occurs shortly after a manure application, before the solution and active mineral pools have time to reestablish equilibrium. After an exhaustive literature search, it was determined that SWAT’s simulation of P desorption is comparable to other hydrologic models. Models to date regard that P desorption occurs at the same rate as P adsorption. Several research studies have demonstrated that this does not occur; however, models remain unchanged. As research data become available to suffice the P adsorption–desorption dilemma, the developers plan to address this important concept. SWAT currently assumes that the P in manure is added directly to the P pools in the upper soil layer (1 cm). Phosphorus may remain soluble in a manure layer longer than a soil layer, and thus SWAT may underestimate P movement shortly after a manure application. A conceptual model for SWAT that considers a manure layer that slowly moves the P into the soil has been developed. This improvement will take more time to implement and validate. The ability to predict runoff and storage requires understanding the processes of soil cracking (Arnold et al. 2005). Flow through each soil layer is combined with a crack flow model in conjunction with a storage routing technique for percolation to occur. Soil shrinkage cracking allows for a greater distribution of water, nutrients, and pesticides to the subsoil, rendering the solution unavailable for plant uptake and a source of groundwater pollution. Seasonal cracking also contributes to poor estimates of runoff and infiltration in areas with expansive soils. SWAT has incorporated a crack flow model. For a Texas watershed, the model was able to simulate surface runoff accurately for the winter months when the cracks were swelled closed and in the fall for recharge events when crack volume went from 70 to 10 mm. Future research is planned


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•

•

to determine the impact of cracking on groundwater recharge and contaminant transport. The addition of best management practices such as vegetated filter strips, riparian zones, wetlands, as well as others, is known to be of importance so that SWAT can correctly simulate agricultural management in the watersheds. A component that has to be refined initially is the configuration of HRUs. This has to be done to account for more detailed variations in topography and management practices rather than each sub-basin remaining entirely independent of its adjoining sub-basins. A major concern before it will be changed is to determine the overall goal of the model. To accommodate smaller areas so that the watershed simulation will be more accurate, the model’s complexity will have to increase rendering it less user-friendly. The ability to model best management practices means that the hydrology component must be redesigned to allow for more subtle topographical changes between sub-basins, thereby increasing the model’s complexity. All of these adjustments are being considered while trying to maintain a less complex, more user-friendly model. Much work has been completed regarding the autocalibration sensitivity analysis component of SWAT through Griensven (2002). A procedure based on multi-objective calibration that incorporates the Shuffled Complex Evolution algorithm was utilized effectively for autocalibration. The optimization allows for up to 100 output variables to be considered simultaneously. The Shuffled Complex Evolution algorithm accepts as many as 30 objective functions for aggregation into a single global optimization criterion. A weighting problem is avoided due to the use of a statistical method that enables the aggregation of the objective functions for individual variables. A sensitivity analysis using the one-factor-at-a-time approach was successfully employed to identify the significant parameters for the optimization.

7.9 CONCLUSIONS The Soil and Water Assessment Tool model is a physically based semi-distributed parameter model that performs all calculations on a daily time step to quantify effects of watershed management and climate conditions of flow, sediment, nutrient, and pesticide response from an agricultural watershed. SWAT simulates hydrology as a twocomponent system: land hydrology and channel hydrology. Components of P modeled by SWAT include soil P — water — plant interactions such as mineralization, decomposition, and immobilization; P sorption; leaching; and organic and inorganic fertilizer P application. In addition, P movement in surface runoff, including both soluble and sediment attached P, and in-stream P cycle are modeled in SWAT. A GIS interface of the model is available for easy preparation of input files and display of output results. SWAT is also integrated as a component of the Better Assessment Science Integrating Point and Nonpoint Sources suit of models developed by the U.S. EPA for TMDL development. The SWAT model has been extensively applied in many watersheds in the U.S. and other parts of the world to make watershed management decisions.



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REFERENCES Arnold, J.G. and P.M. Allen. 1996. Estimating hydrologic budgets for three Illinois watersheds. J. Hydrol. 176:57–77. Arnold, J.G. and P.M. Allen. 1999. Automated methods for estimating baseflow and ground water recharge from stream flow records. J. Am. Water Resour. Assoc. 35(2):411–424. Arnold, J.G., R.S. Muttiah et al. 2000. Regional estimation of base flow and groundwater recharge in the upper Mississippi basin. J. Hydrol. 227:21–40. Arnold, J.G., K.N. Potter et al. 2005. Estimation of soil cracking and the effect on surface runoff in a Texas blackland prairie watershed. Hydrol. Process. 19(3):589–603. Arnold, J.G., R. Srinivasan et al. 1998. Large area hydrologic modeling and assessment. I: model development. J. Am. Water Resour. Assoc. 34(1):73–89. Arnold, J.G., R. Srinivasan et al. 1999. Water resources of the Texas gulf basin. Water Sci. Technol. 39(3):121–133. Barnwell, T.O., Jr., L.C. Brown et al. 1987. QUAL2E — a case study in water quality modeling software: systems analysis in water quality management. Proceedings of the Symposium Systems Analysis in Water Quality Management London, June 30-July 2, 1987. M. B. Beck (Ed.). Oxford: Pergamon Press. Brown, L.C. and T.O.J. Barnwell. 1987. The Enhanced Water Quality Model QUAL2E and QUAL2E-UNCAS Documentation and User Manual. U.S. Environmental Protection Agency. Chaubey, I., T.A. Costello et al. 2003. Stochastic validation of SWAT model. American Society of Agricultural Engineers Total Maximum Daily Load Environmental Regulation Conference II, Albuquerque, NM, ASAE, St. Joseph, MI. Cotter, A.S. 2002. Critical evaluation of TMDL data requirements for agricultural watersheds. M.S. thesis, Department of Biological and Agricultural Engineering, University of Arkansas, Fayetteville. Cotter, A.S., I. Chaubey et al. 2003. Water quality model output uncertainty as affected by spatial resolution of input data. J. Am. Water Resour. Assoc. 39(4):977–986. Di Luzio, M., J.G. Arnold et al. 2004. A GIS-coupled hydrological model system for the watershed assessment of agricultural nonpoint and point sources of pollution. Trans. GIS 8:113–136. Di Luzio, M., R. Srinivasan et al. 2002. Integration of watershed tools and SWAT model into BASINS. J. Am. Water Resour. Assoc. 38(4):1127–1141. Eckhardt, K., S. Haverkamp et al. 2002. SWAT-G, a version of SWAT99.2 modified for application to low mountain range catchments. Phys. Chem. Earth 27:641–644. Griensven, A.V. 2002. Developments towards integrated water quality modeling for river basin. Ph.D. dissertation., Vrije Universiteit, Brussel. Grizzetti, B., F. Bouraoui et al. 2003. Modelling diffuse emission and retention of nutrients in the Vantaanjoki watershed (Finland) using the SWAT model. Ecol. Model. 169(1):25–38. Hanratty, M.P. and H.G. Stefan. 1998. Ecosystem processes: simulating climate change effects in a Minnesota agricultural watershed. J. Environ. Qual. 27:1524–1532. Jones, G.C.A., C.V. Cole, A.N. Sharpley, and J.R. Williams. 1984. A simplified soil and plant phosphorus model. I. Documentation. Soil Sci. Soc. Am. J. 40:800–805. King, K.W., R.D. Harmel et al. 2001. Impact of a turfgrass system on nutrient loadings to surface water. J. Am. Water Resour. Assoc. 37(3):629–640. Kirsch, K.J. and A.E. Kirsch. 2001. Using SWAT to predict erosion and phosphorus loads in the Rock River Basin, Wisconsin. Intl. Symp. ASAE 701P0007, Honolulu, HI. Kirsch, K., A. Kirsch et al. 2002. Predicting sediment and phosphorus loads in the Rock River Basin using SWAT. Trans. ASAE 45(6):1757–1769.


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Knisel, W.G. 1980. CREAMS: a field scale model for chemicals, runoff and erosion from agricultural management systems. USDA Conservation Research Report No. 26, Washington, D.C. Krysanova, V., D.I. Muller-Wohlfeil et al. 1998. Development and test of a spatially distributed hydrological water quality model for mesoscale watersheds. Ecol. Model. 106(2–3):261–289. Lenhart, T., K. Eckhardt et al. 2002. Comparison of two different approaches of sensitivity analysis. Phys. Chem. Earth 27:645–654. Leonard, R., W.G. Knisel et al. 1987. GLEAMS: groundwater loading effects of agricultural management systems. Trans. ASAE 30(5):1403–1417. Manguerra, H. and B.A. Engel. 1998. Hydrologic parameterization of watersheds for runoff prediction using SWAT. J. Am. Water Resour. Assoc. 34(5):1149–1162. McDonald, M.G. and A.W. Harbaugh. 2003. The history of MODFLOW. Ground Water 41(2):280–283. McElroy, A.D., S.Y. Chiu et al. 1976. Loading function for assessment of water pollution from nonpoint sources. Environmental Protection Agency, EPA 600/2-76-151, Washington, D.C. Menzel, R.G. 1980. Enrichment ratios for water quality modeling — CREAMS: a field scale model for chemicals, runoff, and erosion from agricultural management systems. U.S. Department of Agriculture, Conservation Research Report No. 26, Washington, D.C. Neitsch, S.L., J.G. Arnold et al. 2001a. Soil and Water Assessment Tool theoretical documentation version 2000. Available at http://www.brc.tamus.edu/swat/ doc.html. Neitsch, S.L., J.G. Arnold et al. 2001b. Soil and Water Assessment Tool user’s manual version 2000. Available at http://www.brc.tamus.edu/swat/doc.html. Peterson, J.R. and J.M. Hamlett. 1998. Hydrologic calibration of the SWAT model in a watershed containing fragipan soils. J. Am. Water Resour. Assoc. 34(3):531–544. Santhi, C., J.G. Arnold et al. 2001a. Validation of the SWAT model on a large river basin with point and nonpoint sources. J. Am. Water Resour. Assoc. 37(5):1169–1188. Santhi, C., J.D. Atwood et al. 2001b. Environmental and Economic Impacts of Reaching and Doubling the USDA Buffer Initiative Program on Water Quality. St. Joseph, MI: American Society of Agricultural Engineers. Santhi, C., J.R. Williams et al. 2001c. Application of a watershed model to evaluate management effects on point and nonpoint source pollution. Trans. ASAE 44(6):1559–1570. Sharpley, A.N., C.A. Jones et al. 1984. A simplified soil and plant phosphorus model. II: prediction of labile, organic, and sorbed phosphorus. Soil Sci. Soc. Am. J. 48:805–809. Sophocleous, M.A., J.K. Koelliker et al. 1999. Integrated numerical modeling for basin-wide water management: the case of the Rattlesnake Creek Basin in south-central Kansas. J. Hydrol. 214:179–196. Spruill, C.A., S.R. Workman et al. 2000. Simulation of daily and monthly stream discharge from small watersheds using the SWAT model. Trans. ASAE 43(6):1431–1439. Srinivasan, R. and J.G. Arnold. 1994. Integration of a basin scale water quality model with GIS1. Water Resour. Bull. 30(3):453–462. Srinivasan, R., T.S. Ramanarayanan et al. 1998. Large area hydrologic modeling and assessment. II: model application. J. Am. Water Resour. Assoc. 34(1):91–101. Tripathi, M.P., R.K. Panda et al. 2003. Identification and prioritization of critical subwatershed for soil conservation management using the SWAT model. Biosys. Eng. 85:365–369.



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Wastson, B.M., N. Coops et al. 2005. Simulating leaf area index of eucalyptus forests and pine plantations for a catchment-scale balance model. Engineers Australia 29th Hydrology and Water Resources Symposium, February, 21–23 2005, Canberra, Australia. White, K.L. and I. Chaubey. 2005. Sensitivity analysis, calibration, and validation for a multisite and multi-variable SWAT model. J. Am. Water Resour. Assoc. 41(5):1077–1086. Williams, J.R. and R.W.J. Hann. 1973. Hymo: Problem-Oriented Computer Language for Hydrologic Modeling — User’s Manual. U.S. Agriculture Research Service Southern Region 9:76. Williams, J.R. and R.W. Hann. 1978. Optimal Operations of Large Agricultural Watersheds with Water Quality Constraints. Texas Water Resources Institute. Williams, J.R., C.A. Jones et al. 1984. A modeling approach to determining the relationship between erosion and soil productivity. Trans. ASAE 27:129–144.


8

Modeling Phosphorus with Hydrologic Simulation Program-Fortran David E. Radcliffe University of Georgia, Athens, GA

Zhulu Lin University of Georgia, Athens, GA

CONTENTS 8.1 Brief History of Model Development..........................................................189 8.2 Modeling of Hydrology ...............................................................................190 8.3 Modeling of Phosphorus..............................................................................195 8.4 Modeling of Sediment .................................................................................199 8.5 Calibration ....................................................................................................202 8.6 Case Study: Upper Etowah River Watershed ..............................................203 8.7 Comparing HSPF and SWAT ......................................................................210 8.8 Conclusions ..................................................................................................211 Acknowledgments..................................................................................................212 References..............................................................................................................212

8.1 BRIEF HISTORY OF MODEL DEVELOPMENT The Hydrologic Simulation Program-Fortran (HSPF) is a watershed-scale, semidistributed model developed from the original Stanford model (Bicknell et al. 2001). It is one of the two dynamic models intended for modeling watersheds dominated by nonpoint sources in the U.S. Environmental Protection Agency (EPA) Better Assessment Science Integrating Point and Nonpoint Sources (BASINS) package (U.S. Environmental Protection Agency 2004a). The other model is the Soil Water Assessment Tool (SWAT) described by Arnold et al. (1998) and Neitsch et al. (2002). The functions and processes included in HSPF were derived primarily from the following group of predecessor models:

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Hydrocomp Simulation Programming (HSP) (Hydrocomp, Inc. 1976, 1977) Nonpoint Source (NPS) Model (Donigian and Crawford 1976a) Agricultural Runoff Management (ARM) Model (Donigian and Crawford, 1976b; Donigian et al. 1977) Sediment and Radionuclides Transport (SERATRA) (Onishi and Wise 1979) The original development of HSPF was sponsored by the EPA Environmental Research Laboratory in Athens, Georgia, during the 1970s. HSP was a descendant of the Stanford Watershed model (Crawford and Linsley 1966). It was first released in 1980 as Release 5. Later development was sponsored by the U.S. Geological Survey (USGS) Water Resources Division in Reston, Virginia. Probably the best-known application of the HSPF model is its use as part of the Chesapeake Bay Model (Linker et al. 2002). HSPF is one of three linked model components: a watershed model (HSPF), an airshed model, and a bay model. The model was used to establish a goal in 1987 of a 40% nutrient — nitrogen (N) and phosphorus (P) — reduction to the bay by the year 2000. In the current version, the bay watershed is divided into 94 sub-basins with an average area of 194,000 ha. A bibliography of articles describing HSPF applications is available at hspf.com/hspfbib.html (confirmed February 25, 2006). Aside from the Chesapeake Bay Model, applications modeling phosphorus include Donigian et al. (1996), Donigian and Love (2002), and Hummel et al. (2003).

8.2 MODELING OF HYDROLOGY Most of the material in this chapter is taken from the HSPF User’s Manual for Release 12 (Bicknell et al. 2001), which can be downloaded from the EPA Web site, www.epa.gov/waterscience/basins/bsnsdocs.html (confirmed February 25, 2006). A mixture of English and metric units are used in the user’s manual, and this chapter has aimed for consistency with the manual. HSPF uses elements, zones, and nodes. One type of element is the land segment, which can be a pervious land segment (PLS) or an impervious land segment (ILS). Within the PLSs, there are snow, surface, upper soil, lower soil, and groundwater zones. A segment is a portion of the land assumed to have uniform (lumped) properties. Another type of element is a reach element. Within a reach, water moves through a single zone from an upstream node to a downstream node. A simulation might consist of a single watershed (completely lumped) or multiple subwatersheds connected together (partially distributed). U.S. Environmental Protection Agency (2004b) describes which processes need to be simulated for PLSs, ILSs, and reaches to simulate hydrology. Basic hydrology must include PWATER in the PLSs, IWATER in the ILSs, and HYDR in the reaches elements — there is a process for simulating what happens in the snow layer if that is applicable. PWATER is the portion of the model that simulates the water budget for PLSs. Potential evapotranspiration (PET) is based on U.S. Weather Bureau Class A pan evaporation times a crop factor, further adjusted by the vegetative cover percentage in each PLS. Actual ET is calculated by trying to meet the PET from


Modeling Phosphorus with Hydrologic Simulation Program-Fortran

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five different sources in the following order until PET is satisfied (ET = PET) or until sources are exhausted (ET < PET): from the groundwater zone as seepage, from vegetation interception, from the upper soil zone, from the groundwater zone directly, and from the lower soil zone. The model recognizes that within a land segment there is variability in ET due to differences in, for example, rooting density. Rainfall is distributed in PWATER in the following manner. Some of the rainfall first goes to interception by vegetation (i.e., grass, leaves, stems, and trunks). This vegetation has a storage capacity that accepts water until it is filled. The intercepted water is lost through evaporation. The water that remains may infiltrate to upper zone storage or interflow storage, may enter surface detention storage, or may run off. None of the conventional methods (e.g., curve number, Green-Ampt) or soil parameters (e.g., saturated hydraulic conductivity, field capacity) are used to calculate infiltration and interflow. IBAR is the average infiltration rate over the land segment (in. hr−1 or in. day−1), depending on the time step in use (Figure 8.1). The model recognizes that within a land segment there is variability in infiltration rates and that the actual infiltration rate can be less than or greater than IBAR, as this chapter shows. IBAR is calculated as  LZS  IBAR = INFILT   LZSN 

− INFEXP

(8.1)

where INFILT is a parameter (in. hr−1), LZS is the lower zone water storage (in.), LZSN is the nominal (or average) lower zone water zone storage (in.), and INFEXP is a parameter (unitless). IIMAX line II (interflow + infiltration capacity)

IIBAR

IMAX

MSUPY

Inches of water/interval

Inches of water/interval

IBAR

IIMIN IMIN

line I (infiltration capacity)

0

50 % of area

100

potential surface runoff potential Interflow

potential direct

FIGURE 8.1 Determination of infiltration and interflow. (Redrawn from B.R. Bicknell, J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobs, and A.S. Donigian, Jr., Hydrological Simulation ProgramFortran: HSPF Version 12 User’s Manual, Mountain View, CA, Aqua Terra Consultants, 2001. With permission.)


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This represents infiltration into the lower soil zone; infiltration into the upper soil zone (a relatively thin layer) is described later. In the case that frozen ground occurs for a significant period of time, INFFAC accounts for this effect, but it has been left out of Equation 8.1 for the sake of simplicity. Equation 8.1 shows that as water content in the lower zone water storage increases during a storm, the infiltration rate decreases. Once this zone is saturated (LZS = LZSN), the infiltration rate reaches the minimum asymptotic rate of INFILT. This implies that INFILT is equal to the field saturated hydraulic conductivity. The parameter IMAX in Figure 8.1 is the product of INFILD and IBAR. INFILD is a unitless parameter with a recommended value of 2, so IMAX is twice IBAR. The water that is available in a time step for infiltration, interflow, or runoff is moisture supply in inches, MSUPY (Figure 8.1). The total water that infiltrates the lower soil zone is the area beneath line I and the MSUPY line (clear area). (IBAR is the average infiltration rate, and this is used in determining the total) As IBAR increases, so does the amount of water that infiltrates. The water that goes into potential interflow is the area beneath line II and the MSUPY line and above line I (lightly shaded area in Figure 8.1). Interflow is water that moves laterally to a stream due to a restrictive layer in the unsaturated zone (Fetter 1988). Potential interflow water can become actual interflow or inflow into the upper soil zone. As IBAR increases, so does the amount of water that goes to potential interflow. IIMIN and IIMAX are calculated as follows: LZS

IIMIN = IMIN ⋅ INTFW ⋅ 2 LZSN IIMAX = IMAX ⋅ INTFW ⋅ 2

(8.2)

LZS LZSN

where INTFW is a parameter (unitless). It is apparent from Equation 8.2 that as INTFW increases, line II in Figure 8.1 rises, and the amount of potential interflow increases. Also, as the water content in the lower soil zone increases, so does the amount of potential interflow. The water that is available for potential upper soil zone infiltration, surface detention, or runoff is the area below the MSUPY line and above line II (darkly shaded area in Figure 8.1). The remaining water is potential runoff. The fraction of this water that goes into the upper soil zone (FRAC) is a function of the upper soil zone water content (UZRAT), which is the upper soil zone water storage in inches (UZS) divided by the upper soil zone nominal water storage in inches (UZSN). FRAC decreases as the upper zone water content increases. Note that UZRAT is allowed to be greater than unity. This is a recognition that UZSN varies from the average (nominal) value over the pervious land segment. Once infiltration into the upper soil zone is satisfied, the remaining water goes into surface storage, runoff, and interflow. Surface storage depends in part on Manning’s n for roughness (increases with roughness and n), slope length (increases with slope length), and slope angle (decreases with slope angle). The interflow component assumes a certain storage capacity for interflow water. The rate at which



193

water can enter interflow storage depends on the current storage and the rate at which water is discharging from interflow storage to the stream. The rate of discharge to the stream is a function of the interflow recession parameter IRC. Upper soil zone water can percolate into the lower soil zone. Percolation only occurs when the upper soil zone water content is greater than the lower soil zone relative water content according to the following empirical relationship (units are not consistent on both sides of equation):  USZ LSZ  PERC = 0.1 ⋅ INFILT ⋅ UZSN ⋅  −  USZN LSZN 

3

(8.3)

where PERC is the percolation rate (in. hr-1). The fact that PERC is proportional to INFILT reinforces the idea that INFILT is related to field-saturated hydraulic conductivity. Water that percolates into the lower zone from the upper soil zone, plus infiltrating water, can increase the lower zone soil water storage or pass on through to groundwater. The fraction that goes to increasing the lower soil zone storage depends on the lower zone relative water content, LZRAT, which is LZS divided by LZSN. As the water content increases, less percolation water is retained, and more water passes through to groundwater. Infiltrating and percolating water that reaches groundwater storage can discharge into the stream or can go to deep groundwater storage; this water is essentially lost from the watershed system. DEEPFR is the parameter (unitless) that determines the fraction that is lost. Outflow to the stream from the remaining groundwater depends on the slope of the water table (gradient), the groundwater storage, and two parameters, AGWRC and KVARY: AGWO = AGWRC ⋅ (1 + KVARY ⋅ GWVS ) ⋅ AGWS

(8.4)

where AGWO is the outflow rate (in. hr−1), GWVS is an index to the water table slope, AGWS is the current groundwater storage (in.), AGWRC is a groundwater outflow recession parameter (day−1), and KVARY is a recession parameter — nonzero values cause recession to vary as a function of groundwater levels and will produce seasonal variability in hydrographs. U.S. Environmental Protection Agency (2004c) provides guidance on how to choose hydrological parameters. The primary hydrological parameters are as follows. • •

•

FOREST: only used in snow processes. LZSN: lower zone nominal soil water storage (in.); recommends an initial estimate of 1/8 mean annual rainfall + 4 in. (humid regions); min-max values are 3 to 8 in.; lower values of LZSN will cause more stream flow (less water lost to ET); default = 4 to 6.5 in. depending on land use. INFILT: index to mean soil infiltration rate (in. hr−1); provides a range related to soil hydrologic groups (A: 0.4 to 1.0; B: 0.1 to 0.4; C: 0.05 to


194


•

•

•

•

• • • •

•

•

• •

•

•

0.1; D: 0.01 to 0.05); default is 0.16 in. hr−1; suggests that Z *INFILT* INTFN should approximate the long-term infiltration rate, or permeability, in the soil survey database (untested approach); higher values cause less runoff and less storm flow in streams. LSUR: length of overland flow path (ft) for the pervious land segment; average length of travel for water to reach a stream; typical values range from 200 ft for slopes of 15% to 500 ft for slopes of 1%; default = 300 ft; higher values should cause storm hydrograph to spread out (lower peak value). SLSUR: slope of pervious land segment; recommends using digital elevation data to get this — check change in elevation of pixels in a transect perpendicular to stream, divide by distance between centers of pixels — make multiple measurements and average; probably has little effect on hydrology but may affect erosion; default = 0.036 to 0.55, depending on land use. KVARY: nonzero values cause seasonal variation in groundwater flow; increasing the value should cause faster recession during wet months; default is 0; recommends starting with 0 and adjusting if necessary. AGWRC: groundwater recession rate; default = 0.98; recommends finding this through calibration; higher value causes slower recession; suggests using higher values for forests. PETMAX: used only in snow processes. PETMIN: used only in snow processes. INFEXP: exponent in the infiltration equation; default = 2.0 and recommends using the default value. INFILD: ratio of maximum infiltration rate in a pervious land segment, IMAX, to average infiltration rate, IBAR; default = 2.0 and recommends using the default value. DEEPFR: fraction of infiltrating water that goes into deep groundwater storage and is lost from the watershed; default = 0.10; recommends finding value through calibration; higher value causes less stream flow overall. BASETP: the fraction of a pervious land segment area that has vegetation able to transpire water directly from groundwater (i.e., riparian or marsh land vegetation); default = 0.02; recommends calculating this based on area that is riparian or marsh land vegetation. CEPSC: rainfall (in.) intercepted by vegetation; default = 0.10; recommends different values depending on land cover. UZSN: upper zone nominal soil water storage (in.); recommends different values depending on slope, vegetation, and depression storage; overall rule of thumb is 0.10 LZSN; default = 1.128 in. NSUR: n in Manning’s equation for overland flow; larger values of n indicate a rougher surface and slower flow; default is 0.20; probably has little effect on water flow but may affect erosion. INTFW: interflow parameter; increasing interflow value delays water getting to the stream (otherwise it would become overland flow), so it lowers the hydrograph peak and spreads the curve out; default is 0.75; recommends using calibration to find value.



•

•

195

IRC: interflow recession rate, analogous to groundwater recession rate; increasing value causes the hydrograph to spread out and decreases peak value; default = 0.50. LZETP: index to lower zone ET related to root distribution; varies between 0 and 1 with 1 representing maximum potential for plant uptake; gives typical ranges for different types of vegetation; default is monthly varying values from 0.2 in winter months to 0.4 in summer months.

There are a few parameters associated with the ILSs. Unless the impervious land area is a large portion of the modeled watershed, these parameters will not have much effect on model predictions. The most important factor is what percentage of urban areas is assumed to be impervious; the default is 50%. A few parameters are also associated with the reaches, which will have little effect on stream flow, although they may be important for sediment and P transport. Another source of information on hydrological as well as water-quality parameters is HSPF Parameter (HSPFParm) (Donigian et al. 1999). This is a database of parameter values that have been used by experienced users in 45 HSPF model runs in 14 states (available at http://hspf.com/hspfprms.html).

8.3 MODELING OF PHOSPHORUS HSPF has a specific routine for modeling P. The module matrix in U.S. Environmental Protection Agency (2004b) shows which modules need to be activated in the pervious land, impervious land, and reach segments to model P: • • •

PERLND: activate PWATER, SEDMNT, MSTLAY, and PHOS IMPLND: none RCHRES: for inorganic P activate HYDR, ADCALC, SEDTRN, OXRX, and NUTRX for organic P add PLANK

A surface zone, as well as the upper soil, lower soil, and groundwater zones, is considered. A flow diagram for the pervious land portion of the P routine is shown in Figure 8.2. Soil P is in organic, soluble, and adsorbed pools. Phosphate is adsorbed and desorbed using either first-order kinetics (i.e., subroutine FIRORD) or instantaneous adsorption using a Freundlich isotherm (i.e., subroutine SV). This chapter covers only the instantaneous approach. A Freundlich isotherm from the user’s manual is shown in Figure 8.3. On the y axis, X is the P adsorbed in parts per million of soil (mg of P per kg of soil), and on the x axis, C is the P in solution in parts per million of solution (mg of P per L of solution). The y axis intercept of curve 1 and curve 2 is XFIX, the amount of P permanently adsorbed (mg of P per kg of soil). CMAX is the maximum equilibrium concentration of P in soil solution, and XMAX is the corresponding maximum adsorbed concentration of P. Adsorbed P is described by the following equation: 1

X = K 1 ⋅ C N 1 + XFIX


(8.5)

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PLTP Plant phosphorus

Plant uptake of phosphorus Atmospheric deposition

Atmospheric deposition Phosphate immobilization

Desorption of phosphate P4SU Phosphate in solution

ORGP Organic phosphorus

P4AD Phosphorus adsorbed Adsorption of phosphate

Organic phosphorus mineralization

FIGURE 8.2 Flow diagram for P reactions. (Redrawn from B.R. Bicknell, J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobs, and A.S. Donigian, Jr., Hydrological Simulation Program-Fortran: HSPF Version 12 User’s Manual, Mountain View, CA, Aqua Terra Consultants, 2001. With permission.)

XMAX XJCT

XDIF

Curve 2

X, ppm Curve 1 XFIX

CMAX C, ppm

FIGURE 8.3 Freundlich adsorption isotherm. (Redrawn from B.R. Bicknell, J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobs, and A.S. Donigian, Jr., Hydrological Simulation Program-Fortran: HSPF Version 12 User’s Manual, Mountain View, CA, Aqua Terra Consultants, 2001. With permission.)



197

where N1 is the Fruendlich exponent (N1 = 1 is a linear isotherm) and K1 is the Fruendlich distribution coefficient (units of L per kg when N1 = 1). These parameters — XFIX, N1, K1, and CMAX — must be supplied for surface, upper, lower, and groundwater zones. P mineralization and immobilization are modeled using first-order kinetics with temperature corrections. The routine requires values for the mineralization rate, KMP, and immobilization rate, KIMP, at 35°C in units of inverse days or hours, depending on the time step. These parameters must also be specified for each zone. The temperature correction equation for P mineralization takes the form KMPK = KMP ⋅ TH TMP −35

(8.6)

where TMP is the temperature (°C) in the zone, and TH is the correction coefficient (typically 1.06). There is a similar equation for temperature correction of the immobilization rate. Soil temperature is modeled by HSPF. Plant uptake is based on a first-order rate or a yield approach. In the first-order rate approach, for each zone the plant uptake rate parameter (in units of inverse time) is _KPLP where the underlined space is S, U, L, or K, representing the surface, upper, lower, and active groundwater zones. After correction for temperature, the uptake rate takes the form _KPLPK (in units of inverse time). Plant uptake occurs from the soluble P pool (Figure 8.2). The amount of plant uptake each day is calculated as the rate times the mass of P in the soluble pool in each zone. The temperature correction equation takes the same form as Equation 8.6. The yield approach to plant uptake of P is designed to be less sensitive to soil nutrient levels and nutrient application rates than the first-order rate option. It allows crop needs to be satisfied, subject to nutrient and moisture availability, without being affected by soil nutrient level. In this method, a total annual target is specified by the user and is then divided into monthly targets during the crop growing season. The target is further divided into the four soil layers. Soluble P can percolate down through the soil zones, which requires use of the MSTLAY module. In the PWATER module, which is used for general hydrology, some moisture that infiltrates can reach the groundwater in a single time step — that is, a day or an hour. This has little effect on hydrology, but it is not realistic for P in many cases. The MSTLAY module takes the fluxes and storages computed in PWATER and adapts them for runoff, interflow, and percolation through the soil layers. The revised storages, in inches of water, are also expressed in units of mass per area units for use in the adsorption and desorption calculations. Percolation occurs from the surface layer through each of the underlying layers. Percolation of P from the surface layer to the upper soil zone is described by the following equation: FSP = SLMPF ⋅

SDOWN SMST

(8.7)

where SDOWN is the amount of water percolating down (in.), SMST is the amount of water stored in the surface layer (in.), SLMPF is an arbitrary reduction factor (< 1), and FSP is the fraction of the soluble P in the surface zone that percolates (between 0 and 1).


198


Percolation of P from the upper zone to the lower soil zone is described by the following equation: FUP =

UZS UDOWN ⋅ UZSN ⋅ ULPF UMST

(8.8)

where ULPF is the factor for retarding percolation (since this variable is in the denominator, it must be > 1 to cause retardation), UDOWN is the amount of water percolating down (in.), UMST is the moisture storage (in.), and FUP is the fraction of the soluble P in the upper zone that percolates (between 0 and 1). There is a similar equation for percolation from the lower zone to ground water storages. The surface layer can lose P in surface runoff. Soluble P enters runoff directly and is adsorbed, and organic P can be removed with sediment. The concentration of soluble P in runoff is assumed to be the same as the concentration in the surface layer. Particulate P is removed from the surface layer in proportion to the fraction of the surface soil layer removed by erosion, although the mass of soil in the surface layer is a parameter value that does not vary even when material is removed. As such, an enrichment ratio accounting for the fact that most of the P lost in erosion is adsorbed to the clay-size fraction (Sharpley 1985) is not employed. Phosphorus can be added to the system as organic or adsorbed P through atmospheric deposition or through the special actions block where fertilizer and manure applications are described. The special actions block is a table of annual or monthly inputs. Many processes can be modeled for P in reaches. Most of these occur in the NUTRX module. They include longitudinal advection of dissolved P, benthal release of dissolved P, adsorption and desorption of P to suspended sediment in the water column using a linear adsorption coefficient ADPM(J), which varies for different sediment size fractions J, and desorption and scour and longitudinal advection of adsorbed P. In the PLANK module, sources and sinks of P include uptake by phytoplankton or benthic algae and respiration and inorganic excretion by zooplankton. Atmospheric deposition is also considered. No guidance document exists — such as the one for selecting values for hydrological parameters — for selecting values for P parameters. The primary parameters for modeling P are as follows: • • • • • • • • • • •

SKPLP, UKPLP: P plant uptake parameter for surface zone, upper zone THPLP, THDSP: temperature correction factor for plant uptake, desorption KIMP: first-order immobilization rate constant (day−1) KMP: first-order mineralization rate constant (day−1) CMAX: maximum equilibrium concentration of P in soil solution (mg L−1) XFIX: concentration of P permanently adsorbed to soil (mg L−1) K1: Freundlich distribution coefficient N1: Freundlich exponent ORGP: initial P storage in each layer for organic P P4AD: initial P storage in each layer for adsorbed P P4SU: initial P storage in each layer for solution P



• • • • • • • • •

199

PLTP: initial P storage in each layer for plant P IP4SU: initial P storage in upper layer for interflow pool SLMPF: factor for reducing P percolation from the surface to the upper soil zone; values < 1 cause a reduction; default = 0.5 ULPF: factor for reducing P percolation from the upper to the lower soil zone; values > 1 cause a reduction; default = 2.0 LLPF: factor for reducing P percolation from the lower soil zone to groundwater; values > 1 cause a reduction; default = 2.0 BRCON(I): benthal release rate of P (mg m−2 per time interval) for aerobic and anaerobic conditions ADPM(J): P adsorption Kd for suspended sand, silt, and clay fractions BNUT: constant concentration of P on bed sediments (mg P mg−1 sediment) CMMP: orthophosphorus Michaelis-Menten constant for P-limited algal growth (mg P L−1); default is 0.015 mg L−1

8.4 MODELING OF SEDIMENT In most cases, to model P transport the movement of sediment will also have to be modeled. Erosion processes that take place on each PLS are described in the SEDMNT module. Many of the routines are taken from the Agricultural Research Model (ARM) (Donigian et al. 1977). SLSED represents external lateral input from an upslope land segment that can be input as a time series by the user. NSVI is any net external additions or removals of sediment caused by human activities or wind. DET represents soil that is detached by rainfall and enters detached sediment storage. AFFIX represents the opposite process: detached sediment that reattaches to soil, which occurs on days when it does not rain. Once soil is in the detached sediment storage, it can be washed off in WSSD if the transport capacity is sufficient. Also, soil can be lost through erosion by scouring (i.e., gully erosion) without being detached by rainfall splash, which is represented by SCRSD. The total soil lost by washoff and scouring is SOSED. The equation for detachment is  RAIN  DET = DELT 60 ⋅ (1.0 − CR ) ⋅ SMPF ⋅ KRER ⋅   DELT 60 

JRER

(8.9)

where DET is the detached sediment (tons per acre per time interval), DELT60 is the number of hours per interval (dividing by 60 min), CR is the fraction of land covered by snow (SNOCOV) and vegetation (COVER), SMPF is the supporting management factor, KRER is the detachment coefficient dependent on soil properties, RAIN is the rainfall (in. per time interval), and JRER is the detachment exponent dependent on soil properties. To simulate reattachment on days when there is no rainfall, the detached soil sediment storage is decreased by multiplying it by the factor (1.0 – AFFIX) where AFFIX is a parameter.


200


The equation for transport capacity is  SURS + SURO  STCAP = DELT 60 ⋅ KSER ⋅   DELT 60 

JSER

(8.10)

where STCAP is the transport capacity (tons acre−1 time−1), KSER is the coefficient for transport of detached sediment, SURS is the surface detention storage of water from water modeling routines (in.), and SURO is the surface runoff (in. per time interval). If the transport capacity is less than the detachment rate, then erosion is limited by the transport capacity and vice versa. The equation for scouring is

SCRSD =

 SURS + SURO  SURO ⋅ DELT 60 ⋅ KGER ⋅  SURS + SURO  DELT 60 

JGER

(8.11)

where SCRSD is the scour of undetached soil (tons acre−1 time−1), KGER is the coefficient for scour, and JGER is the exponent for scour. Sediment losses from ILSs are also modeled. These are considered solids that wash off impervious surfaces, such as dust deposited and then washed off in storms. The model uses build-up and wash-off curves for ILSs — terminology that comes from modeling urban areas. Build-up of solids is described by the following equation: SLDS = ACCSDP + SLDSS ⋅ (1.0 − REMSDP )

(8.12)

where SLDS is the solids in storage at the end of the day (tons acre−1), SLDSS is the solids in storage at the beginning of the day (tons acre−1), ACCSDP is the accumulation rate of solids storage (tons acre−1 time−1), and REMSDP is the fraction of solids removed each day, by wind or street sweeping. If no runoff occurs, solids will build up and approach an asymptote, which is ACCSDP divided by REMSDP. Wash off of solids is described by the following equation:  SURS + SURO  STCAP = DELT 60 ⋅ KEIM ⋅   DELT 60 

JEIM

(8.13)

where STCAP is the solids transport capacity (tons acre−1 time−1), KEIM is the coefficient for transport of solids, and JEIM is the exponent for transport of solids. Sediment transport in the reaches is described by the SEDTRN module. Suspended sediment storage exchanges with the bed load through deposition and scouring. Three options exist for modeling reach sand transport: the Toffaleti method (Toffaleti 1969), the Colby method (Colby 1964; Colby and Hembree 1955), and the power function method. These three methods are used to calculate sand transportation



201

capacity in the reach. If the transportation capacity is greater than the sand storage, then sand is scoured from the stream bed. If the transportation capacity is less than the storage, then deposition occurs. The transport of cohesive sediment (i.e., silt and clay) is modeled using deposition and scouring based on shear stress exerted on the bed surface. The Toffaleti method requires modeling temperature and specifying the median bed sediment size, D50. The Colby method also uses D50. The power function method is the simplest to describe, so some of the details are shown here. It uses the following equation for sand transportation capacity: PSAND = KSAND ⋅ AVVELE EXPSND

(8.14)

where PSAND is the potential suspended sand load (mg L−1), KSAND is the sandload suspension coefficient, AVVELE is the average velocity of stream reach (ft sec−1), and EXPSND is the exponent. Sand is scoured or deposited depending on whether the capacity to transport is less than or greater than the current sand suspended load. Silt and clay scouring are treated differently because they resist scouring due to cohesion. The rate of scour of silt and clay sediment is described by the following equation:  TAU  S = M ⋅ − 1.0  TAUCS 

(8.15)

where S is the rate at which sediment is scoured from the bed (mass area−1 time−1), M is the erodibility coefficient (kg−2 time−1), TAU is shear stress, (lb ft−2 or kg m−2), and TAUCS is critical shear stress for detachment of bed sediment (lb ft−2 or kg m−2). There is no scouring as long as TAU < TAUCS. The rate of deposition of suspended silt and clay is described by the following equation:  TAU  D = W ⋅ CONC ⋅ 1 −  TAUCD 

(8.16)

where D is the rate at which sediment settles out of suspension (mass area-1 time−1), W is settling velocity in still water (in. sec−1), CONC is the concentration of suspended silt or clay (mass volume−1), and TAUCD is critical shear stress below which sediment deposits (lb ft−2 or kg m−2). There is a new technical note selecting values for sediment parameters (U.S. Environmental Protection Agency 2006). Donigian and Love (2003) can also be used as a guidance document. The primary parameters for modeling sediment are as follows: •

•

SMPF: supporting management practice factor; a table shows values for alternate practices and slopes in U.S. Environmental Protection Agency (2006). KRER: splash detachment soil coefficient; default = 0.14; ARM manual (Donnigian et al. 1977) says that this is equal to the product of the USLE factors K*P where K is soil erodibility and P is the practice factor (usually 1)


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• •

•

• • • • • • • • • • •

• • • • • •

JRER: splash detachment exponent; default = 2.0; HSPFParm runs all use 2.0 AFFIX: fraction by which detached sediment storage decreases each day due to reattachment; default = 0.03; HSPFParm runs used 0.01 for all land uses except forest, which had a value of 0.002 COVER: fraction of land surface shielded from rainfall by vegetation or mulch; default = 0.88; HSPFParm runs use monthly values that vary by land use (e.g., forest > urban) NVSI: deposition or wind removal of sediment from pervious land; default = 0 KSER: coefficient in sediment transport; default = 0.10; HSPFParm varies values from 0.04 to 8.30 JSER: transport exponent; U.S. Environmental Protection Agency (2006) recommends 2.5 KGER: scour or gully erosion coefficient; default = 0.01; HSPFParm runs use a range of values JGER: scouring exponent; default = 1.0; HSPFParm runs all use 1.0 BEDWID: width (ft) of bed; default = 16 ft BEDWRN: depth (ft) of bed sediment; when exceeded produces a warning message; default = 100 ft POR: porosity of bed; default = 0.50; HSPFParm runs varied from 0.6 to 0.8 DB50: median diameter of bed sediment used with Tofaleti and Colby methods KSAND: coefficient in the sand transport equation; default = 0.10; HSPFParm runs use values 0.001 to 0.1 EXPSND: exponent in sand transport equation; default = 3.92; HSPFParm runs use values 1.0 to 6.1; U.S. Environmental Protection Agency (2006) recommends a starting value of 2.0 W: fall velocity of sand in still water (in. sec−1); default = 0.05; one could use Stoke’s Law for this D: effective diameter of silt–clay particles (in.); default = 0.001; HSPFParm runs used 0.0001 for silt and 0.0004 for clay RHO: density of silt–clay particle (gm cm−3); default = 3.0; HSPFParm runs use 2.4 for silt and 2.0 to 2.4 for clay TAUCD: critical shear stress for silt–clay deposition (lb ft−2); default = 0.10; HSPFParm runs use 0.10 to 0.13 for silt and 0.0002 to 0.12 for clay TAUCS: critical shear stress for silt–clay scouring (lb ft−2); default = 0.30; HSPFParm runs use values 0.002 to 2.15 M: erodibility coefficient for silt–clay (lb ft−2 day−1); default = 0.90; HSPFParm runs use the same values of 0.0075 to 0.40 for silt and clay

8.5 CALIBRATION Most studies have used manual calibration of HSPF, often aided by the use of an expert system tool called HSPEXP, which is described in BASINS Technical Note #5 (U.S. Environmental Protection Agency 1999). HSPEXP offers advice to the modeler on parameter changes that can improve the calibration of flow. No guidance is provided for water-quality calibration. Recent studies such as Doherty and Johnston



203

(2003) have performed an autocalibration of HSPF using the Parameter Estimation (PEST) software developed by Doherty (2004). A limited implementation of autocalibration using PEST with HSPF is available in BASINS 3.1.

8.6 CASE STUDY: UPPER ETOWAH RIVER WATERSHED This chapter illustrates the use of HSPF to predict watershed-scale P transport with a case study on the Etowah River in the Piedmont region of Georgia. The Etowah River is the main tributary of Lake Allatoona, which has a Total Maximum Daily Load (TMDL) limit for P. The objective was to calibrate HSPF using data from the USGS gauging station (#02392000) at Canton, Georgia (Figure 8.4). The USGS data contained measurements of daily flow, water temperature, dissolved oxygen, turbidity, and total P. A study conducted by Kennesaw State University at a sampling site nearby measured suspended sediment concentration (SSC) and turbidity for several years (Rose 1999). These data were used to develop a relationship between SSC and turbidity, and then the USGS turbidity observations were converted into SSC. From the Canton USGS station, the Upper Etowah River watershed was delineated into

10

0

10

20 Kilometers

N

Urban Barren Transitional Cropland Pasture Forest Grass Land Water

FIGURE 8.4 Upper Etowah River basin with the solid dot indicating the watershed outlet at Canton, Georgia. The gray lines indicate the stream network, and the dark lines indicate the watershed and sub-basin boundaries.


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nine sub-basins. The area of watershed was 161,557 ha. The HSPF land-use classes and area percentages were as follows: forest (88.6%), pasture (7.9%), urban (2.2%), row crop (0.9%), barren land (0.07%), water (0.04%), and wetland (0.006%). A threshold for land-use categories was set such that only forest, pasture, and urban land uses were modeled. The case study’s approach to finding parameter values was to use soils information — following the guidance in U.S. Environmental Protection Agency (2004c) — and HSPFParm values for simulations in the Piedmont region of Virginia to find initial values and then to use PEST for autocalibration. Even though the values are adjusted by PEST — within limits set by the user — it is important that the initial values be good estimates of the final values since PEST uses a local optimization method. STATSGO soil data were used, and there were seven mapping units in the study’s delineated watershed. The soils were primarily hydrologic group B (moderate infiltration rate) and C (low infiltration rate). Three parameters were differentiated by land use: INFILT, CEPSC, and LZETP. All the other parameters were lumped across land uses. The soils data were used to find area-weighted average values for permeability of the first layer; this was used to get an initial value for INFILT for forest land use. The assumption was made for the study that INFILT for pasture would be 70% of the forest value and that INFLT for urban would be 50% of the forest value based on simulations in HSPFParm. An area-weighted average of the available soil water content in the first layer from the STATSGO database, multiplied by the depth of the first layer, was used as an initial value for UZSN. A similar approach using the available soil water content and depths in all the remaining soil layers was used to calculate an initial value for LZSN. The final calibrated predicted daily flow is compared with the observed flow at Canton, Georgia, for the period 1983 through 1991 in Figure 8.5. A log axis was used for flow to better show low flows. Overall, there was very good agreement between the model predictions and the observations except during very low flow periods, such as in Fall 1987. Donigian and Love (2003) suggested that sediment calibration of watershed models should consist of two stages: sediment erosion (loads from landscape) calibration and in-stream sediment transport calibration. Donigian and Love (2002, Table 2) provide guidelines for choosing HSPF sediment-related parameters in the SEDMNT and SOLIDS modules. Donigian and Love (2003, Table 1) show typical ranges of expected erosion rates for different land covers. For forest and pasture, the typical ranges of erosion rates are 0.05 to 0.4 and 0.3 to 1.5 tons ac−1 yr −1 (0.11 to 0.9 and 0.7 to 3.4 mg ha−1 yr −1). A few model parameters in SEDMNT (IMPLND was ignored) were adjusted accordingly so that the predicted sediment loads from forest and pasture were within the ranges. Donigian and Love (2003) suggest that the fractions of sand, silt, and clay entering a model reach should reflect the relative percentage of the surface material (i.e., sand, silt, clay) available for erosion in the surrounding watershed but also should include an enrichment factor of silt and clay to represent the likelihood of these finer particles reaching the channel. The case study’s analysis based on the STATSGO database showed that the topsoil percentage of sand, silt, and clay in the Etowah watershed are 48, 30, and 22%, respectively.



Stream Discharge (cms)

1000

205

Observed Simulated

100

10

1 1983

1984

1985

1986

1987 Date

1988

1989

1990

1991

FIGURE 8.5 Simulated and observed daily flow at Canton, Georgia, for 1983 through 1991. Nash-Sutcliffe coefficient of efficiency is 0.79.

These percentages were used as starting values since the degree of enrichment was not known. The final calibrated predicted total suspended solids (TSS) and observed TSS and turbidity for 1983 through 1991 are shown in Figure 8.6. As is typically the case, the measured data for contaminant concentrations are relatively sparse, consisting of monthly values in most years, compared to the daily flow data. As a result, it is difficult to know how well the model performs during storm events. At a minimum, the model should predict storm concentrations at least as high as the observed values, which was the case with the present simulations. Performance during base flow is more readily assessed, and the model tended to underpredict TSS somewhat under these conditions. According to Donigian and Love (2003, 18), HSPF undersimulates low concentrations of suspended solids because the model “employs a relatively gross channel representation, with long reach lengths, that tends to eliminate localized turbulence and scour conditions.” The case study assumed that Mehlich III soil test P could be used as an estimate of the adsorbed P pool in the surface soil zone. Since the concentration of dissolved P in runoff is the same as the concentration in the surface soil zone, Equation 8.5 describes the relationship between soil test P and dissolved P in runoff. Schroeder et al. (2004) measured the concentration of dissolved reactive P (DRP) in runoff from typical Piedmont soils using a rainfall simulator. Similar studies for soils in other states are listed in Schroeder et al. (2004, Table 1). When DRP (mg L−1) was plotted as a function of Mehlich III P (M3 in mg kg−1) in the soil from the 0- to 2-cm


206


Total Suspended Solids (mg/L), Turbidity (NTU)

1000

Simulated TSS Observed TSS Observed Turbidity

800

600

400

200

0 1983

1984

1985

1986

1987 Date

1988

1989

1990

1991

FIGURE 8.6 Simulated daily total suspended solids (TSS) and observed TSS and turbidity at Canton, Georgia, for 1983 through 1991.

depth, the linear equation DRP = 0.0017M3 + 0.15 (Schroeder et al. 2004, Table 4) was the best fit to the data. The slope coefficient (0.0017 kg L−1) is the ratio of dissolved P in runoff divided by soil test P. To get an initial estimate of the Freundlich distribution coefficient, K1, in Equation 8.5, the inverse was used to obtain the value of 588 L kg−1. Since the relationship was linear, the assumption was made that the Freundlich exponent, N1, was unity and was not calibrated this parameter. Estimates of the initial store of adsorbed P in the surface soil zone, SP4AD, were obtained using data from the University of Georgia Agricultural and Environmental Services Laboratories analysis of soil samples submitted by producers in the Etowah basin counties. These data were not available before 1992, so averages were used for the period 1992 to 2000. The lab measures Mehlich I soil test P (M1), so the case study used a relationship between M1 and M3 (M1 = 0.72 × M3 − 1.71) reported by Shuman et al. (1988) to convert the M1 to M3. For pastures, the average M3 soil test P in the three counties that dominate the watershed was 126.1 mg kg−1 (based on 1804 samples). This was converted to pounds per acre (252.1) as the initial estimate of P4AD in pasture. For forest land use, there were very few samples from the counties in the basin, so an average was computed for all Piedmont counties (based on 167 samples). The average M3 concentration was 12 mg kg−1 or 24.1 lb per acre as the initial estimate of P4AD in forest. HSPFParm values were used for KIMP and KMP. It was assumed that all pasture land received an annual broiler manure application of 2 mg ha−1 yr−1 in two field applications: late March and late October. It also was assumed that the manure contained 1.6% P, 90% of which was inorganic



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P based on analysis of broiler manure samples in Georgia conducted by the present authors. Plant uptake of P was modeled using the yield-based option. The annual P uptake by forest and pasture was set to 5.6 kg ha−1 and 28 kg ha−1 (Cabrera 2005; Ducnuigeen et al. 1997). Monthly fractions of total annual P uptake and the fractions of total annual P uptake from soil layers were set according to HSPFParm. It was assumed that 80% of P uptake was from the upper soil layer. Parameters were not adjusted in the ILSs, assuming that urban land use would have little effect on water quality in the study’s watershed. For calibration of P, the total P concentration from the PLANK module was compared with the observed total P concentration. The Discharge Monitoring Reports (DMR) for the period 1998 to 2003 — earlier dates were not available — were used to determine average point source P loads. There were two major permitted point sources in the watershed above Canton: the Jasper Water Pollution Control Plant (average measured effluent discharge of 1668 m3 day−1) and the Pilgrim’s Pride Poultry Processing Plant (average measured effluent discharge of 3335 m3 day−1). There were 13 minor permitted point sources in the watershed with average measured effluent discharge ranging from 9.5 to 758 m3 day−1. Phosphorus loads were reported in the DMR for the Pilgrim’s Pride Plant and for one of the minor point sources but not for any of the other point sources. For the point sources without DMR P loads, the study assumed a P concentration of 1 mg L−1 because this is typically the permitted concentration for point sources, although there is no way of knowing what the actual concentration was. Within each sub-basin with one or more point sources, a point source was added with the cumulative effluent discharge and P load. Before automatic calibration, PEST was used to perform a sensitivity analysis for flow, sediment, and P. The results are shown in Table 8.1. The most flow-sensitive parameter by far was the groundwater recession constant, which controls the shape of the stream hydrograph. Other flow-sensitive parameters were related to upper and lower zone soil water storage, the interflow recession constant, and evapotranspiration. The groundwater recession constant was also the most sensitive parameter by far for predicting sediment. The next most sensitive parameters were a group of sediment parameters related to stream transport. The most sensitive parameter for predicting total P was the y-intercept value for the Freundlich P asdorption isotherm in topsoil, XFIX. Other parameters related to P adsorption were also sensitive: N1 and K1. The second, fourth, and fifth most sensitive parameters for predicting P were parameters related to flow that affect runoff, INFILT_F and INFILT_P, and evapotranspiration, LZETP_P. Initial adsorbed P in pasture was a sensitive variable, and so was the variable controlling benthic release of P in streams. Oddly, P prediction was not sensitive to any of the sediment parameters. This may be due to the fact that there was little erosion from pasture and forest land uses and that most of the P lost is soluble P. The sensitivity analysis was used to decide which parameters to use in auto calibration with PEST. The study first calibrated for flow and then for sediment and P concentrations in the Etowah River at Canton, Georgia. The final calibrated predicted and observed total P 1983 through 1991 are shown in Figure 8.7. As was the case with TSS, the observed P data set was sparse. Model predictions matched


208


TABLE 8.1 Top 15 Parameters in Terms of Sensitivity to Flow, Sediment, and P Parameter

Sensitivity to Flow

Parameter

Sensitivity to Sediment

Parameter

Sensitivity to P

AGWRC UZSN LZETP_F IRC INFILT_F LZSN LZETP_P CEPSC_F INTFW INFILT_P DEEPFR LZETP_U LSUR NSUR INFILTU

8.647√ 0.0625√ 0.0589√ 0.0575√ 0.0494√ 0.0377√ 0.0298√ 0.0182 0.0165 0.0161 0.0079 0.0052 0.0040 0.0040 0.0038

AGWRC EXPSND TAUCSS TAUCSC KSAND TAUCDS M LZETP_F LZSN UZSN IRC INFILT_F LZETP_P INFILT_P INFILT_U

1.4283 0.2347√ 0.1996√ 0.1996 0.0645 0.0344√ 0.0197√ 0.0180 0.0156 0.0138 0.0118 0.0094 0.0085 0.0068 0.0053

XFIX INFILT_F N1 INFILT_P LZETP_P K1 IRC INTFW SPFAD_P AGWRC BRPO4 UZSN SLMPF KMP LZETP_F

0.2260√ 0.0879 0.0767 0.0752 0.0605 0.0605√ 0.0538 0.0367 0.0303√ 0.0276 0.0238√ 0.0191 0.0173√ 0.0170√ 0.0159

Notes: A check mark indicates that variables were used in autocalibration.

2 Simulated Observed

Total Phosphorus (P mg/L)

1.6

1.2

0.8

0.4

0 1983

1984

1985

1986

1987

1988

1989

1990

1991

Date

FIGURE 8.7 Simulated daily total P and observed total P at Canton, Georgia, for 1983 through 1991.



209

TABLE 8.2 Initial Values, Bounds, and Final Values of HSPF Parameters Calibrated in the Upper Etowah River Basin Case Study Parametera

Module

Initial Value

INFILT_F LZETP_F LZETP_P LZETP_U LZSN UZSN AGWRC IRC EXPSND TAUCD_S TAUCD_C TAUCS_S TAUCS_C M SLMPF KMP XFIX K1 P4AD_P BRPO4

PWATER

0.29 0.7 0.5 0.3 5.29 0.79 0.98 0.5 3.92 0.1 0.2 0.4 0.4 0.2 0.9 0.04 10 588 252 0.01

SEDTRN

MSTLAY PHOS

NUTRX

Bounds 0.05–0.4 0.6–0.8 0.4–0.6 0.1–0.4 2–15 0.05–2 0.85–0.999 0.3–0.85 1–6.1 0.1–0.13 0.0002–0.12 0.002–2.15 0.002–2.15 0.05–0.4 0.001–1 0.001–1 1–100 1–1000 0.5–400 0.001–1

Calibrated Value 0.1734 0.8 0.57 0.34 9.23 1.38 0.986 0.566 4.51 0.1 0.1 0.316 0.316 0.05 0.925 0.047 1 525 231 0.0093

aExtensions _F, _P, and _U indicate forest, pasture, and urban land use, respectively. Extensions _S and _C indicate silt and clay, respectively.

or exceeded observed P concentrations during storm events, as one would hope. Predicted storm flow peak concentrations were usually in the range of 0.3 to 1.5 mg L−1. Base-flow concentrations of P were simulated accurately as well, usually less than 0.1 mg L−1. The values of the most important variables and initial values, bounds for calibration, and final calibrated values of all parameters are shown in Table 8.2. For the flow-related variables (PWATER module), autocalibration resulted in changes that caused more runoff than the initial parameter values (decrease in the infiltration parameter and increases in the upper and lower soil water zone storage parameters). Most of the changes in the sediment parameters caused greater suspended sediment during base flow (increase in sand transport exponent and decreases in critical shear stress threshold values). Changes in the P-related parameters during autocalibration were a mixture of variables that increased runoff P (i.e., lower initial adsorbed P in pasture land use) and decreased runoff P (i.e., decrease in the Freundlich partition coefficient). The predicted average P loads from point and nonpoint sources for the period of calibration are shown in Table 8.3. Point sources accounted for only 3% of


210


TABLE 8.3 Simulated Average P Loads from Different Land Uses at Canton, Georgia, for the Period 1983 through 1991 Source Urban nonpoint Forest nonpoint Pasture nonpoint Point

Land Use Area (ha)

Specific Yield (kg ha−1 yr −1)

1,206 143,276 15,202 NA

Average Annual Load (kg yr −1)

(%)

0.80 0.20 2.75

9,620 28,000 41,828

12 34 51

NA

2,532

3

the average annual P load at Canton, Georgia. Pasture land use accounted for most (51%) of the average annual load despite the fact that the number of acres in pasture was small compared to forest land use. The pasture load was high due to the high specific yield of P per hectare of land (2.75 kg ha−1 yr−1) compared to forest land use (0.20 kg ha−1 yr−1). The urban load was relatively small due to low total land area.

8.7 COMPARING HSPF AND SWAT As noted in the introduction, HSPF is one of two dynamic watershed-scale models that are part of the BASINS software. The other model is SWAT. Since the present authors have some experience in running both models, this section briefly compares their approaches to modeling flow, sediment, and P. Both models are calibrated, so at least some of the parameter values are adjusted. However, estimates of parameter values are needed to minimize the number of calibrated parameters if manual calibration is used and to make it more likely that a global optimum is found if autocalibration is used. In general, the SWAT parameters for flow tend to be conventional soil parameters (e.g., available water content, saturated hydraulic conductivity, soil drainage class), whereas HSPF parameters for flow are unique to the model (e.g., INFILT, INFEXP, INTFW, UZSN). As a result, the SWAT soil parameters can be obtained from soil survey data. In fact, the BASINS version of SWAT can read some of these parameters directly from a soil survey database. The only way to obtain initial values for many HSPF parameters is to go to the HSPFParm database. HSPF models infiltration using a unique equation (Equation 8.1) and includes interflow (Equation 8.2). SWAT uses the curve number approach for runoff, which can only be used on a daily time step. There is an option for using the Green-Ampt equations for infiltration and an hourly time step in SWAT, but most users have not exercised this option. SWAT uses a Modified Universal Soil Loss Equation approach for estimating erosion from uplands. HSPF uses a series of equations that estimates detachment and transport capacities to model erosion. Again, SWAT uses more conventional soil parameters, whereas the HSPF parameters are relatively unique and best



211

determined from HSPFParm. Stream processes for sediment transport are described in more detail in HSPF than in SWAT. SWAT does not include a sediment-settling velocity, threshold shear-stress values, or different particles sizes of sediment. On the surface, the soil P routines in both models appear similar, but there are some important differences. SWAT uses three pools of inorganic P: labile, active, and stable pools. HSPF uses two pools of inorganic P: phosphate in solution and adsorbed P (Figure 8.2). SWAT implements the P routine developed in EPIC and described in Jones et al. (1984) and Sharpley et al. (1984). In SWAT, it is clear that labile P refers to anion exchange resin extractable P, but in HSPF it is not clear whether phosphate in solution refers to dissolved P or some other form. In SWAT, labile P is converted to soluble P in runoff using a phosphorus soil partitioning coefficient, but in HSPF the concentration in runoff is the same as the concentration of solution P in the surface layer. However, the relationship between P in solution and sorbed P in the surface layer (Equation 8.5) used in HSPF can be interpreted as a relationship between runoff P concentration and labile P in the topsoil, in which case the Freundlich partitioning coefficient is similar to the phosphorus soil partitioning coefficient in SWAT. An enrichment ratio is used to predict particulate P in runoff in SWAT but not in HSPF. In-stream P processes are modeled in greater detail in HSPF than in SWAT. SWAT models algal growth in streams and the movement of P among soluble, organic, and algal P pools. Organic P can settle out, and inorganic P can be released from the stream bed. HSPF includes these processes and adds to this the interaction of P with suspended sediment and scouring of bed sediment that contains P. HSPF also models phytoplankton uptake and release of P and zooplankton release of P. Saleh and Du (2004) compared SWAT and HSPF predictions of flow, sediment, and nutrients (i.e., N, P) in the Upper North Bosque River watershed in Texas. They found that HSPF did a better job of predicting daily flow than SWAT — based on the Nash-Sutcliffe model efficiency — and attributed this to use of the curve number approach in SWAT, which does not account for rainfall intensity. HSPF also did a better job of predicting sediment, but SWAT was a better predictor of nutrient loading. They attributed this to the ease of modeling agricultural practices such as fertilizer and manure applications in SWAT. Both models allow the user to simulate farming practices that occur on specific dates such as tillage and fertilizer and manure applications, but it is considerably easier to do in SWAT than in HSPF.

8.8 CONCLUSIONS HSPF is a state-of-the-art, dynamic, watershed-scale model that is being used in many projects modeling P dynamics and transport, most notably the Chesapeake Bay Model. It is a semidistributed model that divides a watershed into sub-basins. Within each sub-basin it models water, sediment, and P movement in land segments representing the dominant land uses and in a stream-reach segment. The equations describing infiltration and interflow in HSPF are unique to the model, and as a result the parameters for these processes are not readily measured. U.S. Environmental Protection Agency (2004c) is a good guide on selecting parameter values for


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modeling water movement in HSPF. Donigian and Love (2003) and U.S. Environmental Protection Agency (2006) are helpful in finding parameters for modeling sediment. HSPFParm is a database of parameter values that has been used by experienced users in 45 HSPF model runs. A technical note is needed to guide users in finding parameters for modeling P with HSPF. As a case study, HSPF was used to model flow, sediment, and P in the Upper Etowah River Basin; the study found good agreement between predictions and observations after calibration for the period 1983 through 1991. The model showed that nonpoint sources dominated the P load in the watershed and that the largest source of P was pasture land use associated with poultry operations. The most sensitive parameters for predicting P were those related to soil adsorption and initial stores of soil adsorbed P, infiltration, and benthic release of P.

ACKNOWLEDGMENTS This work was supported by a grant from the USDA-CSREES Water Quality grant GEO-2003-04944 entitled “A Framework for Trading Phosphorus Credits in the Lake Allatoona Watershed.”

REFERENCES Arnold, J.G., R. Srinivasan, R.S. Muttiah, and J.R. Williams. 1998. Large-area hydrologic modeling and assessment. Part I: model development. J. Am. Water Resour. Assoc. 34:73–89. Bicknell, B.R., J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobs, and A.S. Donigian, Jr. 2001. Hydrological Simulation Program-Fortran: HSPF Version 12 User’s Manual. Mountain View, CA: Aqua Terra Consultants. Cabrera, M.L. 2005. Personal communication. University of Georgia, Athens. Colby, B.R.1964. Practical computations of bed material discharge. J. Hydrol. Div. ASCE 90(HY2) 217–246. Colby, B.R. and C.H. Hembree. 1955. Computation of total sediment discharge, Niobrara River near Cody, Nebraska. U.S. Geological Survey Water Supply, Paper 1357. Crawford, N.H. and R.K. Linsley. 1966. Digital simulation in hydrology: Standford watershed model IV. Technical Report 39, Department of Civil Engineering, Stanford University, CA. Doherty, J. 2004. PEST — Model-Independent Parameter Estimation User’s Manual, 5th ed. Brisbane, Australia: Watermark Numerical Computing. Doherty, J. and J.M. Johnston. 2003. Methodologies for calibration and predictive analysis of a watershed model. J. Am. Water Resour. Assoc. 29:251–265. Donigian, Jr., A.S., D.C. Beyerlein, H.H. Davis, Jr. and N.H. Crawford. 1977. Agricultural Runoff Management (ARM) Model version II: refinement and testing. U.S. Environmental Protection Agency, EPA 600/3-77-098, Environmental Research Laboratory, Athens, GA. Donigian, Jr., A.S., R.V. Chinnaswamy, A.S. Patwardhan, and R.M. Jacobson. 1996. Watershed modeling of pollutant contributions and water quality in the LeSueur Basin of Southern Minnesota. Pp. 109–111 in WATERSHED '96 — Moving Ahead Together. Conference Proceedings, June 8–12, Baltimore, MD.



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Donigian, Jr., A.S., and N.H. Crawford. 1976a. Modeling pesticides and nutrients on agricultural lands. U.S. Environmental Protection Agency, EPA 600/2-7-76-043, Environmental Research Laboratory, Athens, GA. Donigian, Jr., A.S., and N.H. Crawford. 1976b. Modeling nonpoint pollution from the land surface. U.S. Environmental Protection Agency, EPA 600/3-76-083, Environmental Research Laboratory, Athens, GA. Donigian, Jr., A.S., J.C. Imhoff, and J.L. Kittle, Jr. 1999. HSPFParm: an interactive database of HSPF model parameters, version 1.0. U.S. Environmental Protection Agency, EPA823-r-99-004, Washington, D.C. Donigian, Jr., A.S., and J.T. Love. 2002. The Connecticut watershed model — a tool for BMP impact assessment in Connecticut. WEF-Watershed 2002, February 23-27, 2002. Ft. Lauderdale, FL, WEF-2002 Specialty Conference Proceedings on CD-ROM. Donigian, Jr., A.S. and J.T. Love. 2003. Sediment calibration procedures and guidelines for watershed modeling. WEF TMDL 2003, November 16–19, 2003, Chicago, IL. WEF Specialty Conference Proceedings on CD-ROM. Ducnuigeen, J., K. Williard, and R.C. Steiner. 1997. Relative nutrient requirements of plants suitable for riparian vegetated buffer strips. Interstate Commission on the Potomac River Basin, Report Number 97-4, Virginia Department of Environmental Quality, Richmond, VA. Fetter, C.W. 1988. Applied Hydrology, 2nd. ed. Columbus, OH: Merrill Publishing Company. Hummel, P.R., J.L. Kittle, P.B. Duda, A. Patwardhan. 2003. Calibration of a watershed model for metropolitan Atlanta. WEF TMDL 2003, November 16–19, 2003. Chicago, IL. WEF Specialty Conference Proceedings on CD-ROM. Hydrocomp, Inc. 1976. Hydrocomp Simulation Programming: Operations Manual, 2nd ed. Palo Alto, CA: Hydrocomp, Inc. Hydrocomp, Inc. 1977. Hydrocomp Water Quality Operations Manual. Palo Alto, CA: Hydrocomp, Inc. Jones, C.A., C.V. Cole, A.N. Sharpley, and J.R. Williams. 1984. A simplified soil and plant phosphorus model. I: documentation. Soil Sci. Soc. Am. J. 48:800–805. Linker, L.C., G.W. Shenk, P. Wang, K.J. Hopkins, and S. Pokharel. 2002. A short history of Chesapeake Bay modeling and the next generation of airshed, watershed, and estuarine models. Presented at the Watershed Conference, February 23–27, Fort Lauderdale, FL. Neitsch, S.L., J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King. 2002. Soil and Water Assessment Tool theoretical documentation. U.S. Department of Agriculture Agricultural Research Service, Report 02-01, Grassland, Soil, and Water Research Laboratory, Temple, TX. Onishi, Y. and S.E. Wise. 1979. Mathematical Model, SERATRA, for Sediment-Contaminant Transport in Rivers and its Application to Pesticide Transport in Four Mile and Wolf Creeks in Iowa. Richland, WA: Battelle, Pacific Northwest Laboratories. Rose, P. 1999. Lake Allatoona Phase I Diagnostic-Feasibility Study for 1992–1997. Kennesaw, GA: A.L. Burruss Institute of Public Service. Kennesaw State University. Saleh, A. and B. Du. 2004. Evaluation of SWAT and HSPF within BASINS program for the Upper North Bosque River watershed in central Texas. Trans. ASAE 47(4):1039–1049. Schroeder, P.D., D.E. Radcliffe, M.L. Cabrera, and C.D. Belew. 2004. Relationship between soil test phosphorus and phosphorus in runoff: effects of soil series variability. J. Environ. Qual. 33:1452–1463. Sharpley, A.N. 1985. The selective erosion of plant nutrients in runoff. Soil Sci. Soc. Am. J. 49:1527–1534. Sharpley, A.N., C.A. Jones, C. Gray, and C.V. Cole. 1984. A simplified soil and plant phosphorus model. II: prediction of labile, organic, and sorbed phosphorus. Soil Sci. Soc. Am. J. 48:805–809.


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Shuman, L.M., P.L. Raymer, J.L. Day, and M.J. Cordonnier. 1988. Comparison of four phosphorus extraction methods on three acid southeastern soils. Comm. Soil Sci. Plant Anal. 19:579–595. Toffaleti, F.B. 1969. Definitive computations of sand discharge in rivers. J. Hydrol. Div. ASCE 95(HY1):225–246. U.S. Environmental Protection Agency. 1999. BASINS Technical Note 5: Using HSPEXP with BASINS/NPSM. Available at http://www.epa.gov/waterscience/basins/bsnsdocs.html. U.S. Environmental Protection Agency. 2004a. A powerful tool for managing watersheds. Available at http://www.epa.gov/OST/BASINS/. U.S. Environmental Protection Agency. 2004b. BASINS Technical Note 3: NPSM/HSPF Simulation Module Matrix. Available at http://www.epa.gov/waterscience/basins/ bsnsdocs.html. U.S. Environmental Protection Agency. 2004c. BASINS Technical Note 6: Estimating hydrology and hydraulic parameters for HSPF. Available at http://www.epa.gov/waterscience/ basins/bsnsdocs.html. U.S. Environmental Protection Agency, 2006. BASINS Technical Note 8: Sediment parameter and calibration guidance for HSPF. Available at http://www.epa.gov/waterscience/ basins/bsnsdocs.html.


9

Phosphorus Modeling in the Annualized Agricultural Nonpoint Source Pollution (AnnAGNPS) Model Yongping Yuan U.S. Department of Agriculture-Agricultural Research Service, Oxford, MS

Ronald L. Bingner U.S. Department of Agriculture-Agricultural Research Service, Oxford, MS

Indrajeet Chaubey University of Arkansas, Fayetteville, AR

CONTENTS 9.1 9.2 9.3 9.4

9.5

Model Introduction ......................................................................................216 Watershed Processes Considered in AnnAGNPS........................................216 Model Inputs and Outputs ...........................................................................217 AnnAGNPS Model of Phosphorus Processes .............................................219 9.4.1 Soil Initial Phosphorus Content.......................................................220 9.4.2 Organic P Simulation Processes ......................................................221 9.4.3 Inorganic P Simulation Processes....................................................222 9.4.3.1 Calculation of Inorganic P Additions to a Cell ...............222 9.4.3.2 Calculation of Intermediate Inorganic P Mass Balance..................................................................223 9.4.3.3 Calculation of Inorganic P Losses from the Soil Profile .........................................................224 9.4.4 Total Runoff Losses .........................................................................226 Model Application........................................................................................226 9.5.1 Study Watershed and Monitoring Information................................226 9.5.2 Input Data Preparation .....................................................................227 215


216


9.5.3 Sensitivity Analysis..........................................................................229 9.5.4 Model Calibration and Validation....................................................232 9.6 Model Limitations........................................................................................238 9.7 Conclusions ..................................................................................................238 References..............................................................................................................238

9.1 MODEL INTRODUCTION The Annualized Agricultural Nonpoint Source Pollution (AnnAGNPS) model is an advanced technological watershed evaluation tool that has been developed through a partnership between two U.S. Department of Agriculture (USDA) agencies — the Agriculture Research Service (ARS) and the Natural Resources Conservation Service (NRCS) — to aid in the evaluation of watershed responses to agricultural management practices (Bingner and Theurer 2001). AnnAGNPS is a continuous-simulation, daily time-step, pollutant loading model designed to simulate long-term chemical and sediment movement from agricultural watersheds (Bingner et al. 2003). The spatial variability of soils, land use, and topography within a watershed is accounted for by dividing the watershed into many user-specified, homogeneous, drainage-area-determined cells. For individual cells, runoff, sediment, and pollutant loadings can be predicted from precipitation events that include rainfall, snowmelt, and irrigation. Each day, AnnAGNPS simulates runoff, sediment, nutrients, and pesticides leaving the land surface and being transported through the watershed channel system to the watershed outlet before the next day is considered. The model routes the physical and chemical constituents from each cell into the stream network and finally to the watershed outlet and has the capability to identify the sources of pollutants at their origin and to track them as they move through the watershed system. The AnnAGNPS model has evolved from the original single-event Agricultural Nonpoint Source (AGNPS) model developed in the early 1980s by the USDA-ARS (Young et al. 1989, 1995). The AGNPS model was developed to simulate runoff and water-quality response of agricultural watersheds ranging from a few hectares to 20,000 hectares from a single rainfall event. The AGNPS model has been applied throughout the world to investigate various water quality problems. The AnnAGNPS model includes significantly more advanced features but retains many of the important features of AGNPS. (The complete suite of AnnAGNPS model, composed of programs, pre- and post-processors, technical documentations, and user’s manuals, is currently available at http://www.ars.usda.gov/Research/docs.htm?docid=5199.)

9.2 WATERSHED PROCESSES CONSIDERED IN AnnAGNPS The hydrology components considered within AnnAGNPS are rainfall, interception, runoff, evapotranspiration (ET), infiltration/percolation, subsurface lateral flow, and subsurface drainage. The runoff from each cell is calculated using the Soil Conservation Service (SCS) curve number (CN) method (Soil Conservation Service 1985). The modified Penman equation (Jenson et al. 1990; Penman 1948) is used to calculate the potential ET, and the actual ET is represented as a fraction of potential ET. The fraction is a linear


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function of soil moisture between wilting point and field capacity. For percolation, only the downward drainage of soil water by gravity is calculated (Bingner et al. 2003). Lateral flow is calculated using Darcy’s equation, and subsurface drainage is calculated using Hooghoudt’s equation (Freeze and Cherry 1979; Smedema and Rycroft 1983). Amount of sheet and rill soil erosion loss — not field deposition — for each runoff event is calculated using the Revised Universal Soil Loss Equation (RUSLE) model (Renard et al. 1997). A delivery ratio, which quantifies the amount of sediment deposited in the field and the amount of sediment delivered to the stream, is calculated using the Hydrogeomorphic Universal Soil Loss Equation (HUSLE) model (Theurer and Clarke 1991). Ephemeral gully erosion is based on the Ephemeral Gully Erosion model (Merkel et al. 1988). The model uses the Bagnold equation (Bagnold 1966) to determine the sediment transport capacity of the stream and a modified Einstein equation to determine the sediment transport in the stream system (Bingner et al. 2003). Sediment is partitioned into five classes: clay, silt, sand, small aggregates, and large aggregates. The model estimates particle-size distribution of deposited sediment by taking into account the density and fall velocity of each class. The AnnAGNPS model calculates a daily mass balance within each cell for soil moisture, nitrogen (N), phosphorus (P), organic carbon (OC), and pesticides. Plant uptake of nutrients, fertilization, residue decomposition, mineralization, and transport are major factors considered to determine the fate of nutrients in the watershed. Both soluble and sediment adsorbed nutrients are considered by the model. The pesticide component is adopted from the Groundwater Loading Effects of Agricultural Management Systems (GLEAMS) model (Leonard et al. 1987). The AnnAGNPS model allows simulation of any number of pesticides and treats each pesticide separately with independent equilibrium assumed for each pesticide. Both soluble and sediment-adsorbed fractions of each pesticide are calculated on a daily time scale. Factors affecting fate and transport of pesticides include foliage washoff, vertical transport in the soil profile, and degradation.

9.3 MODEL INPUTS AND OUTPUTS A complete list of AnnAGNPS input data sections is shown in Figure 9.1. These data can be grouped into the following categories: climate, watershed physical information, land-management operations, chemical characteristics, and feedlot operations. Daily precipitation, maximum and minimum temperatures, dew point temperature, sky cover, and wind speed are climate data required by the model to perform continuous simulation. Climate data used with AnnAGNPS can be historically measured, synthetically generated using the climate generator program (Johnson et al. 2000), or a combination of the two. Geographic information systems (GIS) data layers of a watershed are needed to characterize the watershed. The GIS data layers must be in sufficient spatial detail to permit the model to accurately reflect the real landscape it represents. Using the GIS layers of digital elevation model (DEM), soils, and land use, a majority of the large data input requirements can be developed using a customized ArcView GIS interface. Those input requirements include watershed and cell delineation, cell land slope, slope direction, cell land use and soil type, and stream reach data, can be


218

AnnAGNPS Identifier

Gully

Watershed Data Point Source

Simulation Period

Feedlot

Daily Climate Feedlot Management

Verification Data

Field Pond

Cell Data

Soils

Management Field

Tile Drain

Global Output Field Pond Management

Reach Data

Reach Channel Geometry

Impoundment

Reach Nutrient Half Life

Fertilizer Application

Pesticides Application

Fertilizer Reference

Pesticides Reference

Required

Management Operation

Strip Crop

Contours

Runoff Curve Number

Irrigation

Non-Crop

Required if Referenced

FIGURE 9.1 A complete list of AnnAGNPS input data sections. © 2007 by Taylor & Francis Group, LLC

Crop

Optional


Management Schedule

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developed by using a customized ArcView GIS interface. Additional input requirements, which include developing the soil layer attributes to supplement the soil spatial layer, describing crop operations and management practices, defining channel hydraulic characteristics, and entering many other optional data sections as needed by the watershed (Figure 9.1), can be organized using the AnnAGNPS Input Editor. The Input Editor is a graphical user interface developed to aid users in selecting appropriate input parameters. Much of the information needed to characterize crop characteristics, field operations (e.g., crop rotation, tillage, planting, harvesting), chemical characteristics, feedlots, and soils can be obtained from databases imported from RUSLE or from other USDA-NRCS data sources. Feedlot information includes daily manure production rates, manure characteristics, amount of manure removed from the field lot, and residual amount of manure available from previous operations. The model outputs include runoff, sediment, nutrient, and pesticide at a temporal scale ranging from daily to yearly. All model outputs can be obtained at any desired location such as specific cells, stream reaches, feedlots, gullies, or point sources. The model also has capabilities to provide source accounting information in terms of the fraction of a pollutant loading passing through any reach location that originated from a user-specified pollutant source area. Cronshey and Theurer (1998), Geter and Theurer (1998), and Theurer and Cronshey (1998) provide detailed information on available model outputs.

9.4 AnnAGNPS MODEL OF PHOSPHORUS PROCESSES Simulation of P transport and transformation processes at a watershed scale is very challenging because of the complexities and uncertainties related to the processes. A complete understanding of the relationship of various P pools and their chemical, physical, and biological interactions in the soil profile is essential for a full description of the P cycle in soils and plants (Jones et al. 1984). A model based on mathematical descriptions of fundamental chemical, physical, and biological mechanisms of the soil P behavior would be ideal for P modeling. In general, the chemical component in AnnAGNPS exists in two phases: dissolved (solution) in the surface runoff and attached (adsorbed) to clay-size particles resulting from sheet and rill erosion. To simulate P loading, daily soil mass balances of P in a cell are maintained for each computational layer. The daily mass balances of P are adapted from the Erosion Productivity Impact Calculator (EPIC) model (Sharpley et al. 1984; Sharpley and Williams 1990). The P processes simulated in AnnAGNPS are shown in Figure 9.2. More specifically, P is partitioned into inorganic P and organic P, and a separate mass balance is maintained for each. Inorganic P is further broken down into (1) labile P, or P readily available for plant uptake; (2) active P, or P that is more or less reversibly adsorbed to the soil; and (3) stable P, or adsorbed P that is fixed or relatively irreversibly chemisorbed to the soil adsorption complex or as discrete insoluble P minerals. The model simulates the effect of P adsorption that controls P availability to plant uptake and runoff loss, and the model also simulates P movements between labile P and active P and between active P and stable P. Sediment-attached


220


Inorganic Erosion loss

Active

Runoff loss

Plant uptake

Organic Organic fertilizer

Inorganic fertilizer

Mineralization

Desorption Solution Adsorption

Erosion loss

Active and Stable (Humic)

Residue mineralization

Plant residue

Decay

Fresh

Stable

FIGURE 9.2 Phosphorus processes simulated in AnnAGNPS.

P estimated from soil erosion is assumed to be associated with the clay-size fraction of the soil and consists of both organic and inorganic P. Major processes considered are residue decomposition and mineralization, fertilizer application, plant uptake, runoff, and erosion losses. Plant uptake of P is modeled through a simple crop-growth stage index either specified by the user or by the model (Bingner et al. 2003). Phosphorus losses from each AnnAGNPS cell within a stream reach are added to an AnnAGNPS reach. Phosphorus is reequilibrated between dissolved P and sediment-attached P in the reach during transport to the watershed outlet.

9.4.1 SOIL INITIAL PHOSPHORUS CONTENT The initial soil P content is needed to initialize AnnAGNPS simulation. Usually, calibration is recommended to define the initial soil P content. The input P levels in the soil profile are input as concentrations, but AnnAGNPS performs calculations on a mass basis. To convert a concentration to a mass, AnnAGNPS uses a conversion factor, conv (Equation 9.1). The conversion factor converts nutrient concentration in soil to mass (in kilograms) using Equation 9.1: conv = 10,000 ρ b D Acell

(9.1)

where conv is the intensive unit-to-extensive-unit conversion factor (kg), ρb is the bulk density of composite soil layer (g/cm3 or mg/ m3), D is thickness of soil layer (mm), and Acell is the AnnAGNPS cell area (ha).


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9.4.2 ORGANIC P SIMULATION PROCESSES All AnnAGNPS mass balances are based on AnnAGNPS cells and are maintained for two composite soil layers. The first soil layer is 203 mm in depth from the surface, typically defined as the tillage layer by RUSLE. The second soil layer is from the bottom of the tillage layer to either an impervious layer or the user-supplied depth of the soil profile. The mass balance equation for organic P simulation is as follows: orgPt = orgPt −1 +

(resP + orgPfer − hmnP − orgPsed ) 1,000,000 conv

(9.2)

where orgPt is organic P concentration in the composite soil layer for the current day (mg/kg), orgPt–1 is organic P concentration in the composite soil layer for the previous day (mg/kg), resP is organic P addition to a cell from decomposed fresh crop residue (kg), orgPfer is organic P addition to a cell from fertilizer application (kg), hmnP is the mineralization from the humus active organic P pool (kg), and orgPsed is organic P loss from a cell by attaching to sediment (kg). Decomposition is calculated once a day. Equations for residue decomposition were adapted from RUSLE. Only surface decomposition is calculated for crop land. Cell organic P from fertilizer application is the product of the fertilizer applied for the current day and the organic P fraction in the fertilizer. The organic P fraction can be obtained from the fertilizer reference database in AnnAGNPS. The P mineralization equation is adapted from the EPIC model (Sharpley and Williams 1990). Temperature and aeration, represented by soil moisture, are considered for P mineralization (Sharpley and Williams 1990). AnnAGNPS assumes that organic phosphorous is associated with the clay fraction of the soil. Sedimentattached organic P is calculated by Equation 9.3: orgPsed = forgP × sed clay × 1000

(9.3)

where forgP is a decimal fraction of organic P in clay in soil layer (g/g), and sedclay is the amount of clay in the mass of sediment (mg). The decimal fraction of organic P is: forgP =

orgP fclay × 1,000,000

(9.4)

where orgP is the organic P concentration in the composite soil layer (mg/kg), and fclay is the fraction of clay to total composite soil, provided by the soil database. Organic P mass balance is maintained for the second soil layer the same way as the first layer except that fertilizer application and rainfall-induced runoff and sediment loss are not considered. AnnAGNPS assumes that fertilizer application, rainfall-induced runoff, and sediment loss are associated only with the top soil layer. Equation 9.5 represents the mass balance for the second layer: orgPt = orgPt −1 −


hmnP 1,000,000 conv

(9.5)

222


9.4.3 INORGANIC P SIMULATION PROCESSES AnnAGNPS simulates three different pools of inorganic P in the soil. It adapts the principles of the soil mineral P model developed by Jones et al. (1984). Mineral P is transferred among three forms: labile P in solution (available for plant use and runoff loss), active P, and stable P. AnnAGNPS assumes that inorganic P added from fertilizers initially goes to the labile P pool and the active P pool, based on a value of the P sorption coefficient. Fertilizer P that is labile at application may be quickly transferred to the active mineral pool. Many studies have shown that after an application of inorganic P fertilizer, solution P concentration in the soil decreases rapidly with time due to reaction with the soil. This initial fast reaction is followed by a much slower decrease in solution P that may continue for several years (Barrow and Shaw 1975; Munns and Fox 1976; Rajan and Fox 1972; Sharpley 1982). Flow between the active and stable mineral pools is governed by a P exchange rate. Within each inorganic P pool, addition from fertilizer application is calculated first, followed by the mineralization of organic P. Then, losses through runoff, erosion, and plant uptake are calculated. At the end of each day, the mass balance is updated for each P pool. The simulation is a sequence of adjusting the mass balance of each inorganic P pool. 9.4.3.1 Calculation of Inorganic P Additions to a Cell Fertilizer additions are simulated in one of two ways: well mixed with the top soil layer or unincorporated on the soil surface. On a daily basis, AnnAGNPS checks if there is a tillage operation and the percentage of soil disturbance from the tillage operation. If the soil disturbance exceeds 50% of the top soil layer, any fertilizer applications are considered as mixed. Otherwise, it assumes the applied fertilizer stays on the soil surface. In addition, when the soil disturbance exceeds 50% of the soil, it incorporates not only the applied fertilizer on the current day but also any fertilizer left on the soil surface from previous applications. Therefore, when soil disturbance exceeds 50% of the top soil layer, mnaP = surf _ inorgP

(9.6)

where mnaP is the mass of inorganic P added to the soil profile from the current operation (kg) (and it is assumed to be well mixed with the first soil layer), and surf_inorgP is the surface inorganic P in a cell, added through fertilization at the soil surface (kg). If a fertilizer is applied in the current operation, then mnaP = mnaP + inorgPfer

(9.7)

where inorgPfer is inorganic P applied during the current operation (kg). It is calculated using the rate of fertilizer applied for the current day times the inorganic P fraction (from the fertilizer reference database mass/mass). When soil disturbance is less than 50% of the soil, the fertilizer on the soil surface remains on the soil surface and nothing is incorporated into the soil profile. If a fertilizer is applied for the current operation, then surf _ inorgP = surf _ inorgP + inorgPfer © 2007 by Taylor & Francis Group, LLC

(9.8)

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Then, AnnAGNPS checks if a rainfall event occurred, and if so, soil inorganic P is adjusted to reflect the rainfall impact. When a rainfall event occurs, it dissolves the soluble P on the soil surface. When the rainfall generates runoff, AnnAGNPS assumes that inorganic P on the soil surface is totally dissolved in the water and is either carried away with runoff or is carried into the soil profile with infiltration. The amount of inorganic P carried away with runoff or carried into the soil profile with infiltration is determined based on the amount of runoff and infiltration from the rainfall event.

surf _ sol _ P =

inf _ sol_ P =

Q surf _ inorgP (Q + inf ) inf surf _ inorgP (Q + inf )

(9.9)

(9.10)

where surf_sol_P is mass of inorganic P in runoff (kg), inf_sol_P is the amount of inorganic P carried into the soil profile by infiltration (kg), Q is the amount of surface runoff (mm), and inf is the amount of infiltration (mm). Then, the amount of inorganic P carried into the soil profile by infiltration is added to the mnaP value to reflect the impact of the current rainfall event. 9.4.3.2 Calculation of Intermediate Inorganic P Mass Balance The intermediate inorganic P mass balance refers to P pools with P additions but prior to any P losses to runoff, erosion, and plant uptake. Bottom soil-layer inorganic P does not change with this operation. A portion of the incorporated inorganic P is added into the labile P pool:

labPi = labPstart − mpr +

Psp mnaP 1,000,000 conv

(9.11)

where labPi is the concentration of intermediate labile inorganic P in the composite soil layer (mg/kg), labPstart is the concentration of labile inorganic P at the beginning of a day, and it is equal to the labile P at the end of the previous day (mg/kg), mpr is the flow rate of P between labile and active P pools on the current day (+ implies flow from labile to active pool; – implies flow in the opposite direction) (mg/kg/d) (Sharpley and Williams 1990), Psp is the soil type-dependent P sorption coefficient (dimensionless) (Sharpley and Williams 1990), and mnaP is mass of inorganic P added to a cell soil profile (kg). The rest of the incorporated inorganic P is added into the active P pool: actPi = actPstart + mpr +


(1 − Psp) mnaP 1,000,000 − aspr conv

(9.12)

224


where actPi is the concentration of intermediate active inorganic P in the composite soil layer (mg/kg), actPstart is the concentration of active inorganic P at the beginning of a day (equal to the active P at the end of the previous day) (mg/kg), and aspr is the flow rate of P between active and stable P pools on the current day (+ implies flow from active to stable pool; – implies flow in the opposite direction) (mg/kg/d) (Sharpley and Williams 1990). Stable P pool size is calculated as follows: stbPi = stbPstart + aspr

(9.13)

where stbPi is concentration of intermediate stable inorganic P in the composite soil layer (mg/kg) and stbPstart is the concentration of stable inorganic P at the beginning of a day (equals to the stable P at the end of the previous day) (mg/kg). Then, the inorganic P pools are further adjusted to add the organic P from mineralization. This mineralized P is partitioned among three inorganic P pools based on the fraction of each inorganic P pool to total inorganic P. hmnP flab 1,000,000 conv

(9.14)

actPi+1 = actPi +

hmnP × fact 1,000,000 conv

(9.15)

stbPi+1 = stbPi +

hmnP × fstb 1,000,000 conv

(9.16)

labPi+1 = labPi +

where hmnP is the mineralization from the humus active organic P pool in the soil layer on the current day (kg), flab is the fraction of labile P to total P (total P is the sum of labile P, active P, and stable P), fact is the fraction of active P to total P, and fstb is the fraction of stable P to total P. 9.4.3.3 Calculation of Inorganic P Losses from the Soil Profile This calculation includes sequential adjustments to the P pool size to reflect losses from a cell. 9.4.3.3.1 Loss through Surface Runoff When a rainfall event occurs, runoff interacts with soil and carries soluble inorganic P in the soil profile away from fields. AnnAGNPS assumes the effective depth of runoff interaction with soil to be 10 mm. All soluble inorganic P in the top 10 mm of soil is carried away by the runoff. Soil soluble inorganic P in the top soil layer available for runoff loss is calculated as soil_ sol_ inorgP =


labP (1 + Kd _ inorgP)

(9.17)

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where soil_sol_inorgP is the concentration of soluble P available for runoff loss in a cell soil profile on the current day (mg/kg) and Kd_inorgP is the linear partitioning coefficient for inorganic P (the ratio of the mass of adsorbed P to the mass of P in solution). Soluble inorganic P removed by runoff from the top 10 mm of soil is calculated as cell_ soil_ sol_ inorgP = edi

soil _ sol _ inorgP Conv Depth 1,000,000

(9.18)

where cell_soil_sol_inorgP is the inorganic P removed from the top soil layer through runoff (kg), edi is the effective depth of interaction factor, AnnAGNPS uses 10 mm, and depth is the depth of the top soil layer (mm). The labile P pool is adjusted to reflect the loss to surface runoff. labPi+ 2 = labPi+1 −

cell_ soil_ sol_ inorgP 1,000,000 conv

(9.19)

9.4.3.3.2 Loss to Soil Erosion Soil erosion also carries inorganic P away from fields. The inorganic P loss through erosion is calculated the same way as organic P. AnnAGNPS assumes that the inorganic P is also associated with clay fraction. The amount of sediment-attached inorganic P is calculated first; then it is partitioned between the active and stable P pools based on the amount of each pool. actPi+ 2 = actPi+1 −

sed _ inorgP _ actP 1,000,000 conv

(9.20)

stbPi+ 2 = stbPi+1 −

sed _ inorgP _ stbP 1,000,000 conv

(9.21)

where sed_inorg_actP is the sediment loss from active P (kg) and sed_inorg_stbP is the sediment loss from stable P (kg). 9.4.3.3.3 Loss through Plant Uptake of Inorganic P In AnnAGNPS, the amount of crop nutrient uptake is calculated in a crop-growth stage subroutine that determines the crop-growth stage based on crop data specified by a user. Four growth stages —initial, development, mature, and senescence — are simulated by AnnAGNPS. The length of each growth stage can be specified by a user or by the model (Bingner et al. 2003). The amount of nutrient uptake is calculated based on the crop-growth stage and differs by growth stage. The crop nutrient uptake is also limited by available nutrients in the composite soil layer. The calculated crop uptake P in the crop-growth stage subroutine affects the inorganic P mass balance. Phosphorus uptake on a given day is calculated as follows: uptP =

growth_ P_ uptake yield P _ uptake_ harvest Acell stage_ length


(9.22)

226


where uptP is the amount of inorganic P taken up by the plant on the current day (kg), growth_P_uptake is the fraction of P uptake for the current growth stage, yield is the yield at harvest (kg/ha), P_uptake_harvest = P uptake per yield unit at harvest (mass of P/mass of harvest unit, dimensionless), and stage_length is the the number of growing days for the current growth stage (days). Plant P uptake is adjusted based on the availability of P in the soil. If uptP calculated in Equation 9.22 is greater than the available labile P in the soil layer, then a limited crop P uptake is calculated as uptPlimited = 0.99

labPi+2 conv 1,000,000

(9.23)

where uptPlimited is the mass of labile P taken up by the plant on the current day (kg) and labPi+2 is the labile P concentration in the soil (mg/kg). The mass of crop uptake P is subtracted from the labile P pool at the end of each day.

9.4.4 TOTAL RUNOFF LOSSES The total mass of inorganic P lost through surface runoff is composed of loss from the soil profile (Equation 9.18) and loss from the soil surface (Equation 9.9). Due to the low mobility of P, leaching loss of soluble P is not simulated. Phosphorus losses from each AnnAGNPS cell within a stream reach are added to an AnnAGNPS reach. Phosphorus is reequilibrated between dissolved P and sediment-attached P in the reach based on the P partitioning coefficient during the process of being transported to the watershed outlet. Detailed P transformation in the reach is not simulated.

9.5 MODEL APPLICATION AnnAGNPS is currently utilized in many locations of the U.S. by the Environmental Protection Agency (EPA), NRCS, and others to estimate the impact of best management practices on nonpoint pollution (Yuan et al. 2002). Several studies have been performed to evaluate the performance of AnnAGNPS in predicting runoff, sediment, and nitrogen losses (Baginska et al. 2003; Suttles et al. 2003; Yuan et al. 2001, 2003). Suttles et al. (2003) evaluated AnnAGNPS performance on P simulation in a coastal plain agricultural watershed in Georgia, and Baginska et al. (2003) performed a similar evaluation on a small experimental catchment in the Sydney region of Australia. This section presents the AnnAGNPS application to the Deep Hollow (DH) watershed and evaluates the performance of AnnAGNPS on P simulation using comparisons with measurements from the DH watershed of the Mississippi Delta Management Systems Evaluation Area project (MDMSEA).

9.5.1 STUDY WATERSHED

AND

MONITORING INFORMATION

Data collected at the DH watershed by Yuan et al. (2001) were used to evaluate the performance of the AnnAGNPS P component. The DH watershed, located in Leflore County, Mississippi, is one of three watersheds studied in the MDMSEA, which seeks to develop and assess alternative innovative farming systems for improved


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water quality and ecology in the Mississippi Delta. The main crops grown in the DH watershed are cotton and soybeans. The watershed contains 15 soil series varying in texture from loamy sand to silty clay, but three series cover 80% of the total area (Yuan et al. 2001). Detailed records of agricultural operations including tillage, planting, harvesting, fertilization, cover crop planting, and pesticide usages have been maintained since 1996 (Yuan et al. 2001). A rate of 72.9 kg/ha phosphate fertilizer was applied to cotton fields on October 6, 1998, with equipment that knifes in the material at a depth of 100 mm without further mixing with soil. No fertilizer was applied to soybean fields or during the winter wheat cover crop-growth period. In the period of 1995 to 1996, the U.S. Geological Survey (USGS) installed a gauging station to monitor runoff, sediment, nutrient, and pesticide loadings at one of the inlets to the DH Lake (Yuan et al. 2001). Data collected at this monitoring site were used for this study. The drainage area for the monitored site was 11 ha. Runoff was monitored using a critical flow flume. Both discrete and composite samples were taken during rainfall events for sediment and nutrient analyses. Rainfall was monitored at the flume using a tipping bucket rain gauge. Total P and orthophosphate concentrations were determined for water samples. Total P and orthophosphate mass loads were calculated by using discrete samples when available (Rebich 2004). Loads were also calculated by using composite samples for runoff events when discrete samples were not available (Rebich 2004).

9.5.2 INPUT DATA PREPARATION Established input files for model runoff and sediment evaluation — watershed topography, soil type, climate data, and actual field operations and management (Yuan et al. 2001) — were modified for this study. Yuan et al. (2001) described the development of input information for AnnAGNPS simulations (complete information on input file preparation can be found at the AGNPS website at http://www.ars.usda.gov/ Research/docs.htm?docid=5199). The subwatersheds (AnnAGNPS cells), land use, soil information, and stream network for the monitoring site are presented in Figure 9.3. Based on this input file, fertilizer application was timed according to actual field records. Fertilizer application reference information was set up based on AnnAGNPS guidelines and databases. Detailed soil information was obtained from the Soil Survey Geographic (SSURGO) Database (Natural Resources Conservation Service 2005). SSURGO provides most of the soil parameters needed for AnnAGNPS simulation, such as soil texture, erosive factor, hydraulic properties, pH value, and organic matter. However, information on soil nutrient contents was not available from this database. Determining initial soil nutrient values needed for the model was a very difficult task. Soil testing is one way of gaining soil nutrient values. Location, timing, and method of sampling impact the nutrient values obtained from soil testing (Self and Soltanpour 2004). However, soil testing may not be a feasible way to gain soil nutrient values at a watershed scale because of limited resources. First, a watershed may include thousands of fields. Second, each field has different soil types and field managements. Third, nutrient level may vary from one location to another within a field. Consequently, obtaining representative values for the watershed is challenging.


228


Stream location

41 42

Gauging station 43

32

52

33 62

22

53

51

61 63

23

Cell ID 22 23 32 33 41 42 43 51 52 53 61 62 63

Area (ha.) 0.62 2.2 0.32 0.39 2.85 0.53 0.94 0.53 0.12 0.59 0.81 0.24 1.15

Soil Type 284B Tensas silty clay loam 284B Tensas silty clay loam 284B Tensas silty clay loam 284B Tensas silty clay loam 178A Dundee loam 284B Tensas silty clay loam 284B Tensas silty clay loam 164B Dubbs very fine sandy loam 12A Alligator clay 178A Dundee loam 178A Dundee loam 12A Alligator clay 284B Tensas silty clay loam

Hydrologic Soil Group D D D D C D D B D C C C D

Land Use Soybeans Cotton Soybeans Soybeans Cotton Soybeans Cotton Cotton Cotton Cotton Cotton Soybeans Cotton

FIGURE 9.3 Subwatersheds (cells), land use, soil information, and stream network for the monitoring site. (From Y. Yuan, R.L. Bingner, and R.A. Rebich, Trans. ASAE 44(5), 1183–1190, 2001. With permission.)

Therefore, a sensitivity analysis is needed to identify how initial soil nutrient levels impact the simulation result. Literature searches have found that total P in surface soils ranges from 50 to 1500 mg/kg and decreases with depth (Havlin et al. 1999). Organic P typically varies between 15 and 90% of the total P in soils. Thus, as base values for sensitivity analysis, initial soil organic P content was set to 500 mg/kg for the top layer and 250 mg/kg for the subsequent layers; initial soil inorganic P content was set to 250 mg/kg for all soil layers. Detailed crop information such as crop yield, growth period, and amount of residue produced was imported from the RUSLE crop database. However, plant nutrient uptake information was not available from this database. Determining plant


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nutrient uptake for this study was another challenge because information on plant nutrient uptake is usually not available at a watershed scale. AnnAGNPS requires plant nutrient uptake, which is expressed as a ratio (weight of P/weight of dry matter at harvest), through the crop data section. AnnAGNPS converts the plant P uptake value into a daily value based on crop-growth stage. To gain information on plant nutrient uptake, an intensive literature search was conducted. Research on various cottons in Alabama and Louisiana showed that an average of 58 kg N/ha and 9.1 kg P/ha was removed when seed cotton was harvested under optimum fertilization condition (Bassett et al. 1970; Boquct and Breitenbeck 2000; Mullins and Burmester 1990). Based on the total dry matter production of cotton at harvest (Bassett et al. 1970; Boquct and Breitenbeck 2000; Mullins and Burmester 1990), cotton N uptake was set at 0.017, and cotton P uptake was set at 0.0023 (Boquct and Breitenbeck 2000; Mullins and Burmester 1990). Similarly, soybean N uptake was set at 0.092 and soybean P uptake at 0.0095 (Flannery 1986), whereas winter wheat N uptake was set at 0.022 and winter wheat P uptake at 0.0025 (Baethgen and Alley 1989). Taking these as base values, a sensitivity analysis is also needed to identify how plant P uptake impacts the simulation result.

9.5.3 SENSITIVITY ANALYSIS The purpose of a sensitivity analysis is to investigate input parameters, especially those that are difficult to measure or whose expected effect on model output is unclear (Lane and Ferreira 1980). The purpose of this sensitivity analysis was to identify parameters with effects that were greatest on P losses so that model users could focus their data collection on the more sensitive parameters. In a study of the Water Erosion Prediction Project (WEPP) model sensitivity, Nearing et al. (1990) used a single value to represent sensitivity of the output parameter over the entire range of the input parameter tested. The index described by Equation 9.24 (Nearing et al. 1990) was selected for sensitivity testing of the AnnAGNPS P losses. O2 − O1 O12 S= I 2 − I1 I12

(9.24)

where I1 and I2 are the least and greatest values of input used, respectively, I12 is the average of I1 and I2, O1 and O2 are the output values in response to the two input values, and O12 is the average of O1 and O2. The parameter S represents the ratio of a relative normalized change in output to a normalized change in input. An index of 1 indicates a one-to-one relationship between the input and the output, such that a 1% relative change in the input leads to a 1% relative change in the output. A negative value indicates that input and output are inversely related. The greater the absolute value of the index, the greater the impact that an input parameter has on a particular output. Because it is dimensionless, S provides a basis for comparison among input variables.


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TABLE 9.1 Input Parameters Considered in the Sensitivity Analysis Values Input Parameters

A

B(Base Value)

P Mixing Code P application rate (kg/ha) Initial soil P Organic P content in Inorganic P the top soil layer (mg/kg) Plant P uptake Cotton (ratio) Soybean Winter wheat

YES NA 50 25

NO 72.9 500 250

0.0003 0.0075 0.0005

0.0023 0.0095 0.0025

Note: NA

C NA 353.0 NA NA

0.0043 0.0115 0.0045

= no value selected for sensitivity analysis for that situation.

As noted previously, soil nutrient content and plant nutrient uptake are difficult parameters to measure. Because the impact of fertilizer application on nutrient losses is a public concern, sensitivity analysis was performed for inorganic fertilizer application. The study investigated the sensitivity of the P losses from a watershed to changes in the following input parameters: (1) P mixing code, (2) P application rate, (3) initial P content in the top soil layer, and (4) plant P uptake. Phosphorus mixing code reflects how well the applied fertilizer is mixed within the depth of application. If the P mixing code is set to “YES,” applied fertilizer is well mixed within the depth of application. If the P mixing code is set to “NO,” the entire applied fertilizer remains on the soil surface. Values used for sensitivity analysis are listed in Table 9.1. For the P application rate, the actual amount of fertilizer applied was used as the base value. Base-value selections for initial soil P content and plant P uptake were discussed in Section 9.5.2. Each parameter varied individually within a range as reported in the literature (Baethgen and Alley 1989; Bassett et al. 1970; Boquct and Breitenbeck 2000; Mullins and Burmester 1990). The AnnAGNPS sensitivity analysis simulation was performed over a 4-year period. Annual average P loss was used as the output parameter for the sensitivity analysis. To evaluate the sensitivity of P mixing code (Table 9.2), four AnnAGNPS simulations were performed: two for P application rate B and two for P application rate C. Base values listed in Table 9.1 were used for initial soil P content and plant P uptake for all four simulations. No sensitivity index can be calculated for this analysis because no quantitative number is associated with P mixing code “YES” or “NO.” A percent error, which indicates relative changes of P losses from P mixing code “YES” to “NO,” was calculated (Table 9.2). First, the difference between P losses from P mixing codes “YES” and “NO” was calculated, and then the percent error was calculated as a ratio between the difference and P loss from P mixing code


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231

TABLE 9.2 Sensitivity Analysis for the Effect of Mixing Code on P Losses Annual Average P Losses (kg/ha) P Application Rate B P Mixing Code YES NO Percent error (ratio)

P Application Rate C

Attached P

Dissolved P

Attached P

Dissolved P

1.683 1.680 0.001

15.610 16.514 −0.055

1.707 1.695 0.007

18.713 22.702 −0.176

Notes: Application rate B = 72.9 kg/ha; application rate C = 353.0 kg/ha. Initial soil P content and plant P uptake remain as base values listed in Table 9.1. The percent error is calculated as the ratio of the difference between results from P mixing code “YES” and “NO” and results from P mixing code “NO.”

TABLE 9.3 Sensitivity Indexes, S, of Selected Parameters on P Losses Sensitivity Index (S) for P Mixing Code “YES” Input Parameters

Attached P Dissolved P

Sensitivity Index (S) for P Mixing Code “NO” Attached P

Dissolved P

P application rate (kg/ha)

72.9 353.0

0.01

0.14

0.01

0.24

Initial soil P content in the top soil layer (mg/kg)

Organic P

500 50 250 25

0.54

0.05

0.57

0.05

0.19

0.94

0.22

0.84

Plant P uptake (ratio)

Cotton

–0.003

–0.03

–0.003

–0.03

–0.014

–0.12

–0.013

–0.11

–0.004

–0.03

–0.004

–0.03

Inorganic P

Soybean Winter wheat

0.0003 0.0043 0.0075 0.0115 0.0005 0.0045

“NO.” The impact of P application rate on model predictions (Table 9.3) was performed using P application rates of 72.9 kg/ha and 353 kg/ha, and base values listed in Table 9.1 were used for initial soil P content and plant P uptake. The sensitivity index, S, was calculated using Equation 9.24 for sediment-attached P and dissolved P (Table 9.3). Similarly, the impact of initial soil P content and plant P uptake on model predictions was performed (Table 9.3).


232


Sensitivity analysis results (Table 9.3) indicate that the most sensitive variables of those selected for analysis of P losses were initial soil P contents. This is consistent with previous studies (e.g., Fang et al. 2002; Pote et al. 1996, 1999; Sharpley 1995), which demonstrated that P losses to surface runoff were significantly correlated with soil P levels. Attached, or particulate, P loss is more sensitive to the initial soil organic P than soil inorganic P, but is not sensitive to fertilizer application rate and plant P uptake (Table 9.3). In contrast, dissolved P loss is very sensitive to the initial soil inorganic P, less sensitive to P application rate, and not sensitive to plant P uptake (Table 9.3). Because no sensitivity index can be calculated for the P mixing code, the sensitivity of P losses to P mixing code differs from the other parameters analyzed. It is similar, however, to P application rate in that the dissolved P is sensitive to the P mixing code whereas the attached P is not. The sensitivity of P losses to the P mixing code increases with the increase of P application rate as expected (Table 9.2).

9.5.4 MODEL CALIBRATION

AND

VALIDATION

Since initial soil P content had the greatest impact on P losses among parameters tested for sensitivity (Table 9.3), the initial soil P content was adjusted to give good correspondence with the observed P losses. Initial soil P content selection for calibration was based on many studies of P summarized in Havlin et al. (1999). The first simulation was performed using 100 mg/kg for initial soil organic P content and 15 mg/kg for initial soil inorganic P content, which represents the lower level of soil P content. The second simulation was performed using 500 mg/kg for initial soil organic P content and 250 mg/kg for initial soil inorganic P content, which represents the average level of soil P content. The third simulation was performed using 1000 mg/kg for initial soil organic P content and 500 mg/kg for initial soil inorganic P content, which represents the high level of soil P content. The selection of initial soil P contents involved many trials and errors. The first 27 months were used to calibrate the model, and the last 22 months were used to validate the model. For plant P uptake, base values used for sensitivity analysis (Table 9.1) were chosen because these values were typical values under optimum fertilization. It is assumed that fertilizer applied in this study was the optimum value for crop uptake. AnnAGNPS predicts P loss in dissolved and sediment-attached phases; thus, the predicted total P loss was generated by summing dissolved and sediment-attached P losses (Table 9.4). The predicted and observed P losses listed in Table 9.4 do not include all P losses from the watershed. Although an attempt was made to collect samples for every storm event, some storm events were not sampled due to unforeseen circumstances such as equipment malfunctions. Therefore, comparisons between model simulations and observations were made only when monitoring data were available. Linear regression and Nash-Sutcliffe coefficient of efficiency (Nash and Sutcliffe 1970) were calculated to evaluate the model’s performance (Table 9.4). The Nash-Sutcliffe coefficient of efficiency, E, ranges from −∞ to 1, with 1 indicating the model is a perfect prediction (Nash and Sutcliffe 1970). Calibration results showed that AnnAGNPS underpredicted total P loss and overpredicted dissolved P loss. Calibration demonstrated that increases in either


Rainfalla Year

Month

Runoff (mm)

Sediment Loss (mg/ha)

Dissolved P Loss (g/ha)

Total P Loss (g/ha)

(mm)

Observed

Predicted

Observed

Predicted

Observed

Predicted

Observed

Predicted

1996

October November December

63.8 122.4 127.5

4.8 27.4 70.6

25.6 49.5 71.2

0.02 0.07 0.13

0.15 0.09 0.18

23 67 59

65 196 131

23 115 211

164 254 261

1997

January February(110)b March(170.7)b April May June July August(58)b September(76)b October November December

182.1 81.8 0.0 86.5 152.4 130.3 41.1 49.1 0.0 85.6 56.4 133.3

129.5 70.4 0.0 30.9 82.7 37.6 4.1 0.0 0.0 5.5 13.1 56.8

101.4 45.8 0.0 26.3 70.8 31.4 3.1 5.7 0.0 21.2 16.6 73.9

0.70 0.23 0.00 0.15 1.10 1.24 0.12 0.00 0.00 0.05 0.06 0.72

0.23 0.07 0.00 0.04 0.57 0.33 0.02 0.00 0.00 0.19 0.29 0.37

145 64 0 115 123 117 9 0 0 5 19 41

126 179 0 123 124 124 0 0 0 127 63 178

437 231 0 262 768 925 47 0 0 37 124 314

269 229 0 169 388 291 0 0 0 162 106 265

1998

January(142)b February(98)b March(95)b April May

106.6 90.0 88.7 130.8 111.5

59.3 36.5 37.7 72.6 84.6

69.6 35.3 18.9 48.9 64.3

0.58 0.47 0.18 0.46 0.81

0.51 0.22 0.08 0.43 2.08

39 41 9 101 13

121 55 119 177 63

378 389 86 468 748

174 69 216 305 524

31.0

12.3

7.8

0.29

0.09

27

61

144

86

June


233

(Continued)

Phosphorus Modeling

TABLE 9.4 Monthly Observed Rainfall, Observed and Predicted Runoff, Sediment Loss, Dissolved P, and Total P Losses

234

TABLE 9.4 (CONTINUED) Monthly Observed Rainfall, Observed and Predicted Runoff, Sediment Loss, Dissolved P, and Total P Losses Rainfalla Year

Month

Runoff (mm)

Sediment Loss (mg/ha)

Dissolved P Loss (g/ha)

(mm)

Observed

Predicted

Observed

Predicted

Observed

Predicted

Observed

Predicted

53.6

48.8

0.23

0.42

142

242

255

463

0.0

0.0

0.0

0.00

0.00

0

0

0

0

September(74)b

0.0

0.0

0.0

0.00

0.00

0

0

0

0

27.2

0.0

0.0

0.00

0.00

0

0

0

0

November

141.2

39.9

50.8

0.11

0.70

262

129

394

573

December

205.2

155.0

134.4

0.51

1.51

454

258

1092

1331

1992

2661

7446

6299

October

Total (C)c

= 0.52X + 62.3 R2 = 0.45

Regression (C) c,d

Y

Nash-Sutcliffe Coefficient (C)c

0.35

0.58 250 56

1532 46

1601 73

0.22

45

122

288

270

0.30

313

122

569

314

0.10

0.12

56

51

132

70

2.2

0.00

0.00

0

0

0

0

0.0

0.1

0.05

0.01

0

0

0

0

0.0

0.0

0.0

0.00

0.00

0

0

0

0

40.5

0.0

3.6

0.00

0.00

0

0

0

0

224.3 50.0

214.8 7.2

147.3 8.1

1.68 0.04

1.89 0.04

March

120.4

58.1

45.9

0.24

April

110.0

65.4

47.5

0.19

May

73.7

6.5

7.0

June

29.8

0.0

July

7.1

August


= 0.71X + 38.5 R2 = 0.61

187 6

January February

September

Y


166.1

August(29)b

July

1999

Total P Loss (g/ha)

24.4

0.0

0.7

0.00

0.00

0

0

0

0

November

96.0

1.0

2.7

0.03

0.01

18

65

30

93

December

64.0

11.6

8.9

0.08

0.01

49

123

154

137

January February March April May June July August September October

52.3 47.2 156.0 289.3 34.8 103.6 23.9 2.0 50.5 9.4

9.2 7.8 77.0 213.6 0.0 28.8 0.0 0.0 0.0 0.0

3.4 1.3 50.5 210.0 0.0 26.6 0.0 0.0 0.0 0.0

0.10 0.07 0.12 0.37 0.00 0.28 0.00 0.00 0.00 0.00

0.01 0.01 0.08 0.35 0.00 0.04 0.00 0.00 0.00 0.00

26 25 306 1073 0 99 0 0 0 0

0 0 127 242 0 125 0 0 0 0

116 95 457 1152 0 316 0 0 0 0

0 0 204 592 0 162 0 0 0 0

4019.8

1785.9

1587.1

11.58

11.66

2203

1283

4888

3516

Total (V)e Regression (V)

d,e

Nash-Sutcliffe Coefficient (V)e

Y

= 0.82X + 2.63 R = 0.94 2

0.91

Y

= 0.89X + 0.03 R = 0.51 2

0.22

Y

= 0.24X + 34.2 R = 0.51 2

0.34

Y

Phosphorus Modeling

2000

October

= 0.83X – 24.1 R2 = 0.88 0.85

Notes: Validation period for runoff and sediment was 49 months because no calibration was performed for runoff and sediment simulation. Thus, total, regression and Nash-Sutcliffe Coefficient under runoff and sediment are for the whole simulation period. a

Rainfall reported under rainfall column reflects only the amount of rainfall associated with monitored data. Months when not all storms were successfully monitored for runoff and sediment. The number in parentheses shows total rainfall during that month. c First 27 months of calibration for P. d Y = observed; X = predicted. e Last 22 months of validation for P. b

235


236


organic or inorganic initial soil P content increased both dissolved and sedimentattached P losses. Based on the sensitivity analysis, attached P loss is more sensitive to the initial soil organic P than soil inorganic P. Thus, attempts were made to increase total P loss by increasing the initial soil organic P content, which resulted in an increase in the dissolved P loss. Because dissolved P loss is more sensitive to the initial soil inorganic P than soil organic P, attempts were also made to decrease the dissolved P loss by decreasing the initial soil inorganic P content, which resulted in a decrease in the total P loss. For final calibration simulation, 750 mg/kg of initial soil organic P and 25 mg/kg of initial soil inorganic P were used. Because of the complex and contradictory response of changing initial soil P contents, the regression of monthly predicted dissolved P loss with observed dissolved P loss resulted in an R2 of 0.45, slope of 0.52, and E of 0.35. Regression of monthly predicted total P loss with observed total P loss resulted in an R2 of 0.61, slope of 0.71, and E of 0.58 (Table 9.4). For the validation study, the results of runoff and sediment simulation (Yuan et al. 2001) are also presented in Table 9.4 because P movement depends on runoff and sediment movement. No calibration was performed for runoff and sediment simulation because satisfactory runoff and sediment prediction results were achieved using uncalibrated reference values. Over the 49-month simulation period, AnnAGNPS-predicted runoff was 89% of the observed total runoff, and AnnAGNPS-predicted dissolved P loss was 94% of the observed total dissolved P loss (Table 9.4). However, AnnAGNPSpredicted dissolved P loss was only 58% of the observed dissolved P loss (Table 9.4) for the validation period. AnnAGNPS-predicted monthly runoff matched well with observed monthly runoff, but the predicted monthly dissolved P loss did not match well with the observed monthly dissolved P loss. The regression of the monthly predicted dissolved P loss with the observed dissolved P loss was fair with an R2 of 0.51, slope of 0.24, and E of 0.34, which also indicated a fair model performance in predicting dissolved P loss. A time series comparison of observed and predicted dissolved P loss at the study site (Figure 9.4) shows both overpredictions and underpredictions by AnnAGNPS. AnnAGNPS-predicted total P loss during the validation period was 72% of the observed total P loss (Table 9.4). E was 0.85, which indicated that the model’s performance in predicting monthly total P loss was good. The regression of the monthly predicted total P loss with the observed total P loss resulted in an R2 of 0.88 and a slope of 0.83. Although a time-series comparison of observed and predicted total P loss at the study site (Figure 9.5) shows both overpredictions and underpredictions by AnnAGNPS, observed and predicted total P loss generally coincided better than observed and predicted dissolved P loss (Figure 9.4 and Figure 9.5). Both runoff and sediment predictions impact the total P loss prediction. AnnAGNPS-predicted sediment loss over the 49-month simulation period was 101% of the observed sediment loss (Table 9.4). Sediment-attached P loss during the validation period was 83% of the observed sediment-attached P loss. The observed sediment-attached P loss was calculated as the difference between the total P loss and the dissolved P loss. Simulation results may be improved through a better determination of input parameters. For example, actual field analysis of crop information at harvest may


Phosphorus Modeling

237

Dissolved P loss (g/ha)

1200 Observed

1000

Predicted

800 600 400 200

0 Oct-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99 Sep-99 Mar-00 Sep-00

Time (months) FIGURE 9.4 Time series comparison of observed and predicted dissolved P loss. 1800

Total P loss (g/ha)

1600

Observed

1400 Predicted

1200 1000 800 600 400 200 0 Oct-96

Mar-97

Sep-97

Mar-98

Sep-98

Mar-99

Sep-99

Mar-00

Sep-00

Time (months) FIGURE 9.5 Time series comparison of observed and predicted total P loss.

provide a better estimation of plant P uptake parameters than using literature values. In addition, after calibration of initial soil P contents, additional calibration of plant P uptakes may also improve simulation results. Plant P uptake directly impacts the prediction of dissolved P loss because the crop utilizes dissolved P for growth. Variation of the solution P would impact the P loss to runoff and sediment because the amount of P in the solution pool would impact the transfer among three inorganic pools. Furthermore, uncertainties in soil variables such as content of CaCO3, OC, clay, base saturation, and soil pH value, which were obtained from the SSURGO database, would impact the accuracy of the P availability index calculation. The flow rate between P solution and active pools is determined based on soil moisture, temperature, P availability index, and the amount of P in each pool. As more soluble


238


P moves to the active P pool, less soluble P is available for runoff loss. In many circumstances, the determination of soil- and crop-related input parameters is the most difficult task for watershed simulations.

9.6 MODEL LIMITATIONS The difference in the agreement of P losses may be attributed to limitations in Ann AGNPS simulation of P processes, such as P movement between organic and inorganic pools and movement of inorganic P between solution and active pools and between active and stable pools. Such processes are very complicated and difficult to describe mathematically. AnnAGNPS does not simulate dissolution processes or immobilization and leaching of P. Therefore, it is not appropriate to apply Ann-AGNPS to situations where leaching is an important component. Since the P component simulated in AnnAGNPS is a simplification of P processes in nature, the model predictions may be improved with enhancements within AnnAGNPS that more completely describe the P processes and movements. In addition, enhancement of P in stream processes is also needed if the model is to be applied to large watersheds.

9.7 CONCLUSIONS AnnAGNPS P component was described and evaluated in this chapter. AnnAGNPS models dissolved P in runoff and sediment-attached P resulting from sheet and rill erosion. To simulate P losses, AnnAGNPS maintains daily soil mass balances of P for each computational area (AnnAGNPS cell) and keeps track of both organic and inorganic P mass balances. Major processes considered are residue decomposition and mineralization, fertilizer application, plant uptake, runoff, and erosion losses. Application of AnnAGNPS in the DH watershed demonstrated that AnnAGNPS adequately simulated monthly total P. The simulation of monthly dissolved P was not as satisfactory as monthly total P. The differences between simulated and observed results may be attributed to the simplification of P processes in AnnAGNPS and uncertainties in input selections. Initial soil P contents are the most sensitive parameters of those selected for sensitivity analysis in determining P losses.

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Bingner, R.L. and F.D. Theurer. 2001. AnnAGNPS: estimating sediment yield by particle size for sheet and rill erosion. Proc. 7th Interagency Sediment. Conf. 1:1–7. Bingner, R.L., F.D. Theurer, and Y. Yuan. 2003. AnnAGNPS technical processes. Available at http://www.ars.usda.gov/Research/docs.htm?docid=5199. Boquct, D.J. and G.A. Breitenbeck. 2000. Nitrogen rate effect on partitioning of nitrogen and dry matter by cotton. Crop Sci. 40(6):1685–1693. Cronshey, R.G. and F.D. Theurer. 1998. AnnAGNPS — non-point pollutant loading model. Proc. First Fed. Interagency Hydrol. Model. Conf. 1:9–16. Fang, F., P.L. Brezonik, D.J. Mulla, and L.K. Hatch. 2002. Estimating runoff phosphorous losses from calcareous soils in the Minnesota River Basin. J. Environ. Qual. 31(6):1918–1929. Flannery, R.L. 1986. Plant food uptake in a maximum yield soybean study. Potash and Phosphate Institute, Conway, AR. Freeze R.A. and J.A. Cherry. 1979. Groundwater. Englewood Cliffs, NJ: Prentice Hall. Geter, W.F. and F.D. Theurer. 1998. AnnAGNPS — RUSLE sheet and rill eosion. Proc. First Fed. Interagency Hydrol. Model. Conf. 1:17–24. Havlin, J.L., J.D. Beaton, S.L. Tisdale, and W.L. Nelson. 1999. Soil Fertility and Fertilizers: An Introduction to Nutrient Management, 6th ed. Upper Saddle River, NJ: Prentice Hall. Jenson, M.E., R.D. Burman, and R.G. Allen. 1990. Evapotranspiration and irrigation water requirements. Am. Soc. Civ. Eng. Man. Rep. Eng. Pract. 70. Reston, VA: ASCE. Johnson, G.L., C. Daly, G.H. Taylor, and C.L. Hanson. 2000. Spatial variability and interpolation of stochastic weather simulation model parameters. J. Appl. Meteorol. 39(6):778–796. Jones, C.A., C.V. Cole, A.N. Sharpley, and J.R. Williams. 1984. A simplified soil and plant phosphorus model. I: documentation. Soil Sci. Soc. Am. J. 48(4):800–805. Lane, L.J. and V.A. Ferreira. 1980. Sensitivity analysis. Pp. 113–158 in CREAMS: A FieldScale Model for Chemicals, Runoff, and Erosion from Agricultural Management Systems, W.G. Knisel (Ed.). Washington, D.C.: USDA–SEA. Leonard, R., W.G. Knisel, and D.A. Still. 1987. GLEAMS: Groundwater Loading Effects of Agricultural Management Systems. Trans. ASAE 30(5):1403. Merkel, W.A., D. Woodword, and C.D. Clarke. 1988. Ephemeral gully erosion model. Pp. 315–323 in Modeling of Agricultural, Forest, and Range Hydrology, K.L. Campbell (Ed.). St. Joseph, MI: American Society of Agricultural Engineers. Mullins, G.L. and C.H. Burmester, 1990. Dry matter, nitrogen, phosphorous accumulation by four cotton varieties. Agron. J. 82(4):729–736. Munns, D.N. and R.L. Fox. 1976. The slow reaction which continues after phosphate adsorption: kinetics and equilibrium in some tropical soils. Soil Sci. Soc. Am. J. 40(1):46–51. Nash, J.E. and J.V. Sutcliffe. 1970. River flow forecasting through conceptual models. Part I: a discussion of principles. J. Hydrol. 10(3):282–290. Nearing, M. A., L. Deer-Ascough, and L. M. Laflen. 1990. Sensitivity analysis of the WEPP hillslope profile erosion model. Trans. ASAE 33(3): 839–849. Natural Resources Conservation Service. 2005. Soil Survey Geographic (SSURGO) database, U.S. Department of Agriculture, Washington, D.C. Available at http://www.ncgc. nrcs.usda.gov/products/datasets/ssurgo/index.html. Penman, H.L. 1948. Natural evaporation from open water, bare soil, and grass. Proc. Royal Soc. London A 193:120–145. Pote, D.H., T.C. Daniel, D.J. Nichols, A.N. Sharpley, P.A. Moore, Jr., D.M. Miller, and D.R. Edwards. 1999. Relationship between phosphorous levels in three ultisols and phosphorous concentrations in runoff. J. Environ. Qual. 28(1):170–175.


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Pote, D.H., T.C. Daniel, A.N. Sharpley, P.A. Moore, Jr., D.R. Edwards, and D.J. Nichols. 1996. Relating extractable soil phosphorous to phosphorous losses in runoff. Soil Sci. Soc. Am. J. 60(3):855–859. Rajan, S.S.S. and R.L. Fox. 1972. Phosphate adsorption by soils. 1: influence of time and ionic environment on phosphate adsorption. Commun. Soil. Sci. Plant Anal. 3:493–504. Rebich, R.A. 2004. Suspended sediment and agrochemicals in runoff from agricultural systems in the Mississippi Delta: 1996–2000. Pp. 104–118 in Water Quality Assessment in the Mississippi Delta, Regional Solutions, National Scope, M.T. Nett, M.A. Locke, and D.A. Pennington (Eds.). Washington, D.C: ACS. Renard, K.G., G.R. Foster, G.A. Weesies, D.K. McCool, and D.C. Yoder, coordinators. 1997. Predicting Soil Erosion by Water: A Guide to Conservation Planning with the Revised Universal Soil Loss Equation (RUSLE). Washington, D.C.: U.S. Department of Agriculture, Agriculture Handbook 703. Self, J.R. and P.N. Soltanpour. 2004. Soil sampling, Colorado State University Cooperative Extension. Available at http://www.ext.colostate.edu/pubs/crops/00500.html. Sharpley, A.N. 1982. Prediction of the water extractable phosphorus content of soil following a phosphorus addition. J. Environ. Qual. 11(2):166–170. Sharpley, A.N. 1995. Dependence of runoff phosphorous on extractable soil phosphorous level. J. Environ. Qual. 24(5):920–926. Sharpley, A.N., C.A. Jones, C. Gray, and C.V. Cole. 1984. A simplified soil and plant phosphorus model. II: prediction of labile, organic, and sorbed phosphorus. Soil Sci. Soc. Am. J. 48(4):805–809. Sharpley A.N. and J.R. Williams. 1990. EPIC—Erosion Productivity Impact Calculator. 1: model documentation, Washington, D.C.: U.S. Department of Agriculture, Technical Bulletin 1768. Smedema L.K. and D.W. Rycroft. 1983. Land Drainage. Ithaca, NY: Cornell University Press. Soil Conservation Service. 1985. Section 4: Hydrology in National Engineering Handbook, Washington, D.C.: U.S. Department of Agriculture. Suttles, J.B., G. Vellidis, D. Bosch, R. Lowrance, J.M. Sheridan, and E.L. Usery. 2003. Watershed-scale simulation of sediment and nutrient loads in Georgia coastal plain streams using the Annualized AGNPS model. Trans. ASAE 46(5):1325–1335. Theurer, F.D. and C.D. Clarke. 1991. Wash load component for sediment yield modeling. Proc. 5th Fed. Interagency Sediment Conf. 7:1–8. Theurer, F.D. and R.G. Cronshey. 1998. AnnAGNPS-reach routing processes. Presented at the First Federal Interagency Hydrologic Modeling Conference, April 19–23, Las Vegas, NV. Young, R.A., C.A. Onstad, D.D. Bosch, and W.P. Anderson. 1989. AGNPS: a nonpoint-source pollution model for evaluating agricultural watersheds. J. Soil Water Conserv. 44(2):168–173. Young, R.A., C.A. Onstad, D.D. Bosch, and W.P. Anderson. 1995. AGNPS: an agricultural nonpoint source model. Pp. 1011–1020 in Computer Models of Watershed Hydrology, V.P. Singh (Ed.). Highlands Ranch, CO: Water Resources Publications. Yuan, Y., R.L. Bingner, and R.A. Rebich. 2001. Evaluation of AnnAGNPS on Mississippi Delta MSEA watersheds. Trans. ASAE 44(5):1183–1190. Yuan, Y., S.M.M. Debney, and R.L. Bingner. 2002. Cost effectiveness of agricultural BMPs for sediment reduction in the Mississippi Delta. J. Soil Water Conserv. 57(5):259–267. Yuan, Y., R.L. Bingner, and R.A. Rebich. 2003. Evaluation of AnnAGNPS nitrogen loading in an agricultural watershed. J. Am. Water Resour. Assoc. 39(2):457–466.


10

ANSWERS-2000: A Nonpoint Source Pollution Model for Water, Sediment, and Phosphorus Losses Faycal Bouraoui European Commission–DG Joint Research Centre, Institute for Environment and Sustainability, Ispra, Italy

Theo A. Dillaha Virginia Polytechnic Institute and State University, Blacksburg, VA

CONTENTS 10.1 Introduction .................................................................................................241 10.2 ANSWERS-2000 ........................................................................................242 10.2.1 Underlying Concepts.....................................................................242 10.2.2 Water Cycle ...................................................................................242 10.2.3 Sediment Detachment and Transport........................................... 247 10.2.4 Phosphorus Transformations and Losses......................................248 10.3 Validation and Applications........................................................................252 10.4 Recent ANSWERS Developments .............................................................257 10.5 Conclusions ................................................................................................ 257 References..............................................................................................................258

10.1 INTRODUCTION Nutrients — nitrogen (N) and phosphorus (P) in particular — are indispensable for crop and animal production. However, used in excess they have detrimental effects on the environment and human health. Agriculture is the principal source of nutrient losses worldwide (Novotny 1999). Combating diffuse pollution from agriculture is complicated due to the temporal and spatial lag between the management actions 241


242


taken at the farm level and the environmental response (Schröder et al. 2004). Beside the correct identification and quantification of sources, cost-effective P mitigation requires the delineation of critical P source areas, which contribute disproportionate amounts of P to receiving waters. According to Dickinson et al. (1990), targeting and prioritizing nonpoint source (NPS) pollution control potentially could triple pollutant reduction, is financially attractive, and minimizes the extent of area affected negatively by restrictive land practices. Modeling is essential to the implementation of cost-effective and environmentally friendly management strategies to optimize nutrient use and to reduce their losses in terrestrial ecosystems. Modeling, especially when using a distributed approach, can help prioritize critical source areas at various scales within a catchment and assess the impact of landscape factors on nutrient delivery. The Areal Nonpoint Source Watershed Environmental Response Simulation (ANSWERS) (Beasley et al. 1980, 1982; Dillaha and Beasley 1983) is a watershedscale, distributed-parameter, physically based research model originally developed to simulate the impacts of watershed management practices on runoff and sediment loss. P and N transport components were added to the original event-based version of the model by Storm et al. (1988) and Bennett (1997), respectively. Bouraoui and Dillaha (1996) developed a continuous version of the model, ANSWERS-2000, which includes N and P transformations, transport, and losses. The following sections provide a detailed description of the continuous version of the ANSWERS model, with a focus on water, sediment, and P transport.

10.2 ANSWERS-2000 10.2.1 UNDERLYING CONCEPTS ANSWERS-2000 is a process-oriented, distributed-parameter, continuous simulation model developed to simulate long-term runoff, sediment, N, and P losses in agricultural watersheds as affected by land management strategies such as the implementation of best management practices (BMPs). The ANSWERS model is based on the hypothesis that “at every point within a watershed, relationships exist between water flow rates and those hydrologic parameters which govern them, e.g., rainfall intensity, infiltration, topography, soil type, etc. Furthermore, these flow rates can be utilized in conjunction with appropriate component relationships as the basis for modeling other transportrelated phenomenon such as soil erosion and chemical movement within that watershed” (Beasley and Huggins 1981, p. 4). ANSWERS-2000 represents a watershed as a matrix of square uniformly sized elements, where an element is defined as a homogeneous area within which all hydrologically significant parameters (e.g., soil properties, surface condition, vegetation, topography) are similar. Spatial variability is represented by allowing parameter values to vary in an unrestricted manner between elements.

10.2.2 WATER CYCLE Simulated hydrologic processes include interception, surface retention, infiltration, surface runoff, evapotranspiration (ET), and water movement through the root zone. The model maintains a daily water balance as follows: SWd+1 = SWd + P − ( R + DR + TD + AET ) © 2007 by Taylor & Francis Group, LLC

(10.1)

Answers-2000: A Nonpoint Source Pollution Model

243

where SW represents the soil water content (cm) for the day (d), P is precipitation (cm), R represents surface runoff (cm), DR is the drainage below the root zone (cm), TD is tile drainage (cm), and AET is evapotranspiration (cm). Drainage and evapotranspiration are represented as one-dimensional processes, whereas runoff and tile drainage are represented as two-dimensional processes. The model uses a dual time step: a daily time step on days without rainfall, and a 60-sec time step during periods of rainfall (Figure 10.1). The rainfall excess (i.e., rainfall minus interception) is subject to infiltration and runoff for each time step and element. Infiltration starts once the interception volume is filled. Interception volume is dependent on the plant type and stage of growth. Infiltration is simulated using the Green-Ampt (Green and Ampt 1911) equation. It assumes (1) a step water retention function describing the relation between soil water pressure, y (cm), and volumetric water content, q (cm3 cm−3); and (2) a step hydraulic conductivity function K (cm/h). The infiltration process is represented as a saturated wetting front advancing down through the soil profile with q = qs and K = Ks (where Ks is the hydraulic conductivity for volumetric water content at natural saturation qs) behind the wetting front and q = q0 (initial soil moisture content) and K = 0 ahead of the wetting front. The basic Green-Ampt equation to compute cumulative infiltration is   F Ks t = F − (θ s − θ 0 ) ψ f ln 1 +  (θ s − θ 0 ) ψ f  

(10.2)

where t is the time (h), F is the cumulative infiltration (cm), and yf is the wetting front matric potential (cm). The wetting front matric potential represents the suction gradient pulling the water downward from the saturated zone to the unsaturated zone. The wetting front matric potential is assumed to be invariant and is calculated in ANSWERS-2000 using the pedotransfer function given by Rawls and Brakensiek (1985):

ψ f = ex

(10.3)

where x is given by x = 6.531 − 7.33 η + 15.8 CL 2 + 3.81 η2 + 3.40 CL SA − 4.98 SA η + 16.1 SA 2 η2 + 16.0 CL 2 η2 − 14.0 SA 2 CL

(10.4)

− 34.8 CL 2 η − 8.0 SA 2 η where CL is the clay fraction (%), SA is the sand fraction (%), and h is the porosity (%). The hydraulic conductivity is also computed by default using the pedotransfer developed by Rawls and Brakensiek (1985): 3 (η − θ r )  ρ  Ks = 0.0002 C   (1 − η)2  θ r  2


2

(10.5)

244


Beginning simulation DAY = 1

Rainfall excess>0

No

Evapotranspiration

Yes t=0 N & P uptake and transformation Infiltration and runoff submodels

No

t = t + 60s

Soil moisture> field capacity

Runoff> 0 Yes

Yes Soluble P losses

Water percolation

Sediment submodel

Sediment-bound P losses

No

Runoff ended?

DAY = DAY +1

Yes

No

Simulation period over? Yes Output summary

FIGURE 10.1 Flowchart for the ANSWERS-2000 model.


No


245

where r represents the soil bulk density (g cm−3), qr is the residual water (cm), and C is the soil texture coefficient, which is given by C = − 0.17 + 0.181 CL − 0.00000069 CL 2 SA 2 − 0.00000041 SA 2 SI 2 + 0.000118 SA 2 ρ 2 + 0.00069 CL 2 ρ 2 + 0.000049 SA 2 CL

(10.6)

− 0.000085 SI CL 2 where SI is the silt fraction (%). However, if measured values of the Green-Ampt parameters are available they should be used directly in the model. The infiltration rate f (cm h−1) is obtained by differentiating Equation 10.2 with respect to time:   F f = Ks ln 1 +  (θ s − θ 0 ) ψ f  

(10.7)

ANSWERS-2000 takes into account ponding under unsteady rainfall as presented by Chu (1978). Once the infiltration rate is determined, runoff is routed to the watershed outlet using Manning’s equation. Every square element of the discretized watershed acts as an overland flow plane with a computed slope and slope direction. For overland flow, the hydraulic radius is taken equal to the average detention depth. The slope direction is used to apportion runoff between the adjacent receiving cells. Channel elements collect flow from overland flow elements and route the runoff to the watershed outlet using Manning’s equation. Channel elements are described in terms of their slope, width, and Manning’s roughness coefficient. All water draining below the root zone is added to a single reservoir representing a shallow aquifer. Groundwater contribution to surface water is represented as a fraction of the reservoir (shallow aquifer) being added to each channel element. Once a runoff event has ended, the internal soil moisture redistribution takes place. If soil moisture content exceeds field capacity, there is potential for percolation. The rate of percolation depends on the amount of water in excess of field capacity. Travel time of percolating water through the soil matrix is regulated by the hydraulic conductivity. This conductivity varies from near zero when the soil is at field capacity to a maximum value when the soil is at saturation and is expressed by Savabi et al. (1989) as

θ Kad = Ks    η


   −2.65      θd    log     η   

(10.8)

246


where Kad is the adjusted hydraulic conductivity (cm h−1) and qd is the field-capacity water content (cm3 cm−3). Travel time through a particular soil layer (TT, h) is computed using a linear storage equation:  θ − θd  TT =   di  Kad 

(10.9)

where di is the depth of the specific layer (cm). Percolation during a specific time step is determined using an exponential function: ( − ∆t )   DR = (θ − θ d ) d i 1 − e TT   

(10.10)

where ∆t is the time step (h) and DR is the percolation (cm) during ∆t. Evapotranspiration is determined based on Ritchie’s (1972) equation. Potential ET is computed by E0 =

0.504 H 0 ∆ γ+∆

(10.11)

where E0 is the potential evapotranspiration (cm day−1), H0 is the net solar radiation (l), ∆ represents the slope of the saturation vapor pressure curve at the mean air temperature(mbar °C−1), and g is psychrometric constant (mbar °C−1). The net solar radiation is obtained from the daily solar radiation and the albedo. The leaf area index, LAI, is used to split the potential ET into potential soil evaporation and potential plant transpiration. Soil evaporation is assumed to take place in two different stages. During the first stage, soil evaporation is energy limited and occurs at a rate equal to the potential evaporation rate. The potential soil evaporation is computed by Es = E0 e( −0.4 LAI )

(10.12)

where Es is the potential soil evaporation (cm). The upper limit of the first stage evaporation, U (cm), is determined by U = 0.9 (α s − 3)0.42

(10.13)

where a s is the soil evaporation parameter (cm day−0.5). The soil evaporation parameter depends on soil water transmission characteristics. When the cumulative soil evaporation exceeds the upper limit of the first stage (U ), the second stage begins. The second stage begins when the surface starts to dry and water from within the soil starts to evaporate. During the second stage, also called the falling rate stage, the soil evaporation rate is given by

(

Es 0 = α s t 0.5 − (t − 1)0.5


)

(10.14)


247

where Es0 is the soil evaporation rate (cm day−1) for day t, and t is the time (days) since stage-two evaporation started. The potential plant transpiration, Ep0, is given by Ep 0 =

E0 LAI 3

Ep 0 = E0 − Es

0 ≤ LAI ≤ 3

(10.15)

LAI > 3

If soil moisture is a limiting factor, plant transpiration is reduced accordingly. Plant growth is represented by a varying LAI and by simulating root growth. Ten values of the LAI are input to the model for each crop for 10 stages of plant growth. A linear interpolation is made daily between the different values. Root development is simulated using a sin function given by Borg and Williams (1986) as    D  Rd = Rdx  0.5 + 0.5 sin  3.03  p  − 1.47   D      m 

(10.16)

where Rd is the root depth (cm), Rdx is the maximum root depth (cm), Dm is the number of days to reach maturity, and Dp is the number of days after planting.

10.2.3 SEDIMENT DETACHMENT

AND

TRANSPORT

Soil particles can be detached by rainfall impact and from shear stress and lift forces generated by overland flow. Detachment of soil particles by raindrop impact depends on the kinetic energy of the raindrops and is calculated as described by Meyer and Wischmeier (1969): DETR = CE 3 CDR SKDR Ai R 2

(10.17)

where DETR (kg s−1) is the rainfall detachment rate, CDR and SKDR are the cropping and management and the soil erosivity factors from the Universal Soil Loss Equation (USLE) (Wischmeier and Smith 1978), Ai (m2) is the area increment, R (m s−1) is the rainfall intensity, and CE3 is a calibration constant. The detachment of soil particles by overland flow was described by Meyer and Wischmeier (1969) and modified by Foster (1976) as follows: DETF = CE 4 CDR SKDR Ai SL Qw

(10.18)

where DETF (kg s−1) is overland flow detachment rate, SL is the slope steepness (%), Qw is the flow per unit width (m2 s−1), and CE4 is a calibration coefficient. Values of 6.54 106 and 52.5 were proposed for CE3 and CE4, respectively, by Bouraoui and Dillaha (1996). The model allows seasonal variations of the cropping and management factor. It is varied from a maximum value at planting day to a minimum value when plants reach maturity. The CDR factor is assumed to vary linearly between these two values based on the LAI. The soil erosivity factor is assumed constant and does not vary with time.


248


Detachment and transport are calculated for various particle classes according to the particle size distribution of the sediments. Yalin’s (1963) equations as extended by Mantz (1977) for small particles are used to calculate actual transport capacity for each particle. The transport capacity (TC, kg s−1-m−1) is expressed as TC = 146 SL Qw 0.5

for Qw ≤ 0.046

TC = 14600 SL Qw 25

for Qw > 0.046

(10.19)

Sediments are transported both as suspended and bedload. It is assumed that particles of diameter less than 10 µm do not deposit due to the extremely low fall velocity (Dillaha and Beasley 1983). The fraction of larger particles depositing in case of transport capacity deficit is a function of the fall velocity of discrete particles in water:  A  REi = min  FVi ; 1 Q  

(10.20)

where RE is the fraction of particles larger than 10 µm in class i that are deposited, FVi is the fall velocity for particle i (m s−1), A is the surface area (m2) of an overland flow or channel element, and Q is the surface runoff (m3 s−1). The actual transport rate, TF (g s−1), for each particle class in a mixture is calculated using Yalin’s equation: TFi = Pei Sgi ρw g d i V

(10.21)

where rw is the density of water (g cm−3), g is the acceleration due to gravity (m s−2), d is the equivalent sand diameter of particle i (cm), V is the shear velocity, Sg is the particle specific gravity (g cm−3), and Pe is computed as follows:   ln(1 + σ i )   δ i Pei =  0.635 δ i 1 −   σ i   n  δi

∑

(10.22)

1

where s (a function of Sg and d) represents the dimensionless excess of tractive force, which is a function of critical shear stress. A more detailed description of the ANSWERS-2000 erosion module is given by Dillaha and Beasley (1983) and Dillaha (1981). Some basic assumptions of the model are that flow detachment occurs only if there is excess transport capacity and that flow detachment and deposition can not occur simultaneously for the same particle class.

10.2.4 PHOSPHORUS TRANSFORMATIONS

AND

LOSSES

ANSWERS-2000 simulates the transformations of N and P following the approach described by Knisel et al. (1993). The following section focuses on P transformation



Stable Mineral P

249

Active Mineral P

Uptake Plants

Labile P

Fertilizers

Mineralization Residue

Active Organic P

FIGURE 10.2 Flowchart of the P cycle simulated in the ANSWERS-2000 model.

and fate. Details on the nitrogen transport portion of the model are available in Bennett (1997). A flowchart of the P cycle considered in ANSWERS-2000 is given in Figure 10.2. The model considers the following soil P compartments: active organic P, labile P, active mineral P, a stable (inactive) mineral P, and a stable (fresh) organic P pool. The ratio of potentially mineralizable P to total organic P is assumed to be identical to the ratio of potentially mineralizable N to soil organic N (Knisel et al. 1993). Mineralization rate is determined as MINP = CMN SORGP

(

POTMIN SWFA TEMPFA POTMIN + SOILN

)

0.5

(10.23)

where MINP is the mineralization rate (kg ha−1day−1), SORGP is the soil organic P content (kg ha−1), CMN is a mineralization constant (0.0003 day−1) (Sharpley and Williams 1990), and SWFA and TEMPFA are unitless soil water and temperature correction factors, respectively. The mineralized P is added to the pool of labile P. The active and stable inorganic P pools are dynamic, and at equilibrium the stable mineral P pool is assumed to be four times the active mineral P pool (Sharpley and Williams 1990). Dissolved inorganic P losses are a function of the labile P content in the topsoil and runoff. Due to the large adsorptivity of P and since ANSWERS2000 does not consider preferential flow, the P losses through percolation are neglected. The amount of dissolved inorganic P potentially lost is given by PSOL =

0.1 PLAB 1 + 0.1 K phos

(10.24)

where PSOL represents dissolved inorganic P (kg), PLAB is labile P (kg), and Kphos is the partition coefficient for P, which is a function of the clay content of the soil (Knisel et al. 1993): K phos = 100 + 2.5 CL


(10.25)

250


Crop uptake of P is based on a supply-and-demand approach. Only dissolved labile P is available for crop uptake. The potential supply of dissolved labile P is expressed as the product of the concentration of dissolved labile P and plant transpiration. The cumulative P demand on day i, TDMP, (kg ha−1) is based on the plant growth (PGRT): TDMPi = PGRT YP DMY

CP 100

(10.26)

where PGRT corresponds to the ratio between the actual LAI and the maximum LAI, YP is the yield potential (kg ha−1), DMY is the ratio of total dry matter to harvestable yield, and CP is the crop P concentration (% crop biomass). The daily demand is then taken as the difference in cumulative demand between two consecutive days. If the demand is greater than the supply, then the actual uptake is limited to the supply; otherwise the uptake is not limited and is met fully. The P losses via particulate or dissolved form occur only during a runoff producing rainfall event. Sediment-bound P transport is derived from the sediment transport submodel and is based on the conservation of mass written as ( j+1) ∆t

Pj+1

∫

dP =

∫

( j+1) ∆t

Pi dt −

j∆t

Pj

∫

Po dt

(10.27a)

j∆t

or in the discrete form as Pj+1 − Pj =

Pi j + Pi j+1 2

∆t −

Po j + Po j+1 2

∆t

(10.27b)

where Pi is the sediment-bound P inflow (kg s−1), Po is the sediment-bound P outflow (kg s−1), P is the sediment-bound P in transit (kg), and the subscript j refers to the jth time interval. Equation 10.27b can be rearranged as    2 Pj+1 2P + Po j+1  = Pi j + Pi j+1 +  j − Po j      ∆t  ∆t

(

)

(10.28)

To compute the sediment outflow at any time step, a storage outflow relationship is required. At any time step, if the discharge is equal to zero, all the sediment is deposited; no P outflow occurs. The input of sediment-bound P comes from adjacent cells or from within the cell with newly detached sediment. The amount of sedimentbound P added from within the cell is expressed as PCELL = P0 SEDNEW

(10.29)

where PCELL is the newly generated sediment-bound P (kg s −1), SEDNEW is newly generated sediment (kg s−1), and P0 is the concentration of P in the cell



251

soil (kg kg−1-soil). The sediment-bound nutrient inflow at the end of the time increment, Pij+1, is determined by Pi j+1 = PI + PCELL

(10.30)

where PI represents the inflow from adjacent cells. The outflow of sediment-bound P is determined as the concentration of sediment-bound P in transit multiplied by the runoff volume, Q, which can be expressed as Po j+1 =

Pj+1 S

(10.31)

Q

where S represents the storage volume at the end of the time increment. The value of Poj+1 is then replaced into Equation 10.28 to determine the value of the sedimentbound P in storage and then to calculate the outflow of sediment-bound P for each time step. The initial concentration of sediment-bound P is distributed among the different particle sizes in proportion to the specific surface areas of the particle size classes: Xi = X0

SSAi SSA0

(10.32)

where Xi is the P content of soil particle size class i (kg kg−1-particle size class i ha−1), X0 is the nutrient content of the soil (kg kg−1-soil), SSA0 is specific surface area of the original soil (m2 kg−1-soil), and SSAi represents specific surface area of the particle size class i (m2 kg−1-soil). For each time step, the amount of sediment-bound P leaving a particular cell is determined by summing the P content of all particles leaving the cell as follows: n

X phos =

∑ X SED i

i

(10.33)

i =1

where Xphos is the amount of P lost (kg ha−1), SEDi is the amount of particle size class i lost (kg ha−1), and n represents the number of particle size classes. ANSWERS2000 can consider up to 10 different particle size classes. The dissolved inorganic P component is also based on a mass balance approach. The dissolved inorganic P present in runoff water is composed of dissolved P inflow from adjacent cells and dissolved P from within the cell. During a runoff event, it is assumed that there is an instantaneous equilibrium between the dissolved inorganic P present in the top 10 mm of the soil profile —called effective depth of interaction (EDI) — and the total water present, transiting or in storage in the EDI. No transformations of the P besides deposition are assumed to occur in the stream.


252


10.3 VALIDATION AND APPLICATIONS The model uses cell size up to 1 ha and is adapted for small watersheds (≤300 km2). Basic input requirements for ANSWERS-2000 are daily climate data, breakpoint precipitation (i.e., rainfall intensity) records, soil textural composition, organic matter content, and land use and land management data on tillage, fertilization, planting and harvest dates, and initial content of the labile pool. The stable and active organic and mineral P pools are initialized as detailed by Knisel et al. (1993) based on the organic matter content. ANSWERS was applied on two small plots: P2(1.4 ha) and P4(1.3ha) located in the Southern Piedmont Conservation Research Center near Watkinsville, Georgia. The site is characterized by a gently rolling relief with annual temperatures ranging from 14 to 18°C and annual precipitation from 1150 to 1400 mm. Soils in the P2 watershed consist of Cecil sandy loam (62%), Cecil sandy clay loam (28%) and Cecil loam (10%) (Figure 10.3). The P4 watershed soils consist of Cecil sandy clay loam (73%) and Cecil sandy loam (27%). The model was validated using a 3-year time series of climatic data. The management schemes for both plots are presented in Table 10.1, and ANSWERS-2000 was parameterized accordingly. To evaluate the potential use of the model on ungauged watersheds, no attempt was made to calibrate the model during this verification study. Soil texture, management practices, land use, and fertilizer applications (see Table 10.1) and other parameters necessary to initialize the model were taken from Smith et al. (1978). 1

2

3

4

5

6

7

8

9

1 2

Cecil loam

3

Cecil sandy loam

4 Cecil sandy clay loam

5 6

Overland flow direction

7

Channel flow direction

8 9 10 11 12 13

12.5 m

FIGURE 10.3 Soil map and discretization scheme for the P2 plot.



253

TABLE 10.1 Land-Management Schemes for the P2 and P4 Plots Date

P2

04-25-1974

Watersheds tilled with chisel (20 cm deep) Fertilizer application and incorporation (15 cm) NH4-N 38 kg PO4-P 33 kg Fertilizer application and incorporation (15 cm) NH4-N 107 kg Harvest corn

04-29-1974 06-11-1974 09-16-1974 10-19-1974 04-15-1975 04-29-1974 05-14-1975 05-21-1974 06-25-1975 10-03-1975 10-30-1975

P4

NH4-N 38 kg PO4-P 33 kg NH4-N 100 kg Plant rye Harvest rye

Fertilizer application and incorporation (15 cm) NH4-N 11kg, NO3-N 11 kg PO4-P 21 kg

Plow and plant corn Fertilizer application and incorporation (15 cm) NH4-N 112 kg Harvest corn

NH4-N 11kg, NO3-N 11 kg PO4-P 31 kg Plow and plant corn

NH4-N 112 kg Harvest corn

The discretization scheme for P2 (1.4 ha) is shown in Figure 10.3. The time series for the runoff and the dissolved inorganic P predictions are shown in Figure 10.4 for the P2 watershed, and the overall performance of the model is summarized in Table 10.2. The uncalibrated model predicted mean monthly runoff, sediment, and dissolved inorganic P losses extremely well, as shown in Table 10.2. Predicted runoff, sediment, and dissolved inorganic P losses were within 44, 40, and 37% of measured losses, respectively. Measured losses of sediment-bound P loss were not available. The model performed better on the P2 watershed than on the P4 watershed probably due to the poor representation of the grassed waterways characterizing the P4 watershed. However, no attempt was made to calibrate the model at this stage. The model was also calibrated and validated on the 1153 ha Owl Run watershed in Virginia. About 70% of the watershed is dedicated to agriculture, with corn (12.8%), hay (20.1%), and pasture (15.9%) as major land uses. The Owl Run watershed has a humid continental climate with an average annual precipitation of 1040 mm. The watershed soils are mainly silt loam with moderate permeability. There is no base flow during dry periods at any of the monitoring stations. Meteorological variables are collected at a main weather station in the watershed, and precipitation data is collected at seven additional sites within or bounding the watershed. Additional information on the Owl Run monitoring project and systems are reported by Mostaghimi et al. (1989). The model was run for a full corn growing season for a period of five months, from May 1991 to September 1991, during which five major runoff-producing storms occurred. Information on the parameterization of the model is given by Bouraoui and Dillaha (1996). Over the five-month simulation period,


254


180

2

160

4

140

6

120

8

100

10

80

12

60

14

40

16

20

18

PO4-P (g)

0

0

runoff (cm)

200

Measured PO4-P Predicted PO4-P Measured Runoff Predicted Runoff

20 AY

M

74

G

74

V O

AU

74

EB

75

AY

F

N

75 AU

M

G

75

FIGURE 10.4 Monthly time series for the measured and predicted runoff and PO4-P for the P2 watershed.

cumulative predicted runoff, sediment, and dissolved inorganic P losses were within 7, 12, and 39% of observed values, respectively (Table 10.3). In general, the model accurately predicted losses during the largest storms; however, it underestimated the losses during smaller events (Bouraoui and Dillaha 2000). The poor performance during the smaller events was believed to be related to the underprediction of the runoff volumes during smaller storms. The model was then used on the 212 ha Nomini Creek watershed in Virginia to test the impact of changing from conventional to conservation tillage. Soils are

TABLE 10.2 Monthly Mean Measured, Predicted, and Coefficient of Efficiency for the Runoff, Sediment, and Dissolved Inorganic P for the P2 and P4 Plots Validation P2 plot Runoff (cm) Mean measured Mean predicted Efficiencya

1.74 1.80 0.78

a

Sediment Load (kg) 463.8 276.1 0.54

P4 plot PO4-P Load (kg)

Runoff (cm)

Sediment Load (kg)

PO4-P Load (kg)

25.8 28.3 0.36

1.30 1.87 0.21

115.8 119.7 0.26

27.48 17.2 –0.11

Represents the coefficient of efficiency as defined by J.E. Nash and J.V. Sutcliffe, J. Hydrol. 10, 282–290, 1970.



255

TABLE 10.3 Observed and Predicted Cumulative Runoff, Sediment, and Inorganic P Losses from the Owl Run Watershed Runoff (mm) Observed Predicted % Difference a a

Sediment (kg)

31.0 28.7 –7

PO4-P (kg)

90,159 101,049 +12

339 208 –39

100 × (Predicted – Observed)/Observed

mainly sandy loam with moderate permeability. Major crops in the watershed include corn, soybeans, wheat, and barley. The climate is humid continental with an average annual precipitation of 1000 mm. A first run (Scenario 1) was performed with all the cropland in conventional tillage to identify the areas with the highest sediment losses. Validation of the hydrology is shown in Figure 10.5 for a storm that occurred on May 26, 1989. The distributions of sediment losses (gains) for that storm are illustrated in Figure 10.6. Five additional scenarios were then developed to simulate increasing levels of conservation tillage. Scenarios 2, 3, 4, and 6 had 8.5, 21.5, 32.7, and 100% of the cropland in conservation tillage, respectively. Scenario 5 had 32.7% of the cropland in conservation tillage like Scenario 4; however, the location of the conservation tillage fields was different. As the percentage of conservation tillage increased, conservation tillage was expanded to fields with progressively lower

500

1.2

1

measured runoff predicted runoff predicted PO4-P loss

450 400 350 300

0.6

250 200

0.4

PO4-P (g)

Runoff (mm)

0.8

150 100

0.2

50 0 200

0 400

600

800

1000 1200 Time (mn)

1400

1600

1800

FIGURE 10.5 Predicted and measured runoff for the May 26, 1989, rainfall event for the Nomini Creek watershed. The dashed line represents the PO4-P losses occurring during the storm.


256


sed_loss Value -835 - -750 -750 - -600 -600 - -450 -450 - -300 -300 - -150 -150 - 0 0 -150 150 - 300 300 - 450

FIGURE 10.6 Sediment loss (kg) distribution over the Nomini Creek watershed for the May 26, 1989, storm. Negative values indicate a net loss, whereas positive values refer to a net gain of sediments.

sediment yields. The unit reduction (i.e., percentage reduction in runoff, sediment, and total P at the watershed outlet per unit percentage of the watershed converted to conservation tillage) for runoff, sediment, and total P is illustrated in Figure 10.7. The conversion from conventional to conservation tillage did not have a major impact on runoff. Converting all cropland from conventional to conservation tillage reduced sediment losses by about 55%. The most efficient unit reductions were obtained by targeting the change in tillage to areas responsible for the most sediment losses. The estimated cost of reduction is around $1.58 t−1 year−1 for Scenario 1, whereas it is about three times higher for Scenario 6 (Bouraoui and Dillaha 2000). A similar behavior is observed for total P — obtained by summing dissolved and particulate P losses. Scenario 2 with the highest degree of targeting was the most effective in reducing P, with a reduction cost of $3.54 kg−1 yr−1. This scenario was 47% more cost effective than the no-targeting Scenario 6.



500

Runoff Sediment Total P

400

Unit reduction (%)

257

300 200 100 0 Scenario 2

Scenario 3

Scenario 4

Scenario 5

Scenario 6

FIGURE 10.7 Unit reduction as a result of converting cropland from conventional to conservation tillage on the Nomini Creek watershed.

10.4 RECENT ANSWERS DEVELOPMENTS As of the writing of this chapter in the fall 2004, ANSWERS is undergoing a major revision. The current and evolving versions of the model are equipped with an ArcView interface and expert system, QUESTIONS (Veith et al. 2002), which assists the user in creating required model data files and in displaying model output. In addition, new sediment detachment, channel erosion, detention facility, impervious land use and channel, and atmospheric deposition and wash-off submodels have been added to the model. The new sediment detachment and channel erosion submodels, developed by Byne (2000), are based on unit stream power and critical shear theory used in the Water Erosion Prediction Project (WEPP) model (Alberts et al. 1989). The submodels for impervious land uses and channels and atmospheric deposition were developed by Zeckoski (2002). An additional version of the model is under development that better simulates moisture movement in a multilayered unsaturated zone and pesticide fate in surface and subsurface flow. Procedures to link ANSWERS subsurface flow components with MODFLOW (Harbough et al. 2000) and MT3DMS (Zheng and Wang 1999) to simulate groundwater and pesticide movement in the saturated zone are ongoing. (Additional information and downloads of the ANSWERS model are available at http://dillaha.bse.vt.edu/answers.)

10.5 CONCLUSIONS The ANSWERS–2000 was developed to simulate water, erosion, and N and P exports from agricultural watersheds. The model is spatially distributed, making it a powerful tool for localizing critical areas, siting BMPs, and evaluating the effectiveness of local management practices such as filter strips, riparian buffer, and detention ponds. In addition, the model can track source and sink areas of sediments and P in view of an integrated management of P at the field and watershed level. The model is based on a dual time step: minutes during a storm event and daily in-between storms.


258


The model can thus produce on a time-continuous basis daily and subdaily hydrograph and pollutograph (i.e., sediment bound and dissolved P). The model is adapted to small-scale agricultural watersheds (up to 300 km2); however, the model should not be applied in areas where the contribution of P from the groundwater is significant.

REFERENCES Alberts, E.E. et al. 1989. USDA water erosion prediction project, hillslope profile and watershed model documentation. U.S. Department of Agriculture, NSERL Report 10, Agricultural Research Service, Purdue University, West Lafayette, IN. Beasley, D.B. and L.F. Huggins. 1981. ANSWERS (Areal Nonpoint Source Watershed Environment Response Simulation) User’s Manual. West Lafayette, IN: Department of Agricultural Engineering, Purdue University. Beasley, D.B., L.F. Huggins, and E.J. Monke. 1980. ANSWERS: a model for watershed planning. Trans. ASAE 23(4):938–944. Beasley, D. B., L.F. Huggins, and E.J. Monke. 1982. Modeling sediment yield from agricultural watersheds. J. Soil Water Cons. 37(2):113–117. Bennett, M.R. 1997. Modeling nitrogen transport with the ANSWERS model. M.S. thesis, Virginia Polytechnic Institute and State University, Blacksburg. Borg, H. and D.W. Williams. 1986. Depth development of roots with time: an empirical description. Trans. ASAE 29(1):194–197. Bouraoui, F. and T.A. Dillaha. 1996. ANSWERS-2000: runoff and sediment transport model. J. Environ. Eng. ASCE 126(6):493–502. Bouraoui, F. and T.A. Dillaha. 2000. Nonpoint source nutrient transport model. J. Environ. Eng, ASCE 26(11):1045–1055. Byne, F.W. 2000. Predicting sediment detachment and channel scour in the process-based planning model ANSWERS-2000. M.S. thesis, Virginia Polytechnic Institute and State University, Blacksburg. Chu, S.T. 1978. Infiltration during unsteady rain. Water Resour. Res. 14(3):461–466. Dickinson, W.T., R.P. Rudra, and G.J. Wall. 1990. Targeting remedial measures to control nonpoint source pollution. Water Resour. Bull. 26(3):499–507. Dillaha, T.A. 1981. Modeling the particle size distribution of eroded sediments during shallow overland flow. Ph.D. dissertation. Purdue University, West Lafayette, IN. Dillaha, T.A. and D.B. Beasley. 1983. Distributed parameter modeling of sediment movement and particle size distributions. Trans. ASAE 26(6):1766–1772, 1777. Foster, G.R. 1976. Sedimentation, general. Proc. Natl. Symp. Urban Hydrol. Hydraul. Sediment Control University of Kentucky. Lexington, KY. Pp. 129–138. Green, W.H. and G. Ampt. 1911. Studies of soil physics. Part I: the flow of air and water through soils. J. Agric. Sci. 4:1–24. Harbough, A.W. et al. 2000. MODFLOW-2000: The U.S. Geological Survey Modular GroundWater Model — User Guide to Modularization Concepts and the Ground-Water Flow Process. U.S. Geological Survey, Open-File Report Reston, VA. Knisel, W.G., R.A. Leonard, and F.M. Davis. 1993. The GLEAMS model plant nutrient component. Part I: model documentation. U.S. Department of Agriculture Agricultural Research Service, Tifton, GA. Mantz, P.A., 1977. Incipient transport of fine grains and flakes by fluids-extended Shield’s diagram, J. Hydraul. Div., Proc. ASAE 103(HY6):601–615.



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Meyer, L.D. and W.H. Wischmeier. 1969. Mathematical simulation of the processes of soil erosion by water. Trans. ASAE 12(6):754–758. Mostaghimi, S. et al. 1989. Watershed/water quality monitoring for evaluating BMP effectiveness — Owl Run watershed: Pre-BMP evaluation. Department of Conservation and Historic Resources, Report N-P1-8811, Division of Soil and Water Conservation, Richmond, VA. Nash, J.E. and J.V. Sutcliffe. 1970. River flow forecasting through conceptual models. Part I: a discussion of principles. J. Hydrol. 10:282–290. Novotny, V. 1999. Diffuse pollution from agriculture: a worldwide outlook. Water Sci. Technol. 39(3):1–13. Rawls, W.J. and D.L. Brakensiek. 1985. Prediction of soil water properties for hydrologic modeling. Pp. 293–299 in Proceedings of Watershed Management in the Eighties, E.B. Jones and T.J. Ward (Eds.). Denver, CO: American Society of Civil Engineers. Ritchie, J.T. 1972. A model for predicting evapotranspiration from a row crop with incomplete cover. Water Resour. Res. 8(5):1204–1213. Savabi, M.R. et al. 1995. USDA-water erosion prediction project, hillslope profile and watershed model documentation. U.S. Department of Agriculture, NSERL Report 10, Agricultural Research Service, Purdue University, West Lafayette, IN. Schröder, J.J. et al. 2004. The effects of nutrient losses from agriculture on ground and surface water quality: the position of science in developing indicators for regulation. Environ. Sci. Policy 7:15–23. Sharpley, A.N. and J.R. Williams. 1990. EPIC — Erosion/Productivity Impact Calculator. 1: model documentation. U.S. Department of Agriculture, Technical Bulletin 1768, Washington, D.C. Smith, C.N. et al., 1978. Transport of agricultural chemicals from small upland piedmont watersheds. U.S. Environmental Protection Agency, EPA-600/3-78-056, Environmental Research Laboratory, Athens, GA. Storm, D.E. et al. 1988. Modeling phosphorus transport in surface runoff. Trans. ASAE 31:117–127. Veith, T.L. et al. 2002. Questions: a user-friendly interface to ANSWERS-2000. Biological Systems Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg. Wischmeier, W.H. and D.D. Smith. 1978. Predicting rainfall erosion losses — a guide to conservation planning. U.S. Department of Agriculture, Agriculture Handbook 537. Yalin, Y.S. 1963. An expression of bed-load transportation. J. Hydraul. Div. ASCE 89(HY3):221–250. Zeckoski, R. 2002. Simulation of runoff and pollutant losses in urbanizing watersheds. M.S. thesis. Virginia Polytechnic Institute and State University, Blacksburg. Zheng, C. and P.P. Wang. 1999. MT 3DMS: a modular three-dimensional multi-species transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems; documentation and user’s guide. U.S. Army Engineer Research and Development Center, Contract Report SERDP-99-1, Vicksburg, MS.


11

Watershed Ecosystem Nutrient DynamicsPhosphorus (WEND-P Models) Robert L. Kort U.S. Department of Agriculture Natural Resources Conservation Service, Colchester, VT

E. Alan Cassell University of Vermont, Burlington, VT

Stefanie G. Aschmann U.S. Department of Agriculture Natural Resources Conservation Service, Portland, OR

CONTENTS 11.1 Introduction .................................................................................................261 11.2 History and Development ...........................................................................262 11.3 Purpose........................................................................................................263 11.4 The Modeling Framework ..........................................................................263 11.5 Phosphorus Processes .................................................................................268 11.6 Case Studies................................................................................................269 11.7 Model Availability.......................................................................................275 11.8 Conclusions .................................................................................................275 References..............................................................................................................275

11.1 INTRODUCTION Changing land uses and land-management practices on a watershed scale often cause an imbalance in phosphorus (P) cycling, resulting in water-quality problems both inside and outside the watershed in question. A number of watershed-scale models have been developed to trace movement of P from areas of concentration to receiving water bodies (U.S. Environmental Protection Agency 1992, 1997). These models primarily 261


262


focus on hydrologic and soil chemical processes to predict the likelihood of water contamination due to land-based P loading. Watershed Ecosystem Nutrient DynamicsPhosphorus (WEND-P) differs markedly from most of these models. Instead of focusing on hydrologic mechanisms of P movement, WEND-P examines the long-term storage, process, and cycling mechanisms by which the mass balance of P can change in various land uses and under various management scenarios throughout a specified watershed. This approach, when combined with the hydrologic approach, provides a more complete picture of P within a watershed and helps land managers devise strategies for addressing P pollution considering short-term economic, social, and environmental goals as well as long-term watershed ecosystem health.

11.2 HISTORY AND DEVELOPMENT WEND-P is a watershed-scale modeling process that uses dynamic simulation technology integrated with mass balance concepts to evaluate the flow of P into, out of, and within a watershed. The utility of integrating dynamic simulation and mass balance was initially demonstrated in modeling studies of P dynamics resulting from best management practices (BMP) implementation at the field scale (Cassell and Clausen 1993) and in understanding P dynamics in reaches of flowing streams (Hoffmann et al. 1996). The first watershed-scale WEND-P model (WEND-P1) was developed by Alan Cassell of the University of Vermont and Robert Kort of the Natural Resources Conservation Service to evaluate long-term trends in P export from the Winooski River watershed to Lake Champlain in northern Vermont (Cassell et al. 1998b). WEND-P1 reflects the type of agriculture, forest management, industry, and other conditions that characterize the Winooski River watershed as a rapidly urbanizing watershed where dairy is the dominant form of agriculture and where food processing and electronics are the main industries. This first WEND-P model attempted to identify the major sources of P in the watershed and to determine how land use and policy changes could affect export of P from the watershed over time. In 1999, a second WEND-P model (WEND-P2) was developed for the Inland Bays watershed in Southern Delaware (Cassell and Meals 1999). The Inland Bays watershed, like the Winooski River watershed, is urbanizing rapidly. As in the Winooski River watershed, animal production is a major source of P. However, poultry operations rather than dairies dominate agriculture in the Inland Bays watershed. Additionally, the topography and hydrology are very different between these two watersheds. The characteristics of the Inland Bay watershed were captured by changes to the original model structure. Dairy agriculture in the original model was replaced with poultry, natural drainage with tile drains and drainage ditches, northern hardwood forests with natural areas, and milk processing with tourist industries. In 2000, a third WEND-P model (WEND-P3) was developed for the Little Cobb River watershed in south-central Minnesota following a similar procedure (Cassell et al. 2000). The Little Cobb River watershed is a rural, nonurbanizing watershed in which the swine industry is rapidly growing. These modeling efforts have been discussed in the literature (Aschmann et al. 1999; Cassell et al. 1998a, 2001). The WEND modeling process has also been used to track the movement of pathogens in watersheds (Cassell et al. 2002) and to analyze the impacts of conservation practice systems on P movement within and through an agricultural unit (Watzin et al. 2003). © 2007 by Taylor & Francis Group, LLC

Watershed Ecosystem Nutrient Dynamics-Phosphorus (WEND-P Models)

263

Though many of the generic processes and algorithms in each of the WEND-P models remained the same, many were also improved in the later model versions. •

•

In the original WEND-P model (WEND-P1), P leaching was assumed to occur only after all of the P-adsorbing sites in the soil had been filled. In subsequent models, P adsorption isotherms for the watershed soils were used to determine when and how much leaching would occur. Animal manure in the original model was based on a given number of kilograms of animal biomass per hectare in order to account for the nondairy animals in the watershed. Subsequent models based manure production on the number of animal units in the watershed.

11.3 PURPOSE WEND-P models thus far have been used to describe P cycling and export from large (> 5000 ha) watersheds on a yearly time step. The models typically include a comprehensive accounting of mass balance of P for three general land-use sectors — agriculture, urban, and forest or natural — appropriate to the watershed under consideration. The activities within each land-use sector depend on the specific watershed being modeled and may include a variety of commercial, manufacturing, agricultural, tourist, or residential uses. The purpose of WEND-P models is to compare the impacts of alternative management options in different land-use sectors on P cycling and P export from watersheds over decades. The models may consider the impact of watershed hydrology on P losses but are not based on hydrology. They evaluate changes in P mass balance rather than P movement due to transport mechanisms. The information supplied by WEND-P models is generally complementary to information from hydrologic models, so both types of models may be used effectively in the same watershed to help land-use planners and management policymakers more clearly understand the role of watershed activities on P losses.

11.4 THE MODELING FRAMEWORK Several hypotheses provide the framework for developing WEND-P models: • •

•

An ecosystem paradigm provides a holistic view of P dynamics within complex watersheds. The ecosystem paradigm within the context of dynamic simulation modeling is useful for describing the long-term dynamic impacts of nutrient management activities on P export from watershed ecosystems. Dynamic watershed-scale P mass balances must consider all significant import fluxes, export fluxes, internal cycling fluxes, and P storage in watershed ecosystems.

Thus, it is necessary not only to gather information on the export of suspended and dissolved P in stream flow but also to identify and quantify other watershed-scale pathways of P export and import as well as storage mechanisms within the watershed ecosystem.


264


Conceptualizing watersheds as ecosystems is based on application of fundamental principles: • • • • • •

Every watershed ecosystem possesses a defined boundary across which P must move to enter or leave. Watershed ecosystems contain one or more sectors for storing all the P. All sectors are connected so that P can be transferred from one sector to any other sector in the watershed. Activities within a sector determine how it uniquely processes P. Mass balance principles are applied by accounting for all the P inputs and outputs of the watershed as well as all sectors within it. Processes function within and among the sectors and provide for feedback.

The conceptual framework for P is generic and transferable to many watersheds. The elements of this relatively straightforward framework guide the development of the P infrastructure on which each WEND-P watershed model is based. This is, however, a somewhat different approach than used in most models familiar to watershed professionals, and its successful use is dependent on the accurate and comprehensive accounting of P in the modeling framework. Figure 11.1 is a generic compartment flux or P infrastructure diagram representing a watershed ecosystem. It maps how a complex ecosystem processes P. Components of this are the following: • •

•

The watershed ecosystem: the watershed boundary defines the extent of the ecosystem. Compartments (rectangles): • Compartments within the watershed store all the P in the ecosystem. • The ecosystem contains unique sectors that describe P cycling in agriculture, urban, and forest land uses, long-term storage of P that is environmentally unavailable, and the drainage network through which the P moves out of the watershed. • Each sector includes a unique infrastructure to describe how P is cycled and stored. • Sectors have an identifiable boundary over which P may flow. Pathways (arrows): • Arrows identify and quantify the pathways of all significant P imports, exports, and internal cycling fluxes (loads) within a watershed. • Horizontal arrows are watershed imports and exports of P. • Arrows inside the ecosystem boundary are pathways through which P is cycled among the sectors and moved into the environmentally benign long-term storage sector. • The vertical arrow exiting the watershed ecosystem at the bottom is the flux of P that enters the receiving body of water. • P movement is controlled by a complex array of feedback mechanisms — no one sector operates independent of the others.



265

Ecosystem Structure P Import

FOREST SECTOR

AGRICULTURE SECTOR

P Import

Animals

P Export

P Export Field

Long-Term Storage Sector URBAN SECTOR

P Import

WEND Model Boundary

P Export

DRAINAGE NET SECTOR

River Channel

Watershed Ecosystem Boundary

P EXPORT IN RIVERS

FIGURE 11.1 Conceptual structural framework for WEND-P models. Rectangles and circles are locations of P storage; arrows are fluxes or pathways through which P moves within and among the forest, urban, and agriculture land-use sectors. The arrows that cross the watershed ecosystem boundary are the inputs and outputs of P for the watershed.

The P infrastructure diagrams on which a particular WEND-P model is based are detailed and specific to each watershed. Their construction requires local knowledge and expertise, a diverse set of demographic and resource data, and identification of specific algorithms. Detailed compartment flux diagrams developed for agriculture and urban sectors of the Inland Bays watershed ecosystem are shown in Figure 11.2 and Figure 11.3, respectively. Developing customized diagrams for each watershed contributes to a holistic understanding of the watershed infrastructure that controls P cycling and export. Such an understanding is useful in evaluating alternative P management options. WEND-P models of the P infrastructure diagrams are developed to comprehensively describe the major natural or anthropogenic processes (i.e., compartments and pathways) unique to a particular watershed. In building a model, the complexity of a watershed infrastructure is first decomposed into a number of relatively simple algorithms each of which describes a particular process (Figure 11.4). These algorithms


266


WEND Model Boundary

Inland Bays Watershed Boundary

US

Agriculture Sector Boundary

Live Birds

POULTRY

US Chicks

NAS US

Soil Weathering Spray Irrigation US Commercial Fertilizers US Waste Residues Ditch Sediments Irrigation Water Cropland Groundwater

Amendments Bedding Chicken Dead Birds Compost House Compost Bulk Litter Litter Water Spreading Feed

NAS

Litter

US US DNS

DNS

Surface Runoff Grain Harvest Atm Deposition

VEGETABLE

Litter Overcast Vegetable Harvest

Commercial Fertilizers Waste Residues

Vegetable Fields

US

DNS

Irrigation Water

DNS US

Ditch Sediments DNS

Spray Irrigation

Groundwater

Surface Runoff Soil Weathering

Manure Atmospheric Deposition

AS

. FIGURE 11.2 Agriculture P infrastructure diagram. Rectangles are locations of P storage; arrows are pathways for P movement whereas small squares are modeling decision nodes that control the flow pathways active in any given simulation run. Heavy arrows are pathways through which P moves between the agriculture sector (AS) and the drainage net sector (DNS). Linkages with the urban sector (US) and natural area sector (NAS) (i.e., the forest sector) are also shown.

are then linked to mimic the relationships shown on the infrastructure diagram. Within each sector are segment models for the cycling and storage of P, and embedded in these are process models built from individual biological, chemical, and physical relationships. This bottom-up approach to WEND-P model development results in embedding in a model the ability to track simultaneously over time P cycling, storage, and export at different hierarchical levels — that is, at the sector and watershed-scale levels. WEND-P model development takes place in the object-oriented dynamic simulation modeling framework provided by STELLA (isee systems 2006). In the WEND models, • • • • • •

Characteristics of each sector are spatially lumped; that is, there is no spatial explicitness. Data parameters that define each sector are annual average or typical watershed values. Data requirements are similar to needs for economic and resource inventory studies and management program evaluations. Response to perturbation is dynamic because feedback mechanisms operate. Algorithms can be quite complex. Models are built to conveniently allow input data to be changed.



267

WEND Model Boundary

Inland Bays Watershed Boundary

Urban Sector Boundary

Domestic Activities

Population Change

Dom Solid Disposal Wastes Com Solid Wastes Residues Dom Wastewater Sewered Effluent

AS Food

AS

Consumer Products

Spray Irrigation Unsewered

NAS

AS

Raw Materials

Commercial Activities

Cleansers

Poultry Processing

Live Birds AS Soy Bean Oil Grain & Supplements

AS DNS

Groundwater Atmospheric Deposition

Feed Formulation

Finished Products Wastewater

AS LTS DNS AS NAS

DNS DNS

AS NAS DNS

Effluent Viscera & Feathers Processed Birds & “paws” Wastes

Effluent

AS

DNS

Chicken Feed Pervious Areas

Impervious Areas

AS Fertilizer Surface Runoff

DNS

FIGURE 11.3 Urban P infrastructure diagram. Rectangles are activities in which P is stored; arrows are pathways for P movement whereas small squares are modeling decision nodes that control the flow pathways active in any given simulation run. Heavy arrows are pathways through which P from the urban sector (US) enters the drainage net sector (DNS). Linkages with the agriculture sector (AS), natural area sector, and long-term storage sector (LTS) are also shown.

• • • •

•

Sensitivity analyses are easily conducted in this framework. The impact of alternative management scenarios on P dynamics in individual watersheds is easily analyzed and compared. Simulation modeling provides a framework that enhances the understanding of watershed processes. Computations use an annual time step and are carried out over decades of time. WEND-P models do not have the temporal sensitivity to examine event or seasonal P dynamics. P export predicted by WEND-P models may not compare directly with measured watershed export because in-stream P dynamics are not considered in WEND-P simulations. P export from the watershed is equal to the loads from a WEND-P model when the alluvial processes in the drainage network are balanced, so there is no change in P storage over the long-term.


268


Overall System Complexity (No. Components & Interactions)

Level of Model Component Linkages (Hierarchy of Interactions)

Real Watershed

High Med Low

Simplification

Sector Models Process Models

Conceptual Watershed Infrastructure

Segment Models

Basic Algorithns

Decomposition

Synthesis (Rebuilding Complexity)

Basic Model Elements

Model Development Process FIGURE 11.4 Building WEND-P models is a process of simplifying and decomposing the complexities contained in a real watershed into basic modeling elements (individual algorithms) and then synthesizing complexity hierarchically by linking the basic model elements that describe unique watershed infrastructures (e.g., infrastructures such as those in Figure 11.2 and Figure 11.3).

11.5 PHOSPHORUS PROCESSES Though the infrastructure diagrams of a WEND-P model (Figure 11.2 and Figure 11.3) provide the structural framework for how P is imported, cycled, and exported in a watershed ecosystem, the algorithms within a STELLA model compute the actual rates at which P moves and the amount of P stored. These algorithms define the different processes that drive watershed P dynamics, be they some natural biological, chemical, or physical process or an anthropogenic process implemented to manage how P is moved and stored. For example, the computation of rates for soluble and particulate P export in surface runoff from a watershed is essential for WEND-P models to maintain P mass balance over time. To do this, WEND-P model algorithms calculate and keep track of soil P levels for each sector in the watershed. The rate of export for particulate P in surface runoff from a sector is computed as the product of an assigned soil erosion rate and the concentration of P in the soil. The concentration of soluble P in surface runoff, as well as infiltrating water, is a function of soil P according to a P adsorption isotherm applicable to the watershed of



269

interest. Average annual rate of surface runoff and infiltration is based on a regional water-quantity budget. The product of the average annual surface runoff and the concentration of soluble P is the rate of soluble P export in surface runoff. The total rate of P export from a given watershed sector is the sum of the export of soluble and particulate P. The detailed model for this brief example and details of how anthropogenic processes in WEND-P models may be changed to simulate the implementation of new management conditions in a watershed are available in the literature (Cassell and Meals 1999; Cassell et al. 1998b, 2000).

11.6 CASE STUDIES The original WEND-P1 model developed for the Winooski River watershed in Vermont was adapted and customized to reflect the uniqueness of two other watersheds: the Inland Bays watershed in Delaware and the Little Cobb River watershed in Minnesota. Characteristics of the three watersheds are presented in Table 11.1. Simulations were run to evaluate how different management scenarios influence the long-term export of P for all three watersheds. This includes an initial baseline simulation (business as usual) and scenarios that favored either environmental protection

TABLE 11.1 Important Characteristics of Case-Study Watersheds Winooski River Area (ha) Percent agriculture Percent urban Percent forest Percent water Predominant agriculture Animal population Animal population (total number/year) Predominant crops Total population Visitor-day/year Industry Topography Drainage a b

Inland Bays

Little Cobb River

77,000 36 12 24 28 Chickens

23,376 94 2 3 1 Hogs

Not available —

13,000,000 71,500,000

80,000 136,000

Silage, corn, hay, pasture

Corn, wheat, soybean

153,880 330,000 Electronics, food processing Mountains, hills/valleys Naturala

50,270 5,200,000 Food processing

Hay, alfalfa, corn, soybean 1,500 Nil None

Flat Tile drainb

Flat Tile drain

275,399 13 8 74 5 Dairy

Refers to the stream and river networks typical of New England with few tile drains. Implies that tile drainage of agricultural fields is common.


270


P Fluxes - metric tons/year 1600

P Input/Output Pattern Total Import of P

Accumulation

800

Total Export of P 0 0

40

20

P Loadings - metric tons/year 240 Total Loading

60

80 Time - years

P Export in Runoff

Agriculture Loading

Urban Loading 120

Forest Loading 0

0

20

40

60

80 Time - years

FIGURE 11.5 Dynamics of P export from the Winooski River watershed: WEND-P1 model. Current conditions are assumed to remain unchanged into the future. The vertical plot is the model estimates of present-day P export. The total loading is the sum of the loading from agriculture, urban, and forest sectors. Though the total load is increasing, the proportion due to agriculture is decreasing. The watershed is urbanizing.

(comprehensive agricultural or urban growth management) or rapid growth and development. Figures 11.5 through 11.9 provide graphs of these scenario analyses, and Table 11.2 summarizes the present-day phosphorus mass balances. The Winooski River watershed has significant amounts of urbanization and farming, but forest is its dominant land use. Over an 80-year period (Figure 11.5) there is an accumulation of P in the watershed as the total input of P exceeds the output at all times. As urban land increases there is a corresponding decrease in forest and agricultural land and total loading increases, largely due to population growth. Relatively little P is exported from the forest sector compared to the urban and agriculture sectors. It is interesting to note how P export for the environmental scenario in Figure 11.6 pretty much stabilizes at a level considerably higher than that for forest sector loading.



271

Alternative Watershed Management Strategies

Export of P - metric tons/year 240

Growth

Baseline 120 Period of Implementation

Environmental

0 0

20

40

60

80 Time - years

FIGURE 11.6 Dynamics of P export from the Winooski River watershed: WEND-P1 model. Two P management strategies — Environmental and Growth — are implemented between years 20 and 30 and are compared to the management scenario in which current conditions are assumed to remain unchanged (Baseline). The Baseline Strategy is the Total Loading as shown in Figure 11.5. The Environmental Strategy includes implementation of practices for limiting P discharge from urban activity and agricultural lands as well as enhanced local recycling of material that contains P. The Growth Strategy assumes that the P management infrastructure remains at present-day levels, whereas policies encourage a relatively rapid population and commercial and industrial growth.

The Inland Bays is a flat watershed with very intensive use by both agriculture and people. Projecting present trends over the next 40 years (Figure 11.7) shows an ever-increasing trend line for P export to the Bays. Imposing annual variations on the average year rainfall shows an anticipated variation in yearly P export so great that it is hard to see the relatively slow changes in the trend that are occurring. A number of P management options are explored in Figure 11.8, but even a comprehensive watershed management approach shows P exports after 30 years to be back at present-day levels. The model suggests that growth management is the only way for P export to the Inland Bays 40 years from now to be where it is today. The Little Cobb River watershed is flat and is rapidly becoming a major hogproducing area. The implementation of erosion control in equal increments over a 5-year period produces reductions in P export even when grow-out is occurring over the 40-year simulation. This is very different from what is found for the other two watersheds investigated, demonstrating the uniqueness of every watershed. Table 11.2 summarizes the initial (time 0) P balance for each of the studied watersheds. It indicates that total P inputs exceed total P outputs for all three watersheds and a resulting net accumulation of P (mostly in the soils). A relatively


272


Baseline Conditions

Export of P to Inland Bays -metric tons/year

Mean Rainfall = 43 inches/yr (StdDev 15% mean)

120

Normal Years (trend line)

Wetter Years Trial 1

60

Dryer Years Trial 3 Trial 2 0

0

10

20

30

40

Time-Years FIGURE 11.7 Dynamics of P export from the Inland Bays watershed: WEND-P2 model. Current conditions are assumed to remain unchanged into the future. The heavy plot represents simulated P export for years of average rainfall, whereas the thinner lines are simulated patterns of P export when rainfall is assumed to vary randomly from year to year in accordance with observed variation in annual rainfall.

small fraction of the P that enters these watersheds is being exported in surface runoff. This fraction is the monitored export that tends to drive present-day waterquality issues. WEND-P modeling experience in several watersheds suggests the following: •

• • • •

Total inputs of P exceed total outputs of P under present conditions: P is accumulating in the watersheds modeled and is projected to continue accumulating unless there is change in P management strategies. Different watershed management alternatives can have a substantial impact on watershed P export. Monitored P export from study watersheds is consistent with values calculated by the WEND-P model. Different factors drive P dynamics for different scales. The models suggest the watersheds will never return from agriculture and urban to predevelopment P conditions. This is evidenced by the significant difference between P loads from forested and natural areas — the predevelopment land uses — and P export even when a policy of aggressive environmental management is implemented for the watersheds as they are today.



273


Export of P - metric tons/year 100

Phytase Baseline Comp Ag Comp Urban 70 Comp Watershed

Growth Management Period of Implementation 40

0 (1996-1998)

10

20

30 40 Time - Years

FIGURE 11.8 Dynamics of P export from the Inland Bays watershed: WEND-P2 model. Five P management strategies are implemented between years 5 and 10 and are compared to the management scenario in which current conditions are assumed to remain unchanged (Baseline). The Baseline strategy is the normal trend line as shown in Figure 11.7. The Phytase and comprehensive agriculture (Comp Ag) strategies incorporate P management practices that reduce the export of P only from the agriculture sector, whereas the Comp Urban strategy incorporates P management practices that reduce export only from the urban sector. The Comp Watershed strategy incorporates P management practices that reduce P export from both sectors. The Phytase, Comp Ag, Comp Urban, and Comp Watershed strategies all assume the growth of population, and agricultural and urban activity continues to increase at present-day levels. The Growth Management strategy incorporates policies that reduce the rate of growth at which population and agricultural and urban activity changes over future years.

•

•

•

A relatively small fraction of P entering the studied watersheds is being exported in surface runoff, yet water-quality issues often focus only on this fraction. Short-term water-quality monitoring programs may be ineffective in determining the impact of management actions due to year-to-year data variability (Figure 11.7). Management actions to achieve short-term goals may be counterproductive over the long term. Management policies favoring land treatment by erosion control tend to increase the accumulation of P in watershed soils. When watershed P inputs and outputs tend to be balanced, P levels in soils can be managed or even reduced.


274



P Export to Drainage Net metric tons/year 46

Grow Out

Baseline 23

Grow Out+EC 0

0

10

Erosion Control

40 30 Time - Years

20

FIGURE 11.9 Dynamics of P export from the Little Cobb River watershed: WEND-P3 model. Three P management strategies are implemented between years 5 and 10 (erosion control in a stepwise fashion) and are compared to the management scenario in which current conditions are assumed to remain unchanged (Baseline). For the Grow Out and Grow Out + EC (erosion control) scenarios practices are implemented that simulate anticipated maximum sustained growth levels and maximum sustained growth levels plus improved erosion control, respectively. The Erosion Control scenario simulates implementation of improved erosion control only.

TABLE 11.2 Summary of Present-Day Mass Balance for Phosphorus for the Three Case-Study Watersheds Winooski River Total input (mt P/year) Total output (mt P/year) Net accumulation (mt P/year) Export in runoff (mt P/year) Export (as % Input)

~ 900 ~ 550 ~ 350 ~ 100 ~ 11

Inland Bays

Little Cobb River

~ 2700 ~ 950 ~ 1750 ~ 60 ~2

~ 680 ~ 250 ~ 430 ~ 30 ~ 4.5

Note: All watersheds are accumulating P that the WEND-P models indicate is largely accounted for by soil enrichment. For all watersheds the P exported in surface runoff is a relatively small fraction of the P imports.



275

11.7 MODEL AVAILABILITY WEND-P models or model documentation for the Winooski River, Inland Bays, and Little Cobb River watershed studies are available on request from USDA-NRCS ([email protected]). The models require STELLA software that is available for both the Macintosh and Windows platforms. STELLA is available for purchase through isee systems, http://www.iseesystems.com/. The existing WEND-P models may be used as templates for creating new models, but they cannot simply be transported. Each model represents an individual watershed with unique characteristics. Adapting these existing model frameworks to new watersheds requires a detailed analysis of the activities occurring within each land-use sector in a new watershed. The uniqueness of individual watersheds requires modification of WEND-P models or creation of new models to simulate these activities. For example, manufacturing and service industries utilize different amounts of P in different ways, feedlots and pastures cycle P differently, and timber production differs from pulpwood production or wildlife habitat management in the amount and rate of P cycling.

11.8 CONCLUSIONS WEND-P models can complement hydrologic P transport models by providing insights into long-term impacts of management strategies that hydrologic models typically overlook. These models indicate that implementing policies that better balance P imports and exports on a watershed basis is the most effective way to reduce P export over the long-term. Because short-term monitoring programs seldom indicate a clear impact of management actions on water quality, WEND-P can complement monitoring studies by indicating long-term trend responses that are not otherwise apparent. Another initially unanticipated advantage of the WEND-P modeling process is that it necessarily produces a detailed understanding of how resources and activities in a watershed function. By default this also provides a multidisciplinary framework for decision making. Such a framework is essential for effective long-term reduction of P export and allows management programs to be tailored to fit the uniqueness of each individual watershed. WEND-P does not describe all of the microprocesses that affect P transport to water bodies, but because of its long-term, process-based approach it can be a useful tool in the arsenal of land-management decision makers concerned with P pollution in watersheds.

REFERENCES Aschmann, S.G., D.P. Anderson, R.J. Croft, and E.A. Cassell. 1999. Using a watershed nutrient dynamics model, WEND, to address watershed-scale nutrient management challenges. J. Soil Water Cons. 54(4):630–635. Cassell, E.A. and J.C. Clausen. 1993. Dynamic simulation modeling for evaluating water quality response to agricultural BMP implementation. Water Sci. Technol. 28(3–5):635–648.


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Cassell, E.A., J.M. Dorioz, R.L. Kort, J.P. Hoffmann, D.W. Meals, D. Kirschtel, and D.C. Braun. 1998a. Modeling phosphorus dynamics in ecosystems: mass balance and dynamic simulation approaches. J. Environ. Qual. 27:293–298. Cassell, E.A., R.L. Kort, and D.L. Braun. 1998b. The Vermont-Lake Champlain basin watershed phosphorus management study, dynamic simulation modeling for watershed ecosystem analysis of phosphorus budgets, University of Vermont and USDA-Natural Resources Conservation Service, Burlington and Winooski, VT. Cassell, E.A., R.L. Kort, D.W. Meals, S.G. Aschmann, J.M. Dorioz, and D.P. Anderson. 2001. Dynamic phosphorus mass balance modeling of large watersheds: long-term implications of management strategies. Water Sci. Technol. 43(5):153–162. Cassell, E.A. and D.W. Meals. 1999. Dynamic simulation modeling of phosphorus budgets for the Inland Bays watershed, Delaware case study. U.S. Department of Agriculture, Final Report, Watershed Science Institute, Natural Resources Conservation Service, Lincoln, NE. Cassell, E.A., D.W. Meals, S. Aschmann, D.P. Anderson, and B.H. Rosen. 2000. Dynamic simulation modeling of phosphorus budgets for agricultural watersheds dominated by swine farming: the Little Cobb River watershed, MN case study. U.S. Department of Agriculture, Final Report, Watershed Science Institute, Natural Resources Conservation Service, Lincoln, NE. Cassell, E.A., D.W. Meals, S.G. Aschmann, D.P. Anderson, B.H. Rosen, R.L. Kort, and J.M. Dorioz. 2002. Use of simulation mass balance modeling to estimate phosphorus and bacteria dynamics in watersheds. Water Sci. Technol. 45(9):157–168. isee systems. 2006. STELLA Technical Documentation. Lebanon, NH: isee systems inc. Hoffmann, J.P., E.A. Cassell, J.C. Drake, S. Levine, D.W. Meals, and D. Wang. 1996. Understanding phosphorus cycling, transport and storage in stream ecosystems as a basis for phosphorus management. Technical Report 20, Lake Champlain Basin Program, Grande Isle, VT. U.S. Environmental Protection Agency. 1992. Compendium of watershed-scale models for TMDL development. EPA 841-R-92-002, Office of Water, Washington, D.C. U.S. Environmental Protection Agency. 1997. Compendium of tools for watershed assessment and TMDL development. EPA 841-B-97-006, Office of Water, Washington, D.C. Watzin, M.C., E.A. Cassell, and D.W. Meals. 2003. Analyzing the effects of conservation practices using network modeling. U.S. Department of Agriculture, Final Report, Watershed Science Institute, Natural Resources Conservation Service, Washington, D.C.


12

Modeling Phosphorus with the Generalized Watershed Loading Functions (GWLF) Model Elliot M. Schneiderman New York City Department of Environmental Protection, Kingston, NY

CONTENTS 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8

History of Model Development................................................................277 Spatial and Temporal Resolution .............................................................279 Predicting Infiltration and Runoff ............................................................279 Predicting Phosphorus in Runoff .............................................................284 Predicting Phosphorus Leaching ..............................................................285 Simulating Management and BMPs.........................................................285 Simulating In-Stream Processes ...............................................................286 Example Simulations ................................................................................287 12.8.1 Use of GWLF to Evaluate BMPs ...............................................287 12.8.2 Accuracy of GWLF: Comparison of Simulated to Measured Loads ......................................................................289 12.8.3 Simulation of Runoff Volumes and Source Areas......................292 12.9 Sensitivity Analysis...................................................................................295 12.10 Availability of Model................................................................................295 References..............................................................................................................296

12.1 HISTORY OF MODEL DEVELOPMENT The Generalized Watershed Loading Functions (GWLF) model was originally developed at Cornell University by Douglas Haith and associates (Haith and Shoemaker 1987; Haith et al. 1992) as “an engineering compromise between the empiricism of export coefficients and the complexity of chemical simulation models” (Haith et al., 1992, p.1). The GWLF approach conceptualizes the watershed as a system of different land areas — hydrologic response units (HRUs) — that produce surface runoff and erosion and a single groundwater reservoir that supplies base flow. 277


278


Dissolved and suspended substances (i.e., nutrients, sediment) in stream flow are estimated at the watershed outlet by loading functions that empirically relate substance concentrations in runoff, sediment, and base flow to watershed- and HRU-specific characteristics. The strength of this approach lies in its fairly robust hydrologic formulation of a daily water balance and in the ability to adjust loading functions through calibration and for specific watershed conditions to an ever increasing body of knowledge and data on the factors that influence the export of substances in stream flow from a watershed. In addition to the original model there are currently several versions of GWLF in use. ArcView GWLF (AVGWLF) (Evans et al. 2002) was developed by Pennsylvania State Institutes of the Environment for Pennsylvania watersheds. AVGWLF provides a geographic information systems (GIS) interface to GWLF, has a modified sediment algorithm for channel erosion, and incorporates best management practices (BMP) reduction factors. Variable Source Loading Function (VSLF) Model (Schneiderman et al. 2002, 2006) was developed by the New York City Department of Environmental Protection (NYC DEP) for the New York City water supply. VSLF has a modified runoff algorithm to account for saturation-excess runoff; adds optional snowmelt, evapotranspiration (ET), and groundwater algorithms for tuning hydrologic simulation to varied physiographic settings; modifies the sediment algorithm; adds BMP reduction factors; utilizes Vensim visual modeling software (http://www.vensim.com) for transparent viewing of model structure and for viewing tables, graphs, and statistics for all model variables at daily, weekly, monthly, annual, and event time steps; and has builtin model calibration and testing tools. BasinSim (Dai et al. 2000) is a Windows-based version of the original GWLF model developed at Virginia Institute for Marine Science. For research at the Choptank River Basin tributary of Chesapeake Bay, Lee et al. (2000, 2001) and Fisher et al. (2006) converted GWLF to Visual Basic with an ArcView and ArcMap GIS interface and added error analysis and adjustments for nonlinear agricultural land-use effects and hydric soils. These versions of GWLF have incorporated various different modifications from the original BASIC program, but all, including the various teaching tool versions, adhere to the basic water balance formulation and loading function philosophy. The various versions of GWLF are commonly used to predict how stream flow and nutrient loads from a watershed are affected by land-use, watershed-management, and climatic conditions. The U.S. Environmental Protection Agency (EPA) has classified GWLF as a model of mid-range complexity that can be used for developing Total Maximum Daily Load (TMDL) limits for impaired water bodies (U.S. Environmental Protection Agency 1999). GWLF has been applied to the Choptank River Basin tributary of Chesapeake Bay (Lee et al. 2000, 2006), including an application to historical land cover changes (Fisher et al. 2006); the New York City water supply watersheds (New York City Department of Environmental Protection 2005; Schneiderman et al. 2002, 2006); and throughout Pennsylvania (http://www.avgwlf.psu.edu). A Web search at the time of this writing shows that a version of GWLF is being used in at least 12 U.S. states — Arizona, Georgia, Illinois, Iowa, Kansas, Michigan, Mississippi, North Carolina, Pennsylvania, New York, Utah, and Virginia — to meet EPA requirements for development of TMDLs.


Modeling Phosphorus with the GWLF Model

279

12.2 SPATIAL AND TEMPORAL RESOLUTION GWLF has flexibility in the spatial and temporal resolution of model output. The basic time step for the hydrologic water balance calculations is daily, which can be aggregated up to larger time steps. The original GWLF model aggregates hydrologic and water-quality output to a monthly representation, mainly because it does not account for drainage-area-based delays on flood peaks following storms. Daily output from GWLF will generally give too fast a response to rain events because the model computes a daily water balance but does not include routing. VSLF incorporates a time delay for runoff at the watershed outlet using an exponential decay function that can be calibrated. VSLF provides daily, weekly, monthly, annual, and event time step outputs, as desired. Spatial resolution depends on how a GWLF model application is set up. In GWLF the watershed area is divided into HRUs, which are land areas that share a similar hydrologic response to rain or snowmelt events and may not be contiguous. Runoff, erosion, and nutrients associated with runoff and erosion are explicitly tracked for each HRU and can be spatially mapped back to the HRU land areas. Fine resolution division of a watershed into many HRUs can produce model output on a field scale. Water, nutrient, and sediment loads are summed to provide watershed-scale loading estimates as well.

12.3 PREDICTING INFILTRATION AND RUNOFF Runoff and infiltration are predicted in GWLF using the Soil Conservation Service (SCS) curve number (CN) method (Soil Conservation Service 1972). Daily runoff depth Q is calculated by Q=

( P − I a )2 (P − Ia ) + S

(12.1)

where P (mm) is the depth of rain and snowmelt, Ia (mm) is the initial abstraction of rain and snowmelt retained by the watershed prior to the beginning of runoff generation, and S (mm) is a parameter that represents the potential maximum soil water retention when runoff begins. Ia is estimated as an empirically derived fraction of available storage (typically assumed to be 0.2 S). Potential soil water retention, S, depends on the moisture status of the soil of the HRU and varies daily between a maximum Smax (mm) when the HRU soil is dry and a minimum Smin (mm) when the HRU soil is wet. Effective soil water retention for average watershed moisture conditions Savg (mm) is calculated from the SCS CN (CN2):  100  Savg = 254  − 1  CN 2 

(12.2)

CN2 values can be derived by calibration to base-flow-separated stream flow data (Natural Resources Conservation Service 1997) or from tables compiled by the


280


U.S. Department of Agriculture (USDA) (Soil Conservation Service 1986) for different combinations of land use and soil hydrologic group. Soil hydrologic groups rank soils by their infiltration characteristics, and are used to qualify the propensity of an HRU to generate excess runoff. The upper and lower limits of S are estimated in relation to Savg, based on empirical analysis of rainfall and runoff data for experimental watersheds (Hawkins 1978): Smax = 2.381 Savg

(12.3)

Smin = 0.4348 Savg

(12.4)

and

The daily value of S is determined in the original GWLF model by the watershed antecedent moisture (am) condition, determined by the sum of precipitation occurring during the previous five days (P5-day). S is set to Smax for the dry condition (P5-day = 0) and then declines linearly to Savg and Smin as P5-day increases, as given in Figure 12.1. The relationship of S to P5-day is different for the dormant vs. the growing season. Breakpoint values (from Ogrosky and Mockus 1964) for the dormant and growing season curves, respectively, in Figure 12.1 are am1 = 1.27

Smax growing

dormant

S Savg

am1

am1

am2

Smin

am2

0

1

2

3

4

5

6

5-day Antecedent Precipitation (cm) FIGURE 12.1 Variation in soil water retention parameter, S, as a function of 5-day antecedent precipitation for growing and dormant seasons. am1 and am2 represent breakpoint values between different antecedent precipitation conditions.



281

and 3.56 cm, and am2 = 2.79 and 5.33 cm. When snowmelt occurs, it is assumed that the HRU soils are at their wettest condition; hence, S is set to Smin, irrespective of P5-day. An alternative method for calculating S as a direct function of soil moisture content is used in VSLF (Schneiderman et al. 2006). Using the method of Arnold et al. (1998), S varies from storm to storm as  S = Smax 1 − 

  SW  ( SW + e w1− w2SW )   

(12.5)

where SW is the average soil water content (cm3/cm3) and w1 and w2 are shape coefficients. The shape parameters w1 and w2 are calculated by    FC w1 = ln  − FC  + w2 FC   1 − Smin /Smax  

(12.6a)

and       FC SAT ln   − SAT   − FC  − ln   1 − 2.54 Smax    1 − Smin /Smax   w2 =  SAT − FC

(12.6b)

where FC is the amount of water in the soil at field capacity (cm3/cm3) and SAT is the amount of water in the soil when saturated (cm3/cm3). When the top layer of the soil is frozen, the available storage is modified by Sfrz = Smax [1 − exp( R2frzx S )]

(12.7)

where Sfrz is the available storage adjusted for frozen ground, S is the available storage for a given soil moisture content calculated with Equation 12.5, and R2frzx is a parameter that adjusts for frozen ground conditions. R2frzx is set to –0.000826 in the SWAT model but can be calibrated. Stormwater runoff is the primary mechanism for transporting soluble phosphorus (P) from the point where it accumulates on or near the ground surface to the stream and outlet of the watershed. Accurate model predictions of P loads and effects of watershed management depend on realistic prediction of runoff source areas. GWLF, like many CN-based water-quality models, uses the SCS CN method in a way that implicitly assumes that infiltration excess is the runoff mechanism. Each HRU in a watershed is defined by land use and a hydrologic soil group classification via a CN value that determines runoff response. CN values for different land use and hydrologic soil group combinations are provided in tables compiled by the USDA


282


(e.g., Soil Conservation Service 1972, 1986). The hydrologic soil groups used to classify HRUs are based on infiltration characteristics of soils (e.g., Natural Resources Conservation Service 2003) and thus clearly assume infiltration excess as the primary runoff-producing mechanism. The traditional infiltration-excess-based CN method for runoff estimation in GWLF limits the original model’s utility to watersheds where infiltration excess is the dominant runoff-generating mechanism. In humid, well-vegetated areas with shallow soils, such as in the northeastern U.S., infiltration excess does not explain observed storm runoff patterns. On shallow soils characterized by highly permeable topsoil underlain by a dense subsoil or shallow water table, infiltration capacities are generally greater than rainfall intensity, and storm runoff is usually generated by saturation excess on VSAs (Beven 2001; Dunne and Leopold 1978; Needelman et al. 2004; Srinivasan et al. 2002). To improve the accuracy of runoff source area predictions in watersheds where saturation excess is the dominant runoff-generating mechanism, Schneiderman et al. (2006) created a new version of GWLF (VSLF) that simulates runoff from VSAs. In VSLF the watershed is subdivided into wetness index classes by mapping a wetness index (e.g., the topographic index ln a/tan b of the TOPMODEL; Beven and Kirkby 1979) and by defining discrete classes ordered along an axis of increasing available moisture storage. Steenhuis et al. (1995) and Schneiderman et al. (2006) showed that the CN Equation 12.1, when interpreted as representing a saturation excess runoff generation process, gives rise to a characteristic relative soil moisture distribution that is invariant from storm to storm:  σe  1 = − 1 S  (1 − As ) 

(12.8)

where σe (mm, effective local moisture storage) is the amount of water that can be stored in the soil at a point location in the watershed when runoff from the watershed begins, S is the average soil water retention parameter for the entire watershed calculated by Equation 12.5 through 12.7, and As is the fraction of watershed area with lower local moisture storage than the point location. Figure 12.2 shows the relative moisture distribution curve of Equation 12.8 plotted along an axis of increasing fraction of watershed with lower local moisture storage. Runoff q (mm) at a given point location in the watershed is simply q = P – Ia – se for P > σe + Ia

(12.9)

Given the CN-based relative moisture distribution (Equation 12.8), runoff for any point location along the As fraction of watershed area with lower local moisture storage axis is calculated as   1 q=P− − 0.8 ⋅ S  (1 − As ) 


(12.10)


283

10 9 8 7 6

σe /S

5 4 3 2 1 0 0

0.2

0.4

0.6

0.8

1

As FIGURE 12.2 Distribution of effective local moisture storage, σe, normalized to the watershed average potential soil water retention parameter, S, along an axis of increasing fraction of watershed area with lower local moisture storage, As.

Runoff qi for a discrete wetness index class, bounded on one side by the fraction of the watershed that has lower local moisture storage, As,i, and on the other side by the fraction of the watershed that has greater local moisture storage, As,i+1, is given by 2⋅  qi = P −  

( 1− A

s,i

− 1 − As,i+1

( As,i+1 − As,i )

) − 0.8 ⋅ S  

(2.11)

Runoff and nutrient loads from each wetness and land-use HRU are tracked separately in the model. A wetness index class may coincide with multiple land uses. Whereas runoff depth within an index class in VSLF will be the same irrespective of land use, the concentration of pollutant in runoff may vary by both land use and index class. Wetness index classes are thus subdivided by land use to define HRUs with unique combinations of wetness class and land use. In the original GWLF model, runoff is calculated for each defined soil and land use HRU using Equation 12.1. In VSLF, runoff is calculated for each wetness and


284


land use HRU with Equation 12.11. For the entire watershed, runoff depth Q is the areally weighted sum of runoff depths qi for all discrete wetness and land-use contributing areas: n

Q=

∑ q (A i

s,i+1

− As,i )

(12.12)

i =1

Total runoff depth, Q, calculated by this equation is the same as that calculated by Equation 12.1 (Schneiderman et al. 2006), so runoff volume estimates for the watershed as a whole with VSLF are compatible with the original GWLF and other models that use the traditional SCS CN equation. The main hydrological difference is that VSLF distributes storm runoff according to a moisture storage distribution rather than by land use and soil type. This has important implications for predictions of chemical constituents of runoff.

12.4 PREDICTING PHOSPHORUS IN RUNOFF Dissolved P loads in runoff from each HRU are calculated daily in GWLF as the product of simulated runoff and empirically derived HRU-specific nutrient concentrations. Haith et al. (1992) compiled runoff concentrations for different land uses from the literature for rural land uses. Urban dissolved nutrient concentrations were compiled in the Nationwide Urban Runoff Program (U.S. Environmental Protection Agency 1983). Literature concentration values from these and other sources provide an initial basis for determining these parameters. Runoff concentration data for specific watersheds can be used when available. In the original GWLF, dissolved nutrient concentrations are input as constants, with the exception of agricultural land uses on which winter spreading of manure or fertilizer occurs. For these land uses, seasonal variability in nutrient concentrations is introduced, with elevated concentrations applied to snowmelt and rain on snow. Use of literature-based concentrations of nutrients in runoff in GWLF presents a number of challenges. Literature-based concentrations generally provide a range of values for a given land use, and the choice of an appropriate value for a given watershed requires an act of judgment. Since the GWLF parameters represent concentrations in runoff as expressed at the outlet of a watershed, scale differences between study sites on which literature values are based and the watershed being modeled may affect the translation. Even concentration data for runoff in the study watershed may not translate directly to GWLF parameters if the data are sampled at the plot or field scale. Model calibration may be necessary and is recommended where loading data are available. Schneiderman et al. (2002) calibrated nutrient concentrations with a single adjustment factor that was applied to all nutrient concentrations. In this way the relationships between concentrations associated with different land uses are maintained, as all concentrations shift up or down with the multiplicative factor. In effect, the literature values are used to establish the relative concentrations for different land uses, and calibration establishes the absolute values.



285

The use of constant concentrations for nutrients in runoff is deserving of some discussion. On the local plot or field scale, P concentrations would be expected to vary with changes in soil P content in the upper soil layer (Sharpley 1995) or with the timing and intensity of manure or fertilizer applications (Walter et al. 2001). On the watershed scale, however, where the simulation unit (in GWLF and other lumped-parameter HRU models) is the HRU composed of many plots or fields at different stages of fertility and soil P cycles, the temporal variations that exist on the fine scale may cancel out on the broad scale. The New York City Department of Environmental Protection (2005) used the Soil Water Assessment Tool (SWAT) (Bicknell et al. 2001) model, which simulates daily P concentrations in soil and runoff by keeping a mass balance of P, to investigate temporal variation in soil and runoff P concentrations for agricultural land uses in New York City watersheds. The results of an extensive sensitivity analysis suggested that with the exception of agricultural fields that are subject to tillage, predicted soil and runoff P concentrations at a watershed scale were fairly constant. Tilled agricultural fields demonstrated a distinct pattern of reduction of concentrations in runoff (due to mixing of high P upper-layer soil with lower P lower-layer soils) at the time of tillage, followed by a gradual increase in concentrations with time after tillage. VSLF was modified to allow seasonally varying concentrations for cases like this where such variations occur on a watershed scale.

12.5 PREDICTING PHOSPHORUS LEACHING GWLF assumes that the major pathways by which P is exported from a watershed are in runoff from different HRUs and in base flow. GWLF does not predict leaching of P explicitly. In actuality, the importance of P leaching as a pathway for export of P on a watershed scale is uncertain. Observations of elevated P concentrations in base flow in P-enriched watersheds could be considered evidence for transport of leached P from P-saturated soils, but this has not been demonstrated conclusively. Elevated P concentrations in base flow could just as well be caused by high P availability at groundwater discharge sites, including seeps and stream banks. The effects of factors that influence base flow P levels, including leaching of P into shallow groundwater and P entrainment at groundwater discharge zones, is accounted for in GWLF by model and input adjustments to the concentration of P in base flow. In the original GWLF model, the P concentration in base flow was an empirical function of the aerial percentage of active agriculture in the watershed (Figure 12.3). VSLF has an option to allow user input of a base-flow concentration value that is representative of the watershed being studied.

12.6 SIMULATING MANAGEMENT AND BMPS The general approach to simulating management and BMPs with GWLF is to translate the effects of BMPs, either individually or combined, into model parameter adjustments, which are then applied in subsequent scenario runs of the model. For example, hydrologic effects of watershed management and BMPs may be


286


P concentration in baseflow (mg/l)

0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0%

20%

40%

60%

80%

100%

Percent Agriculture

FIGURE 12.3 Dissolved P concentration in base flow as a function of percent of agricultural land use within a watershed.

expressed through modifications in curve number (affecting runoff), soil water capacity (affecting percolation), melt coefficient (affecting snowmelt), or vegetative cover coefficients (affecting ET). Water-quality effects of BMPs are expressed by modifying HRU-specific P concentrations in runoff, P concentration in base flow, pointsource concentrations, septic system failure rates, Universal Soil Loss Equation (USLE) parameters that control erosion rates, sediment delivery ratio, and HRUspecific P concentrations in soils. GWLF-VSA and AVGWLF have reduction factors built into the model to streamline the application of BMP effects on model parameters. The reduction factor approach to simulating effects of watershed management is supported by an ever increasing body of knowledge in the literature on the effectiveness of BMPs. Phosphorus removal efficiencies of urban BMPs are measured and compiled for stormwater treatment practices (Winer 2000). Gitau et al. (2005) compiled a database of BMP effectiveness for agricultural BMPs. Gitau and Veith cover the effect of P control BMPs in Chapter 15 of this volume. The USLE methodology (Wischmeier and Smith 1978) provides coefficient values for various management practices. Results of watershed-specific field studies on BMP effectiveness can be utilized where available.

12.7 SIMULATING IN-STREAM PROCESSES GWLF simulates in-stream processes as a lumped statistical process where the stream is treated as a single unit. The effect of channel length and physical properties on the timing of base-flow discharge at the outlet of the watershed is treated as a simple exponential time delay that can be calibrated from stream flow data. Though the original GWLF model does not permit a time delay for runoff — runoff at the



287

watershed outlet occurs on the day of precipitation — the VSLF does so by treating runoff delay similarly to base flow. In-stream processing of chemical constituents of stream flow is represented minimally in the original GWLF model. The timing of P export at the watershed outlet in GWLF is delayed with the exponential time delay of base flow and, in VSLF, runoff. VSLF and AVGWLF simulate stream-channel erosion by simple loading functions whereby a single channel-erosion calculation representing the entire channel system is determined. VSLF also simulates transformation of P between dissolved and particulate phases under low flow conditions (Schneiderman et al. 2002).

12.8 EXAMPLE SIMULATIONS 12.8.1 USE

OF

GWLF

TO

EVALUATE BMPS

New York City DEP used GWLF to evaluate the effectiveness of New York City’s watershed management programs to control phosphorus loads to the Cannonsville Water Supply Reservoir (New York City Department of Environmental Protection 2001). The Cannonsville Reservoir, located in the Catskill Mountains of New York and a part of the New York City water supply system, is considered vulnerable to problems of eutrophication caused by excessive nutrient loadings, especially P. Sources of P include agricultural and urban runoff, failing septic systems, and wastewater treatment plants (WWTPs). Cannonsville reservoir generally borders between eutrophic and mesotrophic conditions depending on the meteorology and reservoir operations for any particular year (Effler and Bader 1998). To help alleviate and prevent eutrophication, the NYC DEP has invested significant resources in watershed management programs to help control nutrient loading to New York City’s water supply reservoirs. Evaluation of the effectiveness of these programs is a critical component of New York City’s watershed management programs. Four watershed management programs addressing both point and nonpoint sources were evaluated using GWLF: wastewater treatment plant upgrades, agricultural BMPs, urban stormwater BMPs, and septic system upgrades. The GWLF model, calibrated for the Cannonsville watershed, was first used to estimate P loads for a 34-year time series of historical meteorology under premanagement, or baseline, conditions. P reductions due to each watershed management program were then estimated from BMP implementation and effectiveness data. These reductions were incorporated in a management scenario application of the model. The baseline scenario represents the watershed loads that would have occurred over the 34-year time period under the current land-use conditions with no BMPs and no reductions in wastewater loads; the management scenario represents the watershed loads for the same 34-year time period with all BMPs, septic system upgrades, and WWTP upgrades in effect. Using the 34-year meteorologic time series as input to drive the model enabled a comparison of the management scenario with the baseline scenario for a realistic range of climatic conditions for the watershed (see Table 12.1).


288


TABLE 12.1 Dissolved Phosphorus Removal Rates, Percent Land Use Affected by Best Management Practices, and Percent Reduction by Land Use for Agricultural and Urban Best Management Practices and Septic System and Wastewater Treatment Plant Upgrades

Agricultural BMPs

Percent BMP Dissolved Removal Rate

Animal waste system 10.0 Barnyard runoff management 30.0 Conservation tillage –42.0 Contour strip crop 35.0 Grass filter strip 26.0 Nutrient management plan 27.0 Riparian forest buffers 62.0 Percent reduction in load for land use ->

Percent Land Use Area Affected by BMP Corn

Alfalfa

Grass

4.3

4.3

1.1

1.6 0.3

1.6 0.3

0.2

12.7 3.5 0.0 0.6 6.9

24.8 5.5 0.0 0.9 12.7

3.2 1.2 1.9 0.0 3.6

Commercial Pervious

7.9 3.3 1.8 0.0 6.1

Percent of Population Served by Different System Types Septic System Upgrades Septic Type ->

Normal

Ponded

Baseline 74.0 Management 93.5 Percent reduction in load for land use -> WWTP Upgrades

20.8 5.2 75

Short Circuited

2.6 0.7 75

Daily WWTP Load (kg/day)

Baseline Management Percent reduction in load for land use ->

9.50 1.58 83.4

Note: BMP = best management practices; WWTP = Wastewater treatment plant.


Direct Discharge

2.6 0.7 75


289

Dissolved P reduction factors were estimated from watershed management and BMP implementation data (Table 12.1). Watershed-scale P reduction factors for agricultural and urban stormwater runoff were estimated by combining available data on P removal efficiency of individual BMPs (derived from literature review) with the areal extent of BMP implementation in the watershed (derived from watershed management program data). Combined effects of multiple BMPs on land-use-specific loads were compounded — rather than simply added — for agricultural land uses because individual agricultural farm fields are typically impacted by multiple BMPs. For urban land uses, combined effects of multiple BMPs applied in a watershed were treated additively, assuming a single urban BMP system is implemented at each urban stormwater management site. Septic system P reductions were estimated based on program targets of 75% remediation assuming current funding levels. WWTP reductions were based on New York State point source discharge permitted flows and effluent P limits. The final reduction factors given in Table 12.1 represent the percent of reduction in load from each individual land use. The estimated reduction in dissolved P loading due to combined implementation of all four watershed management programs was substantial, exceeding 25% (Figure 12.4). Reductions in total watershed loads depended on a combination of the effectiveness of implemented BMPs, the extent of BMP implementation, and the watershed-wide contribution of P sources under baseline conditions. Urban stormwater management provided relatively minor reductions (0.1%) in dissolved P due to the small amount of urban land-use areas in this watershed. Wastewater treatment plant upgrades (16.0%) and the implementation of agricultural BMPs (8.1%) provided most of the estimated loading reduction.

12.8.2 ACCURACY OF GWLF: COMPARISON TO MEASURED LOADS

OF

SIMULATED

Accuracy of GWLF model predictions can be tested by comparing simulated to measured loads. Whereas the original GWLF model was published as a model that could be used without calibration, it and the various versions of GWLF currently in use can be calibrated. NYC DEP (Schneiderman et al. 2002) tested a modified version of GWLF with calibration of nutrient, sediment, and baseflow recession parameters. The calibration was limited in that runoff parameters (CNs) were not calibrated, and accuracy of the runoff component of stream flow was not tested. The calibrated model provided reasonable estimates of total stream flow, dissolved P, and total P. Goodness-of-fit of model predictions vs. stream measurements as measured by the Nash-Sutcliff coefficient of model efficiency (Nash and Sutcliffe 1970) exceeded 0.8 for stream flow, 0.6 for dissolved P, and 0.7 for total P during both calibration and validation periods (Figure 12.5). Calibration was found to improve results substantially for estimation of stream flow during low flow periods and for particulate and total P.


290

20000

16000

Baseline scenario Management scenario

14000 12000 10000 8000 6000 4000 2000 0

Forest / Agricultural Grass Shrub Runoff Runoff

Urban Runoff

Groundwater Flow

Septic Systems

WWTPs

% Reduction for Land Use

23.5%

-0.1%

3.4%

0.5%

75.0%

83.3%

% Reduction for Total

8.1%

0.0%

0.1%

0.1%

2.6%

16.0%

Total

27.1%

FIGURE 12.4 Dissolved P loadings (kg/yr) for baseline and management scenarios including corresponding percent reductions broken down by land use for Cannonsville watershed. The management scenario includes combined implementation of all four watershed management programs.



Dissolved Phosphorus (kg/yr)

18000

15 10 5 0 5

10

15

20

25

20 15 10 5 0

30

0

Modeled dissolved P (kg/mo)

r2 = .70

3000

2000

1000

8000 r2 = .62 6000

4000

2000

0

0

3000

2000

1000

0

0

Observed dissolved P (kg/mo)

Observed dissolved P (kg/mo)

15,000

30000 Modeled total P (kg/mo)

r2 = .96 12,000 9,000 6,000 3,000

r2 = .74 25000 20000 15000 10000 5000

Observed total P (kg/mo)

30000

9,000 12,000 15,000

25000

6,000

20000

3,000

15000

0

10000

0

0

0

Modeled total P (kg/mo)

5 10 15 20 25 30 Observed streamflow (cm/mo)

5000

Modeled dissolved P (kg/mo)

Observed streamflow (cm/mo)

8000

20

r2 = .84

25

6000

25

0

30

4000

r2 = .87

2000

30

291

Modeled streamflow (cm/mo)

Modeled streamflow (cm/mo)


Observed total P (kg/mo)

FIGURE 12.5 Correlations between observed and modeled monthly stream flow, dissolved P and total P during the calibration period (water year 1992), and verification period (water year 1993 to 1996, excluding January 1996). Solid line is the line of perfect fit; dashed line is the regression line; and R2 is the Nash-Sutcliffe model error statistic.


292


12.8.3 SIMULATION

OF

RUNOFF VOLUMES

AND

SOURCE AREAS

With the development of the VSLF, NYC DEP revisited the accuracy of model predictions for the Cannonsville Reservoir watershed, with particular emphasis on accuracy of runoff estimates and on identification of predicted runoff source areas. The base flow separation technique of Arnold et al. (1995) provided runoff estimates based on stream flow records that were used to calibrate VSLF runoff parameters and to test the accuracy of modeled runoff predictions. Comparison of modeled to base-flow-separated runoff for the West Branch Delaware River at Walton (USGS Gage 01423000) upstream of the Cannonsville reservoir using the uncalibrated original GWLF vs. the calibrated VSLF model revealed that the uncalibrated original GWLF model substantially underestimated runoff during both the growing and the dormant season, whereas CN calibration and incorporation of the Arnold et al. (1998) method for calculating available moisture storage (Equation 12.5 through 12.7) in VSLF greatly improved runoff estimates (Figure 12.6). Similar analyses for 31 USGS-gaged catchments in the Catskill Mountain region of New York revealed the same pattern (Figure 12.7). Comparison of runoff predictions for the original GWLF and the VSLF models show that the underlying runoff generating mechanism (infiltration excess vs. saturation excess) the models use to estimate runoff has significant implications for evaluating source areas for runoff and chemical constituents of runoff. The original GWLF model runoff predictions are controlled by land-use patterns, whereas VSLF runoff predictions follow the pattern of soil wetness due to saturation as depicted in a wetness index. In an example subarea of Cannonsville watershed, depicted in Figure 12.8, GWLF predicts most of the runoff coming from cornfields and predicts that all areas of a particular land use generate runoff equally. 10

10

Grow seas bias/R2: .01/.75 Dorm seas bias/R2: -.06/.84

8

Simulated event runoff

Simulated event runoff

Grow seas bias/R2: -.64/.52 Dorm seas bias/R2: -.65/.44

6

4

2

8

6

4

2

growing dormant

growing dormant

0

0 0

2

4

6

8

Baseflow-separated event runoff

10

0

2

4

6

8

10

Baseflow-separated event runoff

FIGURE 12.6 Scatterplots (with growing and dormant season bias and Nash-Sutcliffe performance parameters) of base-flow-separated vs. -simulated event runoff for West Branch Delaware River at Walton, using the original GWLF model with default CNs vs. the GWLFVSLF model with calibrated CNs.



293

GWLF Default CNs Growing Season GWLF Default CNs Dormant Season

VSLF Calibrated CNs Growing Season VSLF Calibrated CNs Dormant Season -1.0

-0.5

0.0

0.5

1.0

R2

GWLF Default CNs Growing Season GWLF Default CNs Dormant Season

VSLF Calibrated CNs Growing Season VSLF Calibrated CNs Dormant Season

-1.0

-0.5

0.0

0.5

1.0

Bias FIGURE 12.7 Nash-Sutcliffe (R2) and bias performance statistics for simulated vs. base- flow-separated runoff during growing and dormant seasons using the original GWLF model with default CNs vs. the VSLF model with calibrated CNs. Box depicts the 10th percentile, median, and 90th percentile values, the tails extend from the minimum to the maximum values. Data are based on results of model runs for 31 U.S. Geological Surveygaged watersheds in the Catskill Mountain region of New York.


294


a) Land Use

stream water road-rural

b) Wetness Index

corn alfalfa grass

forest-deciduous forest-coniferous grass-shrub

Dry 0.1

c) GWLF : April Runoff

Wet 5.6

6.5 7.1 7.8 Wetness Index

9.1 27.8

d) VSLF : April Runoff

Dry 0.0

Runoff Depth (cm)

e) GWLF : April Dissolved P

Low 0.0

Wet 10.7

f) VSLF : April Dissolved P

High 0.1 km

Dissolved P (kg/ha) 0

0.5

1

FIGURE 12.8 Maps for an example subarea of the Cannonsville watershed of (a) land use; (b) wetness index; (c) mean April runoff (cm) predicted by GWLF; (d) mean April runoff predicted by VSLF; (e) mean April P export (kg/ha-month) predicted by GWLF; and (f) mean April P export predicted by VSLF. Corn fields are outlined in white.



295

In contrast, the spatial pattern of runoff predicted by VSLF follows the pattern of the wetness index, with high wetness index areas generating most of the runoff. The implications of the runoff generating mechanism for P predictions are visible in Figures 12.8e and 12.8f. In the original GWLF model all areas of a particular land use generate P equally, as shown in Figure 12.8e. VSLF simulates a more complex distribution of P generation in which the effects of both land use and topographic position (through the wetness index) result in P losses as shown in Figures 12.8f. By more realistically capturing the complexities of P generation on the landscape, VSLF may be useful for evaluating watershed management practices that precisely target P sources. For example, precision agricultural management can focus on reducing P availability in those specific portions of farm fields that generate most of the runoff through selective fertilizer spreading practices.

12.9 SENSITIVITY ANALYSIS Sensitivity of GWLF model response to variation in model input parameters is very straightforward. Loading functions tend to be fairly simple, with often a single parameter directly controlling simulated flow or chemical load in a linear or exponential relationship. By keeping the loading function relationships simple, the problem of estimating many parameters and the need to determine which subset of a large parameter set has the greatest effect on model output are avoided. In the hydrologic submodel, runoff volumes are an exponential function of the CN, whereas runoff timing is determined by a single linear reservoir coefficient (in VSLF). Base flow is determined by a simple recession coefficient, snowmelt by a melt coefficient, and ET by a vegetative cover coefficient for each HRU type. Water-quality loading functions are equally transparent with regard to the sensitivity of the model, with concentration coefficients that are linear (i.e., nutrients) or exponential (i.e., total suspended solids) factors, which, when combined with runoff and erosion amounts, directly determine model output loads.

12.10 AVAILABILITY OF MODEL The original GWLF model is a compiled program that is available, along with documentation, from the author, Dr. Douglas Haith, at Cornell University (dah@cornell. edu). VSLF can be obtained from the NYC DEP, Bureau of Water Supply, Division of Water Quality Control, Watershed Modeling Section (eschneiderman@ dep.nyc.gov). This version is developed using Vensim visual modeling software and can be applied to any watershed using the Vensim Reader (available for free from http://www.vensim.com). AVGWLF is available from the Pennsylvania State Institutes of the Environment (http://www.avgwlf.psu.edu). The software is designed for use in Pennsylvania and application to other states requires code and algorithm changes and the assistance of the software developers. BasinSim is available from the Virginia Institute of Marine Science (http://www.vims.edu). These are all noncommercial versions of GWLF.


296


REFERENCES Arnold, J.G., P.M. Allen, R. Muttiah, and G. Bernhardt. 1995. Automated base flow separation and recession analysis techniques. Ground Water 33(6):1010–1018. Arnold, J.G., R. Srinivasan, R.S. Muttiah, and J.R. Williams. 1998. Large area hydrologic modeling and assessment part I: model development. J. Am. Water Resour. Assoc. 34(1):73–89. Beven, K.J. 2001. Rainfall-Runoff Modelling: The Primer. Chichester, U.K.: John Wiley & Sons. Beven, K.J. and M.J. Kirkby. 1979. A physically-based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull. 24:43–69. Bicknell, B.R., J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobs, and A.S. Donigian, Jr. 2001. Hydrological Simulation Program-Fortran: HSPF Version 12 User’s Manual. Mountain View, CA: Aqua Terra Consultants. Dai, T., R.L. Wetzel, R.L. Tyler, and E.A. Lewis. 2000. BasinSim 1.0: A Windows-based watershed modeling package. Virginia Institute of Marine Science, College of William and Mary, Williamsburg, VA. Dunne, T. and L. Leopold. 1978. Water in Environmental Planning. New York: W.H. Freeman and Co. Effler, S.W. and A.P. Bader. 1998. A limnological analysis of Cannonsville Reservoir, NY. Lake Reservoir Manage. 14(2–3):125–139. Evans, B.M., D.W. Lehning, K.J. Corradini, G.W. Petersen, E. Nizeyimana, J.M. Hamlett, P.D. Robillard, and R.L. Day. 2002. A comprehensive GIS-based modeling approach for predicting nutrient loads in watersheds. J. Spatial Hydrol. 2(2):1–18. Fisher, T.R., J.D. Hagy, III, W.R. Boynton, and M.R. Williams. 2006. Cultural eutrophication in the Choptank and Patuxent estuaries of Chesapeake Bay. Limnol. Oceanogr. 51(1, part 2):435–447. Gitau, M.W., W.J. Gburek, and A.R. Jarrett, 2005. A tool for assessing BMP effectiveness for phosphorus pollution control. J. Soil Water Conserv. 60(1):1–9. Haith, D.A. and L.L. Shoemaker. 1987. Generalized Watershed Loading Functions for stream flow nutrients. Water Resour. Bull. 23(3):471–478. Haith, D.A., R. Mandel, and R.S. Wu. 1992. Generalized Watershed Loading Functions Version 2.0 User’s Manual. Ithaca, NY: Cornell University. Hawkins, R.H. 1978. Runoff curve numbers with varying site moisture. Proc. Am. Soc. Civ. Eng. J. Irrig. Drain. Div. 104(IR4):389–398. Lee, K.-Y., T.R. Fisher, T.E. Jordan, D.L. Correll, and D.E. Weller. 2000. Modeling the hydrochemistry of the Choptank River Basin using GWLF and Arc/Info. 1: model calibration and validation. Biogeochemistry 49:143–173. Lee K.-Y., Fisher T.R., and E.J. Rochelle-Newall. 2001. Modelling the hydrochemistry of the Choptank River Basin using GWLF and Arc/Info. 2: model application. Biogeochemistry 56:311–348. Nash, J.E. and J.V. Sutcliffe. 1970. River flow forecasting through conceptual models. Part 1 — a discussion of principles. J. Hydrol. 10:282–290. Natural Resources Conservation Service. 1997. National Engineering Handbook, Part 630 Hydrology, Section 4, Chapter 5. Natural Resources Conservation Service. 2003. National Soil Survey Handbook, title 430-VI. Available at http://soils.usda.gov/technical/handbook/. Needelman, B.A., W.J. Gburek, G.W. Petersen, A.N. Sharpley, and P.J.A. Kleinman. 2004. Surface runoff along two agricultural hillslopes with contrasting soils. Soil Sci. Soc. Am. J. 68:914–923.



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New York City Department of Environmental Protection. 2001. New York City’s 2001 Watershed Protection Program Summary, Assessment and Long-Term Plan. Valhalla, NY: New York City Department of Environmental Protection. New York City Department of Environmental Protection. 2005. Multi-Tiered Water Quality Modeling Program Semi-Annual Status Report — EPA Filtration Avoidance Deliverable Report. Valhalla, NY: New York City Department of Environmental Protection. Ogrosky, H.O. and V. Mockus. 1964. Hydrology of agricultural lands, Chapter 21 in Handbook of Applied Hydrology, V.T. Chow (Ed.). New York: McGraw-Hill Publishing Co. Schneiderman, E.M., D.C. Pierson, D.G. Lounsbury, and M.S. Zion. 2002. Modeling of hydrochemistry of the Cannonsville Watershed with Generalized Watershed Loading Functions (GWLF). J. Am. Water Resour. Assoc. 38(5):1323–1347. Schneiderman, E.M., T.S. Steenhuis, D.J. Thongs, Z.M. Easton, M.S. Zion, A.L. Neal, G.F. Mendoza, and M.T. Walter. 2006. Incorporating variable source area hydrology into a curve number based watershed model. Hydrol. Process., in press. Sharpley, A.N. 1995. Dependence of runoff phosphorus on extractable soil phosphorus. J. Environ. Qual. 24:920–926. Soil Conservation Service. 1972. National Engineering Handbook, Part 630 Hydrology, Section 4, Chapter 10, U.S. Department of Agriculture, Washington, D.C. Soil Conservation Service. 1986. Urban Hydrology for Small Watersheds, U.S. Department of Agriculture, Technical Release 55, Washington, D.C.: U.S. Government Printing Office. Srinivasan, M.S., W.J. Gburek, and J.M. Hamlett. 2002. Dynamics of stormflow generation — a field study in east-central Pennsylvania, USA. Hydrol. Process. 16(3):649–665. Steenhuis, T.S., M. Winchell, J. Rossing, J.A. Zollweg, and M.F. Walter. 1995. SCS runoff equation revisited for variable-source runoff areas. ASCE J. Irrig. Drain. Eng. 121:234–238. U.S. Environmental Protection Agency. 1983. Results of the nationwide urban runoff program. NTIS PB 84-185552, Washington, D.C. U.S. Environmental Protection Agency. 1999. Protocol for developing nutrient TMDLs. EPA 841-B-99-007, Office of Water, Washington, D.C. Walter, M.T., E.S. Brooks, M.F. Walter, T.S. Steenhuis, C.A. Scott, and J. Boll. 2001. Evaluation of soluble phosphorus loading from manure-applied fields under various spreading strategies. J. Soil Water Conserv. 56(4):329–336. Winer, R. 2000. National Pollutant Removal Performance Database for Stormwater Treatment Practices, 2nd ed. Ellicott City, MD: Center for Watershed Protection. Wischmeier, W.H. and D.D. Smith. 1978. Predicting rainfall erosion losses — a guide to conservation planning. U.S. Department of Agriculture, Agriculture Handbook 537, Washington, D.C.


Section III Phosphorus Indices, Best Management Practices, and Calibration Data


13

Phosphorus Indices Jennifer Weld The Pennsylvania State University, University Park, PA

Andrew N. Sharpley U.S. Department of Agriculture-Agricultural Research Service, University Park, PA

CONTENTS 13.1

History of Development.............................................................................301 13.1.1 Background ..................................................................................301 13.1.2 Development ................................................................................304 13.2 Index Framework .......................................................................................306 13.2.1 Parameters....................................................................................306 13.2.2 Calculating a Phosphorus Index Value........................................322 13.3 Inclusion of Best Management Practices Factors .....................................323 13.3.1 Examples of Index Site Assessment and Interpretation..............323 13.4 Integration of P Indices into Existing Models or Nutrient Management Planning Software.............................................325 13.5 Field Testing ..............................................................................................326 13.6 Availability of P Indices ............................................................................327 13.7 Conclusions ................................................................................................327 References..............................................................................................................328

13.1 HISTORY OF DEVELOPMENT 13.1.1 BACKGROUND In response to mounting water-quality concerns, many states have developed guidelines for land application of phosphorus (P) and watershed management based on the potential for P loss in agricultural runoff (U.S. Department of Agriculture and U.S. Environmental Protection Agency 1999). These actions have been spurred, in part, by a federal initiative in which the U.S. Department of Agriculture (USDA) and U.S. Environmental Protection Agency (USEPA) created a joint strategy to implement Comprehensive Nutrient Management Plans (CNMPs) on animal feeding operations with a national deadline of 2008.

301


302


Alaska and Hawaii adopted the P Index P Index Soil test crop response P Index and/or environmental P threshold or soil test crop response

FIGURE 13.1 Summary of P management strategies adopted by state USDA-NRCS agencies for revision of the 590 nutrient management practice standard. (From Sharpley, A.N. et al. 2003. Journal of Soil and Water Conservation 58: 137–152. With permission)

Under the USDA–USEPA joint strategy, USDA’s Natural Resources Conservation Service (NRCS) is charged with implementing a new nutrient management policy. As a result, the NRCS planning standard addressing nutrient management (590 standard), which was based on nitrogen (N), has been rewritten to include a P-based planning standard. In each state, NRCS state conservationists must decide which of three P-based approaches will be used in nutrient management planning policy. These approaches are agronomic soil test P (STP) recommendations, environmental STP thresholds, or a P Index to rank fields according to their vulnerability to potential P loss. States have already selected the P-based strategies for their 590 standard. The P Index has been selected for most states’ 590 standards (Figure 13.1). Reasons for widespread adoption of the P Index approach are that other P management options (i.e., agronomic and environmental STP) are inflexible, overly restrictive, and do not account for the critical role of transport mechanisms in determining a site’s P loss potential. Generally, most P exported from agricultural watersheds derives from only a small part of the landscape during a few relatively large storms, where hydrologically active areas of a watershed contributing surface runoff to stream flow are coincident with areas of high soil P or recent manure applications. Even in regions where subsurface flow pathways dominate P transport (e.g., some areas of the coastal plains), areas contributing P to drainage waters are localized to soils with high soil P saturation and hydrologic connectivity to the surface drainage network.


Phosphorus Indices

303

TABLE 13.1 Factors Influencing P Loss from Agricultural Watersheds and Their Impact on Surface Water Quality Factors

Erosion Surface runoff Subsurface flow

Soil texture Irrigation runoff Connectivity to stream Channel effects

Proximity of P-sensitive water Sensitivity P input

Soil P Applied P

Application method Application timing

Description Transport Total P loss strongly related to erosion. Can carry soluble P released from soil or other P sources. In sandy, organic, or P-saturated soils, P can leach through the soil. Phosphorus can also move through the soil by preferential flow through macropores. The presence of artificial drainage can capture this subsurface flow and move it directly to surface water. Influences relative amounts of surface and subsurface flow occurring. Improper irrigation management can induce surface runoff and erosion of P. The closer the field to the stream, the greater the chance of P reaching it. Eroded material and associated P can be deposited or resuspended with a change in stream flow. Dissolved P can be sorbed or desorbed by stream channel sediments and bank material and be taken up by or mineralized from biota. Some watersheds are closer to P-sensitive waters than others (i.e., point of impact). Shallow lakes with large surface area tend to be more vulnerable to eutrophication. Source Management As soil P increases, P loss in surface and subsurface flow increases. The more total or soluble P (mineral fertilizer or manure), the greater the risk of P loss. Site Management P loss increases in the order: subsurface injection; plowed under; and surface broadcast with no incorporation. The sooner it rains after P is applied, the greater the risk for P loss.

Source: Adapted from A.N. Sharpley, J.L. Weld, D.B. Beegle, P.J.A. Kleinman, W.J. Gburek, P.A. Moore, and G. Mullins, Journal of Soil and Water Conservation 58, 137–152, 2003. With permission.

To be effective, risk assessment must consider critical source areas within a watershed that are most vulnerable to P loss in surface runoff. Critical source areas are dependent on the coincidence of transport (i.e., surface runoff, erosion, and subsurface flow) and source factors (i.e., soil, fertilizer, manure) as influenced by site management (Table 13.1). Transport factors mobilize P sources, creating pathways of P loss from a field or watershed. Source and site management factors are typically well defined and reflect land-use patterns related to soil P status, mineral fertilizer and manure P inputs, and tillage.


304


13.1.2 DEVELOPMENT The P Index was originally developed to identify the vulnerability of agricultural fields to P loss (Lemunyon and Gilbert 1993). The original Index accounted for and ranked transport and source factors controlling P loss in surface runoff from a given site. Each site factor affecting P loss was weighted, assuming that certain factors have a different effect on P loss than others. A P Index value, reflecting site vulnerability to P loss, was determined by selecting the rating value for each site factor, multiplying that value by the appropriate weighting coefficient, and summing the weighted products of all factors. Since its inception, three major changes have been introduced to many revised versions of the P Index. First, source and transport factors are related in a multiplicative rather than additive fashion to better represent actual site vulnerability to P loss (Gbuerk et al. 2000). For example, if surface runoff does not occur at a particular site, its vulnerability should be low regardless of the soil P content. In the original P Index, a site’s risk could be ranked as very high based on site-management factors alone, even though no surface runoff or erosion occurred (Lemunyon and Gilbert 1993). On the other hand, a site with a high potential for surface runoff, erosion, or subsurface flow but with low soil P has a low risk for P loss, unless P as mineral fertilizer or manure is applied. Second, an additional transport factor reflecting distance from the stream has been incorporated into the P Index. The contributing distance categories in revised P indices are based on hydrologic analysis that considers the probability, or risk, of occurrence of a rainfall event of a given magnitude resulting in sufficient runoff to potentially transport P offsite. The third major change in Index formulation has been the use of continuous, open-ended parameter scaling for erosion, STP, and P application rate, as either fertilizer or manure. This enables indices to better address the effect of the very high erosion and STP values of the original P Index on P loss potential and to avoid having to subjectively quantify these categories. Finally, the open-ended scaling of erosion, STP, and P rate avoided the unrealistic situation where a one- or two-unit increase in any of these parameters could change risk category and dramatically alter P Index rating and its interpretation. Though the P Index concept has been broadly adopted, its development from a concept into a field-assessment tool has followed several different trends throughout the United States. The variations reflect not only regional differences in P transport but also philosophical differences as to how P risk from a site should be assessed using a P Indexing approach. Current research and field evaluations play a significant role in the continued modification of P indices to best fit and address regional and state conditions. This has resulted in many states incorporating unique factors that extend beyond the scope of the three previously described P Index modifications adopted by many revised P indices. As mentioned already, computation of final P Index values can be additive, as originally proposed by Lemunyon and Gilbert (1993), or multiplicative, as proposed by Gburek et al. (2000) (Table 13.2 and Table 13.3). Seventeen of the reviewed indices use the multiplicative approach, whereas 20 use the additive approach.


Phosphorus Indices

305

TABLE 13.2 The P Index Approach Using Pennsylvania’s Index Version 1 as an Example PART A: SCREENING TOOL Evaluation Category > 200 mg P kg−1 < 150 ft

Soil Test P (Mehlich-3) Contributing Distance

If yes to either factor then proceed to Part B

PART B: SOURCE FACTORS Soil Test P (mg P kg−1)

Soil test (Mehlich-3P) Fertilizer P rate Manure P rate P source application method

Manure P availability

Soil Test P Rating = 0.20a Soil Test P (mg P kg−1) Fertilizer P (lb P2O5/acre) Manure P (lb P2O5/acre) 0.2 0.4 0.6 0.8 1.0 Placed or Incorporated Incorporated > 1 Incorporated >1 week Surface applied injected 2" 500 ft

2 Low

2 500 to 350 ft

Soil Loss (ton/acre/yr) 4 Medium 1 Some 4 350 to 250 ft

6 High

6 150 to 250 ft

8 Very high 2a Patterned 8 < 150 ft

Transport Sum = Erosion + Runoff Potential + Sub-Surface Drainage + Contributing Distance Modified connectivity

0.7 1.0 1.1 Riparian buffer: Grassed waterway or none Direct connection: applies to distance applies to distance < 150 ft > 150 ft Transport Factor = Modified Connectivity × (Transport Sum/22) Phosphorus Index Value = 2 × Source Factor × Transport Factor

a

Or rapid permeability soil near a stream.

Source: Adapted from J.L. Weld, D. Beegle, W.J. Gburek, P.J. Kleinman, and A.N. Sharpley. 2003. The Pennsylvania Phosphorus Index: Version 1, Extension PUBLICATIONS.CAT US 180 5m3/03ps 4591. With permission.


306


TABLE 13.3 General Interpretations and Management Guidance Using Pennsylvania’s P Index P Index Value

Rating

< 59

Low

60 –79

Medium

80 –100

High

> 100

Very high

General Interpretation If current farming practices are maintained, there is a low risk of adverse impacts on surface waters. Chance for adverse impacts on surface waters exists, and some remediation should be taken to minimize P loss. Adverse impact on surface waters. Conservation measures and P management plan are needed to minimize P loss. Adverse impact on surface waters. All necessary conservation measures and P management plan must be implemented to minimize P loss.

Management Guidance N-based applications

N-based applications

P application limited to crop removal of P

No P applied

Source: Adapted from J.L. Weld, D. Beegle, W.J. Gburek, P.J. Kleinman, and A.N. Sharpley. 2003. The Pennsylvania Phosphorus Index: Version 1, Extension PUBLICATIONS.CAT US 180 5m3/03ps 4591. With permission.

In addition to using the multiplicative approach, the Pennsylvania P Index varies the transport factor from 0 to 1 (Table 13.2). The original P Index outlined an approach to identify sites with a high vulnerability to P loss based on evaluation of a variety of P source and transport factors. Most states (44 of 47) (Table 13.4) have maintained this original approach and have examined site vulnerability to P loss. However, in response to questions regarding the relationship between P Index values and actual P loadings, several states have taken a different approach. This approach adopted by Arkansas, Georgia, and Iowa uses source, transport, and management factors common to most other indices, but instead of estimating a vulnerability to or potential for P loss, calculates an estimated P loss that is used either directly or converted to a relative PI Index value (Table 13.4).

13.2 INDEX FRAMEWORK 13.2.1 PARAMETERS P indices include assessments of both source management and transport factors to facilitate the assessment and identification of critical source areas. These factors have been chosen because they determine P loss in most cases (Table 13.1).


State

Alabama

Alaska

Arizona

Arkansas

Colorado

Delaware

Florida

Reference

NRCS (2001a)

NRCS (2001b)

Walther et al. (2000)

DeLaune et al. (2004a, 2004b)

Sharkoff et al. (2000)

Sims and Leytem (2002)

NRCS (2000a)

Soil P test

Mehlich-1 P Mississippi extract

Application rate

lb P2O5/ac/year

Application method

Injection Incorporation Sprinkler application Surface applied Days to incorporation

Application timing Management

Animal access to surface waters

Mehlich-3 P

lb P2O5/ac/year Injection Incorporation Sprinkler application Surface applied Season applied Cover at application —

Source Factors Olsen-P (High pH) Mehlich-3 P Bray P-1 (Low pH)

Olsen-P (High pH) Bray P-1 (Low pH) Mehlich-3 P lb P2O5/ac/year

FIV based on Mehlich-3 P

FIV based on Mehlich-1 P

lb P2O5/ac/year

lb P2O5/ac/year Waste water volume

lb P2O5/ac/year

lb soluble P/ac/year

Injection Incorporation Surface applied

Incorporation Surface applied



Irrigation Incorporation Surface applied

Time to planting

Season applied

Organic P source availability Grazing intensity

Season applied Time to incorporation Organic P source availability

Time to incorporation

Grazing and feeding management

Season applied Time to incorporation Polyacrylamides Cover crops

Phosphorus Indices

TABLE 13.4 P Index Approaches and Modifications

Organic P source availability

(continued)

307


308

TABLE 13.4 (CONTINUED) P Index Approaches and Modifications State

Alabama

Alaska

Arizona

Arkansas

Colorado

Delaware

Florida

Reference

NRCS (2001a)

NRCS (2001b)

Walther et al. (2000)

DeLaune et al. (2004a, 2004b)

Sharkoff et al. (2000)

Sims and Leytem (2002)

NRCS (2000a)

Water (RUSLE) Gully erosion

Surface runoff class

Hydrologic soil group Field slope

Subsurface drainage/ flooding

Underground outlet systems

Contributing distance Connectivity

Distance to water

Water (RUSLE/USLE) Wind (WEQ) Irrigation Hydrologic soil group Field slope Average precipitation —

Transport Factors Water (RUSLE) Water (RUSLE) Wind (WEQ) Irrigation (QS value) Soil permeability Curve number class Field slope Field slope Precipitation

—

Flooding frequency

—

Water (RUSLE)

Water (RUSLE) Irrigation

Soil permeability class Field slope

Hydrologic soil group Field slope Artificial drainage

—

Drainage Water table depth Leaching rating

Leaching potential Soil properties

—

Distance from field to water Vegetated buffer width

Existence of a discharge Wetlands Buffer strip Detention/treatment area


Watershed

Filter strip width


Existence of a discharge Presence of a buffer

— Buffer width

—

Filter strips Contour buffer strips


Erosion

State Reference

Distance to critical habitat water

Value of water body

Additive Risk assessment

Additive Risk assessment

Georgia Cabrera et al. (2002)

— Additive Risk assessment

Illinois NRCS (2002a)

Soil P test

Mehlich-1 P

Bray P-1 Mehlich-3

Application rate

lb P2O5/ac/year

Application method

Injection Incorporation Sprinkler application Surface applied Season applied Time to incorporation

Percent of annual recommended rate Injection Incorporation Surface applied


Solubility factor for P sources

—

Incorporation before or after a runoff event —

—

Multiplicative Loss assessment Iowa NRCS (2004a)

Additive Risk assessment Kansas Davis et al. (2004b)

State watershed categories

Value of water body

Multiplicative Risk assessment


Kentucky NRCS (2001c)

Louisiana NRCS (2000b)

Source Factors Bray P-1 Mehlich-3 P Olsen P lb P2O5/ac/year

Bray P-1 Mehlich-3 P Olsen P lb P2O5/ac/year

Mehlich-3 P





Season applied Time to incorporation Soil conservation practices Tillage

Time to planting Time to incorporation

Season applied Cover at application —

Season applied Time to incorporation

—

—

Phosphorus Indices

Receiving water priority Index Value Determination

Strong Bray P

lb P2O5/ac/year

Varied weighting factors for organic P sources (continued)

309


310

TABLE 13.4 (CONTINUED) P Index Approaches and Modification State Reference

Georgia Cabrera et al. (2002)

Illinois NRCS (2002a)

Water (RUSLE) Bioavailability factor

Water (RUSLE)


Curve number Location

Hydrologic soil group

Subsurface drainage/flooding

Leaching curve number Percolation index Depth to water table

Discharge into a tile inlet

Contributing distance Connectivity

—

Buffer width

Receiving water priority


—

Distance to surface water Discharge to waterway or surface drain outlet —

Kansas Davis et al. (2004b)

Transport Factors Water (RUSLE) Ephemeral Classic gully Curve number Precipitation

Water (RUSLE) Sprinkler Furrow irrigation Soil permeability class Field slope

Tile drainage Field slope Soil texture Precipitation Watershed Distance to stream

Buffer presence and width —

—

Distance to stream

Connected to stream

—

Kentucky NRCS (2001c)

Louisiana NRCS (2000b)

Land cover percent

Water (RUSLE)

Hydrologic soil group Field slope —


Distance from application to surface water Vegetated buffer width

Edge of field distance to surface water

Impaired watershed County location

Ranked very low to very high

Soil drainage class Depth to water table Artificial drainage

Vegetative buffer width


Soil erosion

Iowa NRCS (2004a)

Maine

Reference

NRCS (2001d)

Coale (2000)

Soil P test

Multiplicative Soluble, runoff, particulate, and leachate assessment

Modified Morgan

Application rate Application method

— —

Application timing

—

Management

Adequate land base to handle manure nutrients

FIV based on Mehlich-1 P lb P2O5/ac/year Injection Incorporation Surface applied Season applied Time to incorporation Organic P source availability

Additive Erosion, runoff, and subsurface drainage assessments Michigan Grigar and Lemunyon (1998) Source Factors Bray P-1


Additive Risk assesssment


Minnesota

Mississippi

Montana

NRCS (2001e)

NRCS (2000c)

Fasching (2001)

Bray P-1 Olsen P

Manure lb P/ac/yr Injection Incorporation Surface applied Time to incorporation

— —

Manure N lb/ac/yr N leaching index Soil management group

—

—

Mississippi soil test P method lb P2O5/ac/year Injection Incorporation Surface applied Time to planting Time to incorporation —

Phosphorus Indices

State

No average PI value Individual risk factors evaluated by field Maryland

Index Value Determination

Olsen-P (High pH) Bray P-1 (Low pH) lb P2O5/ac/year Injection Incorporation Surface applied Time to planting

—

(continued)

311


312

TABLE 13.4 (CONTINUED) P Index Approaches and Modification State

Maine NRCS (2001d)

Reference

Soil erosion

Highly erodible land designation —


—

Contributing distance

—

Connectivity

—

Receiving water priority

State environmental protection classification


Water (RUSLE)

Soil permeability class Field slope Soil drainage class Depth to water table

Edge of field distance to surface water Vegetated buffer width

Maryland Clean Water Action Plan classification

Michigan Grigar et al. (1998) Transport Factors Residue at planting Hydrologic soil group Field slope —

Watershed Presence of surface water Vegetated buffer width Application setbacks —

Minnesota NRCS (2001e)

Water (RUSLE)

—

—

Distance to surface water Presence of a 100-ft filter strip

—

Mississippi NRCS (2000c)

Water (RUSLE)

Soil permeability class Field slope —

Distance to water

—

—

Montana Fasching (2001)

Water (RUSLE) Furrow irrigation Sprinkler irrigation Soil permeability class Field slope —

Distance to concentrated surface water flow Presence of grassed waterway

—



Maryland Coale (2000)

Manure priority matrix Field decision tool

State

Nebraska Kucera (2000)

Reference

Multiplicative Risk assessment New Hampshire NRCS (2001f)

Soil P test

Olsen-P (High pH) Bray P-1 (Low pH)

Mehlich-3 P


lb P2O5/ac/year Injection Incorporation Surface applied Time to planting

lb P2O5/ac/year Injection Incorporation Surface applied Season applied

Management

Soil conservation BMPs

Mehlich-3 calcium Soil pH

Soil erosion

Water (RUSLE) Furrow irrigation Sprinkler irrigation

Water (RUSLE)

Application timing


Field decision matrix with no PI value

New Jersey NRCS (2001g)

New Mexico Flynn et al. (2000)

Source Factors Rutgers values based on Mehlich-3 P — Injection Incorporation Surface applied Time to planting

—

Transport Factors Water (RUSLE)

Multiplicative Risk assessment New York Czymmek et al. (2001)

Additive Risk assesssment North Carolina Havlin et al. (2002)

Olsen-P (High pH) Bray P-1 (Low pH)

Morgans P

Mehlich-3 P

lb P2O5/ac/year Injection Incorporation Surface applied Time to planting

lb P2O5/ac/year Injection Incorporation Surface applied Season applied Time to incorporation —

lb P2O5/ac/year Surface application

Water (RUSLE)

Water (RUSLE) Fe-P soil fraction Field slope

Grazing and feeding management

Furrow irrigation

Phosphorus Indices

Index Value Determination

—

Soil management group

(continued )

313


314


Nebraska Kucera (2000)

Reference Surface runoff class



—

Distance to concentrated surface water flow

Connectivity

Presence of grassed waterway

Receiving water Priority Index Value Determination

— Additive Risk assesssment


Field slope Curve number or saturated soil conductivity Flooding frequency

—

Buffer width

— Multiplicative Risk assessment

New Jersey NRCS (2001g) Curve number Field slope

—

Watershed Edge of P application to surface water —


New Mexico Flynn et al. (2000) Soil permeability class Field slope

—

Edge of field distance to a stream or lake

New York Czymmek et al. (2001) Presence of concentrated flow

Estimated runoff (in.yr)

Soil drainage class Flooding frequency

Impact of artificial drainage Estimated subsurface flow (in./yr)

Flow distance to a blue line stream

Vegetated buffer width

—

—

—


North Carolina Havlin et al. (2002)

Particulate and dissolved P risk assessments

—

Buffer width Sediment retention practices — Particulate, soluble, leachate, and source P risk assessment



New Hampshire NRCS (2001f)

Reference

Soil P test

Application rate Application method Application timing

North Dakota NRCS (2002b)

Olsen-P (High pH) Bray P-1 (Low pH) Mehlich-3 P lb P2O5/ac/year Injection Incorporation Surface applied Season applied Time to incorporation

Ohio NRCS (2002c)

Bray-Kurtz P-1

lb P2O5/ac/year Incorporation Surface applied Cover at application Time to incorporation —

Management

Filter strips; cover crop; no-till; contour buffer strips

Soil erosion

Water (RUSLE) Irrigation

Water (RUSLE) Wind




Oklahoma NRCS (2001h) Source Factors Mehlich-3 P

— Injection Incorporation Surface applied Time to incorporation

—

Transport Factors Water (RUSLE) Soil surface loss potential Field slope Depth of soil Rock size and cover

Oregon NRCS (2001i)

Pennsylvania Weld et al. (2003)

Rhode Island NRCS (2001j)

Olsen-P (E. Oregon) Bray P-1 (W. Oregon)

Mehlich-3 P

Modified Morgan

lb P2O5/ac/year Injection Incorporation Surface applied Season applied

lb P2O5/ac/year Injection Incorporation Surface applied Season applied Time to incorporation

lb P2O5/ac/year Incorporation Surface applied

—

Organic P source availability

Residue

Water (RUSLE), sprinkler irrigation, furrow irrigation, wind Hydrologic soil group Field slope

Water (RUSLE)

Water (RUSLE)


Field slope Presence of surface runoff

Time to incorporation

315

(continued) © 2007 by Taylor & Francis Group, LLC

Phosphorus Indices

State

316

TABLE 13.4 (CONTINUED) P Index Approaches and Modification State Reference

North Dakota NRCS (2002b)

Ohio NRCS (2002c)

—

—



Connectivity

—




Adjacent to a stream

Filter strip 33 ft or wider Concentrated flow to surface channel — Additive Risk Assessment

Flooding frequency

Watershed Application distance to pond, well, sinkhole, intermittent or perennial stream Established buffer strip

Nutrient limited watershed Risk assesssment

Oregon NRCS (2001i)

Pennsylvania Weld et al. (2003)

Rhode Island NRCS (2001j)

Tile drain/soil test P Flooding frequency class

Tile drainage

Drainage class Flooding class



Edge of field distance to receiving surface water

Buffer width and presence

Riparian buffer Direct discharge

Buffer Potential for direct discharge

— Additive Risk Assessment

— Multiplicative Risk assessment



Distance from application to runoff entry to a channel

Oklahoma NRCS (2001h)

South Carolina NRCS (2001k)

Reference

Tennessee NRCS (2001l)

Texas NRCS (2000d) Source Factors TAMU Mehlich-3 Bray P-1; Bray P-2 Olsen-P lb P2O5/ac/year Injection Incorporation Surface applied Season applied Time to incorporation

Soil P test

Mehlich-1

Mehlich-1


Management

lb P2O5/ac/year Injection Incorporation Surface applied Time to planting Time to rainfall/irrigation —

lb P2O5/ac/year Injection Incorporation Surface applied Season applied Cover at application Time to incorporation Varied weighting factors for P sources applied

Soil erosion

Water (RUSLE)

Erosion potential


Curve number Field slope

Hydrologic soil group

Application timing

—

Transport Factors Water (RUSLE) Wind (WEQ)

Curve number Field slope

Utah Goodrich et al. (2000)

—

Vermont Jokela (2001)

Modified Morgan Morgan

— Injection Incorporation Surface applied Time to incorporation

lb P2O5/ac/year Injection Incorporation Surface applied Season applied Time to incorporation

Irrigation efficiency

Modified Morgan reactive aluminum

Cover type Irrigation type Field surface Seasonal precipitation Hydrologic soil group Field slope

Water (RUSLE)

Phosphorus Indices

State

Field slope Curve number or saturated soil conductivity (continued)

317


318


South Carolina NRCS (2001k)

Reference Subsurface drainage/flooding



Distance from edge of application to surface water Buffer zone runoff class — Multiplicative Risk assessment


Texas NRCS (2000d)

Utah Goodrich et al. (2000)

Vermont Jokela (2001)

—

—

Available water holding capacity Depth to water table, bedrock, coarse sandy layer

—

Distance from downstream field edge to surface water

—

Non-application width from surface water conveyance Permanent vegetative Buffer width — Multiplicative Risk assessment

Watershed Edge of field distance to named stream or lake — — Additive Risk Assessment

Runoff containment and discharge —

Buffer width

Winter and Spring/Sumer/Fall risk assessments


—


Connectivity

Subsoil permeability class Depth to water table

Tennessee NRCS (2001l)

Virginia Mullins et al. (2002)

Reference

Soil P test

Mehlich-1 P


lb P2O5/ac/year Injection Incorporation Surface applied Time to incorporation Availability factor for P sources


Soil erosion

Water (RUSLE)


Location, crop Hydrologic soil group Curve number Average annual runoff

Washington NRCS (2001m)

West Virginia NRCS (2002d)

Source Factors Olsen-P (E. Washington) Mehlich-1 P Bray p-1 (W. Washington) lb P2O5/ac/year lb P2O5/ac/year Injection Injection Incorporation Incorporation Surface applied Surface applied Time to planting Season applied — —

Transport Factors Water (RUSLE) Water (RUSLE) Sprinkler irrigation Furrow irrigation Wind Hydrologic soil group Surface runoff from Field slope field (cm)

Wisconsin Jarrell and Bundy (2002)

Bray P-1 lb Soluble P/ac/year Incorporation

Season applied —

Water (RUSLE) Enrichment ratio

Annual runoff Soil solution P concentration

Wyoming NRCS (2002e)

Olsen-P (High pH) Bray P-1 (Low pH) lb P2O5/ac/year Injection Incorporation Surface applied Time to planting Soil P sorption capacity based on soil texture and pH

Phosphorus Indices

State

Water (RUSLE) Irrigation efficiency Flood irrigation efficiency Soil permeability class Field slope

(continued)

319


320


Washington NRCS (2001m)

West Virginia NRCS (2002d)


Location, crop Hydrologic soil group Average annual percolation for row crops/fallow conditions Soil drainage class Soil texture

Tile drain presence/soil test P Flooding frequency class

—


Edge of field distance to intermittent/perenni al stream Buffer width


—

Buffer width and presence —

—

Reference

Wisconsin Jarrell and Bundy (2002) Soil retention properties Depth to water table/groundwater

Wyoming NRCS (2002e) —

Watershed

Connectivity Receiving water Priority Index Value Determination

— Particulate and dissolved P risk assessments

Additive Risk Assessment


—

Buffer strip

— —

Soluble, leaching, and particulate P risk assessments

Source: Adapted from A.N. Sharpley, J.C. Weld, D.B. Beegle, P.J.A. Kleinman, W.J. Gburck, P.A. Moore, and G. Mullins. Journal of Soil and Water Conservation. 58, 137–152, 2003. With permission. © 2007 by Taylor & Francis Group, LLC

Distance from application to surface water



Virginia Mullins et al. (2002)

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Generally, source management factors are soil test P and P application rate, method, and timing; transport factors are erosion, surface runoff, subsurface P loss, and distance to receiving water body. Though these represent the general categories of parameters, many indices have elected to include specialized parameters and categories to appropriately represent their unique regional conditions or areas of environmental concern. Certain variations introduced into the P Index account for factors such as irrigation and flooding, which are unique to certain regions of the country. Other variations in the P Index reflect different approaches to account for best management practice (BMP) impacts, calculate of a P Index value, and estimate of a site’s P loss as compared to its vulnerability to P loss. Unique factors included in various P Index versions vary from STP modifiers (i.e., New Hampshire, Vermont, Wyoming) to estimates of the availability or solubility of the P applied to a site (i.e., Arkansas, Delaware, Florida, Georgia, Louisiana, Maryland, Pennsylvania, Tennessee, Virginia) to flooding frequency (i.e., Arkansas) to BMPs (i.e., Alabama, Arizona, Arkansas, Colorado, Iowa, Nebraska, New Mexico, North Carolina, North Dakota, Rhode Island) to rankings of the priority or sensitivity of receiving water bodies (i.e., Alabama, Alaska, Delaware, Florida, Kentucky, Louisiana, Maine, Maryland, Oklahoma) (Table 13.4). Several states use soil properties to modify STP calculations, due to the influence of these properties on soil P availability and the use of these properties in existing soil testing programs. For instance, in Vermont and Wyoming, reactive aluminum (Al) and P sorption capacity based on soil texture and pH, respectively, are included in the P index to reflect routine soil P test procedures and to more accurately describe the availability of soil P release to runoff (Table 13.4). In Vermont, soils testing low to moderate in extractable Al (< 40 mg kg−1) show a much greater increase in STP and P release to water than soils testing high in extractable Al (> 40 mg kg -1) (Jokela et al. 1998; Magdoff et al. 1999). Though STP, P application rate, and P application method are common source factors across most P indices, several states include an additional source factor that accounts for the relative solubility of applied P (Table 13.4). P solubility has been shown to vary across manure types and manure treatments, and in the index, P solubility can be used as an indicator of dissolved P loss from a site (Kleinman et al. 2002; Moore et al. 2000). In the Virginia index, manure P solubility is indirectly accounted for by giving credit for alum use to decrease manure P solubility (Moore et al. 2000) and by deducting credit for the use of phytase in poultry and swine feed due to its effect on increasing the solubility of P in manure and dissolved P loss in surface runoff (Moore et al. 1998; Smith et al. 2001). A flooding frequency factor is included in several states’ P indices, as identified for soils in the NRCS soil survey database (Czymmek et al. 2001; DeLaune et al. 2004a, 2004b; NRCS 2001f, 2001h, 2001i, 2001j, 2001m). Phosphorus loss from a field during flooding can be an important mechanism of P transport to a stream compared to surface and subsurface runoff. Separate transport factors for receiving water priority and biological response to P addition to a receiving water are accounted for in several indices (Table 13.4). Ranking of receiving waters was designed to emphasize water bodies designated as


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high quality. Often, however, assessments of water body quality and priority have not been designated by the state, making inclusion in a P Index difficult.

13.2.2 CALCULATING

A

PHOSPHORUS INDEX VALUE

The modifications to basic calculations of site vulnerability have been incorporated into many recent versions of the P Index, as illustrated by the Pennsylvania P Index (Table 13.2 and Table 13.3) (Weld et al. 2003). Included as an initial step in the Pennsylvania P Index is a screening tool (Table 13.2, Part A); if a field has an STP greater than 200 mg kg −1 Mehlich-3 P and is 150 ft or closer to a stream or water body, then a more comprehensive evaluation of the field using the full P Index (Table 13.2, Parts B and C) is required. The corollary is that if A field has an STP less than 200 mg kg−1 and is located more than 150 ft from a stream, the full Index need not be run. In this last situation, the field is assumed to be of a lower risk to contribute P, and, for example, in the Pennsylvania P Index N-based nutrient application rates are recommended. Thus, time and effort expended in calculating Index ratings can be directed to those fields that are more likely to be at risk of P loss. Source factors of the P Index, STP, fertilizer and manure rate, method, and timing of application (Table 13.2, Part B) do not all have the same quantitative effect on P loss. In the original P Index, this was addressed with different weighting factors. In the Pennsylvania P Index, a coefficient of 0.2 is used to convert STP to a value that directly relates to P in manure and mineral fertilizers. This conversion is based on field data that show a fivefold greater concentration of dissolved P in surface runoff with an increase in mineral fertilizer or manure addition compared to an equivalent increase in Mehlich-3 STP. In the Pennsylvania P Index, transport potential for each site is calculated by first summing erosion, surface runoff, leaching potential, and connectivity values (Table 13.2, Part C). The summed value is then divided by 22, the value corresponding to high transport potential (erosion is 4 tons ac−1, surface runoff is 8, leaching potential is 0, and connectivity is 8) to determine a relative transport potential (Table 13.2, Part C). This normalization process assumes that when a site’s full transport potential is realized, 100% transport potential is realized. Thus, transport factors < 1 represent a fraction of the maximum potential (Table 13.2, Part C). However, because erosion is open ended, it is possible at high erosion rates to have a transport factor > 1. A final P Index value, representing cumulative site vulnerability to P loss, is obtained by multiplying the summed transport and source factors (Table 13.2). Pennsylvania P Index values are normalized so that the break between high and very high categories is 100 (Table 13.3), representing an initiative by northeastern and mid-Atlantic states to ensure that P Index output is consistent across state boundaries. Normalization is accomplished by calculating a P Index value in which all transport and source factors are assumed to be high. In the Pennsylvania P Index, erosion is set at 4 tons ac−1, and STP is set at 200 mg kg−1 Mehlich-3 P. Breaks between medium and high and between low and medium are calculated using the same method with STP set at 50 and 30 mg kg−1 Mehlich-3 P, respectively. These Mehlich-3 P levels correspond to crop response and fertilizer recommendations for Pennsylvania: > 50 mg kg−1 is sufficient for production, and no P addition is recommended; between


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30 and 50 mg kg−1, no crop response is expected, but maintenance P is recommended; and < 30 mg kg−1 is low, and crops will respond to added P (Beegle, 2005). In Pennsylvania, P Index values correspond to P Index ratings of low, medium, high, and very high (Table 13.3). Each of the P Index rating categories has an associated nutrient management recommendation ranging from N-based nutrient application rates to no P application. These recommendations are representative of most state P Index recommendations. However, as there have been modifications made to P Index factors and calculations, the associated nutrient management recommendations have also been modified by some states. This results in some states having P Indices that are more restrictive than others.

13.3 INCLUSION OF BEST MANAGEMENT PRACTICES FACTORS The inclusion of BMPs and other management practices in the P Index represents a significant developmental difference across the reviewed indices. Of the various P indices, 21 include some type of management practice as a separate factor in the Index (Table 13.4). The rationale for the addition of a management category centers on providing credit for management practices that have been installed and likely impact the loss of P.

13.3.1 EXAMPLES OF INDEX SITE ASSESSMENT AND INTERPRETATION As previously discussed, the P Index can be used to identify the risk of P loss from fields at a farm or watershed scale and provide farmers flexibility in management options to decrease this risk. To address the common misconception that a high or very high Index value will result solely in a decrease in the amount of manure that can be applied, other management scenarios were evaluated. Using the Pennsylvania P Index, hypothetical scenarios are given to highlight the range of options available (Table 13.5). Scenarios considered are a change in the timing of manure application, installation of a riparian buffer, and a reduction in the amount of P in the dairy cow ration. Management of the baseline scenario is for a field on a dairy farm, obtained from a farm-scale testing of the Pennsylvania P Index on 11 farms (Weld et al. 2002). The field was no-till corn and had received manure and starter fertilizer in the past — hence an elevated STP level of 150 mg kg−1 Mehlich-3 P. Planned source management included a 45 kg P ha−1 surface application of dairy manure in November (i.e., application method and availability factors of 0.8) and 10 kg P ha−1 starter mineral fertilizer placed with planting in May (i.e., application factor of 0.2). Erosion was calculated by the Revised Universal Soil Loss Equation (RUSLE), and runoff rating from the no-till field was low (1 and 2, respectively); some subsurface drainage was evident from an old tile drain (Table 13.5). The field was within 150 ft of the stream channel; thus, any runoff was assumed to contribute directly to stream flow. The resulting P Index value for this field was 101 (Table 13.5). Based on Pennsylvania’s nutrient management guidance, the field would be subject to P-based management with no P application recommended.


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TABLE 13.5 Phosphorus Index Management Scenarios Based on Pennsylvania’s P Index Factors

Baseline Management

Manure Application Method a

Riparian Buffer b

Dairy Cattle Ration c

Soil test P (ppm Mehlich-3 P)

150

Source Factors 150

150

150

Soil Test Rating

30

30

30

30

Fertilizer rate (lb P2O5/A) Fertilizer application method

20

20

20

20

0.2

0.2

0.2

0.2

Fertilizer Rating

4

4

4

4

Manure rate (lb P2O5/A) Manure application method Manure P availability

91

91

91

68

0.8

0.6

0.8

0.8

0.8

0.8

0.8

0.8

Manure Rating

58

44

58

44

Source Factor

92

78

92

78

Transport Factors Erosion (ton/acre/yr) Runoff class Subsurface drainage Contributing distance Transport Sum/22 Modified connectivity Transport Factor Phosphorus Index value Management guidance

1 2 1 8

1 2 1 8

1 2 1 8

1 2 1 8

0.55

0.55

0.55

0.55

1.0

1.0

0.7

1.0

0.55

0.55

0.39

0.55

101 No P applied

86 Applied P limited to crop removal

72

87

N-based nutrient application

Applied P limited to crop removal

Notes: Factor that changed in each scenario is highlighted in bold. a

Change in the timing of surface manure application from fall (November) to spring (May).

b

Establishment of an edge-of-field riparian buffer.

c

Decreased amount of P fed to a lactating dairy cow from 0.48 to 0.38% P.

Source: Adapted from A.N. Sharpley, J.L. Weld, D.B. Beegle, P.J.A. Kleinman, W.J. Gburek, P.A. Moore, and G. Mullins, Journal of Soil and Water Conservation 58, 137–152, 2003. With permission.


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In Scenario 1, timing of the surface manure application was changed from fall (November) to spring (May). In fact, applying manure a month earlier in late September or October will decrease the application factor from 0.8 to 0.6 (Table 13.5). Neither of the methods of application in Scenario 1 involved manure incorporation; thus, no-till requirements are met, and erosion or runoff potential is not increased. As a result of a change in timing of manure application, the P Index rating for the field decreased from 101 to 86, with applied P limited to crop removal (Table 13.5). In Scenario 2, the establishment of a riparian buffer at the downslope edge of the field decreases the transport factor from 0.55 to 0.39 (Table 13.5). Although source management remains the same, overall P loss potential as reflected in the P Index value decreased (72) compared to the baseline scenario (101), and nutrient management would revert to being N-based. However, the riparian buffer must be carefully installed and maintained to ensure long-term protection against P loss. In Scenario 3, the dairy ration was modified so that the amount of P fed to lactating dairy cows more closely met animal nutritional requirements (Table 13.5). Wu et al. (2000) showed a direct relationship between the amount of P in excess of cow requirements and fecal P. For instance, a 25% reduction in fecal P excreted when the dairy cow ration was decreased from 0.48 to 0.38% P on a drymatter basis is translated into an equivalent decrease in manure P applied (45 to 34 kg P ha−1). By simply altering the feed P ration, the P Index value for the field was 87 (high risk of loss) compared to the baseline scenario of 101 (very high risk of loss) (Table 13.5). If all three scenarios — rescheduling manure application, establishment of a riparian buffer, and changing the feed management program — were adopted, the P Index rating for the same field would be 52. Clearly, the P Index can identify several opportunities to decrease the overall P Index rating of a field, which in the scenarios given did not include a reduction in the amount of manure applied. This provides the farmer with long-term flexibility of nutrient management and may slow down STP build-up as less manure P is applied.

13.4 INTEGRATION OF P INDICES INTO EXISTING MODELS OR NUTRIENT MANAGEMENT PLANNING SOFTWARE The P Index was developed not as a model but as a field assessment tool. However, due to the reliance of most indices on readily available field information, the integration of the P Index into existing nutrient management software and models is possible. Examples of nutrient management software packages that include a P Index calculator are OnePlan Nutrient Management Software (Ohlensehlen et al. 2005), AFOPro (Kloot et al. 2002), and Manure Management Planner (MMP; Hess and Joern 2005). OnePlan includes a P Index assessment for Idaho that involves the following factors: soil test P, organic and inorganic fertilizer and manure application rate and method, runoff, erosion, distance to surface water, and BMP. In addition to the P Index value, a qualitative ranking and descriptive recommendation is provided on a field-by-field basis for each previously listed P Index factor (Ohlensehlen et al. 2005).


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AFOPro includes a P Index component for Florida, Kansas, South Carolina, and Tennessee. The factors used and the recommendations given are based on statespecific guidelines and indices (Kloot et al. 2002). Manure Management Planner includes several P indices based on state-specific guidelines and recommendations (Hess and Joern 2005). Additional information regarding MMP development can be found in Chapter 14. Though the P Index has been incorporated into the previously mentioned software planning tools, challenges still exist. All indices and associated recommendations must be added to the software on a state-specific basis. Additionally, the P Index calculation is performed independently of other nutrient management calculations, making it a companion but not a truly integrated calculation. Additional considerations when integrating a P Index calculation and evaluation into nutrient management planning software include the definition of a field or planning unit, the recommendation of appropriate P application rates, and the use of soil erosion calculators such as RUSLE2. Accurate field identification ensures that current nutrient applications are being properly evaluated and that areas critical to P loss potential are being managed correctly. To ensure that appropriate P application rates are recommended, all final P application rates need to be evaluated in the P Index and compared to the associated management recommendations. This can create multiple P Index calculations and management scenarios for a filed which can result in challenges for software developers. Finally, the correct use of RUSLE2 and soil loss calculators is essential to estimating soil loss, which is a transport factor in most P indices. Most states educate nutrient management planners to address these issues as a part of the planning process. However, software developers must address these issues as well. The inherent flexibility of the P Index can result in the need for careful consideration when creating software that will incorporate a P Index process.

13.5 FIELD TESTING The P Index has been used to assess the potential for P loss in several regions including the Delmarva Peninsula (Leytem et al. 1999; Sims 1996), Oklahoma (Sharpley 1995), Texas (McFarland et al. 1998), Vermont (Jokela et al. 1997), and Canada (Bolinder et al. 1998). Though a great deal of research justifies the various transport and source factors included in the P Index, there has been little site evaluation of the Index ratings. DeLaune et al. (2004a, 2004b) found annual P loads from two small (0.5 ha) pastures over a 6-year period were highly correlated to the P Index value with a slope of near one and an intercept approaching zero (y = 1.16x – 0.23; R2 of 0.83). Yet few other comparisons of P Index ratings and measured P loss under natural rainfall have been made. In Nebraska, Eghball and Gilley (2002) found correlation coefficients between total P loss from simulated rainfall-runoff plots and P Index ratings as high as 0.84, when erosion factor weighting was increased from 1.5 to 7.5. Using the Pennsylvania Index, Sharpley et al. (2001) were able to accurately describe the potential for dissolved (R2 of 0.79) and total P loss (R2 of 0.83) from 57 recently manured and unmanured 2-m2 runoff plots in an agricultural watershed. In comparison, STP did not predict losses from plots recently amended with


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various sources of P (R2 of 0.42). Because this evaluation relied upon plot data, several factors such as site position and connectivity to the stream channel could not be accounted for. A watershed assessment of a P Index for pastures and cropland in the Texas Blackland Prairie was conducted by Harmel et al. (2005) and for pastures in Arkansas by DeLaune et al. (2004a, 2004b). Both the Texas and Arkansas P indices estimated runoff dissolved P concentration well in their respective studies (Harmel et al. 2005; DeLaune et al. 2004a, 2004b). In addition to evaluating the Texas P Index on both cultivated and pastured watersheds, Harmel et al. (2005) evaluated the Iowa and Arkansas P indices on these watersheds. Considering average annual runoff dissolved P concentration, all three P indices reflected P loss well in the pastured watersheds (Texas P Index r2 = 0.86, Iowa P Index r2 = 0.90, and Arkansas P Index r2 = 0.84). However, in the cultivated watersheds the Texas and Iowa P Indices, r2 = 0.68 and 0.76, respectively, provided better estimates of P loss than the Arkansas P Index, r2 = 0.16. While the Texas and Iowa P indices were developed to evaluate broader agricultural conditions, the Arkansas P Index was developed to specifically evaluate pasture lands. These differences do not reflect a deficiency in the Arkansas P Index, but instead the result of a different development objective. In spite of these studies, watershed-scale evaluations of the indices are urgently needed. Such testing and validation should focus on determining the effect of P-based nutrient management using the P index on P export at a farm or watershed scale.

13.6 AVAILABILITY OF P INDICES A survey of the 50 states enacting CNMP strategies shows that 47 adopted the P Index approach, one adopted an agronomic STP (crop response) approach, and two adopted an environmental STP threshold approach (Figure 13.1). The specific factors included in these indices, how ratings are calculated, and whether the output is a risk- or lossbased estimate are given in Table 13.4. Such widespread adoption of the P Index confirms a general scientific and policy consensus toward this approach as a valid, flexible means on which to base P management recommendations for CNMPs. To achieve the goal of using the P Index as a part of CNMP development and nutrient management planning, most indices are electronically available and can be obtained at no cost. Resources for obtaining a P Index are the National Phosphorus Research Project Web site (http://www.ars.usda.gov/main/docs.htm?docid=2300), state land-grant universities, and state USDA-NRCS offices.

13.7 CONCLUSIONS Clearly, many versions of the P Index are in use across the U.S. supporting P-based nutrient management planning strategies. Development of different Index versions of among states has been driven by local topographic, hydrologic, and management conditions influencing P transport, as well as state-level policy decisions. Consequently, individual indices likely provide a reliable assessment of a given site under the range of conditions for which they were developed, however, the need for watershed level assessments still exists. The fact that many modifications and versions of P indices are


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in use and accepted demonstrates the robustness and flexibility of the P Indexing framework originally proposed by Lemunyon and Gilbert (1993). Future development of the P Indexing approach should not focus on differences among indices but rather should move toward more interactive tools that are closely integrated with parameter databases. These databases include digitized national soil survey information, topographic maps, drainage density, and land use. A wide array of agencies can provide needed information (e.g., NRCS, USGS, Departments of Transportation, National Oceanographic and Atmospheric Administration). Ultimately though, a P Index rating for a given site based on inherent transport factors at a minimum (i.e., transport potential) could be included as a calculated variable of NRCS’s National Soil Survey database. With this rating, only source management factors — STP, fertilizer, manure, and tillage — would be needed to determine overall site vulnerability.

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McFarland, A., L. Hauck, J. White, W. Donham, J. Lemunyon, and S. Jones. 1998. Nutrient management using a phosphorus risk index for manure application fields. Presented at the Proceedings of Manure Management in Harmony with the Environment and Society, Soil and Water Conservation Society, February 10–12, Ames, IA. Moore, P.A., Jr., T.C. Daniel, and D.R. Edwards. 2000. Reducing phosphorus runoff and inhibiting ammonia loss from poultry manure with aluminum sulfate. J. Envrion. Qual. 29:37–49. Moore, P.A., Jr., M.L. Self-Davis, T.C. Daniel, W.E. Huff, D.R. Edwards, D.J. Nichols, W.F. Jaynes, G.R. Huff, J.M. Balog, N.C. Rath, P.W. Waldroup, and V. Raboy. 1998. Use of high available phosphorus corn and phytase enzyme additions to broiler diets to lower phosphorus levels in poultry litter. Pp. 346–352 in Proceedings of the 1998 National Poultry Waste Management Symposium, J.P. Blake and P.H. Patterson (Eds.). Auburn, AL: Auburn University Press. Mullins, G., M.L. Wolfe, J. Pease, L. Zelazny, L. Daniels, M. Beck, M. Brosius, A. Vincent, and D. Johns. 2002. Virginia phosphorus index version 1 technical guide. Virginia Polytechnic Institute and State University, Blacksburg. Available at http://p-index. agecon.vt.edu. Natural Resources Conservation Service (NRCS). 2000a. The Florida phosphorus index. Florida Agronomy Field Handbook, Chapter 1, Exhibit 9, Gainesville, FL. Available at http://nutrients.ifas.ufl.edu/nutrient%20pages/FLPIndex.htm. Natural Resources Conservation Service (NRCS). 2000b. Phosphorus site index for Louisiana. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Alexandria, LA. Natural Resources Conservation Service (NRCS). 2000c. Phosphorus index rating. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Jackson, MS. Natural Resources Conservation Service (NRCS). 2000d. Phosphorus assessment tool for Texas. U.S. Department of Agriculture, Agronomy Technical Note 15, Temple, TX. Natural Resources Conservation Service (NRCS). 2001a. Phosphorus index for Alabama: A planning tool to assess and manage P movement. U.S. Department of Agriculture, Agronomy Technical Note AL-72, Auburn, AL. Natural Resources Conservation Service (NRCS). 2001b. The Alaska phosphorus index. U.S. Department of Agriculture, Technical Note Agronomy 14, Palmer, AK. Natural Resources Conservation Service (NRCS). 2001c. Kentucky phosphorus (P) matrix. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Lexington, KY. Natural Resources Conservation Service (NRCS). 2001d. Environmental assessment and manure allocation tool. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Bangor, ME. Natural Resources Conservation Service (NRCS). 2001e. Phosphorus loss potential and manure application rates. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, St. Paul, MN. Natural Resources Conservation Service (NRCS). 2001f. Phosphorus index calculation sheet. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Durham, NH. Natural Resources Conservation Service (NRCS). 2001g. New Jersey phosphorus index for typical crop production systems. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Somerset, NJ. Natural Resources Conservation Service (NRCS). 2001h. Oklahoma phosphorus assessment worksheet. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Stillwater, OK.


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Natural Resources Conservation Service (NRCS). 2001i. The phosphorus index. U.S. Department of Agriculture, Agronomy Technical Note 26, Portland, OR. Available at http://isnap.oregonstate.edu/P_Index/P_index_technote.pdf. Natural Resources Conservation Service (NRCS). 2001j. Rhode Island phosphorus index (RIPI). U.S. Department of Agriculture, Rhode Island Field Office Technical Guide Section II, Warwick, RI. Natural Resources Conservation Service (NRCS). 2001k. The phosphorus index: South Carolina. Agricultural waste management field handbook, Chapter 11, South Carolina Supplement 2, Columbia. Natural Resources Conservation Service (NRCS). 2001l. Tennessee phosphorus index: a planning tool to assess and manage P movement. U.S. Department of Agriculture, Nashville, TN. Natural Resources Conservation Service (NRCS). 2001m. The phosphorus index. U.S. Department of Agriculture, Water Quality Technical Note 2, Spokane, WA. Natural Resources Conservation Service (NRCS). 2002a. Illinois phosphorus assessment procedure: use and interpretation of the Illinois phosphorus assessment procedure. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Champaign, IL. Natural Resources Conservation Service (NRCS). 2002b. North Dakota phosphorus index screening tool. U.S. Department of Agriculture, Technical Guide Notice ND-9, Bismarck, ND. Natural Resources Conservation Service (NRCS). 2002c. Phosphorus index risk assessment procedure worksheet. U.S. Department of Agriculture, Ohio Field Office Technical Guide Section 1, Columbus, OH. Natural Resources Conservation Service (NRCS). 2002d. Phosphorus index for nutrient management. U.S. Department of Agriculture, Conservation practice standard: nutrient management code 590, Morgantown, WV. Natural Resources Conservation Service (NRCS). 2002e. The phosphorus index: section 12 — nutrient basis for manure application rates Wyoming comprehensive nutrient management plan workbook, Casper, WY. Natural Resources Conservation Service (NRCS). 2004a. Iowa phosphorus index. U.S. Department of Agriculture, Technical Note 25, Des Moines, IA. Available at http://www.ia.nrcs.usda. gov/Technical/Phosphorus/phosphorusstandard.html. Natural Resources Conservation Service (NRCS). 2004b. Kansas site assessment indexphosphorus. U.S. Department of Agriculture, Electronic field office technical guide, Section 2H, Water quality and quantity interpretations, Salina, KS. Ohlensehlen, B., J. Beddoes, and R. Fisher. 2005. One plan nutrient management software planner’s version 1.75 user’s guide. R. Johnson (Ed.). U.S. Department of AgricultureNatural Resources Conservation Service, Boise, ID and University of Idaho, Moscow. Available at http://ftp-fc.sc.egov.usda.gov/ID/technical/pdffiles/users_guide1105.pdf. Sharkoff, J.L., R.M. Waskom, and J.G. Davis. 2000. Colorado phosphorus index risk assessment. U.S. Department of Agriculture, Agronomy Technical Note CO-95, Lakewood, CO. Available at http://efotg.nrcs.usda.gov/references/public/CO/COATN_95v3.pdf. Sharpley, A.N. 1995. Identifying sites vulnerable to phosphorus loss in agricultural runoff. J. Environ. Qual. 24:947–951. Sharpley, A.N., R.W. McDowell, J.L. Weld, and P.J.A. Kleinman. 2001. Assessing site vulnerability to phosphorus loss in an agricultural watershed. J. Environ. Qual. 30:2026–2036. Sharpley, A.N., J.L. Weld, D.B. Beegle, P.J.A. Kleinman, W.J. Gburek, P.A. Moore, and G. Mullins. 2003. Development of phosphorus indices for nutrient management planning strategies in the United States. Journal of Soil and Water Conservation 58:137–152.


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Sims, J.T. 1996. The phosphorus index: a phosphorus management strategy for Delaware’s agricultural soils. Fact Sheet ST-05, Delaware Cooperative Extension Service, Newark. Sims, J.T. and A.B. Leytem. 2002. The phosphorus site index: a phosphorus management strategy for Delaware’s agricultural soils. ST-05. University of Delaware, Newark. Smith, D.R., P.A. Moore, Jr., C.V. Maxwell, and T.C. Daniel. 2001. Dietary phytase and aluminum chloride manure amendments to reduce phosphorus and ammonia volatilization from swine manure. Pp. 502–507 in Proceedings of the International Symposium Addressing Animal Production and Environmental Issues, G.B. Havenstein (Ed.). Raleigh, NC: North Carolina State University. U.S. Department of Agriculture and U.S. Environmental Protection Agency. 1999. Unified National Strategy for Animal Feeding Operations. Washington, D.C:. U.S. Government Printing Office. Walther, D., R. Flynn, M. Sporcic, and L. Scheffe. 2000. Draft phosphorus assessment tool for Arizona. U.S. Department of Agriculture, Natural Resource Conservation Service, Phoeniz, AZ. Available at http://ag.arizona.edu/animalwaste/notebook/ phosphorus.html. Weld, J.L., R.L. Parsons, D.B. Beegle, A.N. Sharpley, W.J. Gburek, and W.R. Clouser. 2002. Evaluation of phosphorus management strategies in Pennsylvania. J. Soil Water Conserv. 57:448–454. Weld, J.L., D.B, Beegle, W.J. Gburek, P.J. Kleinman, and A.N. Sharpley. 2003. The Pennsylvania phosphorus index: version 1. Extension PUBLICATIONS.CAT US 180 5m3/03ps 4591, Publications Distributions Center, The Pennsylvania State University, University Park, PA. Wu, Z., L.D. Satter, and R. Soja. 2000. Milk production, reproductive performance, and fecal excretion of phosphorus by dairy cows fed three amounts of phosphorus. J. Dairy Sci. 83:1028–1041.


14

Challenges to Using and Implementing Phosphorus Indices in Nutrient Management Planning: an MMP Perspective Philip Hess Purdue University, West Lafayette, IN

Bradley Eisenhauer Purdue University, West Lafayette, IN

Brad Joern Purdue University, West Lafayette, IN

CONTENTS 14.1 Introduction.................................................................................................334 14.2 Design Flaws Present in Many First-Generation PIs.................................334 14.2.1 Overview........................................................................................334 14.2.2 Inconsistencies between Prescreening Tools and PIs ...................335 14.2.3 Lack of Sliding Scales in PI Subcategories..................................336 14.2.4 Lack of Sliding Scales in Overall PI Interpretations ...................336 14.2.5 The Chicken–Egg Problem ...........................................................337 14.2.6 The Bermuda Triangle...................................................................339 14.2.7 Temporal Discontinuities ..............................................................340 14.3 Challenges Commonly Encountered by First-Generation PI Users ..........341 14.3.1 Overview........................................................................................341 14.3.2 Some Input Data May Not Be Known during Planning ..............341

333


334


14.3.3 What If a Field Is Not Uniformly Manured? ...............................342 14.3.4 Gaming the System .......................................................................342 14.4 Challenges and Opportunities for Implementing PIs in the Future ..........343 14.4.1 Potential Implementation Approaches ..........................................343 14.4.2 Implementation Challenges...........................................................345 14.4.2.1 Interpreting the Risk Assessment Procedure ................345 14.4.2.2 Supplying Soil Loss Estimates .....................................346 14.4.2.3 Errors or Gaps in Soils Data ........................................346 14.4.2.4 Program Support and Maintenance ..............................347 14.5 Conclusions.................................................................................................348 References..............................................................................................................349

14.1 INTRODUCTION Evaluating the potential risk of phosphorus (P) loss from crop fields to surface- and groundwater resources is an important component of the nutrient management planning process. Nearly all states have developed a P index (PI) or other state-specific P risk assessment tool for this purpose. Though most PIs were originally implemented as paper worksheets or computer spreadsheets, in practice nearly all planners will use PI tools implemented via computer software to speed up the planning process. In developing the Manure Management Planner (MMP) software, we have programmed more than a dozen state-specific PI tools and have evaluated many others as we prepare to program them (MMP, 2006). During this process we discovered several significant challenges to both the use and implementation of PIs that must be addressed before they can be used effectively for writing and implementing nutrient management plans (NMPs). Our experience in programming and evaluating various PIs, and our interactions with planners who use them, inform much of the discussion presented in this chapter. The general topics covered in this chapter include design flaws present in many first-generation PIs, challenges commonly encountered by PI users, and challenges and opportunities related to future PI development and implementation. The information presented in this chapter should be useful to PI developers and programmers, planners using first-generation PIs, and state and federal agency personnel responsible for reviewing NMPs that include PI assessments.

14.2 DESIGN FLAWS PRESENT IN MANY FIRST-GENERATION PIs 14.2.1 OVERVIEW The purpose, use, and interpretation of PIs vary widely from state to state. In some states the PI interpretation is prescriptive and does limit the amount of P that can be applied to fields that fall into certain categories of risk. In other states, the PI


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result is more advisory in nature and is used to identify potential problems associated with P applications and to select fields and practices that present the lowest risk. Ideally, field assessment using a PI or other P risk assessment tool should include two steps. The first step should identify the inherent soil and landscape factors that may limit P applications to a field, and the second step should determine the optimum or maximum rate of P that may be applied based on application time and method. The planner should use the results of the initial assessment to discuss inherent risk factors with the producer and should determine how to address these issues with improved management — if this is an option — and then should use the PI to determine the optimum or maximum P rate. At a minimum, PIs should determine allowable P rates based on time and method of application and other field and management variables. Unfortunately, many PIs were originally designed as post mortem risk assessment tools rather than tools to help planners determine the optimum or maximum rates of P that can be applied to a field. In these PIs, the assessment includes the rate, time of year, and method of manure and commercial fertilizer P applications, and the planner must run multiple scenarios to determine the optimum or maximum rate of P that can be applied. If the objective of a PI is to help the user determine P application rates, then many first-generation PIs fall short of the mark. The following sections discuss some of the design flaws present in many PIs that limit their potential usefulness for developing effective NMPs.

14.2.2 INCONSISTENCIES

BETWEEN

PRESCREENING TOOLS

AND

PIS

Planners typically perform some type of P risk assessment on all crop fields as part of the nutrient management planning process. Due to the repetitive, computationintensive nature of most PIs, PI developers in many states developed a prescreening procedure that eliminates the need to conduct the full PI on a field if certain criteria are met. These prescreening procedures typically look at distance to water body, soil test P level, field slope, or other readily available information. Though prescreening procedures do reduce the total number of PI calculations, they also increase the risk of overlooking potentially problematic fields and management scenarios and also may lead to management decisions that will dramatically change the assessment status of a field during the next round of plan development. For example, if a prescreening procedure looks only at a field’s soil test P level and distance to water, then the field will be exempt from the full PI assessment if its P level is below a certain value and its distance to water is greater than a certain value. If the field is exempt from further assessment, this usually means that manure can be applied annually at a rate that supplies crop nitrogen (N) needs or, in the case of legumes, the amount of N that the crop can utilize. In states where the rate can be increased to account for anticipated losses of N between the time of application and the time of plant N utilization, this can result in many years worth of P being applied between soil tests if the state does not have any other cap on the rate. In this case the planner is doing exactly what the assessment allows, but because


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the prescreening procedure allows the planner to skip the full PI assessment on certain fields, they may be setting up the producer for a shock the next time the soil in those fields is tested. In addition, since most PIs include the time, rate, and method of manure application, we often find that N-based manure applications to fields excluded from the full PI assessment based on prescreening results have PI results that would not allow N-based management if the full PI had been run on these fields. This lack of consistency in assessment makes the use of prescreening approaches questionable in some states. With PI tool automation via computer software, the additional increase in plan-writing efficiency made possible by using prescreening tools probably is not great enough to justify the risk of overlooking potentially problematic fields or of encouraging nonsustainable management strategies in the resulting NMP.

14.2.3 LACK

OF

SLIDING SCALES

IN

PI SUBCATEGORIES

Nonsustainable P management plans often occur when a state does not have a sliding scale on the upper ends of subcategories in traditional, matrix-based PIs. For example, a state that does not have a soil test P limit above which no additional P can be applied assigns the same number of points to any field above a certain soil test P level. In the original PI template, a field is assigned eight points if its soil test level is considered very high (Lemunyon and Gilbert, 1993). A state might set the breakpoint for the very high category at 100 parts per million (ppm), meaning a field with a soil test P level of 101 ppm would be assigned the same 8 points as a field with a soil test P level of 1001 ppm. The consequence of this is that, all other things being equal, no distinction is made in the assessment among fields that may be acceptable candidates for manure application and fields that are probably very poor candidates for manure application. This can create a false sense of security for the producer, who may continue managing the highest testing fields in the same way that caused them to become high testing fields in the first place. States that have implemented PIs with this problem could easily address this issue with a sliding scale on the high risk end categories of all PI inputs in matrix-based PIs.

14.2.4 LACK

OF

SLIDING SCALES

IN

OVERALL PI INTERPRETATIONS

Though many PIs scale open-ended inputs like soil test P, soil loss, and P application rate to avoid abrupt changes in a factor’s risk category due to small changes in input values, the interpretation of the field’s overall PI value is usually not scaled. Instead, most PIs have threshold values that are used to assign a field’s overall PI value to one of several interpretation categories. For example, a PI might have a threshold value of 6.0, where a PI value above 6.0 indicates that no P can be applied and a PI value of 6.0 or below indicates that some P can be applied. What this means for the planner and producer is that there is a significant difference between, say, 6.0 and 6.1, even



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though the magnitude of the numeric difference is small and may simply be due to subtle differences in the way soil loss was estimated, for example. The overall implication of hard thresholds in PIs is that the accuracy, even of open-ended inputs, is critical, particularly soil loss. These thresholds also encourage the planner to play with the inputs when a field’s PI value falls slightly above a threshold rather than suggesting management changes that could actually reduce the risk of P loss from the field. In many PIs, no scientific basis is given for the choice of threshold values. And since the thresholds appear to be arbitrary, planners and producers understandably question why the interpretation is so inflexible. This issue could be resolved with minor modifications to many current PIs.

14.2.5 THE CHICKEN–EGG PROBLEM As stated previously, most PIs are post mortem assessment tools that include the rate, time of year, and method of manure or commercial fertilizer P application. With these PIs, the planner must run multiple scenarios to determine the optimum or maximum rate of P that can be applied. This is a common problem with nearly all PIs and is illustrated in the following scenario. A planner wants to know the greatest possible P application rate that presents an acceptable risk of P loss. The PI requires information about planned nutrient applications and will indicate, once it has this information, if the planned applications are acceptable. For example, if the planner selects an application rate that supplies the planned crop’s N need, two outcomes are possible when this application is analyzed for risk. Either the application presents an acceptable risk, or it does not. If the risk is too great, the rate must be reduced or the management must be changed to lower the risk. However, if the rate is reduced, for example to supply only the crop’s P need, a subsequent PI run might indicate that the risk with the reduced rate is low enough that the rate can be increased. Somewhere in-between the N-based rate and the P-based rate is the optimal rate that the planner wants, but the assessment procedure is unable to determine it. So the planner is forced into a game of trial and error, oscillating between higher and lower rates until the desired rate is eventually discovered. Table 14.1 illustrates this iterative procedure. In practice, determining the ideal rate this way can be a time-consuming and frustrating experience. Though the risk assessment procedure is doing what it was designed to do, which is to assess the risk for a given nutrient application scenario, that is largely all it can do. For each application scenario, the planner must review the available sources of organic and commercial fertilizer nutrients; consider application equipment, timing windows, and labor availability; take into account hauling costs if manure is involved; and discuss these issues with the producer, only to discover after the risk assessment is performed that much of this work may have been for naught. Many planners intuitively understand that what is needed is a way of assessing risk before committing resources to the actual nutrient application planning. We have


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TABLE 14.1 Chicken–Egg Iterative Process for Determining Maximum Manure Application Rate Allowed by PI Iteration

Rate Basis

Planned Rate (Gal/Acre)

1

No manure applied

2 3

Crop N need 1-year crop P removal

3900 700

Very high Low

4

2-year crop P removal

1400

Low

5


2100

Medium

6


2800

High

5-year crop P removal 4.5-year crop P removal 4.25-year crop P removal 4.1-year crop P removal

3500 3200 3000 2900

Very high Very high Very high High

7 8 9 10

0

PI Rating Low

PI Interpretation Use N-based management No P applied Use N-based management Use N-based management Use N-based management P limited to crop removal No P applied No P applied No P applied P limited to crop removal

Notes: In this hypothetical scenario, rates have been rounded up to the nearest 100 gallons. Equilibrium is reached when the highest rate with a high rating is found (iteration 10). In practice, a planner would likely stop iterating when the highest rate with a whole number of years’ P removal is found (iteration 6, but 7 iterations would be required to determine this).

learned that some planners will run the PI report before planning any nutrient applications in MMP, hoping to discover something about the fields’ relative risk independent of any nutrient applications. Since planning nutrient applications can be one of the most time-consuming components of NMP development, planners naturally are looking for ways to expedite this process. Though the preapplication PI report will not be the final one, it may provide important clues about what fields are poor candidates for nutrient applications in any scenario and what fields are likely to be good candidates. We have identified a couple of ways to address this obvious planning need. One would be to develop a preliminary risk assessment procedure that considers only the field’s inherent properties such as soil type, soil properties, field slope, soil test levels, and distance to water, possibly including management factors that the producer would be unlikely to modify, such as crop rotation or even application timing. The results of this preliminary assessment could be fairly simple, for example, dividing fields into two groups: those that are not likely to be good



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candidates for nutrient applications in any scenario and those that are good candidates, or could become good candidates with appropriate management or conservation practices. The planner could then concentrate initially on the good candidates, turning to the poorer candidates only if they are needed to utilize manure. A complete risk assessment would still be done on any field that receives manure, unlike some prescreening procedures, which exempt certain fields from any further assessment. Another approach would be to leave the current risk assessment procedures unchanged but to program the PI software tool to iterate through various rates until it finds the highest rate that still presents an acceptable level of risk for a particular application method and timing scenario. In other words, the PI tool would automate the trial-and-error process that the planner currently has to perform manually.

14.2.6 THE BERMUDA TRIANGLE The previous section describes the circular dependency of planned manure applications and PI interpretation. A third element, estimated soil loss, is often involved as well because planned manure applications can affect estimated soil loss, and estimated soil loss is an input for most PIs. For example, surfaceapplied solid manure can add a significant amount of residue to a field, generally lowering soil loss, whereas incorporating liquid manure can disturb a field’s existing plant residue, generally increasing soil loss. This means that for each change in planned manure application rate, the Revised Universal Soil Loss Equation version 2 software (RUSLE2, 2006) needs to be run again to determine an adjusted soil loss estimate, and the new soil loss estimate must be entered into the PI to calculate an adjusted PI value. This revised PI value is then used to evaluate whether the new application rate is acceptable. If the rate is not acceptable, this three-step process — rate determination, soil loss estimation, PI calculation, hence the term Bermuda Triangle — needs to be repeated until an acceptable rate is discovered. In practice, some planners may not account for the impacts of manure applications in RUSLE2, and fewer still likely determine the impacts of different manure application rates on estimated RUSLE2 soil loss. Should all changes to planned manure applications be reflected in RUSLE2? If changes to the planned crop rotation and yield goals must be reflected in RUSLE2, then the answer to this question is probably yes. Unfortunately, accounting for planned manure applications in RUSLE2 can be tricky. Though some RUSLE2 Crop Management Zone (CMZ) files include cropmanagement scenarios that account for typical manure applications for common crop rotations, these management scenarios may not match the field’s planned crop rotation or may differ in other assumptions about application rate, timing, and associated tillage operations. In these cases, the planner must create a custom cropmanagement scenario and manually enter all planned manure applications and associated tillage operations during the rotation, as well as manually calculate the amount


340


of residue added to the field by each application based on the manure’s dry matter concentration. To manually solve the Bermuda Triangle, planners currently must use three separate software tools. This is a time-consuming, repetitive process. The only way to speed up the rate calculations is to dynamically link all three software tools to automate this iterative process in a manner similar to solving the chicken–egg scenario.

14.2.7 TEMPORAL DISCONTINUITIES Guidance from the assessment procedure’s authors is usually helpful in determining the PI’s temporal scope. Some PIs are designed to assess fields over the entire rotation or planning period, whereas other PIs assess each crop year separately and may or may not combine these results into a summary interpretation. Once a decision has been made to calculate the assessment on an annual or rotational basis, related issues must then be addressed. For example, most risk assessment procedures utilize estimated soil loss by water, which historically has been calculated as a long-term annualized average for the entire rotation. However, if the risk assessment is determined on an annual basis, soil loss also should be determined for each cropping year in the rotation because soil loss estimates can differ considerably from year to year as a field’s crop, tillage, and planned manure applications change. As a result, using a rotational average soil loss may overestimate risk in some years and underestimate risk in other years. Using rotational average soil loss estimates in the PI also makes the process of determining appropriate manure application rates nearly impossible because the impact of a current planned manure application can change the PI result for a previous application. For example, if liquid manure is applied to a corn silage field in the first year of the plan, it will have some impact on rotational average soil erosion. If during the second year of the plan, solid manure is applied to this same field, soil erosion may decrease dramatically for that year and may lower the rotational average soil loss. This change in rotational average soil loss will actually change the PI value for the previous year’s application. Though a previous year’s manure application certainly may impact future applications, applications planned for future years should not impact the previous year’s planned application. The circular interaction cannot be solved with software. Any PI that uses the rotational average soil loss has this inherent design flaw. The solution to this problem is for PIs to use annual soil loss estimates for each crop year in the plan. However, per current PI guidelines, MMP’s PIs use the rotational average soil loss with annual assessments in most states. States that use a rotational risk assessment procedure, or a matrix-based PI that has no inherent temporal context, also face the issue of data that cannot be averaged. For example, many assessment procedures use information about the timing and method of nutrient applications, but these data cannot be averaged. If manure is applied differently to a field throughout the rotation — or even for multiple applications within a given year — one time and method must be selected for use in the



341

assessment. In general, if not specified by the assessment procedure, MMP’s PIs use the time and method that present the greatest risk. In most cases, this approach unfairly penalizes the producer in the overall PI assessment for a field. Secondgeneration PIs should use an annual PI assessment for each crop year and then, if appropriate, should generate a summary report for each field.

14.3 CHALLENGES COMMONLY ENCOUNTERED BY FIRST-GENERATION PI USERS 14.3.1 OVERVIEW Because the purpose, data requirements and interpretation of PIs vary widely across states, planners must have a solid understanding of these and other issues to properly use PIs in the plans they develop. Normally this requires instruction of some kind, either as training specific to the PI or as part of a larger nutrient management planning course. However, based on our experience, many planners, especially those working in multiple states, have received little or no in-depth training on PIs and have acquired their knowledge about various PIs from slide shows, sample nutrient management plans, extension publications, and USDANRCS Nutrient Management 590 standards (NRCS, 2006). Some states have developed nutrient management planning Web sites to provide required data and helpful reference materials at a single location. Even with PI software that automates much of the assessment procedure, planners often struggle with operationspecific issues frequently encountered in the real world but that are not generally covered in training courses or reference materials. This section discusses a few of these common challenges.

14.3.2 SOME INPUT DATA MAY NOT BE KNOWN DURING PLANNING Some PIs depend on knowledge of soil and field conditions such as residue cover, hydrologic condition, soil condition, and field condition (e.g., whether the soil is frozen) in calculating runoff and other factors, even though these inputs will not be known when the NMP is created. With these inputs, MMP’s PI tools make an assumption based on crop rotation or application timing. For example, with field condition, a PI tool for a state in the north-central U.S. might assume that the soil is likely to be frozen during the winter months of December through February and not frozen during other months of the year. Even though in any given year there may be periods during the winter when the soil is not frozen, and there is always the possibility that the soil could be frozen outside of the winter months, from a planning perspective this assumption is simply indicating that it is risky to count on fields being available (unfrozen) during those months. This is consistent with the idea that multiyear NMPs are designed to demonstrate that the producer can manage the operation’s manure properly in a typical year.


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14.3.3 WHAT IF

Modeling Phosphorus in the Environment A

FIELD IS NOT UNIFORMLY MANURED?

Many risk assessment procedures ask for the rate, method, and timing of P applications. Though at first glance this may appear to be an easy question to answer, determining this information can be difficult in a number of situations. For example, most states have regulatory manure application setback areas such as streams, wells, sinkholes, roads, and property boundaries. In general, manure cannot be applied here. If the affected area is small, it may be possible to disregard this area in the field’s assessment. However, if the nonmanured area is large enough that the producer will likely apply commercial fertilizer to it, the result is a field that may have significant differences between its manured and nonmanured parts in the rate, method, and timing of P applications. A good rule of thumb is to subdivide these kinds of fields and then do an independent risk assessment on each subfield. Large fields also are sometimes not completely manured, usually because the producer does not have enough manure to cover the entire field. Ideally, these fields should also be subdivided so that each subfield can be uniformly manured from the same manure source, with the same equipment, and during the same time of year. If fields are not subdivided, MMP’s PI tools calculate a per-acre weighted average rate, even though there may be significant rate differences across the field. The PI assessment results can be misleading in these cases.

14.3.4 GAMING

THE

SYSTEM

Gaming the system is the term we use to describe the process of determining manure application strategies that may be used by some experienced planners once they fully understand the design flaws inherent in the PI with which they are working. The circular chicken–egg problem discussed previously arises when the P application rate is a factor in determining the PI value, whereas the PI value in turn is used to limit the application rate. When RUSLE2 is included in the PI, the issue becomes even more complicated (i.e., the Bermuda Triangle). To further compound the P rate determination dilemma, PIs often lack scaling in PI subcategories or in the final PI interpretation. Matrix-based first-generation PIs have most of these inherent design flaws. These PI design flaws also have another side effect. With P-based management, the maximum rate will usually put the field off limits for further manure applications until the P applied has been removed from the field as harvested crop material. In many cases, this will take several harvests. Reducing the rate to where the PI result allows N-based management may permit annual applications at a rate that in many cases is only slightly less than the multiyear P-based maximum rate. Although allowed by the PI, this can result in a rapid build-up of soil P, which may mean that fields managed in this way will abruptly become unavailable following the next round of soil testing if the state has a soil test P cutoff level above which no further P can be applied. Whether intentional or not, this application strategy could be problematic for the producer and surely is not what the designers of the PI intended. Table 14.2 illustrates this problem.



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TABLE 14.2 Gaming the System by Reducing the Manure Application Rate Enough to Permit Annual Applications

Year

Planned Rate When Using Maximum P-Based Management Rate (Gal/Acre)

1 2 3 4 Total

2900 0 0 0 2900 (4 years of crop P removal)

Planned Rate When Using Maximum N-Based Management Rate (Gal/Acre) 2100 2100 2100 2100 8400 (12 years of crop P removal)

Notes: 2900 gal/acre is the maximum rate determined in Table 14.1, which puts the field off limits to further application for four years. 2100 gal/acre is the highest rate from Table 14.1 that still permits N-based management (annual applications).

14.4 CHALLENGES AND OPPORTUNITIES FOR IMPLEMENTING PIs IN THE FUTURE 14.4.1 POTENTIAL IMPLEMENTATION APPROACHES In developing MMP, we have identified several possible approaches to implementing (programming) PIs. One approach would be to implement the PI as part of the larger nutrient management planning software, in our case MMP. The chief disadvantage to making the PI tool a built-in part of the planning software is that even minor changes or corrections to the PI procedure require a revision of the planning software. Another disadvantage is that the source code for the PI tool probably will not be made available if it is part of a larger program. This approach also runs counter to MMP’s development philosophy, where all state-specific crop-fertilizer recommendations, manure nitrogen availability estimates, manure application rate calculations, and state-specific reports are driven by human-readable data stored external to MMP. Another possible approach would be to create an external program, complete with data entry and storage capabilities, which is independent of the planning software. Traditionally this has meant a Microsoft Excel spreadsheet, which can be difficult to debug, document, and maintain once a certain level of complexity is reached. Spreadsheets date to the very first personal computers but now represent an approach that is out of step with modern software development best practices.


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Linking the spreadsheet to other software also is unlikely, since getting data into or out of a spreadsheet programmatically can be difficult. Though useful for prototyping and proof of concept work, a spreadsheet is rarely the right tool for creating production quality software. Of course, an external PI tool does not need to be implemented as a spreadsheet. A database like Microsoft Access could be used, or the PI tool could be built from scratch as a stand-alone program that does not require Excel or Access. The PI tool could even be implemented as a Web-based calculator. However, as with a spreadsheet, the PI tool would still need to implement its own user interface for data entry, its own program help, and its own data storage. Though this may be acceptable if only one PI tool is being developed, implementing PIs for multiple states this way would likely involve duplication of effort from one tool to the next. This approach also means that data common to both the planning software and the PI tool are stored in both programs and can get out of sync if one program’s data are edited but not the other’s. A third possible approach involves exporting data from the planning software to an existing PI spreadsheet. Since many states already have working spreadsheet versions of their risk assessment procedures, this would seem like an obvious choice because it means that the planning software developers would not necessarily have to understand the PI to utilize it. This type of blind exporting makes sense when the target program has a well-defined application programming interface (API) or data input format, but a PI spreadsheet generally will not have this. Spreadsheet-based PI tools often are designed to be operated only in an interactive calculator mode, meaning they do not have a place to put data for more than one crop field at a time. This approach also has some of the same data linkage and duplication issues as the second approach. Each state PI, too, would require its own link with the planning software, which could involve just as much programming effort as implementing the risk assessment procedure itself. With a PI spreadsheet, this kind of link tends to be fragile since the planning software needs to write to specific cells in the spreadsheet. Any modification to the PI spreadsheet can break this type of link. Still another approach involves creating an external report designed specifically to draw on data entered and stored in the planning software to calculate the risk assessment. Since reports are normally driven by data from database queries, a database like Access can be used to develop the report. This approach avoids most of the problems in the approaches discussed previously, although the assessment report still must be developed on a state-by-state basis. No field data are actually entered in the report tool. This means that all field data must come from the planning software. MMP includes a special assessment data input panel to supply all of the data required by the PI report. This panel serves as a collection site for any additional field data required by various state PIs. It includes dedicated columns for entering commonly used assessment data such as distance to water, buffer width, artificial drainage type, and estimated water, wind, irrigation, gully, and ephemeral erosion. The assessment panel also has several optional columns that can be enabled for entering miscellaneous data unique to a



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particular state. Assessment panel data generally are not used in the nutrient management planning process per se but are simply passed along with field, crop, and nutrient application data to the PI report. There are several advantages to this approach. Since the PI tool draws exclusively on data from the planning software, this means the PI tool does not need its own user interface or data storage. Since data are only entered and stored in one place, the PI tool always uses the current plan data whenever it is run. Any import or export facilities in the planning software can be used to import and export PI input data as well. This approach also allows the PI tool to be modified and distributed independent of the planning software. The PI’s source code also can be included without exposing the planning software’s source code. The PI report’s database queries also can be used in other ways, for example to create a table of assessment results — rather than a full report — that can be inserted into a nutrient management plan document. Finally, this type of P tool can theoretically be developed or modified by third parties rather than by the planning software developers. This is the current approach taken by MMP, and though the resulting reports are of immediate and significant benefit to planners, we consider this approach only a short-term solution necessitated by the need to produce something that increases planner productivity compared to using a spreadsheet-based implementation. Because of MMP’s dependency on both RUSLE2 and PIs in determining and evaluating manure application rates, in the longer term both RUSLE2 and PIs need to be integrated more closely with MMP, although stopping short of becoming part of MMP. To further speed up the planning process, MMP will eventually need to have real-time, on-demand access to RUSLE2 and PI results for any given field, similar to the way MMP automatically recalculates a field’s crop fertilizer recommendations whenever any crop inputs change. This PI tool implementation strategy would help solve the Bermuda Triangle issue.

14.4.2 IMPLEMENTATION CHALLENGES As part of the national MMP project, we have implemented over a dozen statespecific PI tools. Though each has its own specific challenges, the following implementation challenges are common to many risk assessment procedures. 14.4.2.1 Interpreting the Risk Assessment Procedure The overall goals of a state’s risk assessment procedure, as well as its equations and algorithms, are usually well documented or can be determined from existing spreadsheets or planning examples. However, as discussed previously, sometimes the temporal scope of the assessment or other essential details of its use are not clear. For example, a common issue is determining whether a state’s assessment should be applied to one or more individual crop years or to the crop rotation as a whole. Though one implementation solution might be to provide both options, this does not necessarily help the planners using the software, who will then be forced to make this decision.


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14.4.2.2 Supplying Soil Loss Estimates RUSLE2 is the software used to estimate soil loss by water for official USDA-NRCS purposes. RUSLE2 is a complex, stand-alone program with its own user interface and data storage. RUSLE2 brings additional capabilities to soil loss estimation over its table-driven predecessor, RUSLE, although at the expense of increased complexity and data input requirements. Many risk assessment procedures were developed prior to the deployment of RUSLE2, assume that soil loss is something that is easy to estimate, and may not be designed for RUSLE2’s estimates. For example, assessment procedures that ask for both sediment delivery and any vegetative buffer or sediment control structure that reduces sediment delivery may be double counting the impact of these structures on P loss since RUSLE2’s sediment delivery values already take these structures into account. Implementing this sort of assessment procedure merely propagates the data mismatch, rather than eliminates it. Historically, a field’s estimated soil loss, once determined, has sometimes been treated almost like a constant or an inherent property of the field rather than as a snapshot of the complex, dynamic process that is soil erosion. This may have contributed to the development of PIs that consider soil loss as just another input rather than as something that is inextricably linked to the manure applications that the PI is designed to evaluate. Many of the input data required by RUSLE2 also are used by nutrient management planning software. However, without a software link to RUSLE2 these data must be entered manually into RUSLE2. MMP currently addresses this problem by exporting common data such as field ID, slope, and soil type from the MMP plan to RUSLE2. Though this eliminates duplicate entry of common field data, it also means that these data are now stored in more than one place, creating the potential for data to get out of sync. However, this data synchronization problem is not unique to MMP and RUSLE2. In the nutrient management planning world, the same field data also may be stored in GIS mapping software, commercial farm management software, recordkeeping programs, and software such as Customer Service Toolkit, which is used by NRCS field offices to develop conservation plans (Toolkit, 2006). MMP also can import each field’s rotational average soil loss from RUSLE2 — and could import annual, or even seasonal, soil losses — since this is the value used in most PIs. This does not simplify the problem of using RUSLE2 efficiently and correctly, but it does eliminate the manual entry of these values into MMP and means that the soil loss estimates can be stored in the MMP plan file with the other data required to calculate the PI. 14.4.2.3 Errors or Gaps in Soils Data In addition to field and soil loss data, most PIs also are driven by soils data, specifically the underlying properties of the field’s predominant or most limiting soil type. The National Soil Information System (NASIS) database is NRCS’s central repository for U.S. soils data (NASIS, 2006). However, the soils data are not updated at the national level and the completeness and accuracy of data can differ from state to state.



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For example, in NASIS, each component of a soil map unit can be associated with a representative slope length, which is the distance from the overland flow’s point of origin to where the slope decreases enough that soil deposition begins. Slope length is also an input to RUSLE2. Though determining slope length in the field is the preferred method, there are situations where having a rough estimate based on soil type is adequate for RUSLE2. NASIS would be the natural source for these slope length estimates. However, though in some states slope lengths are available in NASIS for most soils, in others these values are missing or appear to be a mix of values in meters and feet. Due to these database issues, and because of the fact that planners should determine slope lengths in the field as part of the site visit, MMP currently does not export slope lengths to RUSLE2 based on soil type. Sometimes there can be a difference between the data that the assessment procedure’s authors had in mind and the data available to the planner. For example, many assessment procedures use some measure of a field’s runoff potential in determining risk. This potential is typically either the NASIS surface runoff class, which is based on soil permeability and field slope, or a class based on soil hydrologic group and field slope. However, the derivation of the NASIS runoff class is not static and may be periodically recalculated. This may result in values that differ from those originally used by the authors of the PI. The content, format, and availability of soils data are also constantly evolving as new methods of delivering soils data to users are developed and tried out. Currently soils data for a single survey — typically one county — can be downloaded from the NRCS Soil Data Mart and imported into a supplied Access database for viewing and summarizing (Soil Data Mart, 2006). Soils data for RUSLE2 are available for downloading along with the RUSLE2 software. MMP includes selected soil data for each state that it supports. For each state where MMP also includes a PI tool, these data include any soil properties required by the PI tool as well. 14.4.2.4 Program Support and Maintenance Questions will naturally arise during the risk assessment phase of NMP development, both about the PI and the PI software implementation tool. In general, questions about the PI should be directed to its authors or the responsible agency, whereas questions about the PI tool should be directed to the tool developers. However, planners sometimes look to the tool developers for help with the PI because they cannot obtain help elsewhere, because the PI tool is the context where their questions arose or simply because they do not make a distinction between the PI and the PI tool. This puts the PI tool developers in the awkward position of being considered experts about the PI. As with many software support issues, there is no easy solution to this problem. Maintaining a piece of software can be as difficult as developing a new program. Maintaining multiple PIs can also be challenging. With MMP’s PI tools we developed an Access database template containing common code and design elements that can be used with all PIs as well as a common report style and method of presentation. Though each PI tool represents a particular state’s thinking on the risk


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of P loss from crop fields, which may differ in both obvious and subtle ways from other states, the high-level structure of all PI tools is similar, differing primarily in the low-level implementation details.

14.5 CONCLUSIONS PIs present a variety of challenges not only to the planners who use them but also to the programmers who have taken on the job of implementing them as part of larger NMP programs. Though implementing PIs can reduce some of the challenges currently facing planners, in other cases, particularly with the complicated interaction of manure application rate, soil loss, and PI interpretation, advances will take place only with considerable future programming efforts. Current state P risk assessment procedures represent an advance over previous efforts to evaluate site and management risks; however, some are not optimized for software implementation, and many were designed more for current-year or post mortem analysis than for multiyear nutrient management planning. Next-generation assessment procedures need to address the issues discussed in this chapter as well as to anticipate emerging trends in nutrient management. For example, most assessment procedures do not address variations in P source availability. The availability of P in alum-treated poultry litter is probably different enough from hog and dairy manure that it needs to be considered in any assessment procedure. Manure allocation strategies need to consider economic factors as well. For example, given two fields with similar risk an economic analysis can help identify the field with the higher priority for manure application. But what about fields with dissimilar risk? Should economics ever trump risk? For example, would an increased level of risk, perhaps on a small area, that realizes larger cost savings elsewhere ever be acceptable? Is there a role for regional or even national P risk assessment procedures? Differences among current assessment procedures, coupled with differences in fertilizer recommendations and assumptions made about applied manure N availability, mean that — all other things being equal — producers are allowed to apply manure at greater rates in some states than in others. A regional assessment procedure might help level the playing field among states. An analogy with RUSLE2 is apt: Even though significantly more complex to program than even the most complicated state PI, the authors of RUSLE2 have been able to deliver a single national program that is driven by standard, localized data and produce a standard result that can be compared across states. A single, quantitative, process-oriented model for estimating the quantity of P lost from a field would be very useful for making objective PI risk assessments. In time, this quantitative model could replace individual state PIs, which are largely qualitative in nature. Most PIs and other risk assessment procedures emerged as the result of numerous meetings and much correspondence between multiple authors from several agencies over a period of months or sometimes even years. Reassembling this group in each state might be the biggest challenge to developing next-generation assessment procedures.



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REFERENCES Lemunyon, J.L. and R.G. Gilbert. 1993. The concept and need for a phosphorus assessment tool. Journal of Production Agriculture. 6:483–486. MMP. 2006. Manure management planner. Purdue University. http://www.agry.purdue. edu/mmp. NASIS. 2006. National soil information system. Natural Resources Conservation Service. http://nasis.nrcs.usda.gov/. NRCS. 2006. Natural Resources Conservation Service Conservation Practice Standard. Code 590. ftp://ftp-fc.sc.egov.usda.gov/NHQ/practice-standards/standards/590.pdf. RUSLE2. 2006. Revised Universal Soil Loss Equation, Version 2. http://fargo.nserl.purdue. edu/rusle2_dataweb/RUSLE2_Index.htm. Soil Data Mart. 2006. Natural Resources Conservation Service Soil Data Mart. http:// soildatamart.nrcs.usda.gov/. Toolkit. 2006. Natural Resources Conservation Service. http://www.itc.nrcs.usda.gov/toolkit/.


15

Quantifying the Effects of Phosphorus Control Best Management Practices Margaret W. Gitau University of Arkansas, Fayetteville, AR

Tamie L. Veith U.S. Department of Agriculture-Agricultural Research Service, University Park, PA

CONTENTS 15.1 Introduction .................................................................................................352 15.2 Modeling BMP Effectiveness in Reducing Phosphorus ............................354 15.2.1 Readily Modeled ...........................................................................354 15.2.2 Less Readily Modeled...................................................................357 15.2.3 Specialized Models .......................................................................357 15.2.4 Caveats...........................................................................................358 15.2.5 Model Comparisons ......................................................................359 15.3 Cumulations and Analyses of Data from Previous Studies .......................360 15.3.1 Developing a BMP Tool ...............................................................360 15.3.2 Example BMP Tool Application...................................................362 15.4 Cost Considerations of BMP Recommendations.......................................363 15.5 Combining Pollution Reduction and Cost .................................................365 15.5.1 Optimizing BMP Selection and Placement ..................................366 15.5.2 Problem Classification...................................................................367 15.5.3 The Genetic Algorithm..................................................................367 15.5.4 Current Challenges in Optimization .............................................369 15.5.5 The Next Step: Multi-Objective Optimization .............................370 15.6 Applications ................................................................................................370 15.6.1 Farm-Level Evaluation, Subdivided by HRUs (TBW) ................371 15.6.2 Watershed-Level Evaluation, Subdivided by HRUs (TBW) ........372 15.6.3 Watershed-Level, Subdivided by Fields (FD-36) .........................375 15.7 Summary .....................................................................................................375 References..............................................................................................................376

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15.1 INTRODUCTION There is continuing concern regarding impairment of surface waters as a result of pollutants emanating from agricultural land uses. A major focus has been surface water pollution resulting from excessive phosphorus (P) loadings (Sharpley and Beegle 2001), a major impact of which is eutrophication of these waters (Harper 1992; Logan 1993; Sharpley 1995; Sharpley et al. 1999). The enormity of the P problem is widely acknowledged; the recent past has seen an emphasis on efforts to reduce P pollution, with due recognition being given to the importance of reducing P at its source (Heathwaite and Sharpley 1999; Logan 1993; Sharpley et al. 1999). Best management practices (BMPs) are agricultural control practices that can be used to reduce P loss to streams and rivers. The widely recognized need for BMPs has resulted in their increasingly extensive application. For the most part, however, these BMPs are being implemented without a sufficient research base on which to establish their overall effectiveness at the farm or watershed scales (Dillaha 1990; NRCS 2004). The question of BMP effectiveness in reducing pollutant loss is not a new one. Researchers have undertaken numerous studies to determine and document the effectiveness of various control measures; these studies have covered a wide variety of BMPs and date back to the early 1970s. Although these studies have tended to focus on agricultural pollutants in general, information on the effectiveness of various BMPs on P control is, nevertheless, discernable. Previous studies have used either field experimentation or modeling to quantify BMP effects, with field experimentation being the most commonly used of the two methods. Field experimentation studies have typically used field-scale, or smaller, plots to assess BMP effectiveness (Baker and Johnson 1983; Franco et al. 1996; Lal 1980; Mendez et al. 1999). Field plots are of convenient size to use in experimentation studies and can be used in conjunction with rainfall simulators where natural rainfall is unreliable. At this scale, however, the range of site characteristics under which BMP performance can be studied is limited. It may also be difficult to study some BMPs, such as contour farming or strip cropping, for which larger areas are needed. Additionally, it is difficult to scale up from the field plot to the field scale or to the watershed scale as watershed-wide aspects such as field-to-field interactions are not accounted for at the plot or field scales. BMPs have also been studied at a watershed scale (Chow et al. 1999; Kramer et al. 1999; Tebrugge and During 1999), thus allowing watershed-wide quantification of BMP effectiveness. Experimental studies at the watershed scale, however, often do not allow for quantification of individual BMP effects, thus leaving questions as to which BMPs are having an impact and the extent of that impact largely unanswered. Additionally, temporal and spatial replication is often difficult, if even possible, with watershedlevel experiments. Often, the success of large-scale experimental studies relies on the occurrence of natural rainfall. With natural rainfall, however, long experimentation periods may be required to eliminate inconsistencies attributable to anomalies in rainfall regime. Short time periods may not be enough to determine the long-term effectiveness of the BMPs (Camacho 1993) or to adequately capture effects of variation (e.g., plant


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height, density) on the effectiveness of a particular management technique. In general, experimental studies require a great deal of investment, particularly in time, money, and land resources, thus limiting the extent to and conditions for which BMP effects may be explored. Recently, there has been a steady shift toward modeling and model-based approaches as primary methods of quantifying BMP effectiveness. A variety of models exist that have been designed to describe the response of land areas and pollutant movement to various BMPs, including the Soil and Water Assessment Tool (SWAT) (Arnold et al. 1998), the Agricultural Non-Point Source (AGNPS) model (Young et al. 1989), the Annualized Agricultural Non-Point Source (AnnAGNPS) model (Bosch et al. 1998), the Areal Nonpoint Source Watershed Environment Response Simulation (ANSWERS) model (Bouraoui and Dillaha 1996), the Chemical Runoff and Erosion from Agricultural Management Systems (CREAMS) model (Knisel 1980), and the Hydrological Simulation Program-Fortran (HSPF) (Johanson et. al. 1980; Bicknell et al. 2001). These models have been discussed in detail in preceding chapters. The advantages of using a modeling approach to quantify BMP effectiveness in pollutant control are that (1) multiple BMPs can be studied simultaneously; (2) the effectiveness, and therefore impact, of each individual BMP can be determined while also determining the combined effect of BMPs at the study scale; and (3) BMP effects can be simulated to reflect varying locations or location-specific conditions. Disadvantages are uncertainty in model predictions due to uncertainty in some model parameters and lack of measured data in some watersheds, which impacts the process of calibration and validation. Nevertheless, models do provide a means to carrying out such otherwise complex studies as BMP effectiveness evaluations. Moreover, model outputs can be considered adequate where comparisons are made with regard to relative as opposed to absolute change or where ranking of output is required (Novotny and Olem 1994). Until recently, the issue of BMP effectiveness has been addressed mainly with regard to reduction in quantity of pollutant loss. However, BMP implementation and maintenance can be costly. Thus, with regard to P control effectiveness, two issues warrant consideration: the ability of BMPs to reduce P loss and the associated cost effectiveness (defined as the annual cost of reducing pollutant loss by one unit). Recent studies that consider both issues are Chesapeake Bay Program (1987), Epp and Hamlett (1996), Osei et al. (2000), Wossink and Osmond (2002), Yuan et al. (2002), Annett et al. (2004), and Johansson et al. (2004). These studies have considered pollutant loss and cost effectiveness mostly in terms of individual BMPs at the field or plot scale. However, as the scale of interest expands to encompass the farm or watershed, interaction effects among BMPs cause BMP relationships, with respect to both P reduction and cost, to quickly become more complex. These complexities suggest the need to determine ways in which individual BMPs can be selected and placed on the landscape such that the watershed-level BMP scenario provides maximum pollutant reduction for the watershed at the least cost. As such, an in-depth decision on BMP selection and placement based on pollutant removal and costs becomes an iterative process that is effectively executed through optimization of BMP scenarios.


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This chapter discusses approaches to quantifying overall BMP effectiveness, considering both P reduction and costs, with an emphasis on modeling and modelbased approaches. The chapter further discusses means by which optimal BMP solutions can be obtained and presents examples in which the various approaches have been used to obtain farm- or watershed-level solutions.

15.2 MODELING BMP EFFECTIVENESS IN REDUCING PHOSPHORUS Theoretically, BMP effects are most accurately simulated when the mechanisms that a BMP uses to control pollutants are represented within the model by physically based equations. For example, crop rotations can be best simulated if the model code directly accounts for resulting changes in soil structure (Table 15.1). Unfortunately, such representation is often impossible. The inability to completely capture the physical system in simple, machine-codable equations requires mechanisms to be approximated using adjustment factors or modified model inputs (Table 15.1). Nevertheless, process depiction is often implied in the interpretation of model output. For example, reduced sediment loss can be taken to imply either that decreased soil detachment (e.g., crop rotations, conservation tillage) or increased deposition (e.g., contour strip cropping) has been simulated.

15.2.1 READILY MODELED The main types of BMPs that have been investigated through modeling are crop rotations, tillage BMPs, and nutrient management plans. This perhaps reflects the ease with which the effects of these BMPs can be simulated, either by changing model inputs or by specifying appropriate factors. Crop rotations, for example, have been modeled by specifying appropriate cropping factor for the Universal and Revised Universal Soil Loss Equations (i.e., USLE-C or RUSLE-C factors) as demonstrated, for example, by Prato and Wu (1991). Additionally, models like SWAT allow crop rotations to be modeled by specifying the cropping sequence within a response unit, which results in specification of a variety of management- and plantrelated factors, including the curve number (CN) and the USLE-C factor. The impacts of varying cropping sequences under conventional tillage results in differences in pollutant loss as demonstrated by Figure 15.1, based on work by Veith et al. (2003a). From Figure 15.1, response units in continuous corn experienced the highest P losses, with P losses remaining at the same level over three years. During the corn-cornsoybean and corn-soybean-soybean rotations, simulated P losses decreased as the crop changed from corn to soybeans. Similarly, contour strip cropping may be simulated by specifying the cropping pattern within a response unit, as demonstrated by Mostaghimi et al. (1997) and Vache et al. (2002). Mostaghimi et al. (1997) modeled strip cropping in AGNPS by specifying cropping patterns, altering curve numbers, and adjusting cropping and support practice factors for response units that were strip cropped. Vache et al. (2002) modeled strip cropping using SWAT by representing the BMP as a rotation.



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TABLE 15.1 Physical Mechanisms and Potential Methods for Modeling Some Commonly Used BMPs, with Example Applications Best Management Practice

Physical Mechanism

Modeling Approaches

Example Applications

Crop rotation

Improve soil structure Decrease detachment Decrease need for nutrient application

Change specified crop and specify associated management; assumes availability of crop parameters, e.g., from in-built crop databases. Change curve number Change RUSLE cropping factor

Warner et al. (1985), Shirmohammadi et al. (1988), Hamlett and Epp (1994), Vache et al. (2002)

Contour strip cropping

Reduce runoff velocity Increase infiltration Facilitate deposition

Change USLE cropping factor Simulate different strips of crop on field

Hession et al. (1989), Mostaghimi et al. (1997)

Nutrient management plan

Minimize availability of nutrients for transport

Specify different options for nutrient management (e.g., application dates, rates, mixing vs. surface application, manure/fertilizer types)

Warner et al. (1985), Shirmohammadi et al. (1988), Hession et al. (1989), Hamlett and Epp (1994), Mostaghimi et al. (1997), Santhi et al. (2001)

Vegetated filter strip

Facilitate deposition Reduce runoff velocity Increase infiltration Increase nutrient uptake

Apply empirical equations Simulate associated processes

Clausen and Meals (1989), Hession et al. (1989), Hamlett and Epp (1994), Vache et al. (2002)

Riparian forest buffer

Facilitate deposition Reduce runoff velocity Increase infiltration Increase nutrient uptake

Simulate associated processes

Inamdar et al. (1999a, 1999b) Perry et al. (1999), Vache et al. (2002)

Conservation tillage

Reduce runoff volume Increase infiltration Decrease detachment Retard particle movement

Adjust amount of residue available on surface Adjust mixing of residues Change USLE cropping factor

Animal waste system and barnyard management

Divert clean water Contain pollutants for treatment (allow time for deposition and composting) Dispose of waste safely

Change pollutant concentrations in affected response unit

Warner et al. (1985), Shirmohammadi et al. (1988), Hession et al. (1989), Hamlett and Epp (1994), Yoon et al. (1996), Mostaghimi et al. (1997) Hession et al. (1989), Mostaghimi et al. (1997)


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4.0 3.5

Total P, kg/ha

3.0 2.5 2.0 1.5 1.0

CSYSY

2000

1999 Year

1998

Ro

0.0

tati

CCSY

on

CCC

0.5

FIGURE 15.1 SWAT-simulated variation in average annual total P loss across different crop rotations. CCC = continuous corn; CCSY = corn-corn-soybean; CSYSY = corn-soybeansoybean. (Based on work by Veith et al. 2003a. With permission.)

The SWAT, AnnAGNPS, and CREAMS models contain tillage databases, from which input parameters are adjusted when a tillage method is changed. These parameters are often related to the depth and extent of mixing associated with the tillage practice and, subsequently, the amount of residue and nutrients available on the soil surface. The ANSWERS model handles tillage by changing the soil surface roughness, amount of residue on the ground, and other factors related to changes in infiltration and soil cover. Tillage practices have also been modeled by specifying different values of USLE-C factors (Prato and Wu 1991) and by altering curve numbers, cropping factors, and roughness factors (Mostaghimi et al. 1997). Models such as SWAT, AGNPS and AnnAGNPs, and ANSWERS allow changes in nutrient management operations, including application dates and rates. SWAT and AGNPS and AnnAGNPs also allow the user to specify the forms of different types of fertilizers and manures and whether the nutrients are incorporated or surface applied. Nutrient management plans work by limiting the amount of nutrients available for transport, a mechanism that may be approximated by adjusting model inputs and nutrient redistribution in the soil following incorporation or application of liquid manure. Santhi et al. (2001), for example, modeled the impact of changes in fertilizer application rate by using the crop P requirement rate for the application rate input in SWAT. Walter et al. (2001) modeled different manure management scenarios by directly specifying application schedules and rates within the Soil Moisture Routing (SMR) model (Zollweg et al. 1996).



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15.2.2 LESS READILY MODELED BMPs that are more difficult to represent within a model are riparian buffers, vegetated filter strips, barnyard management, and animal waste systems. Often a number of assumptions are necessary to model these BMPs. Vache et al. (2002), for example, manipulated cover factors of near-stream response units and streambed erodibility of associated reaches to model the watershed-wide impact of riparian forest buffers using SWAT. Yuan et al. (2002) specified a strip crop with a high roughness coefficient to simulate filter strips using AnnAGNPS, whereas Mostaghimi et al. (1997) modeled vegetated filter strips by dividing affected response units (cells in AGNPs) and modifying the roughness coefficients of subunits representing filter strips. Vache et al. (2002) and Yuan et al. (2002) also specified filter length as a function of slope to better account for sediment settling caused by the filter strips. Practices such as animal waste management systems have often been modeled by directly changing nutrient loadings attributed to affected response units. Hession et al. (1989), for example, assigned high nutrient availability levels to affected hydrologic response units (HRUs) in a pre-BMP scenario and then greatly reduced these levels to simulate a scenario in which waste management facilities were available to serve the area. Generally, the impact of waste storage systems on areas where manure was previously applied without schedule or restriction can be adequately modeled by appropriately adjusting the simulated timings and rates of manure application as well as the periods over which manure is applied. Other practices that have been modeled indirectly include P reduction in feed (Santhi et al. 2001) and livestock exclusion (Mostaghimi et al. 1997). Santhi et al. (2001) reduced the P content of manure in SWAT to reflect the effect of reducing the P content in animal feed on soluble and organic P levels downstream. Mostaghimi et al. (1997) divided individual response units in AGNPS into subunits to represent areas that had been fenced off from cattle. Direct nutrient loading to the fenced-off areas was simulated as zero in order to model the impact of fencing.

15.2.3 SPECIALIZED MODELS Fortunately, specialized models exist for some BMPs that fit less directly into the more commonly used watershed models. For example, the Riparian Ecosystem Management Model (REMM) (Lowrance et al. 2000) and the Spatial Analysis System (SPANS) (Perry et al. 1999) were both developed to model riparian buffer systems. Additionally, Muñoz-Carpena et al. (1999) developed a finite element model to simulate the effectiveness of filter strips for a given event. With REMM, the buffer area behaves as a single unit that receives precipitation and has associated process-based hydrologic, erosion, and nutrient components (Inamdar et al. 1999a, 1999b; Lowrance et al. 2000). The buffer zone receives inputs — water, sediment, and nutrients — from the upland zone, which are then routed through the buffer. The model can be used to evaluate various aspects of a buffer including buffer width and vegetation type (Dukes and Evans 2003). The SPANS model works by manipulating nutrient retention within the buffer zone. Even though


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these specialized models were developed as stand-alone applications, they can be and have been coupled to various nonpoint source (NPS) models to better represent the specific BMP impacts at the hill slope and watershed scales. For example, REMM has been coupled with GLEAMS (Gerwig et al. 2001; Tucker et al. 2000a, 2000b), AnnAGNPS (Yuan et al. 2004), and SWAT (Cerruci and Conrad 2003) such that the hydrologic and nutrient output from the latter models provide input to REMM.

15.2.4 CAVEATS Though models provide a viable means of evaluating BMP effectiveness, some caution must be exercised in interpreting the results so obtained. Because of its complexity, some aspects of the natural system may not be as fully or as accurately modeled as others. For example, the modeling of conservation tillage practices is expected to result in the simulation of reduced sediment and sediment-bound pollutants. However, it may also result in the consistent simulation of decreases in dissolved pollutants. Yoon et al. (1996) for example, found that the ANSWERS model simulated lower dissolved P losses for conservation tillage areas than it did for the same areas in conventional tillage. This model result is contrary to findings from observed data that have shown increases in dissolved P losses when the management practice changed from conventional to conservation tillage (Camacho 1993; Gitau et al. 2005; Yoon et al. 1996). According to Romkens et al. (1973), Baker and Laflen (1983), and Dillaha (1990), increases in dissolved P losses are attributable to reduced soil disturbance associated with conservation tillage and thus an increased availability of soluble nutrients at the soil surface. Thus, expected reductions in runoff due to the practice may not be in significant amounts to counter increases in soil surface P concentrations (Baker and Laflen 1983; Dillaha 1990). Misinterpretation of modeling results can also occur when the level of detail used to represent the BMP is limited. This is the case for filter strips, animal waste systems, and buffers within several current NPS models. For example, the SWAT model contains a filter strip component (Neitsch et al. 2002) in which filter strip effects are modeled only as a function of filter width. However, other factors affect the performance of filter strips, including slope and underlying soils (Dillaha 1990), and vegetation type and age (Schmitt et al. 1999). Additionally, because the SWAT filter strip equation does not distinguish between pollutants, the model simulates the same efficiency for sediment, sediment-bound P, and soluble P. In actuality, filter strips work best at removing sediment and sediment-bound pollutants but do not greatly reduce soluble pollutant loses (Dillaha 1990). Also, since pollutants are preferentially adsorbed to fine sediments (Morgan 1997), filter-strip efficiency in sediment removal would be somewhat higher than the associated efficiency in sedimentattached pollutant removal. Though CREAMS and AGNPS and AnnAGNPS allow multiple filter strip characteristics — including width, roughness, and vegetation type — to be specified within a response unit, their adequacy in simulating transport processes involved with vegetated filter strips has also been challenged (MuñozCarpena et al. 1999).



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Oftentimes, modeled animal waste systems consistently simulate decreases in all forms of P due to the practice. Field studies by Brannan et al. (2000) have shown that the use of animal waste storage systems favors conversion of P from organic to inorganic forms, thus leading to an increase in the amount of available P in manure at the time of application and subsequently resulting in increases in dissolved P loss from areas where the manure is applied. In that study, however, nitrogen (N)-based nutrient management was used; thus, the authors suggested that increases in dissolved P loss associated with the BMP might be eliminated by changing to P-based applications. Regardless of the model used and any model limitations, determinations of BMP efficiencies must consider how the model is used. The approach taken by Vache et al. (2002) in modeling buffers using SWAT, for example, models a whole response unit as a buffer area. As SWAT does not model interactions between adjacent units, this approach is more reflective of the effects of a local land-use change than of a buffer’s impact on upstream critical areas or preferential flow paths and may not adequately reflect the full impact of the buffers without some type of adjustment. When using models to evaluate BMPs, one must keep in mind that discrepancies between simulated and observed results will occur, in part, because of assumptions needed to model the BMPs. Model results must be interpreted while bearing in mind the characteristics of the natural system being modeled and with a reasonable understanding of how the mechanisms of the BMPs, as modeled, differ from those applied in the system.

15.2.5 MODEL COMPARISONS Of the models that have been used in evaluating BMP effects, the CREAMS model appears to offer great flexibility related to incorporating BMPs. This model, however, operates at a field scale, thus limiting its use for watershed-wide BMP assessment. The AGNPS and AnnAGNPS and SWAT models, all partially based on the CREAMS model, offer similar capabilities with regard to BMP simulation. The AGNPS model is an event-based model and is limited in this manner with regard to analyzing long-term effects of BMPs. It is, however, possibly more suitable than a continuous simulation model when structural-type BMPs are being implemented as these BMPs are best evaluated based on their functioning during storm events (Borah and Bera 2003). The HSPF model has very limited BMP simulation capability. The SWAT, AnnAGNPS, HSPF, and ANSWERS models offer detailed discretization of a watershed by allowing the watershed to be modeled as unique hydrologic response units. AnnAGNPS and ANSWERS have an advantage in that pollutants are routed through receiving response units before reaching the stream. Output formats from SWAT, AnnAGNPS, and HSPF allow losses from the hydrologic response units to be analyzed individually, thus providing the ability to separate out individual BMP effects while also allowing a watershed-wide evaluation of BMP effects. In particular, areas from which P losses are likely to cause a threat to water quality (critical P loss areas) can be identified, thus allowing a need-based evaluation of potential BMP solutions.


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15.3 CUMULATIONS AND ANALYSES OF DATA FROM PREVIOUS STUDIES Though modeling is a much more efficient and practical means of evaluating BMPs than is the use of experimental studies, existing models do not always have the capabilities to model the suite of BMPs being evaluated. Additionally, associated computation time may become a limiting factor when an iterative evaluation of BMP solutions is needed. In such cases, the use of BMP effectiveness factors or coefficients provides an alternative means of representing BMPs within models. Chew et al. (1991), for example, used a supporting management factor to model tillage effects within HSPF, whereas Qui and Prato (2001) used values derived from experimental data to represent buffers in SWAT. The use of BMP factors and coefficients offers a simplified means of including BMPs in models. However, it is important that these simplifications represent the most recent knowledge and existing data on BMP effectiveness. Because many studies have been carried out with the aim of determining BMP effectiveness (see Section 15.1) a substantial amount of data exists that can be used to estimate effectiveness. A key consideration in the use of existing data is the reported variability in BMP effectiveness, as shown in Figure 15.2. Such variability is attributable to factors such as slope, soils, and geographic location (Baker and Johnson 1983). Despite the multifarious nature of existing BMP effectiveness data, these data, when considered collectively, comprise BMP effectiveness values for a wide range of site conditions and will generally include site characteristics and other information (e.g., study location) necessary to qualify the data. In this regard, data from previous BMP studies can be accumulated in such a way as to provide insights as to the variability in the data and, subsequently, to provide a simple means of obtaining reliable, sitespecific estimates of BMP effectiveness (Gitau et al. 2005).

15.3.1 DEVELOPING

A

BMP TOOL

A logical starting point in the accumulation process is to assemble existing data into a database from which information can be extracted in a raw or analyzed form and through which there are capabilities for the development of analytical tools. Recently, there have been a number of efforts toward accumulating BMP effectiveness information into databases. Possibly the first effort at BMP data accumulation was the Non-Point Source Database (Robillard et al. 1994), developed in Oracle for operation on a Mac platform. It allowed the user to retrieve raw and summarized information on all BMPs within specified categories, either restricted or unrestricted by site conditions. This database formed part of the RCWP Expert System (Robillard et al. 1994), which allowed database linkage to the AGNPS model. Another database currently in existence is the International Storm Water BMP Database (UWRRC 2004). Developed for storm water BMPs, this database is possibly the most comprehensive of all existing BMP databases. In addition to site characteristics and effectiveness information, it contains a wide range of other supporting information, including BMP design and layout and monitoring instrumentation.



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TP effectiveness, %

100 75 50 25 0

PP effectiveness, %

-25 100 80 60 40 20 0

DP effectiveness, %

100 50 0 -50 -100 -150 -200

AWS

BYRM CONST CSC

CR

FS

NMP

RFB

BMP FIGURE 15.2 Box plots showing variability in reported TP, PP, and DP effectiveness data relative to various best management practices. TP = total phosphorus; PP = particulate phosphorus; DP = dissolved phosphorus. AWS = animal waste systems; BYRM = barnyard runoff management; CONST = conservation tillage; CSC = contour strip crop; CR = crop rotation; FS = filter strips; NMP = nutrient management plan; RFB = riparian forest buffers; Outliers. For DP, values less than –200 have been excluded from the plots to enable the display of the other plots. (From Gitau et al., J. Soil Water Cons. 60(1), 1–10, 2005. With permission.)


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It allows the user to obtain information based on location, watershed size, and general BMP categories but does not contain analytical tools. A third database, the BMP Tool, is one described by Gitau et al. (2001, 2005). Developed in Microsoft Access, this database was aimed at facilitating agricultural BMP effectiveness evaluation in addition to providing straightforward access to basic information on BMP effectiveness. Yagow et al. (2002) developed another database, also in MS Access, that contains BMP cost and yield impact information in addition to basic site characterization information. The most involved part of a cumulation of research findings is the process of article selection, which constitutes the initial portion of the data collection process. Key considerations are appropriate scope of subject matter, use of all or only published material, rules for rejection of articles based on methodology, quantity of data necessary for analyses, and, once all the data have been assembled, the handling of data appearing as outliers within the combined dataset. These considerations and their application in the cumulating process are discussed in detail in Gitau et al. (2005).

15.3.2 EXAMPLE BMP TOOL APPLICATION Table 15.2 shows analyses of factors affecting BMP effectiveness, based on BMP data in existing literature (Gitau et al. 2005). From the analyses, slope had a significant effect on both total P (TP) and particulate P (PP) reduction at the 95% level

TABLE 15.2 Analyses of the Statistical Significance of Slope and Soil Effects on Best Management Practice Effectiveness at the 95% Level of Significance Factor Effects on Effectiveness for: Factor

Statistics

TP

DP

PP

Slope

Number of entries p-value Significance Number of entries p-value Significance Number of entries p-value Significance Number of entries p-value Significance

56 0.0153 S 56 0.0909 NS 77 0.0285 S 71 0.3373 NS

45 0.54 NS 45 0.6619 NS 64 0.1917 NS 52 0.6648 NS

15 0.0071 S 15 0.0026 S 21 0.041 S 12 0.1685 NS

Soil

Location

Scale

Notes: TP = total phosphorus; DP = dssolved phosphorus; PP = particulate phosphorus; S = significant; NS = not significant Source: Gitau et al., J. Soil Water Cons. 60(1), 1–10, 2005. With permission.



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of significance. With soil type represented by hydrologic soil group, soil effects were significant for PP effectiveness at the 95% level and TP at the 90% level. At the 95% level, location effects were significant for both TP and PP reduction. None of the factors showed a significant effect on dissolved P (DP). Study scale showed no significant effect on BMP effectiveness for any of the three forms of P. Based on the factor effect analyses, site slopes and soils were selected as the factors to be used in developing the BMP Tool (Gitau et al. 2005). Data were grouped by both soils and slopes and descriptive statistics computed for the combined data. Descriptive statistics were also computed for DP, PP, and TP data, grouped by hydrologic soil group and individually by slope class. The BMP Tool is most readily applied in a situation where a pollution problem has been identified and there is a need to evaluate potential BMP solutions. It can be applied to either fields or individual response units as defined within an NPS model. For example, a farm in a New York City watershed has undergone a site environmental review (WAC 2001), and individual fields have been categorized based on their risk with regard to P pollution (Figure 15.3 inset). The site environmental review process involves analyses and inventory of water, soil, air, plant, and animal resources on the farm and subsequent determination of the potential water-quality impacts of the farm in relation to watershed water quality goals. The three fields categorized as high risk are all cropland fields. These are on soils of hydrologic soil group C with a 3 to 8% slope. Farm planners feel that BMPs must be implemented on this farm to prevent P loss. Using the BMP Tool and selecting the appropriate soil hydrologic group and slope class, as well as the desired BMP category, estimates of effectiveness for various BMPs can be obtained (Figure 15.3a and 15.3b). These estimates can be converted to reduction coefficients (where reduction = 1 – {BMP effectiveness %/100}), which can then be used in conjunction with NPS models to determine expected pollutant losses in post-BMP scenarios. Establishing a direct link between the tool and a watershed model can increase the efficiency of tool application across a wide variety of site and management conditions. Tool estimates may also be used in developing BMP components within existing tools such as the P index.

15.4 COST CONSIDERATIONS OF BMP RECOMMENDATIONS Though it is important to consider the effectiveness of BMPs in terms of their abilities to reduce pollutant losses, it is also important to determine the cost implications of applying these techniques. The few publications that document cost components are implementation and variable costs, cost-share rates, land rental, and incentive payments. Chesapeake Bay Program (1987), for example, provided some costs (mainly installation) for individual BMPs as priced at various locations within the Susquehanna basin and also provided cost comparisons, such as the dollar amount increase to implement no-till as compared to conventional tillage. Epp and Hamlett (1996) evaluated changes in field costs and revenues associated with individual BMPs and BMP combinations and compared resulting net revenues with baseline net revenues. Consideration of these various cost elements provides some indication of monetary BMP costs but does not reflect pollutant removal aspects. This makes it difficult


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TOOL Main Interface

BMP Effectiveness Assessment

EFFECTIVENESS ASSESSMENTS Click here

to obtain effe estimates Risk Not classified High Low/Medium

Land use

N

INPUT 0

0.25

Estimates dialog Soil Group

Do Estimates

Forest Corn Hay Pasture

80

Cancel

OUTPUT

70 60 50 40 30 20

Estimates Results for: CATEGORY = Erosion Control| BMP Name

10 Soil Group = C Dissolved P %

Slope =

3-8

Particulate P %

% Total P %

Conservation Tillage

25

55

47

Contour Strip Crop

45

65

59

Crop Rotation

75

0 Total P Conservation Tillage

70

Riparian Forest Buffers

(a)

Contour Strip Cropping

Dissolved P Crop Rotation

Particulate P Nutrient Management Plan

(b)

FIGURE 15.3 Example BMP tool application: (a) tool input and output; (b) comparison of erosion control estimates generated by tool; inset: farm land use and environmental review classification with regard to risk of P loss. (From Gitau et al., J. Soil Water Cons. 60(1), 1–10, 2005. With permission.) © 2007 by Taylor & Francis Group, LLC


Barn Yard Management Erosion Control Nutrient Management

SLOPES

Expected effectiveness (%)

CATEGORY

0.5 Kiometers


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to determine the overall worth of a BMP; a BMP may appear expensive based on cash value yet offer pollutant removal benefits far greater than those offered by a monetarily less expensive BMP. Other BMPs may appear to be effective over most of the year but may fail to function as expected under certain conditions such as extreme rainfall events or severe flooding. A more complete cost comparison among BMPs is thus provided by a BMP cost-effectiveness measure that directly relates pollutant removal capabilities to associated costs. Osei et al. (2000) determined individual cost-effectiveness measures of various manure management practices. Butt and Brown (2000) discussed the cost of nutrient reduction with a focus on the Chesapeake Bay and compared the cost-effectiveness of BMPs in the various basins whose waters feed into the bay. Though this study focused mainly on nitrogen, some suggestions were given as to the potential cost of individual BMPs used for reducing TP losses to the Bay. Wossink and Osmond (2002) studied the cost effectiveness of various management practices including forest and grass buffers, nutrient management, cover crops, and controlled drainage from a nitrogen control point of view. The authors discussed the use of break-even costs as a method of comparing BMPs. Other studies in which the cost effectiveness of BMPs has been considered are Srivastava et al. (2002), Veith (2002), Yuan et al. (2002), Gitau (2003), Annett et al. (2004), and Johansson et al. (2004). Many of these studies have determined the suitability of BMPs by comparing cost effectiveness of individual BMPs. This is appropriate if BMPs are applied one at a time to a given field and if all BMPs considered are equally appropriate for the field. One could then say, for example, that for a particular field, crop rotations are more cost effective than are edge-of-field filter strips. However, consideration of cost effectiveness on an individual BMP basis may quickly lead to inappropriate comparisons among noninterchangeable BMPs, such as animal waste systems and conservation tillage. Additionally, adequate pollutant control on a particular area of land may require a combination of BMPs instead of a single BMP. In this case individual BMP costeffectiveness assessments are not sufficient as BMP cost effectiveness cannot be assumed to be directly additive or multiplicative across all BMPs in a given combination. Thus, in addition to comparing individual BMP effects, it is necessary to compare suites of BMPs that together comprise a watershed solution. Water-quality concerns and the subsequent need to implement BMPs is an issue that presents itself at the watershed scale (EPA 1998), causing pollutant removal and cost considerations to be more appropriately considered at this level or, at the very least, the farm level where there is a need to be consistent with farm management operations. Additionally, addressing pollutant loss at the farm or watershed scale enables consideration of the placement of individual BMPs to account for those areas within the farm or watershed that are critical to pollutant loss.

15.5 COMBINING POLLUTION REDUCTION AND COST Few studies have considered costs and cost effectiveness from the watershed point of view, among them Srivastava et al. (2002), Veith (2002), Gitau (2003), and Johansson et al. (2004). Of these, Gitau (2003) and Johansson et al. (2004) focused specifically on P. A variety of workable solutions is discernable when BMPs are


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considered at the watershed scale. However, because economic and management resources are often limited, researchers and government personnel have suggested that selective BMP application schemes are necessary to maximize pollution reduction and improve water quality (Dickinson et al. 1990). By applying BMPs selectively into those areas most contributing to NPS pollution, pollution control is likely to be cheaper and less disruptive overall than applying the same control measures across the watershed (Braden et al. 1989). A number of researchers have addressed the problem of BMP cost effectiveness using NPS or economic models in conjunction with optimization algorithms, heuristics, or decision criteria. By considering baseline P levels, hydraulic and water budget models, and various field experiments, Willis et al. (1994) evaluated effectiveness of several categories of BMPs in reducing P loadings. Heatwole et al. (1987) evaluated cost effectiveness of 15 different BMP scenarios for two Florida watersheds draining into Lake Okeechobee. They then combined results for the two watersheds and provided a ranking of the eight most effective BMP scenarios. The researchers found that cost effectiveness decreased as the number of BMPs applied within a scenario increased. Das and Haimes (1979) developed a reduced gradient optimization algorithm that integrated optimization of point source, NPS, and economic objectives to arrive at a set of final solutions. Their method provided a listing of trade-off values, in cost of pollution control per unit of pollution reduction, for each of the considered pollutants and planning regions. This provided decision makers for each planning region with information about relative costs of pollution reduction methods. Braden et al. (1989) discussed a theoretical nonlinear model and described a corresponding empirical model for optimizing BMP selection on a watershed. The empirical model optimizes pollution reduction and cost by calculating farm profit, field erosion, and sediment transport for numerous watershed scenarios.

15.5.1 OPTIMIZING BMP SELECTION

AND

PLACEMENT

Success in locating the most cost-effective BMP scenario for a specific watershed depends on the ability to consider the complete range of possible scenarios within a watershed, accounting for spatial variation, field-specific BMP effectiveness, and BMP interaction within and among fields. However, the number of ways to allocate BMPs throughout a watershed is exponential with regard to the number of fields. For example, for 10 fields and 4 nonmutually exclusive BMPs, there are (24)10 possible placement scenarios. Evaluation of all possible BMP scenarios becomes an intractable problem, one that is computationally difficult or impossible to solve for an exact solution in a finite amount of time. Advances in computational speed and software now enable evaluation of a large sample of possible scenarios for a watershed in a reasonable time frame. Using an optimization heuristic to determine scenario effectiveness eliminates the laborious task of individual evaluation and lessens the possibility of computational errors and evaluation inconsistencies. Additionally, optimization enables existing knowledge to be used to aid evaluation while lessening the likelihood that prior knowledge limits the scope of possibilities considered.



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Current optimization techniques combine the computational power of computer technology with the user’s knowledge of the modeled system and with probabilistic or algorithmic routines. These techniques evaluate BMP scenarios for fitness — the degree to which the scenario meets user-supplied criteria. For example, a BMP scenario might be considered more fit than another if the first results in less P loss from the watershed outlet than the second scenario. By successively incorporating scenario fitness results throughout the optimization process, an optimization technique determines highly fit scenarios for a watershed under given criteria. Because of internal mechanisms within the optimization technique, scenarios that are highly fit overall will tend to be composed of individual BMPs that are highly fit and are therefore most likely to have the largest impact.

15.5.2 PROBLEM CLASSIFICATION The problem of locating BMPs throughout a watershed for cost-effective pollution control can be stated as a combinatorial optimization problem (Grötschel 1982; Lawler 1976). A combinatorial optimization problem optimizes a set of categorical variables (a watershed-level BMP scenario) based on an objective function that assigns an ordered value (cost effectiveness of pollutant reduction) to that set. Several optimization heuristics are available for solving combinatorial problems: the genetic algorithm (Goldberg 1989), simulated annealing (Eglese 1990), and tabu search (Glover et al. 1993). Numerous heuristic variations or combinations of heuristics and linear or nonlinear optimization algorithms have been applied to solve complex or intractable problems (e.g., Buick et al. 1992; Cooper et al. 1996; Glover et al. 1995; Koza 1992). In particular, the shuffled complex evolution technique (Duan et al. 1993), a combination of the genetic algorithm (GA) and a nonlinear algorithm, has seen growing use in NPS model calibration. However, only the GA has been documented in the available literature for solving the problem of BMP selection and placement. Additionally, the GA has been shown to be well suited to this problem (Gitau et al. 2004; Srivastava et al. 2002; Veith et al. 2003b).

15.5.3 THE GENETIC ALGORITHM The GA has been used since its inception in the 1960s, mainly in industrial engineering and business applications (Goldberg 1989; Mitchell 1999). In a basic GA, populations of individuals progress from generation to generation based on fitness scores that represent the optimization goal. Each individual of a population is modeled as a chromosome, with genes on the chromosome defining relevant traits of the individual. The possible values of each gene form an allele set for the gene. The value of each gene is selected from its allele set through crossover of existing individuals and through random mutation. Each individual is then assigned a fitness score based on how well the combined traits of the individual satisfy the objective of the optimization. For example, each farm scenario is represented as an individual, or chromosome, within the GA. Each field within the farm is represented as a gene with the possible BMPs for that field forming the gene’s allele set. The BMP scenario is


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then associated with a fitness score based on how well the scenario reduces costs and pollutant loss from the farm. The more the BMP scenario minimizes pollutant loss and costs, the more desirable (more fit) that scenario is and hence the higher its fitness score. At each generation, new individuals are added to the population through crossover and mutation, whereas previous individuals with low fitness scores are dropped from the population. New individuals are typically more likely to be formed from highly fit existing individuals, which help drive the GA toward improving solutions. The most fit chromosomes (i.e., the ones with the lowest pollutant losses and costs) from the previous generation are also often carried over into the new generation to ensure that the best-found solution is maintained. The process terminates when no further improvement in cost effectiveness is being achieved. Nearly all GAs have three basic components: a population of individuals, a function to score the fitness of an individual, and crossover and mutation strategies for creating each successive population (Mitchell 1999). A flowchart of the basic GA process is shown in Figure 15.4. The GA begins by creating an initial population of individuals. Highly fit individuals are then probabilistically selected for consideration into the next generation through direct reproduction, mutation, or crossover. Thus, the probability of an individual’s surviving to the next generation increases with increasing fitness. Mutation changes one or more genes within an individual without regard to past or current fitness. Mutation is a purely random

Initialize population of scenarios

Rank scenarios by calculating each scenario’s fitness score Create next population by joining newly ranked scenarios into previous population and then removing lowest scoring scenarios to maintain population size.

Termination criterion met?

Y

Optimal scenario identified

N Create scenarios for next population from probabilistically selected, high-scoring scenarios by: • Combining attributes of two scenarios, • Precisely replicating a previous scenario, and/or • Randomly changing one or more scenario attributes.

FIGURE 15.4 Flow chart of general genetic algorithm.



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mechanism used to avoid local fitness maxima. Crossover combines two existing individuals to create two new individuals, each having values from both of the parents. Crossover helps redirect the search into new areas of the search space. Whether the parent individuals survive to the next generation depends not only on their fitness levels but also on the replacement scheme of the GA. Depending on the nature of the problem, a GA may be set to replace, at each generation, nearly all of the population, only one or two individuals, or an intermediate number of individuals. A GA ends on reaching some termination criterion, which can be defined in a number of ways. For example, termination can be set to occur after a predetermined number of iterations of the optimization process. The termination criterion can also be defined as a minimal improvement in the maximum fitness score; that is, termination occurs either when the change in fitness score is below a predetermined tolerance or when the score increase has remained below a tolerance for a predetermined number of generations. Existing studies can assist in setting GA parameter values, such as population size, crossover rate, and mutation rate (Srivastava et al. 2002; Veith 2002).

15.5.4 CURRENT CHALLENGES

IN

OPTIMIZATION

Since the GA must calculate NPS pollution loading for each scenario, an NPS model evaluation is necessary for each member of each generation. Thus, runtime for the NPS model is an important consideration. To compare the impacts of BMPs with regard to their location in the watershed, discretization of the spatial data is needed such that each field is simulated with one or more discretization units. Additionally, within field variation is desired to fully utilize the spatial data available. Consideration of soil and slope variation within fields can further increase accuracy of sediment loss and economic predictions. Unfortunately, there are currently few farm- or watershedlevel NPS models with both adequate levels of discretization and a computer runtime feasible for the number of evaluations needed by a general optimization heuristic. Srivastava et al. (2002) optimized BMP selection across a watershed by linking a GA with AnnAGNPS and field-level net returns. By optimizing for pollutant reduction while constraining net return, and vice versa, they showed that within the set of possible scenarios the optimization technique did identify those scenarios with higher than average cost effectiveness. Veith et al. (2003b, 2004) built on concepts presented by Srivastava et al. (2002) by comparing optimized scenarios to targeted solutions. They combined a GA with a geographic information system (GIS)-based sediment loss model, farmer enterprise budgets, and public cost-share estimates. Using the GIS-based NPS model allowed more spatial discretization, greater flexibility in representation and assignment of BMPs, and shorter run times than were available with more complex models. Both public and private costs were then incorporated into an economic module of fieldlevel complexity comparable to that of the NPS model. The optimization methodology was found to locate scenarios more cost effective than defined by a uniform targeting strategy (Veith et al. 2004). Gitau et al. (2004) used literature-based BMP efficiencies to provide fieldsupported NPS reduction predictions while further reducing runtime. Thus, the


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optimization methodology used by Gitau et al. (2004) incorporates an enhanced version of the optimization methodology by Veith et al. (2003b) with fixed BMP costs and the BMP Tool by Gitau et al. (2005), described previously. Although Gitau et al. (2004) used SWAT to determine initial field-level pollutant losses from the baseline scenario, data from other sources could equally be used. Economic routines that incorporate important regional and BMP-specific features into cost considerations are an important area of enhancement and are currently being explored by Veith and collaborators.

15.5.5 THE NEXT STEP: MULTI-OBJECTIVE OPTIMIZATION Although this book focuses on P, water-quality concerns and related modeling efforts commonly extend to other nutrients and pathogens. Consideration of multiple NPS pollutants when designing BMP scenarios often adds significant complexity to the problem. A BMP that controls P loss in surface runoff by increasing infiltration may simultaneously increase the likelihood of nitrogen leaching. In addition to concern over multiple environmental constituents, researchers and stakeholders are often concerned about more than just public or private costs. For example, likelihood to adopt, impact to wildlife, and increased labor hours may be of concern. Thus far, research has addressed multiple NPS control objectives by defining a relationship among them such that they can be incorporated into a single objective function. The fitness function developed by Srivastava et al. (2002) uses an exponential relationship to minimize pollutant loss while penalizing those scenarios of high cost, or vice versa. Multiple pollutants are combined with weighting factors to normalize reduction percentages across all pollutants considered. Veith et al. (2003b, 2004) and Gitau et al. (2004) used a two-step lexicographic function that optimizes first for pollution reduction; all scenarios that meet or exceed an established pollutant reduction criterion are then optimized for minimal cost. The objective function accommodates multiple pollutants by summing them using user-determined weighting. With the existing research laying the groundwork for optimizing BMP selection and placement, areas for further development arise quickly. A non-dominating, multiobjective optimization routine by Reed et al. (2003) is currently being evaluated in combination with farm-level management scenarios. The benefit of such a technique is to create pareto-optimal curves of each decision variable. From these curves, tradeoffs and interactions among variables can be determined. Computational speeds are sufficiently fast with dynamic routines such as described in Reed et al. (2003) to enable consideration of NPS models such as SWAT within the optimization routine, should that prove beneficial to the research questions at hand. Additionally, methods by Reed et al. (2003) determine GA parameters dynamically during the problem solution, greatly simplifying the optimization setup process for the user.

15.6 APPLICATIONS This section provides examples on the quantification of BMP effectiveness and the subsequent optimization of BMP selection and placement. The first two examples are based on the Town Brook watershed (TBW) in New York and involve HRU-



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based evaluations at the farm and watershed levels, respectively. In the third example, based on the FD-36 watershed in Pennsylvania, evaluations are specifically restricted to the field and subfield units. Located in Delaware County, New York, the TBW covers an area of 3700 ha and is part of the Cannonsville Reservoir watershed, which in turn is part of the Catskill and Delaware system, a watershed system that supplies the majority of New York City’s potable water. Agriculture in the Catskill and Delaware region is focused on dairy production and supporting cropland practices. As a result, water quality is at risk from excess manure and fertilizer application, barnyard runoff, and soil loss, with P being the main pollutant of concern (Porter et al. 1997). The FD-36 study site is a 39.5-ha subwatershed of Mahantango Creek, a tributary of the Susquehanna River and ultimately the Chesapeake Bay. Land use in FD-36 is typical of that found in northeastern U.S. (50% soybean, small grain, or corn; 30% forest; 19% pasture; 1% farm buildings). The watershed is characterized by shallow, fragipan soils in near-stream areas, and deep, well-drained soils in the uplands. Slopes within FD-36 range from 1 to 25%. Climate is temperate and humid, with average rainfall of 1100 mm yr−1 and stream yield of 450 mm yr−1, based on data collected by the U.S. Department of Agriculture Agricultural Research Service (USDA-ARS) from 1966 to 2004 (Pionke et al. 1999).

15.6.1 FARM-LEVEL EVALUATION, SUBDIVIDED

BY

HRUS (TBW)

Ongoing work to control P loss in the TBW has involved systematic implementation of BMPs across several pilot farms within the watershed. The farm presented here is one of the pilot farms and was selected because its digitized field boundaries and detailed management data were readily available. Land use on the farm is comprised of 44% cropland, in a rotation of corn silage and hay, and of 19% pasture. The remainder of the land is either forested or inactive. For this case study, DP was considered the target pollutant to be controlled because it is readily available for algal uptake (Sharpley and Beegle 2001) and is thus a critical form of P for the Cannonsville Reservoir. For the TBW baseline scenario, management practices of conventional tillage and daily manure spreading, representative of TBW before intervention by the New York City Watershed Agricultural Council (Cornell Cooperative Extension 1987; Lamont 2002), were applied. The SWAT model was then used to simulate baseline P loss values for the farm. All cropland and pasture HRUs on the farm were considered for BMP implementation. Three BMPs were considered, both individually and in appropriate combinations. Specifically, nutrient management plans were considered for both cropland and pasture. Riparian forest buffers were considered on all agricultural land bordering a stream. Contour strip cropping was considered for all cropland. Due to the cool climate in the study region, conservation tillage was not considered a feasible BMP as soil temperatures were often too low to allow proper crop growth under conservation tillage practices. P reduction estimates were obtained for predominant slope and soil conditions on the farm (Table 15.3) from the BMP Tool. Average annual DP loss as simulated by SWAT, BMP reduction coefficients as shown in


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TABLE 15.3 Reduction Estimates for Dissolved P on 3 to 8% and 8 to 15% Slopes and Hydrologic Soil Groups B and C 3 to 8% Slope BMP Contour strip cropping Nutrient management plan Riparian forest buffers a b

8 to 15% Slope

Group B

Group C

Group B

Group C

0.75 0.75 0.38

0.55 0.36 0.38a

0.65a 0.50 0.38b

0.68b 0.43a 0.38b

Estimated based on effectiveness data grouped separately by soils and by slopes. Estimated based on overall average, independent of soil and slope.

Source: Gitau, M.W. et al., Trans. ASAE 47(6), 1923–1931, 2004. With permission.

Table 15.3, and BMP cost data obtained from the Delaware County BMP cost records (Blouin 2002; Lamont 2002) were analyzed with a GA to determine optimal scenarios for BMP selection and placement. The GA generated a number of near-optimal scenarios for the farm by selecting and placing BMPs as was best suited (fit) to maximizing P loss reduction and minimizing costs. Two highly fit scenarios from the optimization run were analyzed for cost effectiveness and for BMP selection and placement (Figure 15.5, Table 15.4). Both scenarios met a pre-established 60% DP pollution reduction target implying that both scenarios suitably reduced P. A cost effectiveness of $1.62 kg−1 P removal per year was obtained for Scenario 1, whereas cost effectiveness for Scenario 2 was $1.91 kg−1 P removal per year. Scenario 1 applied BMPs to less acreage of the farm than did Scenario 2. Additionally, the areas in specific BMPs and BMP combinations, other than buffers, were smaller in Scenario 1 than in Scenario 2, thus the slightly higher costs associated with Scenario 2. Placement of the selected BMPs varied between the scenarios, with some HRUs that had previously not been allocated a BMP in Scenario 1 being allocated one BMP or a combination in Scenario 2.

15.6.2 WATERSHED-LEVEL EVALUATION, SUBDIVIDED BY HRUS (TBW) In the watershed-level evaluation of TBW, the SWAT model was again applied to simulate baseline P loss values. In the SWAT setup, 0% land use and 0% soil thresholds were specified (0/0% definition) to preclude any lumping of soil and land use areas. This was important in capturing all potential areas of P loss, as small-sized areas with high P loss potential might be lost if lumping were allowed. BMP effectiveness estimates and specific BMP cost data were obtained in the same manner described in the TBW field-level example. Optimization was performed using the GA, as with the previous example, but was set to optimize based on TP rather than on DP.



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FIGURE 15.5 Best management practice (BMP) placement for baseline and two near-optimal scenarios for a farm in Town Brook watershed, New York. (From Gitau, M.W. et al., Trans. ASAE 47(6), 1923–1931, 2004. With permission).

Considered BMPs included animal waste systems, barnyard runoff management systems and filter strips, crop rotations, contour strip cropping, nutrient management plans, and riparian forest buffers. The following two scenarios were evaluated. In Scenario 1, the GA was allowed to place BMPs freely on all cropland and pasture HRUs. However, all cropland and pasture HRUs were considered to require BMPs, thus the GA was constrained to put at least one BMP on each cropland or pasture HRU.


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TABLE 15.4 Comparison of P Reduction Potentials and Cost Effectiveness for B Scenarios Determined through Farm- and Watershed-Level Evaluations for Town Brook Watershed, New York Farm-Level Evaluation, Subdivided by HRUs

Simulated P loss (kg) Reduction of P loading from baseline (%) Cost effectiveness ($/yr/kg) BMPs implemented as percent of cropland Contour strip cropping Nutrient management plan Riparian forest buffers Contour strip cropping/nutrient management plan combination

Baseline

#1

#2

1471 — —

587 60 1.62

588 60 1.91

— — — —

8.0 11 0.4 16

9.0 14 0.1 18

Watershed-Level Evaluation, Subdivided by HRUs

Simulated P loss (kg) Reduction of P loading from baseline (%) Cost effectiveness ($/yr/kg) BMPs implemented as percent of cropland Crop rotations Contour strip cropping Nutrient management plan Riparian forest buffers Crop rotation/contour strip cropping combination Crop rotation/nutrient management plan combination Contour strip cropping/nutrient management plan combination

Baseline

#1

#2

3900 — —

1560 60 24

1580 59 34

— — — — —

4 11 60 1 21

— — 61 — 39

—

1

—

—

2

—

Notes: BMP = best management practice; P = phosphorus. Source: Modified from Gitau, M.W. et al., Trans. ASAE 47(6),1923-1931, 2004. With permission.

Scenario 2 comprised the basic BMP implementation scheme currently being implemented within the watershed. The goal of this scheme is to have all cropland be in rotation, all fields have a nutrient management plan, and all barnyard areas have a barnyard runoff management system with filter strips as treatment for



375

barnyard runoff. Thus, BMPs for this scheme are fixed, and no optimization was performed. Table 15.4 shows a comparison of pollutant reduction efficiencies and cost effectiveness of the two scenarios. Overall, Scenario 1 offered the most cost-effective solution, with a cost effectiveness of $24 kg−1 P removal per year compared to the $34 kg−1 P removal per year associated with Scenario 2. In Scenario 1, the GA favored the nutrient management plan and a combination of crop rotations and contour strip cropping, indicating that these BMPs were likely to have the most impact. Riparian forest buffers were also selected for some of the near-stream HRUs. Though there were fewer BMPs associated with Scenario 2 than with Scenario 1, Scenario 2 was less cost effective. The higher costs were attributed to the requirement that all barnyard areas have barnyard runoff management. The GA did not favor the use of barnyard runoff management BMPs; these are costly, yet the potential pollutant reduction benefits associated with them may not be commensurate with their costs. In addition, Scenario 2 had a lower P loss reduction associated with it, further highlighting the need to determine which BMPs would have an impact when designing a watershed-wide solution.

15.6.3 WATERSHED-LEVEL, SUBDIVIDED

BY

FIELDS (FD-36)

For the FD-36 study, land use at a field-level was divided by soil type to form spatial HRUs in SWAT that are homogenous in soil type, land use, and management. Unique management of each field was maintained by simulating all management changes for each field. Thus, field-level results were obtained by combining results from appropriate HRUs and watershed-level results by considering all HRUs. Field-level P losses predicted by SWAT were compared with field-level vulnerabilities to P loss derived by the P index (Veith et al. 2005). The P index and SWAT categorized 73% of the 22 fields similarly in terms of vulnerability to P loss, with Pearson correlation significant at p = .07; all except one of the remaining six fields were over- or underpredicted by a single risk category. This study suggests the benefit of complex NPS models in verifying more readily accessible indexes, which require less detailed input and are generally less prone to substantial misinterpretation by users than are complex simulation models.

15.7 SUMMARY Techniques for quantifying BMP effectiveness have expanded from individual BMPs on experimental hill slope plots to modeling and model-based approaches and, more recently, to watershed-level optimizations of BMP solutions. This chapter explored this progression and has pointed out the assets and roles of each type of technique. Additionally, the chapter has discussed a number of issues to be kept in mind when modeling BMPs and interpreting the resulting impacts to the natural system. Recent work in multi-objective optimization holds exciting promise for further evaluating phosphorus control BMPs, in line with potential secondary effects on other pollutants such as nitrogen. This will increase the overall effectiveness with which natural resources can be protected. Three examples of quantifying BMP


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effectiveness using the approaches discussed were given. These examples demonstrate work at the watershed, farm, and field levels. Continuing and expanding on such work will provide the interdisciplinary methodologies needed to locate BMP suites that are not only effective in reducing pollutant losses, but that are also cost effective at the public and private level and that are socially acceptable to the local community. At the same time, continuing research to better quantify pollutant reduction due to individual BMPs and specific BMP suites is needed as understanding of pollutant fate and transport mechanisms and of how to model those mechanisms become more clear. Ongoing experimentation and simulation of pollutants less well understood than P and of interactions among these pollutants will continue to provide valuable inputs to larger-scale, nonpoint source control modeling efforts.

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Watershed Agricultural Council (WAC). 2001. WAP planners/engineers and Town Brook researchers meeting proceedings. Watershed Agricultural Council, Walton, NY. Willis, L.M., S.B. Forrest, J.A. Nissen, J.G. Hiscock, and P.V. Kirby. 1994. Analysis of on-farm best management practices in the Everglades agricultural area. Pp. 93–99 in Environmentally Sound Agriculture: Proceedings of the Second Conference, K.L. Campbell, W.D. Graham, and A.B. Boltcher (Eds.). Orlando, FL. Wossink, G.A.A. and D.L. Osmond. 2002. Farm economics to support the design of costeffective best management practice (BMP) programs to improve water quality: nitrogen control in the Neuse River Basin, North Carolina. J. Soil Water Conserv. 57(4):213–220. Yagow, G., T. Dillaha, J. Pease, D. Kibler, and D. Bosch. 2002. A BMP database for nutrient reduction. In Proc. March 11–13, 2002 Conf. Total Maximum Daily Load (TMDL) Environmental Regulations, 250–255. 701P0102. Fort Worth, TX: American Society of Agricultural Engineers. Yoon, K.S., A. Shirmohammadi, K.Y. Yoo, and W.J. Rawls. 1996. Simulation of tillage effect on runoff and nutrient losses with the continuous version of ANSWERS model. J. Environ. Sci. Heal. A 31(3):687–718. Young, R.A., C.A. Onstad, D.D. Bosch, and W.P. Anderson. 1989. AGNPS: A nonpoint source pollution model for evaluating agricultural watersheds. J. Soil Water Conserv. 44(2):168–173. Yuan, Y., R.L. Bingner, R.G. Williams, R.R. Lowrance, D.D. Bosch, and J.M. Sheridan. 2004. Integration of AnnAGNPS and REMM for watershed riparian buffer system assessment. Presented at the Proceedings of the American Water Resources Association Summer Specialty Conference “Riparian Ecosystems and Buffers: Multi-Scale Structure, Function, and Management,” June 28–30, Olympic Valley, CA, CD-ROM. Yuan, Y.S., M. Dabney, and R.L. Bingner. 2002. Cost effectiveness of agricultural BMPs for sediment reduction in the Mississippi delta. J. Soil Water Conserv. 57(5):259–267. Zollweg, J.A., W.J. Gburek, and T.S. Steenhuis. 1996. SMoRMod — A GIS-integrated rainfallrunoff model. Trans. ASAE 39(4):1299–1307.


16

Small Watershed Data Collection to Support Phosphorus Modeling Daren Harmel U.S. Department of Agriculture-Agricultural Research Service, Temple, TX

Brian E. Haggard University of Arkansas, Fayetteville, AR

CONTENTS 16.1 Introduction .................................................................................................383 16.2 Project Design Factors................................................................................384 16.2.1 Monitoring Resources ...................................................................385 16.2.2 Flow Characterization ...................................................................386 16.2.3 Water-Quality Characterization.....................................................388 16.2.3.1 Base Flow and Low Flow.............................................388 16.2.3.2 Storm Flow....................................................................389 16.2.4 Automated Storm Sampling Settings ...........................................390 16.2.4.1 Storm Sampling Threshold ...........................................391 16.2.4.2 Sampling Interval..........................................................391 16.2.4.3 Discrete vs. Composite Sample Collection..................395 16.2.5 Alternative Procedures (Regression Methods) .............................395 16.3 Uncertainty in P Transport Measurement ..................................................396 16.4 Summary .....................................................................................................398 References............................................................................................................. 399

16.1 INTRODUCTION Research and development of improved phosphorus (P) modeling methods is often hampered by the lack of adequate data on P transported in runoff from various soil and land use conditions. These data are needed to enhance model representation of soil P cycling, off-site transport, and linkages to downstream impacts. Such enhancements

383


384


are necessary because models are increasingly used to guide legal, regulatory, and programmatic decisions, which directly affect farm income, water-supply protection, and ecological sustainability. Because of these implications, modelers must incorporate state-of-the-art science to accurately represent P mechanisms and to provide corresponding uncertainty estimates, both of which require appropriate P transport data for model calibration and evaluation (Sharpley et al. 2002). The relative lack of water quality and corresponding flow data is attributed to collection difficulties involving natural rainfall variation, adverse weather conditions, travel time, field personnel requirements, and equipment maintenance (Beaulac and Reckhow 1982; Gilley and Risse 2000; Harmel et al. 2003). The resource requirements of discharge data collection and water quality sampling and analysis also limit availability of transport data (Agouridis and Edwards 2003; McFarland and Hauck 2001; Robertson and Roerish 1999; Shih et al. 1994). As a result, few researchers have made the commitment needed to adequately monitor P transport. Many monitoring projects have been recently initiated, or existing projects modified, to provide targeted water resource data in response to water-quality concerns. The paramount objective in typical project design and modification is to accurately characterize runoff and water quality within resource constraints. The major considerations that affect accomplishment of this objective are discussed in this chapter. Automated storm water quality sampling techniques receive particular attention because most monitoring projects designed to support P modeling are assumed to utilize automated samplers to characterize P transport in surface runoff (for discussion see Section 16.2.3). Other topics addressed include: monitoring resources, flow measurement, manual base-flow and storm sampling, and alternative methods. The influence of scale on P transport mechanisms is well established (Sharpley et al. 2002), but the categorization of watershed scales is difficult due to variable sizes, as determined by hydroclimatic setting and arbitrary selection of watershed outlet. With this variability in mind, the methods discussed are generally applicable for data collection at field-scale (< 50 ha) and small watershed (< 10,000 ha) sites. Discharge and water-quality characterization at the basin-scale are not addressed because most agencies and projects are not adequately staffed or equipped to collect data at that scale.*

16.2 PROJECT DESIGN FACTORS The following Sections 16.2.1–16.2.5 discuss project design factors that directly affect the tradeoff between accurate transport data and monitoring resources. Specifically, they determine the quality and quantity of collected P transport data and supporting flow characterization data. This chapter integrates and summarizes the extensive, well-established information on preferred methods of discharge and manual water-quality data collection with more recent research and guidance on automated storm sampling. Extensive guidance is available on certain aspects of hydrologic and water-quality data collection. Preferred methods in discharge data collection, developed by the U.S. * The U.S. Geologic Survey (USGS) is an exception, as they have the expertise and personnel to collect data on larger watersheds.


Small Watershed Data Collection

385

Department of Agriculture (USDA) and the U.S. Geological Survey (USGS) scientists, appear in the Field Manual for Research in Agricultural Hydrology (Brakensiek et al. 1979) and in selected Techniques of Water-Resources Investigations of the USGS (e.g., Buchanan and Somers 1976, 1982; Carter and Davidian 1989; Kennedy 1984). Chow et al. (1988), Haan et al. (1994), and Maidment (1993) also provide comprehensive information on applied hydrology. In its National Field Manual for Collection of Water Quality Data (USGS 1999), the USGS provides guidance for its personnel on preferred methods for manual collection of water quality samples. Other publications provide extensive guidance on manual field measurements in terms of sample collection techniques and quality control (e.g., Wells et al. 1990) and general information on quality assurance (QA), sample collection, and statistical analysis procedures (e.g., Dissmeyer 1994; USDA-NRCS 1996; U.S. EPA 1997). Much of the information on preferred methods for hydrologic (Section 16.2.2) and water-quality data collection (Section 16.2.3) was compiled from these sources. The previously available sources do not, however, provide the much-needed information on design and implementation of automated storm sampling projects to achieve monitoring goals within resource constraints. Because little such practical guidance has been developed, project design is commonly based on field experience (in the best case) or with no knowledge of design factors and potential consequences (in the worst case). Research results (e.g., King and Harmel 2003; McFarland and Hauck 2001; Miller et al. 2000; Robertson and Roerish 1999; Tate et al. 1999) and practical guidance (e.g., Behrens et al. 2004; Harmel et al. 2003; McFarland and Hauck 2001) on storm sampling on small watersheds have only recently been published.

16.2.1 MONITORING RESOURCES Most projects are faced with resource constraints, and monitoring resource requirements are often underestimated by project designers. Agourdis and Edwards (2003) emphasized that the collection and analysis of water quality samples is a difficult, time-consuming, and expensive task; however, this simple truth is commonly not appreciated. Personnel needs, travel time, equipment purchase and maintenance, site location, sites numbers, and laboratory analysis costs should all be carefully examined prior to project initiation. Committed, well-trained field personnel are essential for water monitoring projects. Personnel must be on call and willing to make frequent trips to remote sites for data collection and sample retrieval, whether or not samples are collected automatically (Section 16.2.3). This travel is often necessary with little advance warning and under adverse weather conditions. These trips can also consume considerable time for conducting necessary equipment inspection, maintenance, and repair. In spite of expense and time required, maintenance of flow and water-quality monitoring equipment is an essential step in producing meaningful data. A commitment to proper maintenance limits loss of data and equipment malfunctions, which, if allowed to occur, increases the uncertainty in measured data affecting model calibration and evaluation. Back-up equipment should be purchased and made ready © 2007 by Taylor & Francis Group, LLC

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for rapid replacement of malfunctioning components. Site visits should be made weekly or in alternating weeks to • • • •

check power sources, stage recorders, pumps, sample tubes, sample intakes, dessicant levels calibrate stage recorders to assure flow measurement accuracy retrieve data to limit loss caused by power failures or other malfunctions perform required maintenance and equipment replacement

Personnel should also visit all sampling sites as soon as possible during or after sampling events to collect or retrieve samples, check stage recorder and automated sampler function, and make necessary repairs. Delay in retrieving water quality samples and transporting them to the lab can result in substantial changes in their chemical composition. The acceptable time frame is constituent specific and should be included in project QA guidelines. Decisions regarding project resource allocation should also consider the number and location of sampling sites and the analysis costs of collected water quality samples. Ideally, data collection sites should be established at a range of scales to adequately assess specific land-management impacts and integrated downstream effects. For best results, field-scale sampling sites should be located at the boundaries of homogeneous land use areas in the natural drainage way. Berm construction may be necessary to direct runoff to a single well-defined outlet. Downstream sampling sites should, if feasible, be established at existing flow gauges or hydraulic control structures (Section 16.2.2) with an historical flow record and a current stagedischarge relationship (rating curve). The cost and travel time required to establish and maintain multiple sites must, however, be considered. The number of samples that can be collected and analyzed by a laboratory in a reasonable time frame as determined by project QA guidelines is another important consideration (Novotny and Olem 1994). It is prudent to estimate the number of samples that will be collected to meet reasonable sampling expectations within the project resources. For flow interval sampling strategies (Section 16.2.4.2), the mean annual number of samples can be estimated from historical runoff data. Selection of base-flow and storm sampling methodology (Sections 16.2.3 and 16.2.4) also affects the number of samples collected, which directly influences sample analysis costs.

16.2.2 FLOW CHARACTERIZATION Collection of adequate flow data is vital in monitoring projects designed to support P modeling efforts because runoff and associated sediment is the dominant overland P transport process. Discharge (flow rate) data, along with corresponding dissolved and particulate P concentrations, are needed to determine the mass transport values and differentiate between transport mechanisms. Typically, discharge is determined with the relation between stage (water surface level or flow depth) and discharge. A general description of stage-discharge relationships and their development is provided in most applied hydrology texts (e.g., Brakensiek et al. 1979; Maidment 1993).



387

With this method, stage data are recorded and translated to discharge with the stagedischarge relationship. A stage-discharge relationship alleviates the difficult task of measuring actual flow rates and instead uses stage, which is relatively easy to measure, to determine discharge. Bubblers, pressure transducers, floats, and noncontact sensors are commonly used to provide continuous stage data. Bubblers and pressure transducers are submerged devices that measure stage by sensing the pressure head created by water depth. Noncontact sensors are suspended above the water surface and use ultrasonic or radar technology to measure water level. All of these devices are typically used in connection with an electronic data logger to store a continuous stage record. Float sensors actually float on the water surface and, in conjunction with a stage recorder, produce a graphical or electronic record of stage. Installation of a permanent staff gauge with which to calibrate stage devices is also recommended, but a surveyed reference elevation point should be established at a minimum. The most reliable stage-discharge relationships are associated with hydraulic control structures, such as flumes or weirs, which can provide stable and accurate flow data for a number of years with minimal maintenance. These structures are often precalibrated and thus do not require development of a stage-discharge relationship. This is an important benefit because stage-discharge relationship development is a time-consuming, long-term task requiring measurement of stage, cross-sectional flow area, and flow velocity for a range of stages. Selection of an appropriate structure for local conditions should be based on the following factors: (1) expected flow range and existing headwater-tailwater effects on structure calibration; (2) floating or suspended debris and transported sediment; (3) construction and maintenance costs in relation to expected project life; and (4) need for flow measurement standardization at sites within the project. Detailed selection criteria for hydraulic control structures are provided in Bos (1976) and Brakensiek et al. (1979). For small watershed sites, pre-calibrated hydraulic control structures are highly recommended in spite of the high cost of purchase and installation. These structures are, however, limited in the discharge they can support, which limits their use on many large watersheds. If installation of a structure is not feasible, location of sampling sites at or near established gauge stations with available data is recommended. Other preferred sampling site locations are culverts or concrete channels, which often provide reliable, consistent stage-discharge relationships. Establishing monitoring sites in natural channels subject to morphological shifts in channel geometry or in locations with limited data can create considerable difficulty in maintaining reliable stage-discharge relationships. An important consideration, regardless of channel type or measurement technique, is assurance that measurement can be made for the complete range of expected flow rates. Another method for determining discharge utilizes measurements of crosssectional flow area and flow velocity. This is the typical method for determining or adjusting stage-discharge relationships for sites in natural channels and for uncalibrated structures. With this method, the flow is divided into vertical sections,


388


and mean velocity and cross-sectional flow area are determined for each section. The total discharge for that stage is the sum of discharges for each section. This procedure must be repeated for the range of expected discharges. Several portable devices are available to measure flow velocities. Velocity meters may use revolving cups that spin at a rate proportional to the velocity, or they may use Doppler, electromagnetic, or radar technology to determine flow velocity. When using each of these meters, care must be taken to determine the mean flow velocity within the vertical section of interest. Permanent in-stream velocity meters are also available that provide continuous stage and velocity measurements. In theory, these instruments use corresponding stage and velocity measurements with cross-sectional survey data to produce continuous discharge measurements; however, the flow velocity values may not adequately represent the mean velocity of the entire flow cross-section. If a stage-discharge relationship is not established for a monitoring site and if in-stream velocity measurement is not feasible, mean velocity can be estimated using a derivative of Manning’s equation. Then, cross-sectional survey data can be used with the mean velocity to estimate discharge. Manning’s equation was developed for uniform flow, which is much more likely to occur in constructed channels with uniform perimeters than irregular natural channels. Therefore, Manning’s equation introduces substantial uncertainty into discharge data when applied to natural channels and thus should only be used as a final option.

16.2.3 WATER-QUALITY CHARACTERIZATION Depending on watershed scale and discharge characteristics, base flow and storm runoff sampling may be needed to adequately characterize various P transport mechanisms. At small watershed sites characterized by perennial flow, base flow sampling is needed to evaluate P transport as affected by in-stream processes, direct deposition from wildlife and livestock, groundwater inflow, and point source contribution. Base flow sampling is generally unnecessary at field-scale or ephemeral small watershed sites where P transport occurs predominately in runoff events. Storm sampling is needed at each of these scales to capture the nonpoint source contribution of dissolved and particulate P and potential resuspension of P associated with in-stream sediment. 16.2.3.1 Base Flow and Low Flow Manual grab sampling is typically used to characterize base flow and low flow waterquality. To provide the most beneficial data to support P modeling, base flow waterquality samples should be taken as often as possible and at regular time intervals not less than once per month. Samples can be taken at a single point in the flow, generally in the centroid of flow, because dissolved constituent concentrations typically are assumed to be uniform across the cross-section unless the site is located immediately downstream of a significant point source contribution (Martin et al. 1992, Slade, 2004, Ging 1999). This assumption is discussed in more detail in Section 16.2.3.2.



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16.2.3.2 Storm Flow Characterization of storm water quality is much more difficult. Storm events occur with little advance warning often outside the conventional work hours and by definition accompany adverse weather. As a result, automated water-quality sampling equipment is often used so that personnel are not required to travel to multiple sites during runoff events. In contrast, manual storm sampling requires personnel to travel to each sampling site and manually collect samples during storm events (Table 16.1). The USGS Equal-Width-Increment (EWI) and Equal-Discharge-Increment (EDI) procedures are widely accepted as proper manual storm sampling methods (USGS 1999; Wells et al. 1990). With these procedures, multiple depth-integrated, flow-proportional samples are obtained across the stream cross-section and produce accurate dissolved and particulate P concentration measurements even in large streams. Despite this advantage, manual techniques require substantial collection time for each sample, which creates difficulty in collecting multiple samples at numerous sites. Less intensive manual sampling, such as grab sampling at random times or locations during storm events, provides much less useful data compared to intensive manual or automated sampling. Regardless of the manual sampling technique utilized, samples should be collected throughout the entire range of observed flow to adequately characterize P transport. The major advantage of automated samplers is their ability to use consistent sampling procedures to take multiple samples at multiple sites throughout complete runoff events of various durations. This is especially important at remote and/or small-scale sites because of the difficulty that field personnel have in traveling to sites and collecting adequate data within event durations. Automated samplers, however, are quite expensive to purchase and maintain and thus require considerable

TABLE 16.1 Advantages and Disadvantages of Automated and Intensive Manual Storm Sampling Automated Storm Sampling

Manual Storm Sampling

Advantages

Disadvantages

Advantages

Disadvantages

Reduced on-call travel

Large investment in equipment Single intake (samples taken at one point)

Low equipment cost

Large investment in personnel Frequent on-call travel often in adverse weather and dangerous conditions Time-consuming sample collection

Multiple samples collected automatically Numerous sites feasible Avoid work in dangerous conditions

Difficult to secure intake in the centroid of flow Considerable maintenance and repair requirement


Integrated samples throughout profile and cross-section

Numerous sites difficult to manage

390


financial investment. Another potential disadvantage of automated samplers is their utilization of a single intake point, which is discussed in detail in the following paragraph. It is assumed that most monitoring projects designed to support P modeling will utilize automated sampling. This assumption is based primarily on the ability of automated samplers to take multiple samples at multiple sites with a consistent sampling procedure and on the realization that most monitoring projects will not have the resources to maintain an adequate on-call field staff* to conduct intensive manual storm sampling at multiple sites (Table 16.1). An important difference between automated and intensive manual storm sampling is that automated samplers typically utilize a single intake while the manual EWI and EDI procedures collect integrated samples across the stream cross-section. Thus, the uniformity of water quality across the flow cross-section and within the water profile deserves consideration. It is generally assumed that dissolved constituents can be adequately sampled at a single intake point in small streams because of well-mixed conditions and in larger streams unless located immediately downstream from significant point sources prior to complete mixing (Martin et al. 1992, Slade, 2004, Ging 1999). If doubt arises as to whether dissolved constituents are uniformly distributed, this can be easily evaluated with a hand-held conductivity probe. If conductivity measurements are relatively uniform throughout the cross-section, then the assumption of well-mixed conditions is supported. This assumption is often invalid for sediment and particulate P because their concentrations typically vary within the vertical profile and across the channel. In spite of this variability, a single sample intake is generally adequate at most field-scale sites because of shallow flow depths and well-mixed conditions. In larger streams, however, EWI or EDI sampling is needed to adequately capture the variability of sediment concentrations within the flow profile and across the channel. To use automated samplers in large streams with constituent concentration variability, single intake samples should be supplemented by manual integrated sampling (e.g., Ging 1999). With both types of samples taken at a range of discharges, the relation between concentrations at the sampler intake and the mean cross-sectional concentrations can be established and used to determine mean concentrations from single intake measurements.

16.2.4 AUTOMATED STORM SAMPLING SETTINGS Three settings are critical in programming automated samplers to collect storm water quality samples. Decisions regarding the following settings determine the number, frequency, and collection method of water-quality samples and, therefore ultimately determine the uncertainty of transport measurement (Section 16.3): • • •

Threshold to start and finish sampling (Section 2.4.1) Sampling interval on which to collect samples after sampling begins (Section 2.4.2) Discrete or composite sample collection (Section 2.4.3)

* The USGS, however, is one agency with the expertise and personnel to conduct proper manual storm sampling.



391

Most commercially available automated samplers contain the following components: programmable electronic operation and memory, water level (stage) recorder, sample collection pump, and sample bottles. Typical bottle arrangements allow from 1 to 24 sample bottles. These electronic samplers evolved from automated, mechanical samplers that were initiated with a float-activated water level switch. Alternative mechanical automated sampling procedures have been designed to provide reliable, low-cost operation for small scale monitoring, but these are not used as frequently as electronic automated samplers. Examples are the Low-Impact Flow Event (LIFE) sampler (Franklin et al. 2001; Sheridan et al. 1996) and modifications of the Coshocton Wheel sampler (Bonta 2002; Edwards et al. 1976; Malone et al. 2003; Parsons 1954, 1955). Both of these can be used for indirect measurement of runoff volume from small watersheds. 16.2.4.1 Storm Sampling Threshold The first critical program setting for automated samplers is selecting a threshold to initiate sampling. For runoff-driven storm sampling, a minimum stage or discharge threshold is typically set, but an additional rainfall criterion is commonly included for larger watersheds. When flow depth or rate exceeds this threshold, sampling begins and typically continues as long as flow remains above this threshold; therefore, setting the minimum flow threshold directly affects the number of samples taken and the proportion of the total discharge sampled (Figure 16.1). Results from Harmel et al. (2002) suggest that substantial sampling error is introduced as minimum flow thresholds are increased. Therefore, thresholds should be set so that as much of the storm duration as possible is sampled. To prevent pump malfunction, the sampler intake should be placed so that it is completely submerged at the minimum flow threshold. Ideally, the sampler intake should be located in the center of the channel in well-mixed flow not a pool or immediately upstream below the crest of the hydraulic control structure. The programming option to sample each time flow rises and/or falls past the threshold (i.e., as sampling is initiated and completed) should be avoided because flow fluctuations near the threshold will override the specified sampling interval and result in unnecessary samples. 16.2.4.2 Sampling Interval The second important setting is the interval on which to sample once the sampling threshold is reached. There are two options for determining the sampling interval: time and flow (Figure 16.2). Time-interval sampling is also referred to as timeweighted, time-proportional, or fixed frequency sampling, and flow-interval sampling can be referred to as flow-weighted or flow-proportional sampling. With time-interval sampling, samples are typically taken at equal time increments (such as every 30 min). Variable time intervals (typically with more frequent samples initially, then less frequently as the storm proceeds) can be beneficial, however, if based on adequate knowledge of site hydrology. Time-interval sampling is a simple and reliable procedure since accurate time intervals are easy to measure



60

measured storm load = 35.7 kg samples taken = 5

50

Flow (m3/s)

3

flow load measured load unmeasured

sample 2

40 30

high minimum flow threshold = 1.0 m3/s

1

20 10

0 0:00

4

0 1:00

2:00

60

measured storm load = 46.0 kg samples taken = 10

3 Flow (m3/s)

3:00

flow load measured load unmeasured

sample 2

low minimum flow threshold = 0.1 m3/s

1

0 0:00

50 40 30 20 10

Cumulative Load (kg)

4

Cumulative Load (kg)

392

0 1:00

2:00 Time (hr)

3:00

FIGURE 16.1 Loads measured with different minimum flow thresholds (1.0 and 0.1 m3/s) with a time-interval (10 min) sampling strategy. The bold lines represent the measured portion of total storm load.

and clock failures are rare. However, if small time intervals are used, frequent sampling will quickly produce numerous samples, exceed sampler capacity, and not adequately characterize the entire runoff event (Table 16.2). Time-interval sampling does not eliminate the need for flow measurement, as flow data are necessary for load determination. With flow-interval sampling, samples are collected on flow volume increments, such as every 2000 m3 or 2.5 mm volumetric depth*. Flow-interval sampling requires continuous flow monitoring to determine loads and to determine sampling intervals. * Referring to discharge intervals in volumetric depth units such as mm, which represent mean runoff depth over the entire watershed, as opposed to volume units such as m 3, normalizes discharge over various watershed sizes. This notation allows a consistent transfer of methods and results to watersheds of differing size.



393

2.0

4 flow-interval samples (3 mm) flow concentration

1.5

2

1.0

1

0.5

0 0:00

PO4-P (mg/l)

Flow (m3/s)

3

0.0 1:00

2:00

3:00

4

2.0 time-interval samples (10 min) flow concentration

1.5

2

1.0

1

0.5

0 0:00

PO4-P (mg/l)

Flow (m3/s)

3

0.0 1:00

2:00

3:00

Time (hr)

FIGURE 16.2 Example hydrograph illustrating differences in sample timing for time- and flow-interval strategies. Although both strategies collect nine samples, flow-interval sampling is most frequent at high flow rates, whereas the frequency of time-interval sampling is consistent throughout the event. Thus, the concentrations measured can be quite different.

Flow-interval sampling readily produces the Event Mean Concentration (EMC), a common method for reporting constituent concentrations defined as the arithmetic mean of individual sample concentrations collected on equal discharge intervals. The EMC multiplied by the total flow volume represents the storm load. Statistical sampling theory indicates that the smaller the sampling interval (the more samples taken), the better actual population characteristics are estimated (Haan 2002). Several recent studies confirm this theory regarding storm monitoring (Harmel and King 2005; King and Harmel 2003, 2004; Richards and Holloway 1987; Miller et al. 2000; Shih et al. 1994). Thus, frequent sampling intervals should be used to accurately characterize storm water quality. However, intervals should


394


TABLE 16.2 The Number of Samples Taken Estimated for Watersheds (0.1 to 6300 ha) and the Sampling Capacity Based on a 24-Bottle Configuration for Selected Strategies Sampling Strategy Time-Interval Discrete (min) 5 10 15 30 60 120 180 300 Sampling Strategy Flow-Interval Discrete (mm) 1.0 2.5 5.0 7.5 10.0 12.5 15.0

Number of Samples Range

Mean

Median

8 – 1237 4 – 619 3 – 413 2 – 207 0 – 104 0 – 52 0 – 35 0 – 21

234 117 78 39 20 10 6 4

164 82 55 28 14 7 5 3

Number of Samples Range 0 – 132 0 – 53 0 – 26 0 – 17 0 – 13 0 – 10 0–8

Mean 30 12 6 3 2 2 1

Median 25 10 5 3 2 2 1

Maximum Duration (min) Discrete 120 240 360 720 1440 2880 4320 7200

2/Bottle 240 480 720 1440 2880 5760 8640 14400

Maximum Volume (mm) Discrete 24 60 120 180 240 300 360

2/Bottle 48 120 240 360 480 600 720

Source: K.W. King and R.D. Harmel, Trans. ASAE, 46, 63, 2003. With permission.

not be set at such a high frequency that prevents complete sampling of various duration runoff events and introduces substantial uncertainty. Harmel et al. (2003) and Harmel and King (2005) provide guidance on selecting time and flow intervals for sampling small watersheds. For time-interval sampling, intervals must be adjusted based on watershed size; however, a consistent flow interval can be used on small watersheds regardless of size if volumetric depth intervals that normalize runoff volume by watershed area are used. Several studies have concluded that flow-interval sampling better represents storm loads than time-interval sampling because a greater proportion of the samples are taken at higher flow and transport periods (Abtew and Powell 2004; Claridge 1975; Harmel and King 2005; King and Harmel 2003; Izuno et al. 1998; McFarland and Hauck 2001; Miller et al. 2000; Rekolainen et al. 1991; Richards and Holloway 1987; Shih et al. 1994). In practical terms, it is difficult to choose time-intervals that can completely sample various duration events with adequate frequency to capture constituent concentration fluctuation without exceeding sampler capacity. It is much easier for flowinterval sampling to provide intensive sampling throughout entire events of various magnitudes (Table 16.2) when runoff is expressed in volumetric depth intervals.



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16.2.4.3 Discrete vs. Composite Sample Collection Another important program setting for automated samplers is the option to collect discrete samples (one sample per bottle) or composite samples (more than one sample per bottle). Discrete sampling strategies provide the best representation of temporal variability of constituent concentrations; however, discrete sampling can produce substantial error even with frequent sampling intervals. This effect is evident in large volume/duration runoff events in which sampling capacity is reached prior to the completion of the event. As shown in Table 16.2, numerous samples can be generated, especially by time-interval sampling, but the common 24-bottle limitation allows only a fraction of the samples to be collected. Composite sampling is a powerful alternative because it increases sampler capacity by collecting more than one sample in each sample bottle. Composite sampling with two, three, or four samples per bottle reduces sample numbers to 50%, 33%, and 25% of that collected by discrete strategies. Composite sampling does, however, reduce data on the distribution of within-event constituent behavior, which limits quantification of various transport mechanisms (McFarland and Hauck 2001). An alternative to using the sampler to composite samples involves manual compositing. Samples collected on equal time intervals can be manually composited following the sampling event by combining subsamples proportional to flow volume during each time interval. This technique does produce a meaningful estimate of the EMC but requires considerable postprocessing. Several recent studies have concluded that composite sampling introduces less error than raising minimum flow thresholds or increasing sampling intervals, especially for flow-interval sampling (Harmel and King 2005; Harmel et al. 2000; King and Harmel 2003; Miller et al. 2000). Therefore, composite sampling is recommended for management of the number of samples collected (Section 16.3). For monitoring projects whose primary goal is load determination, not examination of within-event constituent behavior, single-bottle composite flow-interval sampling is a powerful option that reduces analysis costs while intensively sampling complete events of various durations (Shih et al. 1994; Harmel and King 2003). With this strategy, 80 to 160 flow-interval samples of 100 to 200 ml can be composited into a single sample (16 L bottle capacity) to produce the EMC. Another appropriate option involves collecting discrete samples until an adequate understanding of constituent behavior is gained and then converting to composite sampling.

16.2.5 ALTERNATIVE PROCEDURES (REGRESSION METHODS) The previous sections discussed achieving an appropriate balance between measured P transport data quality and project resources under the assumption that resources are sufficient to intensively sample storm water quality (and base flow if significant). In situations with inadequate resources to conduct intensive water quality sampling, regression methods can be used to estimate P transport (Cohn 1995; Cohn et al. 1989). Regression methods, which typically utilize the relation between flow and constituent concentrations to estimate constituent loads, are commonly applied to large watersheds (Haggard et al. 2003; Robertson and Roerish 1999). Current versions have been


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modified from the original simple linear regression approach to account for nonlinearity, seasonality, and other complicating factors (Cohn 1995; Robertson and Roerish 1999). The statistical relation among discharge, concentrations, and other complicating factors is used to estimate missing daily constituent concentrations, which are then summed to give monthly, seasonal, or annual load estimates. A benefit of this statistical approach is its ability to place confidence limits on resulting load estimates. Regression methods can be applied to relatively small water-quality datasets collected over many years; however, water quality sampling designed to provide input to regression methods must adequately describe the relation between discharge and constituent concentration. To achieve that, dissolved and particulate P concentration data must be collected throughout the range of discharge observed at that location. Sampling strategies should target both base-flow and storm events, as fixed interval sampling (e.g., monthly sampling) may not adequately represent the range of discharge. Monthly sampling strategies targeting base flow may underestimate constituent loads by over 40% (Haggard et al. 2003). Robertson and Roerish (1999) suggested that the collection of water samples during storm events may positively bias annual load estimates in smaller streams because storm concentrations are typically larger than average daily concentrations. Constituents associated with sediment transport often exhibit hysteresis across the storm event, with greater concentrations on the rising portion of the hydrograph than the corresponding discharge on the falling portion (Richards and Holloway 1987; Richards et al. 2001; Thomas 1988); therefore, samples should be collected during both the rising and falling portions. This methodology has been widely used, particularly by the USGS, in relatively large streams and rivers across the U.S. as an effective and economical alternative to provide constituent load data (e.g., Green and Haggard 2001; Pickup et al. 2003). The application of this alternative to field-scale and small watersheds has received limited evaluation except for Robertson and Roerish (1999), who concluded that regression methods are relatively imprecise in small watersheds. Thus, application to small watersheds should be conducted with caution.

16.3 UNCERTAINTY IN P TRANSPORT MEASUREMENT An emphasis on the need for uncertainty estimates associated with model outputs has recently re-emerged, as water quality models are increasingly used to guide natural resource decision-making and legislation (Beck 1987; Haggard et al. 2003; Hession et al. 1996; Sharpley et al. 2002). One obstacle to properly estimating model output uncertainty is the lack of understanding related to uncertain calibration and evaluation data. The uncertainty* related to nutrient transport measurement is poorly understood at best. As a result, the effects of uncertain P transport data on calibration and evaluation of P models have historically been ignored. However, if the water resource community is truly serious about uncertainty and its impact on water quality modeling, uncertainty in constituent transport measurements desperately needs intense research attention. * It is important to note that sampling error is defined as sampling variability or sampling uncertainty and does not include mistakes in data collection and processing (Haan 2002).



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This issue of uncertainty also affects monitoring project design, as most projects are faced with balancing resources and accurate discharge and water quality characterization (Agourdis and Edwards 2003; Harmel et al. 2003; Preston et al. 1992; Shih et al. 1994; Tate et al. 1999). The relative differences in uncertainty between discharge measurement alternatives (Section 16.2.2) have been known for some time. However, only recently have research and practical guidance on automated storm water quality sampling been published. Thus, projects utilizing this methodology are often implemented without regard for the effects of sampler settings on data uncertainty. Each of the important automated storm sampling settings (storm sampling threshold, sampling interval, discrete/composite sampling) directly affects the uncertainty of storm water quality data. These settings determine whether constituent behavior (such as first flush and concentration hysteresis) is adequately characterized without exceeding sampler capacity in events of various durations. Recent research has produced the following conclusions regarding uncertainty in storm water quality data: • •

•

•

Raising the minimum flow threshold decreases the proportion of the storm duration that is sampled and increases uncertainty (Harmel et al. 2002). Increasing the sampling interval increases uncertainty (Richards and Holloway 1987; Shih et al. 1994; Miller et al. 2000; King and Harmel 2003, 2004; Harmel and King 2005). Composite sampling may increase uncertainty for time-interval sampling (Miller et al. 2000; King and Harmel 2003) but by a lesser amount than corresponding increases in sampling interval. Composite flow-interval sampling has little effect on uncertainty (King and Harmel 2003; Harmel and King 2005).

A majority of the previous research on uncertainty was conducted by comparing various estimates of constituent flux and thus addressed relative differences (precision) in error without regard to possible deviation from the true flux (accuracy). This approach is attributed to the cost and commitment required to make true flux measurements. As a result, relative comparisons of various storm sampling strategies can be made, but little is known about the true uncertainty of each. In theory, a measurement of the true flux must be made to determine the uncertainty produced by sampling strategy estimates. However, because it is impractical in field studies to capture the entire runoff volume for actual load measurement (Parsons 1954), a true flux must be assumed. For the assumption to be valid, a sufficiently frequent sampling intensity or appropriate subsampling scheme is required. In practical terms, either an automated sampler with a flow-interval sampling strategy with a 1.5 mm or less volumetric depth interval (Harmel and King 2005) or a flow-proportional sampler (Bonta 2002; Edwards et al. 1976; Franklin et al. 2001; Malone et al. 2003; Parsons 1954, 1955; Sheridan et al. 1996) can produce true dissolved constituent loads on small watersheds. In conditions involving large watersheds or extreme in-channel concentration gradients, frequent cross-sectionally integrated sampling throughout the event duration is required to establish the true flux. Conducting such data collection is a difficult task that is beyond the resources and expertise of typical monitoring projects. Research by Harmel and King (2005) was initiated to address uncertainty estimates in measured storm water-quality data from small agricultural watersheds. All © 2007 by Taylor & Francis Group, LLC

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15 of the flow-interval strategies evaluated (sampling intervals up to 5.28 mm volumetric depth with discrete and composite sampling 2 to 5 samples per bottle) produced cumulative load error magnitudes less than ±10%. The ranking of absolute errors in individual event and cumulative load estimation (sediment > NO3-N > PO4P) is attributed to differences in within-event concentration variability as measured by the coefficient of variation, CV, which was also noted by Claridge (1975). The mean CV across sites for within-event concentrations was 0.61 for sediment, 0.39 for NO3-N, and 0.19 for PO4-P. The authors concluded that sampling intervals up to 6 mm should produce similar load accuracy in other locations for constituents that vary relatively little within runoff events, but smaller intervals (1 to 3 mm) should be used to sample widely varying constituents. The focus of this discussion is the uncertainty effects of various automated water quality sampling strategies; however, uncertainty is also introduced into reported nutrient data by uncertainties in discharge measurement, sample preservation/storage, and laboratory analysis (Harmel et al. 2006). Although relative differences between discharge measurement alternatives are well established, few studies on errors associated with sample preservation, storage, and analysis have been published (e.g., Kotlash and Chessman 1998; Jarvie et al. 2002). Research on the relative differences in uncertainty contributed by each of these potential sources has only recently become available (e.g., Harmel et al. 2006).

16.4 SUMMARY In recent years, many monitoring projects have been initiated or modified to provide water quality and discharge data needed to support water resource management. Water-quality modeling in particular relies on measured nutrient transport data for calibration and evaluation. These data are needed to improve model dynamics to more accurately represent soil P cycling and transport and to improve linkages between field-scale losses and downstream transport. In monitoring project design and modification, it is important to utilize data collection methods that accurately characterize runoff and water quality within resource constraints. The design factors that directly impact this balance are monitoring resources, flow characterization, automated vs. manual water quality sampling, and settings for automated storm sampling. Although relatively little information is available on measurement uncertainty effects for certain project design factors, the following guidelines have been established to improve data quality and reduce sampling uncertainty: • • •

Assemble a well-trained field staff willing to be on-call and make frequent site visits. Commit to proper maintenance of monitoring equipment in spite of time and expense. Install pre-calibrated hydraulic control structures or develop reliable stagedischarge relationships.



•

•

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At field-scale and small watershed sites, use automated sampling equipment programmed with a low minimum flow threshold to collect frequent, flow-interval composite samples. At larger watershed sites where particulate P concentrations are not uniform, manually collect frequent EWI or EDI samples throughout complete events, and supplement automated sample collection with EWI or EDI sampling to correct single intake concentrations to represent mean concentrations within the entire channel.

As modeling increasingly impacts water resource policy, management, and regulation, the water resource community needs to direct research attention to the issue of uncertain nutrient transport data and its impact on water-quality model output. Additional data are needed to provide scientifically sound information to decision makers about the uncertainties in calibration and evaluation data and the uncertain nature of model output.

REFERENCES Abtew, W. and B. Powell. 2004. Water quality sampling schemes for variable flow canals at remote sites. J. Am. Water Resour. Assoc. 40:1197–1204. Agouridis, C.T. and D.R. Edwards. 2003. The development of relationships between constituent concentrations and generic hydrologic variables. Trans. ASAE 46:245–256. Beaulac, M.N. and K.H. Reckhow. 1982. An examination of land use-nutrient export relationships. Water Resour. Bull., 18:1013–1024. Beck, M.B. 1987. Water quality modeling: a review of the analysis of uncertainty. Water Resour. Res. 23:1393–1442. Behrens, B., J.H. Riddle, and J. Gillespie. 2004. Tips to improve wet weather monitoring. Am. Publ. Works Assoc. Report. Also presented by Holbrook, K.R., Maximizing reliability of storm water monitoring data, North American Surface Water Quality Conference, Palm Desert, CA, 2004. Bonta, J.V. 2002. Modification and performance of the Coshocton wheel with the modified drop-box weir, J. Soil Water Cons., 57:364–373. Bos, M.G. 1976. Discharge measurement structures, Publication 20, International Institute for Land Reclamation and Improvement, Wageningen, the Netherlands. Brakensiek, D.L., H.B. Osborn, and W.J. Rawls. 1979. Field manual for research in agricultural hydrology, Agriculture Handbook, U.S. Dept. Agriculture, Washington, D.C., 224. Buchanan, T.J. and W.P. Somers. 1976. Discharge measurements at gaging stations, in Techniques of Water-Resources Investigations of the U.S. Geological Survey, book 3, chap. A8. Buchanan, T.J. and W.P. Somers. 1982. Stage measurement at gaging stations, in Techniques of Water-Resources Investigations of the U.S. Geological Survey, book 3, chap. A7. Carter, R.W. and J. Davidian. 1989. General procedure for gaging streams, in Techniques of Water-Resources Investigations of the U.S. Geological Survey, book 3, chap. A6. Chow, V.T., D.R. Maidment, and L.W. Mays. 1988. Applied Hydrology. New York: McGraw-Hill. Claridge, G.G.C. 1975. Automated system for collecting water samples in proportion to stream flow rate. New Zealand J. Sci. 18:289–296. Cohn, T.A., L.L. DeLong, E.J. Gilroy, R.M. Hirsch, and D.K. Wells. 1989. Estimating constituent loads. Water Resour. Res. 25:937–942.


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Cohn, T.A. 1995. Recent advances in statistical methods for the estimation of sediment and nutrient transport in rivers. U.S. Natl. Rep. Int. Union Geod. Geophys. 1991-1994, Rev. Geophys. 33:1117–1123. Dissmeyer, G.E. 1994. Evaluating the effectiveness of forestry best management practices in meeting water quality goals or standards, U.S. Department of Agriculture, Miscellaneous Publication 1520, Forest Service, Southern Region, Atlanta, GA. Edwards, W.M., H.E. Frank, T.E. King, and D.R. Gallwitz. 1976. Runoff Sampling: Coshocton Vane Proportional Sampler, ARS-NC-50. Franklin, D.H., M.L. Cabrera, J.L. Steiner, D.M. Endale, and W.P. Miller. 2001. Evaluation of percent flow captured by a small in-field runoff collector. Trans. ASAE 44:551–554. Gilley, J.E. and M.L. Risse. 2000. Runoff and soil loss as affected by the application of manure. Trans. ASAE 43:1583–1588. Ging, P. Water-quality assessment of south-central Texas — comparison of water quality in surface-water samples collected manually and by automated samplers, U.S. Geological Survey, Fact Sheet FS-172-99. Haan C.T., B.J. Barfield, and J.C. Hayes. 1994. Design Hydrology and Sedimentology for Small Catchments. New York: Academic Press. Haan, C.T. 2002. Statistical Methods in Hydrology, 2nd ed. Ames: Iowa State Press. Haggard, B.E., T.S. Soerens, W.R. Green, and R.P. Richards. 2003. Using regression methods to estimate stream phosphorus loads at the Illinois River, Arkansas. Applied Eng. Agric. 19:187–194. Harmel, R.D., R.J. Cooper, R.M. Slade, R.L. Haney, and J.G. Arnold. 2006. Cumulative uncertainty in measured streamflow and water quality data for small watersheds. American Society of Agricultural and Biological Engineers 49(3):689–701. Harmel, R.D. and K.W. King. 2005. Uncertainty in measured sediment and nutrient flux in runoff from small agricultural watersheds. Trans. ASAE 48:1713–1721. Harmel R.D., K.W. King, and R.M. Slade. 2003. Automated storm water sampling on small watersheds. Applied Eng. Agric. 19:667–674. Harmel, R.D., K.W. King, J.E. Wolfe, and H.A. Torbert. 2002. Minimum flow considerations for automated storm sampling on small watersheds. Texas J. Sci. 54:177–188. Helsel, D.R. and R.M. Hirsch. 1993. Statistical Methods in Water Resources. New York: Elsevier. Hession, W.C., D.E. Storm, C.T. Haan, K.H. Reckhow, and M.D. Smolen. 1996. Risk analysis of total maximum daily loads in an uncertain environment using EUTROMOD. J. Lake Reservoir Manage. 12:331–347. Izuno, F.T., R.W. Rice, R.M. Garcia, L.T. Capone, and D. Downey. 1998. Time vs. flow composite water sampling for regulatory purposes in the Everglades Agricultural Area. Appl. Eng. Agric. 14:257–266. Jarvie, H.P., P.J.A. Withers, and C. Neal. 2002. Review of robust measurement of phosphorus in river water: sampling, storage, fractionation, and sensitivity. Hydrol. Earth Sys. Sci. 6:113–132. Kennedy, E.J. 1984. Discharge ratings at gaging stations, in Techniques of Water-Resources Investigations of the U.S. Geological Survey, book 3, chap. A10. King, K.W. and R.D. Harmel. 2003. Considerations in selecting a water quality sampling strategy. Trans. ASAE 46:63–73. King, K.W. and R.D. Harmel. 2004. Comparison of time-based sampling strategies to determine nitrogen loading in plot-scale runoff. Trans. ASAE 47:1457–1463. Kotlash, A.R. and B.C. Chessman. 1998. Effects of water sample preservation and storage on nitrogen and phosphorus determinations: implications for the use of automated sampling equipment. Water Res. 32:3731–3737. Maidment, D.R. 1993. Handbook of Hydrology. New York: McGraw-Hill.



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Malone, R.W., J.V. Bonta, and D.R. Lightell. 2003. A low-cost composite water sampler for drip and stream flow. Appl. Eng. Agric. 19:59–61. Martin, G.R., J.L. Smoot, and K.D. White. 1992. A comparison of surface-grab and cross sectionally integrated stream-water-quality sampling methods, Water Environ. Res. 64:866–876. McFarland, A. and L. Hauck. 2001. Strategies for monitoring nonpoint source runoff, TIAER Report 0115. Miller, P.S., B.A. Engel, and R.H. Mohtar. 2000. Sampling theory and mass load estimation from watershed water quality data, American Society of Agricultural Engineers, Paper 00-3050, St. Joseph, MI. Novotny, V. and H. Olem. 1994. Water Quality: Prevention, Identification, and Management of Diffuse Pollution. New York: Van Nostrand Reinhold. Parsons, D.A. 1955. Coshocton-Type Runoff Samplers. ARS-41-2. Parsons, D.A. 1954. Coshocton-Type Runoff Samplers, Laboratory Investigations, SCS-TP-124. Preston, S.D., V.J. Bierman, and S.E. Silliman. 1992. Impact of flow variability on error in estimation of tributary mass loads. J. Environ. Eng. 118:402–419. Rekolainen, S., M. Posch, J. Kamari, and P. Ekholm. 1991. Evaluation of the accuracy and precision of annual phosphorus load estimates from two agricultural basins in Finland. J. Hydrol. 128:237–255. Richards, R.P. and J. Holloway. 1987. Monte Carlo studies of sampling strategies for estimating tributary loads. Water Resour. Res. 23:1939–1948. Robertson, D.M. and E.D. Roerish. 1999. Influence of various water quality sampling strategies on load estimates for small streams, Water Resour. Res. 35:3747–3759. Sharpley, A.N., P.J.A. Kleinman, R.W. McDowell, M. Gitau, and R.B. Bryant. 2002. Modeling phosphorus transport in agricultural watersheds: processes and possibilities. J. Soil Water Conserv. 57:425–439. Sheridan, J.M., R.R. Lowrance, and H.H. Henry. 1996. Surface flow sampler for riparian studies. Appl. Eng. Agric. 12:183–188. Shih, G., W. Abtew, and J. Obeysekera. 1994. Accuracy of nutrient runoff load calculations using time-composite sampling, Trans. ASAE 37:419–429. Slade, R. 2004. personal communication. Stone, K.C., P.G. Hunt, J.M. Novak, M.H. Johnson, and D.W. Watts. 2000. Flow-proportional, time-composited, and grab sample estimation of nitrogen export from an Eastern coastal plain watershed. Trans. ASAE 43:281. Tate, K.W., R.A. Dahlgren, M.J. Singer, B. Allen-Diaz, and E.R. Atwill. 1999. Timing, frequency of sampling affect accuracy of water-quality monitoring. California Agric. 53:44–49. Thomas, R.B. 1988. Monitoring baseline suspended sediment in forested basins: the effects of sampling on suspended sediment rating curves. Hydrol. Sci. 33:499. U.S. Department of Agriculture Natural Resource Conservation Service (USDA-NRCS). 1996. National Water Quality Handbook: National Handbook of Water Quality Monitoring, Part 600. U.S. Environmental Protection Agency (EPA). 1997. Monitoring Guidance for Determining the Effectiveness of Nonpoint Source Controls. EPA 841-B-96-004, Washington, D.C. U.S. Geological Survey (USGS). 1999. Handbooks for water-resources investigations, Section A., in National Field Manual for Collection of Water-Quality Data. Wells, F.C., W.J. Gibbons, and M.E. Dorsey. 1990. Guidelines for collection and field analysis of water-quality samples from streams in Texas, U.S. Geological Survey, Report 90-127, Open-File.


Section IV Modeling in the Future


17

Suggestions to Improve Modeling of Phosphorus David E. Radcliffe University of Georgia, Athens, GA

Miguel L. Cabrera University of Georgia, Athens, GA

CONTENTS 17.1 Introduction ...............................................................................................405 17.2 Runoff........................................................................................................406 17.3 Soil Phosphorus Pools and Model Parameters.........................................406 17.4 Leaching of Phosphorus............................................................................408 17.5 Best Management Practices ......................................................................409 17.6 In-Stream Processes ..................................................................................410 17.7 Phosphorus Indices ...................................................................................411 17.8 Calibration and Uncertainty......................................................................411 17.9 Data to Support Phosphorus Modeling ....................................................412 17.10 Summary ...................................................................................................413 References..............................................................................................................413

17.1 INTRODUCTION Much progress has been made in the science of modeling phosphorus (P) fate and transport: from field-scale, event-based, empirical models to dynamic, watershedscale, process-based models. Nonetheless, some improvements are clearly needed in today’s models. This chapter’s purpose is to identify the most necessary changes to improve the modeling of P in the environment. Earlier chapters in this book have been drawn on heavily in developing the ideas presented here. Suggestions are grouped into eight general areas: (1) runoff; (2) soil P pools and model parameters; (3) leaching; (4) best management practices (BMPs); (5) in-stream processes; (6) P indices; (7) calibration and uncertainty; and (8) data for modeling.

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17.2 RUNOFF Most of the current models use the Soil Conservation Service (SCS) curve number approach (McCuen 1982) to estimate runoff. This approach is widely proven and sensitive to land use and soils, but it limits models to a daily time step. Some models use, or have the option of using, infiltration equations such as Green and Ampt (1911). These equations can be used for shorter time steps, but they do not readily reflect differences in land use. Furthermore, the infiltration equations are based on a one-dimensional (vertical) approach to water flow and as a result estimate infiltration excess runoff in contrast to saturation excess runoff (Beven 2001). Research in humid regions has shown that saturation excess runoff is generated during storms in areas low in the landscape that vary in size (variable source area, or VSA) depending on the antecedent soil water content because of lateral subsurface water flow (Hewlett and Troendle 1975). It is essential not only that the correct amount of runoff from a watershed be estimated but also that the area where runoff is generated be identified. Combined with the areas that are sources of high concentrations of P in runoff, these are the critical source areas where management can be focused to reduce P losses (Gburek and Sharpley 1998). Models need to incorporate the VSA concept into their estimations of where runoff occurs. This may move P simulation toward fully distributed watershed models such as AnnAGNPS or ANSWERS-2000. With a fully distributed model, digital elevation model (DEM) data can be used to generate a wetness index (Beven 2001) for each cell, which in turn can be used to identify areas that are likely to receive lateral subsurface flow of water. Alternatively, it may be possible to incorporate the VSA concept into semidistributed models such as Soil Water Assessment Tool (SWAT) and HSPF. According to Steenhuis et al. (1995), the SCS curve number approach for estimating the amount of runoff is consistent with the VSA concept. Schneiderman (Chapter 12, this volume) describes a new version of the Groundwater Loading Function (GWLF) known as VSLF that uses the wetness index to distribute runoff estimated by the SCS curve number method among hydrologic response units (HRUs). In the present authors’ opinion, models must consider both infiltration excess and saturation excess processes in estimating where runoff will occur. Recent work has shown that both soil properties and landscape topography are important in predicting runoff (Soulsby et al. 2005; Tetzlaff et al. 2005).

17.3 SOIL PHOSPHORUS POOLS AND MODEL PARAMETERS Many of today’s watershed-scale models have evolved from field-scale models developed in the 1980s. The soil P routines in these models are derived from concepts current in the 1980s and implemented in the EPIC model (Williams 1995). These routines need to be updated to reflect recent research. The most important improvement will be to add a separate manure pool for P (Vadas et al. 2004). Current models assume that P added in manure instantly becomes part of the soil P pools. However, in grasslands where manure is not incorporated this is not the case, and models can


Suggestions to Improve Modeling of Phosphorus

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underestimate P losses in runoff from storms shortly after manure is applied (Pierson et al. 2001). How these pools interact is an important question. DeLaune et al. (2004) showed that the manure pool dominated soil test P as a source for up to 14 days after application of broiler litter, but it is not known how much longer these pools remain separate. Vadas et al. (2005a) developed equations for a separate manure pool based on laboratory-derived relationships similar to what has been used earlier for soil P pools (see Chapter 3). Vadas is also developing a full model of the manure pool and its interaction with other pools (Vadas 2006). This model estimates dissolved organic P in runoff in addition to dissolved inorganic P. Dissolved organic P in manure has been found to increase as the pH of the manure decreases after application from its original pH of around 8 to a pH of 6, which is typical of agricultural soils (Tasistro et al. 2006). It may also be important to model the contribution to particulate P that comes from the manure pool as well as the P derived from vegetation or residue pools (Sharpley and Smith 1992). Further research is needed to determine how much P loss is due to losses from these pools. Nelson and Parsons (Chapter 4, this volume) note that the EPIC approach leads to an assumption of linear P sorption in soils, but sorption isotherms show that sorption is highly nonlinear. Assuming linear sorption could lead to error in predicting runoff and leaching losses, especially in soils with high concentrations of sorbed P. Nonlinearity also arises in the data used to develop the laboratory-derived relationships because of the effective depth of interaction and water-to-sediment ratio terms (Chapter 3, this volume). For many models, it is not clear what form of measurable soil P (e.g., total, soil test, bioavailable, anion-exchangeable) corresponds to the different model soil P pools (e.g., labile, active, residual). In the original papers by Jones et al. (1984) and Sharpley et al. (1984) describing the EPIC approach, it was clear that the labile P pool corresponded to anion-resin-exchangeable P (Sharpley 2000). Sharpley et al. (1984) recognized that the most commonly measured forms of soil P were the different soil test extractions (Bray-1, Mehlich-1, and Olsen P) and provided regression equations for converting soil test P concentrations to labile P concentrations. This clarity has been lost in the documentation of some of the current models. In the SWAT User’s Manual (Neitsch et al. 2002), a dissolved P pool is described, but the equations are identical to those in the EPIC routines, so this is most likely labile P. In HSPF, two soil P pools — dissolved and adsorbed — are simulated, but no guidance is given on what forms of measurable P correspond to these pools. Models have been found to be sensitive to the initial storages of soil P pools (Chapter 9, this volume). Wherever possible, soil P pools in models should be related to measurable forms of P in soils. The rate of transfer between soil P pools in soil can be important. Vadas et al. (2006) showed that SWAT does not include a delay that was part of the original EPIC routine in transfer between the labile and active P pools when fertilizer is added. As noted by Chaubey et al. (Chapter 7, this volume), several improvements to the P routines in SWAT are under consideration, including slowing the transfer of added (fertilizer) P from labile into active pools and adding a separate manure pool. Most models estimate the dissolved inorganic P concentration in runoff by multiplying the concentration of dissolved or labile P in the topsoil by an extraction


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coefficient. The National P Project (Vadas et al. 2005b) resulted in a very large number of rainfall simulation studies performed across the U.S. where dissolved inorganic P concentration in runoff was regressed on different forms of P in soil. This information on extraction coefficients needs to be incorporated into model databases. HSPF uses a number of soil parameters in the soil P routines — and in the hydrology routines — that are unique to the model and not commonly measured in soils. A database of parameter values used in models by experienced users is provided in HSPFParm (Donigian et al. 1999), which is very useful. A technical note for selecting values for hydrology parameters is available (EPA 2004), as well as a new technical note for sediment parameters (EPA 2006). A similar technical note for selecting P parameters is needed.

17.4 LEACHING OF PHOSPHORUS Concern over leaching of P is relatively new, as recent research has shown it is an important pathway for subsurface losses to nearby streams, especially in deep sands and in systems with tile drains (Nelson et al. 2005; Sims et al. 1998). As noted by Nelson and Parsons (Chapter 4, this volume), leaching also affects the estimation of runoff in that it removes P from the topsoil that would otherwise be available for runoff loss. They point out that in soils with low P sorption capacities, leaching can potentially remove more P from the root zone than crop uptake. Leaching is also important in longterm modeling studies where it becomes a significant component of P mass balances. However, current models either ignore P leaching or treat it in a simplistic manner. AnnAGNPS, ANSWERS-2000, and WEND-P do not model leaching of P or losses by tile drains. SWAT uses a field-capacity water balance (FCWB) approach to estimate vertical flux of water within the soil profile (up to 10 layers) and includes preferential crack flow. The concentration of P in leaching water is determined by the labile P concentration in the top soil layer. HSPF uses an empirical equation to determine percolation of water, and user-specified reduction factors are used to determine how much P is transported with the percolating water. GWLF does not model leaching explicitly, but the concentration of P in groundwater, which affects stream base-flow P concentration, is a user-specified input or a function of the percent of agricultural land use in the basin. A better description of the P leaching process needs to be included in models. Modeling may benefit from some of the same improvements mentioned for improving the modeling of runoff — a separate manure pool because manure P, especially when surface applied, will not be immediately available for leaching and because adsorption is likely to be nonlinear. Models need to be able to estimate tile drain flow and the concentration of P in tile drains. It may be possible to estimate the P concentration in leachate by using a relationship with soil test P in the topsoil. Nathan and Parsons (Chapter 4, this volume) refer to these as quantity–intensity relationships. Preferential flow should also be incorporated into future models if it is not already present. Research has shown that it is especially important in fields with tile drains (Kladivko et al. 1991). Particulate P as well as dissolved P may move via preferential flow (Chapter 4, this volume). Model validation should include comparisons of model estimations with P distributions in the soil profile.



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Model developers seem aware of the need for improving the simulation of P leaching. SWAT2003 has improved tile drain simulation, and further testing of the preferential flow model in SWAT is stated goal (Chapter 7, this volume). ANSWERS2000 is undergoing major revision to link the model’s subsurface flow components with the groundwater model MODFLOW (Chapter 10, this volume).

17.5 BEST MANAGEMENT PRACTICES Today, watershed-scale models are being used to test scenarios for reducing P loads to sensitive water bodies because of limits imposed by Total Maximum Daily Loads (TMDLs) (Reckhow et al. 2001), source water assessment (EPA 1997), or lawsuits (Blackstock 2003). This is usually done in part by reducing loads from nonpoint sources through the use of best management practices (BMPs). Despite the widespread use of models for this purpose, BMPs are usually modeled in a simplistic manner (Chapter 15, this volume). All the models in this volume allow for simulation of BMPs to some degree. The most extensive list of BMPs occurs in SWAT and AnnAGNPS. Common BMPs simulated are crop rotations, tillage, and nutrient management (i.e., timing, type, and rate). However, in most cases a simple reduction factor is used to simulate the effect of BMPs. Often the reduction factor for a given BMP is the same for different pollutants. For example, in SWAT the reduction factor for filter trips is specified by the user, but it is the same for sediment and dissolved P. Research has shown that filter strips are not as effective in removing dissolved P as they are in removing sediment (Chapter 15, this volume). One of the most important BMPs that needs improvement in modeling is the use of riparian buffers, since these are commonly used in implementing TMDLs. Semidistributed models such as SWAT and HSPF do not model overland flow or subsurface flow from one land use to another, so it is difficult to model the effect of buffers beyond using a simple reduction factor. Buffers can be more easily modeled in fully distributed models such as AnnAGNPS or ANSWERS-2000. This, along with identification of variable source areas of runoff, may be another reason for moving toward fully distributed models. Including buffers as separate land uses may require improvements in the leaching and lateral flow predictions as well (Chapter 4, this volume). The SWAT model developers are considering the addition of vegetated filter strips and riparian zones, but it will require reconfiguration of HRUs to allow more detailed variation in topography and management practices (Chapter 7, this volume). The advantages of this approach are being weighed against the fact that increased complexity will make it less user friendly. Lowrance et al. (2000) developed the Riparian Ecosystem Management Model (REMM), which simulates all of the important P and hydrologic processes thought to occur in riparian buffers, given the runoff and subsurface lateral flow inputs from adjoining fields. It may be possible to use REMM to parameterize HRUs that consist of a field with a riparian buffer and thereby avoid developing a fully distributed model. Gitau and Vieth (Chapter 15, this volume) recommend that the cost of BMPs be included in models. They also suggest that the interaction between BMPs needs to be simulated since management scenarios will consider more than one type of BMP.


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Interesting work is being done on using optimization methods to determine the most effective suite of BMPs to achieve a given reduction (Chapter 15, this volume). Multi-objective functions can be used that include cost and the effect on other pollutants such as nitrogen and sediment. This type of capability is also needed in calibration and uncertainty analysis (see Chapter 6). The long-term effectiveness of BMPs must also be considered. WEND-P, which uses a long-term mass balance approach at an annual time step, reminds readers that to be effective in the long term BMPs must affect P storage in the watershed.

17.6 IN-STREAM PROCESSES A clear trend in the modeling of P has emerged to scale up. Models have moved from field scale models such as EPIC and GLEAMS to watershed scale models such as AnnAGNPS, ANSWERS-2000, GWLF, HSPF, SWAT, and WEND-P. At first the watershed models were used for single events on ephemeral or small, first-order streams, but now they are being used for basins that are thousands of square kilometers in area. In modeling P, the objective is often to predict the load to a sensitive lake, reservoir, or estuary. Modeling of P processes in large lakes, reservoirs, and estuaries is usually done with separate, specialized models, and for the near future it does not seem likely that this will change. To estimate accurate loads at this scale, it is essential that in-stream processes affecting the transport of P and sediment be included in models (see Chapters 1 and 5, this volume). Stream processes also affect the form of P that reaches a sensitive water body and the bioavailability of this P. Processes change with flow (i.e., storm vs. base flow) and stream order (Vanotte et al. 1980). Stream water column P concentrations may be heavily buffered by elevated bed sediment (benthic) P concentrations in watersheds with a history of large P losses. This may delay the reduction in P loading to lakes or reservoirs in response to the implementation of BMPs. Most current models ignore or poorly model in-stream processes. Only three of the models discussed in this volume include in-stream processes: HSPF, SWAT, and GWLF. HSPF provides the most comprehensive modeling of in-stream processes, taking into consideration benthic release of dissolved P, sorption and desorption of P to suspended sediment in the water column (which varies for different sediment size fractions), settling of suspended sediment, scouring of bed and bank sediment, uptake by phytoplankton or benthic algae and respiration and inorganic excretion by zooplankton. Atmospheric deposition is also considered. SWAT includes settling of organic P, benthic release of P, and uptake by algae but does not simulate interaction between dissolved P and suspended sediment. GWLF models in-stream processes as a single, lumped stream segment. It includes channel erosion and transformation between dissolved and particulate P under base-flow conditions. It is necessary to know the initial stores of benthic P for models, and studies that have measured equilibrium P concentrations (EPC0) of bed sediments may be useful in this regard (Sharpley et al. 2002). They may also provide an integrated measure of historical local inputs (Page et al. 2005). It may be possible to use measurements of P uptake lengths in streams to determine if models are correctly estimating losses of P in streams. As described by



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Haggard and Sharpley (Chapter 5, this volume), uptake length is measured by applying a constant source of dissolved P to a stream and measuring concentrations of dissolved P in the stream at various distances below the input point. Concentrations typically decay exponentially with distance, and the inverse of the exponential decay coefficient is the uptake length (Newbold et al. 1981, 1983). It should be possible to do a similar experiment with a watershed model by including a point source and examining the concentrations of P in downstream reaches. Concentrations estimated by the model should have a decay coefficient that is on the order of that measured in streams of the region.

17.7 PHOSPHORUS INDICES In the present authors’ opinion, P indices (PIs) can be considered a type of model representing one end of the spectrum in that they are usually used at the field scale and estimate long-term averages (one to five years). In most cases, they estimate a risk index of P loss, not an actual loss, but there are three states where the PI in fact estimates P loss (Chapter 13, this volume). PIs are probably weakest in their treatment of transport, and in this area they need improvements in some of the same areas as the more complex, dynamic, watershed-scale models. These include identification of critical source areas, better treatment of P leaching, and better quantification of the effects of BMPs. Better methods for rapidly calculating erosion under different scenarios are needed, perhaps by linking PI software to Revised Universal Soil Loss Equation, version 2 (RUSLE2) programs. PIs also need to be linked to databases of soils, hydrography, and land use. Other needed improvements include the development of a preliminary risk assessment that only considers a field’s inherent transport risk factors such as soil type, slope, and distance from water body (Chapter 13, this volume). PIs need to be integrated into comprehensive manure management software such as the Manure Management Planner (Chapter 14, this volume).

17.8 CALIBRATION AND UNCERTAINTY Dynamic watershed-scale P models are necessarily calibrated because of the large number of parameters, many of which operate at a scale beyond which measurements can be made — called noncommensurability by Beven et al. (Chapter 6, this volume). Sensitivity analysis can be used to reduce the number of calibrated parameters to only those that have a large effect on estimations. Because watershed models are frequently used in the regulatory arena for TMDLs (Reckhow et al. 2001), source water assessment (EPA 1997), and lawsuits (Blackstock 2003), some measure of the uncertainty of estimations must be included. Methods and software have been developed for performing sensitivity analysis, for automating calibration, and for quantifying uncertainty, but these tools are usually not integral parts of today’s models. In fact, some model users oppose the use of autocalibration tools because they feel that model users should be limited to expert hydrologists (Gupta et al. 2003). The present authors disagree and recommend that calibration and uncertainty tools be integrated into modern models.


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A good example of this type of approach is contained in the latest version of SWAT, which incorporates an autocalibration capability described by van Griensven (2002). It includes sensitivity analysis using the one-factor-at-a-time approach. Once the significant parameters are identified, the Shuffled Complex Evolution (SCE) algorithm is used for autocalibration (Chapter 7, this volume). Another example is a new version of GWLF that has a built-in calibration tool (Chapter 12, this volume). Automated calibration tools may be easier to use with stream-flow data (where daily or more frequent measurements are frequently available) than with P data, which may be collected at monthly intervals in many TMDL data sets. For the near future it may be necessary to accept the idea of equifinality (Chapter 6, this volume); no unique set of parameter values probably provides the most accurate model estimation. But it may be possible to separate parameter values into those that are plausible (behavior) and those that are not (nonbehavior). All of this points to the importance of monitoring data.

17.9 DATA TO SUPPORT PHOSPHORUS MODELING Edge-of-field and stream-monitoring data are essential for calibrating and evaluating watershed-scale models (Chapter 16, this volume). One of the most difficult variables to measure accurately is flow, but it is essential for calculating loads and for calibrating and evaluating models. Advantage should be taken wherever possible of U.S. Geological Survey (USGS) sites that measure daily discharge on large streams. Usually, these sites do not have automated storm samplers installed, so they are an ideal location for partnering among universities, the U.S. Department of Agriculture (USDA), and USGS. The development of automated storm samplers represents a huge advance in the ability to collect stream-water-quality data. Frequently when models are calibrated for the estimation of sediment and P concentrations in streams, there are only one or two samples during a storm. In that situation, the model should estimate concentrations that are at least as large as those measured. Only with a well-defined chemograph can a comparison be made to the model estimations and can there be some assurance that the model processes are correct. Optimum sampling schemes for automated samplers need to be further developed and tested (Chapter 16, this volume). The type of sampling will likely be different depending on whether the aim is to calculate an annual load or to calibrate a dynamic model. Even when monitoring data are not used for calibrating dynamic models, annual loads calculated from monitoring data from small streams with a predominant land use are very useful for comparison with unit area loads calculated from dynamic models as well as export-coefficient loading models. Edge-of-field data should also be used to assess the accuracy of and to improve PIs. Ideally, studies should employ a nested design where edge-of-field and low-order stream-monitoring sites are located within the watershed where the high-order stream is monitored. Last, better quantification of the uncertainty (error) in monitoring data is needed.



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17.10 SUMMARY Much progress has been made in the modeling of P in the environment over the past 30 years. To continue this progress, the following improvements to modeling P are suggested. •

•

•

•

•

•

•

The estimation of the areas where runoff occurs must be improved through the incorporation of saturation excess as well as infiltration excess processes. Better information on where these areas occur will allow identification of the critical source areas where runoff and P sources coincide and where management needs to be focused. Modeling of soil P pools needs to be improved by adding a separate manure pool, relating the forms of P in model pools with forms of P measured in soils, and refining the rates of movement between P pools. Modeling of leaching of P needs to be improved by using a more processbased approach to estimating the flux of percolating water and the concentrations of P in leachate. This is especially important in soils with ditch or tile drainage. A more process-based approach is needed in modeling the effects of BMPs and their interactions. Riparian buffers are especially important in this regard. Simulation of in-stream processes must be improved in most of the current models if they are to be used to predict P loading to sensitive lakes, reservoirs, and estuaries in large watersheds. Stream measurements of equilibrium P concentrations and P uptake lengths offer opportunities to assess model in-stream estimations. Calibration and uncertainty tools need to be an integral part of future models. Uncertainty in model estimations must be quantified as models are increasingly used for regulatory purposes such as TMDL development. Monitoring data are critical for modeling. Long-term studies with a nested design of automated samplers are needed in partnership with the USGS stream-monitoring network.

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