STREAMFLOW CHARACTERISTICS
DEVELOPMENTS I N WATER SCIENCE, 22 OTHER TITLES IN THIS SERIES
G. BUGLIARELLO AND F. GUNT...
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STREAMFLOW CHARACTERISTICS
DEVELOPMENTS I N WATER SCIENCE, 22 OTHER TITLES IN THIS SERIES
G. BUGLIARELLO AND F. GUNTER
1
COMPUTER SYSTEMS A N D WATER RESOURCES
2
H.L. GOLTERMAN
PHY SI 0 LOG ICA L LIMN 0 LOGY
Y. Y. HAIMES, W.A.HALL AND H.T. FREEDMAN
3
MULTIOBJECTIVE OPTIMIZATION I N WATER RESOURCES SYSTEMS: THE SURROGATE WORTH TRADE-OFF-METHOD
4
J.J. FRIED
GROUNDWATER POLLUTION
5
N. RAJARATNAM
TURBULENT JETS
6
D. STEPHENSON
PIPELINE DESIGN FOR WATER ENGINEERS
7
v. HALEK AND J. SVEC
GROUNDWATER HYDRAULICS
8
J.BALEK
HYDROLOGY AND WATER RESOURCES I N TROPICAL AFRICA
9
T.A. McMAHON AND R.G. MElN
RESERVOIR CAPACITY A N D Y I E L D
10 G. KOVACS SEEPAGE HYDRAULICS
1 1 W.H. GRAF AND C.H. MORTIMER (EDITORS) HYDRODYNAMICS OF LAKES: PROCEEDINGS OF A SYMPOSIUM 12-13 OCTOBER 1978, LAUSANNE, SWITZERLAND
12 W. BACK AND D.A. STEPHENSON (EDITORS) CONTEMPORARY HYDROGEOLOGY: THE GEORGE BURKE MAXEY MEMORIAL VOLUME
1 3 M.A. M A R I ~ OAND J.N. LUTHIN SEEPAGE A N D GROUNDWATER
14 D. STEPHENSON STORMWATER HYDROLOGY AND DRAINAGE
15 D. STEPHENSON PlPLELlNE DESIGN FOR WATER ENGINEERS (completely revised edition of Vol. 6 i n t h e series)
16
w. BACK AND
R . LETOLLE (EDITORS)
SYMPOSIUM ON GEOCHEMISTRY OF GROUNDWATER
17 A.H. EL-SHAARAWI (EDITOR) I N COLLABORATION WITH S.R. ESTERBY TIME SERIES METHODS I N HYDROSCIENCES
18 J.BALEK HYDROLOGY AND WATER RESOURCES I N TROPICAL REGIONS
19 D. STEPHENSON PIPEFLOW ANALYSIS
20 I. ZAVOIANU MORPHOMETRY OF DRAINAGE BASINS
21 M.M.A. SHAHIN HYDROLOGY OF THE N I L E BASIN
STREAMFLOW CHARACTERISTICS H. C. RIGGS 3415 Executive Avenue, Falls Church, VA 22042, U.S.A.
ELSEVIER Amsterdam - Oxford
- New York - Tokyo
1985
ELSEVIER SCIENCE PUBLISHERS B.V. Molenwerf 1 P.O. Box 21 1, 1000 A E Amsterdam, The Netherlands
Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York, N Y 10017
ISBN 0-444-42480-6 (v01.22) ISBN 0-444-41669-2 (Series)
0 Elsevier Science Publishers B.V., 1985 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Science & Technology Division, P.O. Box 330, 1000 AH Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registed with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made i n the USA. A l l other copyright questions, including photocopying outside of the USA, should be referred t o the publisher, Elsevier Science Publishers B.V., unless otherwise specified. Printed in The Netherlands
V
PREFACE
A f l o o d d i s c h a r g e may be thousands of t i m e s
Streamflow i s h i g h l y v a r i a b l e .
g r e a t e r than t h e d i s c h a r g e d u r i n g a drought.
Such flow r e g i m e s can be d e s c r i b e d
by v a r i o u s s t a t i s t i c s c o l l e c t i v e l y r e f e r r e d t o a s s t r e a m f l o w c h a r a c t e r i s t i c s . These c h a r a c t e r i s t i c s p r o v i d e i n f o r m a t i o n n e e d e d i n t h e d e s i g n o f s t r u c t u r e s b u i l t i n o r along stream channels, ing t h e a v a i l a b l e w a t e r supply.
f o r e v a l u a t i n g f l o o d h a z a r d s , and f o r d e f i n -
V a r i o u s m e t h o d s may b e u s e d t o c o m p u t e f l o w
c h a r a c t e r i s t i c s ; t h e a l i p r o p r i a t e ones f o r a p a r t i c u l a r s t r e a m depend on i t s flow regime and on t h e amount and t y p e of d a t a a v a i l a b l e . d e f i n i n g f l o w c h a r a c t e r i s t i c s have been proposed,
Although many methods of
and a r e b e i n g used.
descrip-
t i o n s and e v a l u a t i o n s of t h e s e a r e w i d e l y s c a t t e r e d i n t h e l i t e r a t u r e .
book b r i n g s t o g e t h e r some of t h e m o r e u s e f u l m e t h o d s
-
This
ones t h a t a r e simple,
p r a c t i c a l , a n d r e q u i r e o n l y commonly a v a i l a b l e o r r e a d i l y o b t a i n a b l e d a t a . These methods produce r e s u l t s comparable i n a c c u r a c y w i t h t h o s e from more sop h i s t i c a t e d methods f o r many problems. An a n a l y s t needs more t h a n d e s c r i p t i o n s of methods.
He needs t o understand
the hydrology i n t h e r e g i o n s t u d i e d and t h e p r i n c i p l e s of t h e s t a t i s t i c a l techniques used,
and t o have some f e e l f o r t h e r e l i a b i l i t y of h i s d a t a .
Discussions
of t h e e f f e c t s of c l i m a t e , geology, and topography on t h e s t r e a m f l o w regime,
of
s t a t i s t i c a l p r i n c i p l e s , and o f methods f o r c o l l e c t i n g h y d r o l o g i c d a t a respond t o these n e e d s . The a n a l y s t s h o u l d know how h i s i n t e r p r e t a t i o n s w i l l b e u s e d .
Some o f t h e
p r i n c i p a l a p p l i c a t i o n s of s t r e a m f l o w c h a r a c t e r i s t i c s t o w a t e r - r e l a t e d of e n g i n e e r i n g and management a r e i n c l u d e d f o r t h a t purpose.
problems
Also i n c l u d e d i s
i n f o r m a t i o n on t h e changes t o b e e x p e c t e d i n s t r e a m f l o w c h a r a c t e r i s t i c s because of n a t u r a l o r man-made changes on t h e land. The m a t e r i a l i n t h i s book was s e l e c t e d f o r i t s v a l u e t o p r a c t i c i n g hydrolog i s t s ; t h e b o o k i s i n t e n d e d t o b e b o t h a m a n u a l and a s o u r c e o f r e f e r e n c e s .
Engineers s h o u l d f i n d some p a r t s u s e f u l f o r a p p r a i s i n g t h e r e l i a b i l i t y of hydrol o g i c i n f o r m a t i o n on which t h e i r d e s i g n s w i l l be based.
E n v i r o n m e n t a l i s t s may
f i n d t h e i n t e r p r e t a t i o n s of v a r i o u s s t r e a m f l o w c h a r a c t e r i s t i c s h e l p f u l . T h i s i s n o t a hydrology book i n t h e u s u a l sense.
Some i m p o r t a n t e l e m e n t s of
the h y d r o l o g i c c y c l e a r e n o t covered i n d e t a i l b e c a u s e adequate d a t a on them a r e often d i f f i c u l t t o obtain; here.
t h e s e e l e m e n t s a r e n o t used i n t h e t e c h n i q u e s g i v e n
L i k e w i s e , c e r t a i n well-known
too time-consuming
f o r common use.
t e c h n i q u e s a r e n o t i n c l u d e d because they a r e Ground w a t e r i s i n c l u d e d o n l y t o t h e e x t e n t
VI needed t o p r o p e r l y e v a l u a t e t h e s u r f a c e - w a t e r hydrology.
Water q u a l i t y i s
discussed b r i e f l y . The m a t e r i a l h a s been drawn from many s o u r c e s , t h e p r i n c i p a l ones b e i n g t h e l i t e r a t u r e of government a g e n c i e s and p r o f e s s i o n a l s o c i e t i e s .
I am p a r t i c u l a r l y
i n d e b t e d t o t h e U.S. G e o l o g i c a l S u r v e y w h i c h p r o v i d e d me t h e o p p o r t u n i t y t o p a r t i c i p a t e i n many h y d r o l o g i c i n v e s t i g a t i o n s , a n d f o r u s e of e x a m p l e s a n d e x p l a n a t o r y m a t e r i a l f r o m t h e i r many p u b l i c a t i o n s on h y d r o l o g y .
I also
acknowledge t h e p e r m i s s i o n of Pergamon P r e s s t o i n c l u d e p a r t s of my a r t i c l e s i n c l i m a t i c f a c t o r s o f r u n o f f (Chapter 2 ) and i n snowmelt r u n o f f (Chapter 12).
VII
CONTENTS 1
INlRODUCTION
1
General, 1 Probability and Recurrence Interval, 3 Units, 3 Conversion Factors, 3 References, 4 2
FACTORS AFFECTING STREAMFLOW
5
Introduction, 5 Climatic Factors, 5 Effects of the Precipitation Regime, 5 How Temperature Modifies Runoff, 9 Climatic Differences Along a Stream. 15 Effects of Geology. 16 Effects of Topography, 2 2 References, 23 3
COLLECTION OF HYDROLOGIC DATA Streamflow, 2 5 Stage Measurement, 25 Discharge Measurement , 28 Rating Curve, 3 1 Discharge Computation and the Hydrograph. 3 4 Special Gaging Methods, 34 Indirect Measurements, 3 9 Crest-Stage Gaging Stations, 4 0 Time of Travel, 4 0 Sediment Transport, 4 2 Chemical and Biological Quality, 4 4 Weather Observations, 46 Pr ec ip i tat ion, 4 6 Evaporation From Water Surfaces, 4 7 Temperature, 4 9 Snow Accumulation. 4 9 Basin Characteristics, 5 1 Transmission of Hydrologic Data, 5 2 References, 53
25
VIII 4
STATISTICS
51
Introduction, 57 Frequency Curves, 57 Distributions, 57 Cumulative Distributions, 60 Recurrence Interval, 63 Graphical Fitting, 63 Fitting Theoretical Distributions, 67 Evaluation of Fitting Methods, 71 Interpretation of Frequency Curves, 72 Describing Frequency Characteristics, 73 Statistical Inference, 74 Correlation and Regression, 77 Standard Error, 79 Multiple Correlation and Regression, 80 Serial Correlation, 82 Regression Methods, 8 3 Regression Models, 83 Transformations, 84 Example of Simple Linear Regression, 8 5 Multiple Linear Regression, 89 Graphical Regression, 90 Graphical Multiple Regression, 92 Graphical Vs. Analytical Method, 96 Application of the Regression Method, 97 Characteristics of Ifydrologic Data, 100 Effects of Data Characteristics on Analysis, 101 Out1 iers, 103 References, 104 5
STREAMFLOW CHARACTERISTICS AT A GAGED SlTE
Introduction, 107 Means, 107 Frequency Characteristics, 107 Extending Streamflow Records in Time, 109 Flow-duration Curves, 111 Base-Flow Recession Curves, 112 Theory, 113 Derivation, 114 Assumptions as
to
Recharge, 116
Seasonal Variability, 116
107
IX Water-Qua1 ity Characteristics, 116 References, 118 6
RELATION OF GROUND WATER TO SIREAMFLOW
121
Introduction, 121 Aquifer Recharge, 122 Bydrograph Interpretation, 123 Bank Storage in Surface Reservoirs, 127 The Water Resource, 128 References, 128
7
FLOW CHARACTERISTICS AT UNGAGED SITES
131
Introduction, 131 No Data at Site, 131 Regression Analysis, 131 From Rainfall, 134 Interpolation Along a Channel, 134 Some Data at Site, 135 Mean Flow From Monthly Measurements, 136 Low-Flow Characteristics From Base-Flow Measurements, 139 Flow Characteristics From Channel Size, 139 References, 143 8
FLOOD-FREQUENCY ANALYSES Introduction, 145 Annual Floods, 145 Floods Above a Base, 145 Annual and Partial-Duration Frequency Curves, 145 Fitting Annual Frequency Curves, 146 A Uniform Method, 149 Record Extension, 150 Relation to Basin Characteristics, 151 Reliability of Flood-Frequency Curves, 153 Flood Characteristics a t Ungaged Sites, 155 Regression on Basin Characteristics, 155 Index-Flood Method, 156 From Channel Geometry, 156 From Precipitation, 160 Interpolation Along a Channel, 161 Regulated Streams, 162 References, 163
145
x 9
LOW-FLOW CHARACTERISTICS
+
165
Introduction, 165 Frequency Curves, 165 Interpretation, 167 Reliability, 168 Seasonal Frequency Curves, 169 Regulated Streams, 170 Low-Flow Characteristics at Ungaged Sites, 170 Partial-Record Method, 171 Seepage Runs, 172 Interpolation Along a Channel, 173 References, 175 10
THE CHANGING ENVIRONMENT
177
Introduction. 177 Changes Due to Natural Events, 178 Effects of Man's Activities, 182 Surface Storage, 182 Land-Use Changes, 187 Cloud Seeding, 197 Air Pollution, 197 Quantifying Effects of Changes, 198 Environmental Changes, 198 Diversion and Regulation, 201 References, 201 11
APPLICATIONS OF IIYDROLOGIC DATA Introduction, 207 Reservoir Design, 207 Mass Curve, 207 Use of Simulated Streamflows, 208 Annual Mass-Curve Method, 209
Probability Routing, 210 Evaporation, Sedimentation, and Bank Storage, 212 Draft-Storage at Ungaged Sites. 214 Spillway Design Floods, 215 Storage for Flood Control, 216 Dependable Flow Without Storage, 219 Bridge and Culvert Openings, 220 Forecasting Streamflow. 220 Floods, 221
207
XI Snowmelt Runoff, 222 Seasonal Low Flows, 225 Streamflow Droughts, 228 Seasonal Streamflow Drought, 229 Multiyear Streamflow Drought, 229 Adaptation to Drought, 232 Flood-Prone Area Mapping, 233 Estimation of Environmental Impact, 234 References, 235 12
SOURCES OF DATA AND INFORMATION
239
Introduction, 239 Water-Resources Data, 239 Climatic Data, 240 Maps, 241 Current Conditions and Outlooks, 241 Interpreted Data, 242 General, 242 References, 243 INDEX
245
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1
Chapter 1
INTRODUCTION
1.1 GENWAL S t r e a m f l o w changes c o n t i n u a l l y i n r e s p o n s e t o w e a t h e r and t h e modifying e f f e c t of t h e land.
But t h e c l i m a t e over a d r a i n a g e b a s i n f o l l o w s a p a t t e r n
throughout each y e a r and t h i s r e s u l t s i n a y e a r l y c y c l e i n s t r e a m f l o w .
On t h i s
c y c l e a r e imposed t h e v a r i a t i o n s of flow b e c a u s e of t h e p a r t i c u l a r w e a t h e r i n t h e p r e c e d i n g days o r months.
Both t h e c l i m a t e and t h e l a n d v a r y from s t r e a m t o
s t r e a m and t h u s t h e f l o w s a l s o d i f f e r . H y d r o l o g i s t s e x p l a i n t h e movement o f w a t e r on t h e e a r t h b y t h e h y d r o l o g i c c y c l e , an e x t r e m e l y g e n e r a l i z e d c o n c e p t t h a t b e g i n s w i t h e v a p o r a t i o n of m o i s t u r e from t h e oceans and t r a n s p o r t of t h a t m o i s t u r e i n c l o u d masses o v e r l a n d where i t is precipitated.
The p r e c i p i t a t i o n ,
i f r a i n , may b e d i s p o s e d of by r u n o f f on
t h e l a n d s u r f a c e , i n f i l t r a t i o n i n t o t h e s o i l , and by e v a p o r a t i o n .
The i n f i l -
t r a t e d w a t e r may r e m a i n as s o i l m o i s t u r e t o b e l a t e r e v a p o r a t e d or t r a n s p i r e d by p l a n t s , o r some of i t may move down t o a w a t e r t a b l e from which i t may r e a p p e a r as streamflow.
E v a p o r a t i o n and t r a n s p i r a t i o n t a k e an a d d i t i o n a l t o l l f r o m
s t r e a m f l o w b e f o r e t h a t w a t e r r e t u r n s t o t h e ocean.
Obviously t h e t r a n s f o r m a t i o n
of p r e c i p i t a t i o n i n t o s t r e a m f l o w i n a p a r t i c u l a r b a s i n i s e x t r e m e l y c o m p l i c a t e d because of t h e many v a r i a b l e s of w e a t h e r , geology, and topography.
Although t h e
l a n d p h a s e o f t h e h y d r o l o g i c c y c l e i s w e l l u n d e r s t o o d , t h e i n p u t a n d t h e many r e l e v a n t l a n d c h a r a c t e r i s t i c s c a n n o t b e m e a s u r e d a c c u r a t e l y enough t o d e f i n e streamflow completely d e t e r m i n i s t i c a l l y .
C h a p t e r 2 d e s c r i b e s how v a r i o u s meas-
u r a b l e f a c t o r s a f f e c t t h e flow regime.
General p r i n c i p l e s a r e explained i n
t e x t s on hydrology such a s one by L i n s l e y ,
Kohler,
and Paulhus (1982).
Q u a n t i t a t i v e hydrology i s a r a t h e r r e c e n t s c i e n c e .
Streamflow measurements
were n o t w i d e l y a v a i l a b l e u n t i l a f t e r 1888 when t h e U.S. s y s t e m a t i c gaging.
G e o l o g i c a l Survey began
Subsequent demands f o r i r r i g a t i o n w a t e r ,
hydropower,
flood
c o n t r o l , m u n i c i p a l and i n d u s t r i a l w a t e r s u p p l i e s , and s o i l c o n s e r v a t i o n l e d t o major a c t i v i t y i n hydrologic analysis.
F u l l e r and Hazen h a d s t u d i e d t h e f r e -
quency d i s t r i b u t i o n s of f l o o d s b y 1914 and f l o w - d u r a t i o n
c u r v e s and methods o f
e s t i m a t i n g f l o w s of ungaged s t r e a m s w e r e a v a i l a b l e a t t h a t time.
J a r v i s (1936)
and Hoyt (1936) g i v e b r i e f summaries of developments up t h e t h e mid 1930s.
Many
of t h e developments s i n c e t h e n r e s u l t e d from g r e a t e r u s e of s t a t i s t i c s . The a v a i l a b i l i t y o f d i g i t a l c o m p u t e r s f u r t h e r e x p a n d e d t h e c a p a b i l i t y t o u t i l i z e l a r g e a m o u n t s o f d a t a i n a n a l y s e s t h a t w e r e not p r e v i o u s l y f e a s i b l e . The i m p r o v e d u n d e r s t a n d i n g of g r o u n d - w a t e r movement a l s o h a s c o n t r i b u t e d t o
p r o g r e s s i n s u r f a c e - w a t e r h y d r o l o g y : s u r f a c e and ground w a t e r a r e i n t i m a t e l y r e l a t e d i n most r e g i o n s . Streamflow c h a r a c t e r i s t i c s a r e q u a n t i t a t i v e measures o f v a r i a b i l i t i e s of d a i l y ,
monthly,
t h e magnitudes and
and a n n u a l means and of f l o w extremes.
They
c a n b e computed from s t r e a m f l o w r e c o r d s o r by i n d i r e c t means where no r e c o r d s are available;
t h e s e computed v a l u e s a r e of c o u r s e o n l y e s t i m a t e s of t h e long-
term values. Streamflow c h a r a c t e r i s t i c s a r e used i n a wide v a r i e t y of problems such a s d e f i n i n g a v a i l a b l e f l o w w i t h and w i t h o u t s t o r a g e ; f o r e c a s t i n g f l o o d s , d r o u g h t s , and s n o w m e l t r u n o f f : d e s i g n i n g b r i d g e w a t e r w a y openings: p l a n n i n g p r o t e c t i o n from f l o o d s : and e s t a b l i s h i n g r e g u l a t o r y r e q u i r e m e n t s .
P r o b a b l e changes i n f l o w
c h a r a c t e r i s t i c s r e s u l t i n g e i t h e r from n a t u r a l o r a r t i f i c i a l m o d i f i c a t i o n s of a b a s i n a r e needed t o e v a l u a t e t h e impact of such m o d i f i c a t i o n s . The m a t e r i a l p r e s e n t e d h e r e i s d i r e c t e d t o h y d r o l o g i s t s who a r e f a c e d w i t h p r a c t i c a l p r o b l e m s and t o e n g i n e e r s and p l a n n e r s who u s e h y d r o l o g i c d a t a a n d would p r o f i t from knowing how i t was d e r i v e d and how i t s h o u l d b e i n t e r p r e t e d . T h i s book p r o v i d e s s e l e c t e d t e c h n i q u e s and t h e o t h e r i n f o r m a t i o n needed t o e s t i m a t e s t r e a m f l o w c h a r a c t e r i s t i c s and t o e v a l u a t e t h e i r r e l i a b i l i t y . l i t e r a t u r e on hydrology and h y d r o l o g i c a n a l y s i s i s e x t e n s i v e .
The
Any c o l l e c t i o n o f
t e c h n i q u e s i n a book of r e a s o n a b l e l e n g t h would n o t b e complete.
The t e c h n i q u e s
s e l e c t e d f o r i n c l u s i o n i n t h i s book a r e l i m i t e d t o o n e s t h a t a r e r e a s o n a b l y s i m p l e t o d e f i n e and t h a t r e q u i r e o n l y commonly a v a i l a b l e d a t a .
More complex
methods a r e mentioned and r e f e r e n c e d . Any d e s c r i p t i o n of a h y d r o l o g i c t e c h n i q u e i s i n c o m p l e t e w i t h o u t some means of e v a l u a t i n g t h e r e l i a b i l i t y of t h e r e s u l t .
Such e v a l u a t i o n s should b e based on
an u n d e r s t a n d i n g o f t h e hydrology of t h e b a s i n o r r e g i o n , of s t a t i s t i c a l p r i n c i ples,
and of t h e r e l i a b i l i t y of t h e d a t a used.
The c h a p t e r s on F a c t o r s A f f e c t -
i n g Streamflow, C o l l e c t i o n o f Hydrologic Data.
R e l a t i o n o f Ground W a t e r t o
S u r f a c e Water, and S t a t i s t i c s a r e i n c l u d e d t o p r o v i d e t h a t u n d e r s t a n d i n g . tionally,
Addi-
throughout t h e book e v a l u a t i o n s and l i m i t a t i o n s of t h e v a r i o u s tech-
niques are discussed.
This information should help the reader t o s e l e c t the
most a p p r o p r i a t e t e c h n i q u e f o r t h e p a r t i c u l a r a p p l i c a t i o n a s w e l l a s t o make a ( s u b j e c t i v e ) e s t i m a t e of t h e r e l i a b i l i t y of t h e r e s u l t . Many s t a t i s t i c a l t e c h n i q u e s a p p l i c a b l e t o hydrology can b e a p p l i e d w i t h o u t knowledge of s t a t i s t i c a l theory.
F o r example,
a n a l y s i s and m u l t i p l e r e g r e s s i o n can b e used, of e i t h e r s t a t i s t i c s o r hydrology.
computer programs f o r frequency and o f t e n a r e ,
w i t h o u t knowledge
B u t a n a n a l y s t w i t h no s t a t i s t i c a l b a c k -
g r o u n d may make a s s u m p t i o n s o f w h i c h h e i s n o t a w a r e a n d h e may i n c o r r e c t ' l y interpret h i s results.
The m a t e r i a l i n t h e c h a p t e r on s t a t i s t i c s i s d i r e c t e d t o
t h o s e w i t h l i t t l e t r a i n i n g in t h a t f i e l d ;
i t c o n c e n t r a t e s on t h e o r y (non-mathe-
m a t i c a l ) r a t h e r than on c o m p u t a t i o n a l d e t a i l s .
3 By e m p h a s i z i n g a p p l i e d h y d r o l o g y i n t h i s book,
t h e coverage of p r a c t i c a l
s u b j e c t s i s b r o a d e r and t h e a n a l y s e s a r e d e s c r i b e d i n more d e t a i l t h a n i s u s u a l i n one source.
On t h e o t h e r hand t h e h y d r o l o g i c s u b j e c t s a r e l i m i t e d t o t h o s e
useful i n applying the techniques presented.
Consequently, s e v e r a l s u b j e c t s
commonly i n c l u d e d i n h y d r o l o g y t e x t s d o n o t a p p e a r h e r e . unit-hydrograph
method,
ting. channel hydraulics,
Among them a r e t h e
i n f i l t r a t i o n , c h a r a c t e r i z i n g p r e c i p i t a t i o n , f l o w rouevapotranspiration,
computer modeling, and e s t i m a t i o n
of f l o w c h a r a c t e r i s t i c s from p r e c i p i t a t i o n i n a r i d and s e m i a r i d r e g i o n s . 1.2
PROBABILITY AND RECURRENCE INTERVAL F o r many y e a r s e n g i n e e r s h a v e d e s c r i b e d t h e f r e q u e n c y c h a r a c t e r i s t i c s o f
annual e v e n t s i n t e r m s of r e c u r r e n c e i n t e r v a l ,
t h e r e c i p r o c a l of p r o b a b i l i t y .
F o r e x a m p l e , t h e a n n u a l f l o o d w i t h a p r o b a b i l i t y o f 0.01 o f b e i n g e x c e e d e d i n any one y e a r i s commonly c a l l e d t h e 100-year flood.
E i t h e r way of d e s i g n a t i n g
t h a t f l o o d i s c o r r e c t b u t b e c a u s e laymen o f t e n m i s i n t e r p r e t t h e meaning of a f l o o d o f a g i v e n r e c u r r e n c e i n t e r v a l , t h e U.S.
W a t e r R e s o u r c e s C o u n c i l recom-
mended t h a t t h e p r e f e r r e d d e s c r i p t o r b e p r o b a b i l i t y .
Recurrence i n t e r v a l i s
g e n e r a l l y used i n t h i s book b e c a u s e r e c u r r e n c e i n t e r v a l was used i n most of t h e a n a l y s e s s e l e c t e d a s examples.
No p r e f e r e n c e for r e c u r r e n c e i n t e r v a l should b e
imp1 i e d . 1.3
UNITS Some E n g l i s h - s p e a k i n g n a t i o n s u s e t h e B r i t i s h o r I m p e r i a l s y s t e m of u n i t s
a l t h o u g h i n s u r v e y i n g and i n hydrology t e n t h s and h u n d r e d t h s of f e e t a r e used instead of inches.
I n t e r n a t i o n a l j o u r n a l s r e q u i r e u s e of m e t r i c o r S y s t e m e
I n t e r n a t i o n a l d'Unites tists.
(SI u n i t s ) which have been adopted by n e a r l y a l l s c i e n -
A c o m p l e t e and a b r u p t c h a n g e t o t h e m e t r i c s y s t e m i n h y d r o l o g y i s n o t
f e a s i b l e i n t h e United S t a t e s b e c a u s e many e x i s t i n g l a w s , r e g u l a t i o n s , r e c o r d s , and s t a n d a r d s a r e based on t h e B r i t i s h system.
For d e m o n s t r a t i n g p r i n c i p l e s and
explaining techniques e i t h e r system of u n i t s i s adequate.
The p r o b l e m s and
e x a m p l e s g i v e n i n t h i s book a r e i n t h e u n i t s i n w h i c h t h e y w e r e o r i g i n a l l y reported.
R e s u l t s c a n e a s i l y b e c o n v e r t e d f r o m o n e s y s t e m of u n i t s t o t h e
other. 1.4
CONVERSION FACTORS 1 i n c h = 25.4 m i l l i m e t e r s
1 foot
= 1 2 i n c h e s = 304.8
millimeters
1 m i l e = 5280 f e e t = 1.609 k i l o m e t e r s 1 m i l l i m e t e r = 0.039 i n c h e s 1 m e t e r = 39.37 i n c h e s = 3.281 f e e t
1 k i l o m e t e r = 0.621 m i l e s 1 a c r e = 43.560 s q u a r e f e e t
4 1 s q u a r e m i l e = 640 a c r e s 1 s q u a r e meter
=
10.76 s q u a r e f e e t
1 h e c t a r e = 2.471 a c r e s 1 square kilometer 1 cubic f o o t 1 U.S.
=
=
100 h e c t a r e s
7.4805 U.S.
=
0.386 s q u a r e m i l e s
g a l l o n s = 0.028
cubic meters
g a l l o n = 3.785 l i t e r s
1 acre-foot
=
43,560 c u b i c f e e t = 1233.5 c u b i c m e t e r s
1 c u b i c meter = 35.31 c u b i c f e e t 1 million cubic meters
=
810.7 a c r e - f e e t
1 c f s ( c u b i c f o o t p e r second) = 0.028 cms ( c u b i c m e t e r s p e r second) 1 cfs-day = 0.0864 m i l l i o n c u b i c f e e t = 1.983471 a c r e f e e t = 0.6463 m i l l i o n g a l l o n s
1 cfs-year = 723.97 a c r e f e e t ( f o r 365 d a y s ) 1 c f s per square mile f o r one day = 0.03719 inches d e p t h on t h e d r a i n a g e b a s i n Annual r u n o f f i n i n c h e s = 13.58
times annual mean, i n c f s p e r s q u a r e m i l e
1 pound = 0.4536 kilograms 1 g a l l o n = 8.33 pounds ( w a t e r ) 1 c u b i c f o o t = 62.4 pounds ( w a t e r ) 1 kilogram = 2.205 pounds 1 f o o t p e r second = 0.682 m i l e s p e r hour REFERENCES Eoyt. W.G.. States:
1936, S t u d i e s o f R e l a t i o n s o f R a i n f a l l and Runoff i n t h e U n i t e d U.S. G e o l o g i c a l Survey Water-Supply Paper 772, 301 p.
J a r v i s , C.S., 1936, F l o o d s i n t h e U n i t e d S t a t e s , M a g n i t u d e and F r e q u e n c y : Geological Survey Water-Supply Paper 771, 497 p.
U.S.
L i n s l e y , R.K.,, K o h l e r , M.A., and P a u l h u s , J.L.H., 1982, H y d r o l o g y f o r E n g i n e e r s , Third E d i t i o n : New York. McGraw-Hill, 496 p.
5
Chapter 2
FACTORS AFFECTING STREAMFLOW 2.1 INTRODUCTION The process by which precipitation becomes streamflow is well known in a general way.
But for a specific drainage basin it is not possible to quantify
all the relevant variables and to describe the paths that the water takes a t various times.
Nevertheless some knowledge of the probable processes in a basin
is essential if realistic estimates of streamflow characteristics in that basin are to be obtained.
Climate, geology, and topography are the principal basin
characteristics affecting streamflow.
Unusual streamflow patterns usually can
be explained qualitatively by some feature or combination of features of these. This chapter provides such explanations using examples of flows from various regimes.
More information on hydrologic characteristics throughout the world is
given by L'vovich (1980).
The following section, 2.2, is from Riggs (1980) by
permission of Pergamon Press. 2.2
CLIMATIC FACTORS The climatic factors of precipitation, temperature, sunshine, humidity, and
wind all affect stream runoff to some extent, but only precipitation and temperature account for major differences among runoff regimes in regions of similar geology and topography.
Precipitation, the source of runoff, is disposed of in
several ways, some is evaporated from the surfaces on which i t falls, some infiltrates into the soil, and some moves directly to stream channels.
Of the
water that infiltrates the soil, some will be removed later by evaporation and transpiration and some may reach a ground-water body which maintains stream runoff between storms. Temperature, in conjunction with sunshine and wind, determines the evapotranspiration losses.
In temperate and tropical regions of
low annual precipitation, evapotranspiration losses may nearly equal the precipitation.
At the other extreme, evapotranspiration may be
percent of precipitation in regions of high rainfall.
as
l i t t l e as 10
Below-freezing tempera-
tures affect runoff by delaying runoff from snowfall and by modifying the winter runoff because of ice formation. 2.2.1
E f f e c t s of t h e p r e c i p i t a t i o n r e g i m e
The response of Shetucket River to an intense storm rainfall associated with a West Indian hurricane is shown in Figure 2.1.
The extremely high peak dis-
charge is followed by a high base flow resulting from the recharge of ground water in the drainage basin.
6
’”’
The magnitude of a f l o o d peak i s n o t o n l y a f u n c t i o n of t h e r a i n f a l l magnit u d e and d u r a t i o n ,
2000 i
-
b u t a l s o of t h e a r e a l coverage of t h e s t o r m r e l a t i v e t o t h e
v
T
500
5 1
20
10
SEPT F i g . 2.1.
30 1938
10
20 OCT
Runoff from i n t e n s e r a i n f a l l , S h e t u c k e t R i v e r , C o n n e c t i c u t .
d r a i n a g e b a s i n of t h e stream.
Thus t h e c h a r a c t e r of s t o r m s i n a r e g i o n d e t e r -
mines t h e r e l a t i v e magnitudes of u n u s u a l f l o o d s f o r v a r i o u s d r a i n a g e a r e a s i z e s . In some a r i d and s e m i a r i d r e g i o n s t h u n d e r s t o r m s produce e x c e p t i o n a l f l o o d peak discharges per u n i t area for the smaller drainage areas.
Thunderstorms a l s o
produce r e c o r d f l o o d s from s m a l l b a s i n s i n humid r e g i o n s , b u t t h o s e r e g i o n s a r e a l s o s u b j e c t t o more w i d e s p r e a d s t o r m s which produce t h e m a j o r f l o o d s from l a r g e r basins.
The d i f f e r e n c e i n f l o o d p o t e n t i a l between a s e m i a r i d and a humid
r e g i o n i s shown b y p l o t s o f maximum k n o w n f l o o d - p e a k d i s c h a r g e s ( C r i p p e n a n d Bue, 1977) a g a i n s t d r a i n a g e a r e a f o r s e m i a r i d A r i z o n a a n d f o r h u m i d V i r g i n i a (Fig. 2.2).
The l e s s e r f l o o d p o t e n t i a l f r o m l a r g e b a s i n s i n A r i z o n a i s d u e
p r i n c i p a l l y t o t h e l i m i t e d a r e a l e x t e n t of major storms.
I n b a s i n s where snow does n o t accumulate, and where b a s i n c h a r a c t e r i s t i c s a r e n o t unusual,
t h e s e a s o n a l d i s t r i b u t i o n of r u n o f f c l o s e l y f o l l o w s t h e s e a s o n a l
d i s t r i b u t i o n of p r e c i p i t a t i o n . the r e s u l t i n g runoff
F i g u r e 2.3 compares t h e monthly p r e c i p i t a t i o n t o
f o r S e t i Khola.
Nepal,
i n a r e g i o n of h i g h r a i n f a l l .
T y p i c a l d i s t r i b u t i o n o f r u n o f f i n a c l i m a t e w i t h w e t w i n t e r s a n d d r y summers. a l s o f o l l o w s t h e p r e c i p i t a t i o n c l o s e l y so long a s t e m p e r a t u r e i s g e n e r a l l y above f r e e z i n g ( P i g . 2.4). Seasonal v a r i a b i l i t y of l a r g e s t r e a m s t e n d s t o be l e s s t h a n f o r s m a l l ones because l a r g e ones may have s o u r c e s i n d i f f e r e n t c l i m a t e s so t h a t t h e c u m u l a t i v e
7
5 r
x
X
a
s
VIRGINIA (Humid) ARIZONA (Semiarid)
100 1000 DRAINAGE AREA, IN KM*
10,000
Fig. 2.2 Maximum known floods in a humid and a semiarid area.
1000
1
I
1
,
,
I
I
l
l
, , /\
z
8
v)
=
z
8001
600 PRECIPITATION A T P 0/
;
A
-
I
4001
\
I
_I
g
200
///
O'J
RUNOFF
1,
,
c---
\
F M A-M
J MONTH
A
6
1 - L
I
0 N D
Fig. 2.3. Average monthly precipitation and runoff, Seti Khola, Nepal.
I
O
'
j
I
,
F
M
I A
I M J J MONTH
l A
l S
O
N
'
o
Fig. 2.4. Monthly distribution of precipitation and runoff, Tualatin River, Oregon.
8
effect of inputs at various times and the lag in runoff from headwaters is a reduction in the variability of downstream flow among seasons.
This is illus-
trated by the seasonal distribution of flow in the Amazon River and of the precipitation at two sites in the basin (Fig. 2 . 5 ) .
3
0
~
~ J - A S~ O NA D MONTH
~
~
Fig. 2.5. Seasonal distribution of runoff of Amazon River and of precipitation at two sites in the basin. The seasonal distribution of precipitation also influences the low-flow characteristics of a stream.
Frequent storms throughout the year, and especial-
ly during the late summer, tend to maintain streamflow whereas, in a climate characterized by little or no rain during summer, the late summer streamflows may be small or zero.
The ephemeral stream, one which flows only in direct
response to precipitation, and the intermittent stream, which flows for only part of each year on the average, are typical of regions with dry summers. The above comparisons of seasonal runoff to precipitation have been for average conditions.
Variability of weather from year to year accounts for the
considerable variation in monthly runoff, in flood peaks, and in low flows.
The
annual low flow may result from no precipitation for a considerable period or from small amounts of precipitation on each of many days of an extended period,
no amounts large enough to do more than supplement the soil moisture.
A long
period of no precipitation causes a drought both hydrologically and agriculturally, whereas frequent small rainfalls may not produce runoff yet may maintain adequate soil moisture for plants. Annual precipitation on a river basin varies from year to year.
The re-
sulting runoff is more variable than the precipitation because the percentage of precipitation that becomes runoff decreases with decreasing precipitation. Figure 2.6 shows a long record of annual runoffs for Red River of the North, North Dakota, USA.
The period of low runoff in the 1930’s resulted from several
consecutive years of below normal precipitation. mean runoffs shown in Figure 2.7.
More typical are the annual
The large year-to-year variability in runoff
of Rio Guadalquivir in southern Spain is the result of the highly variable
9
L
$05 4
1916 1920 1924 1928 1932 1936 I t 4 0 1944 1&8 YEAR
Fig. 2.6. Annual runoff of Red River of the North, North Dakota.
g
100'
1910 1920
1930
1940 YEAR
1950 1960
Fig. 2 . 7 . Variability of annual runoffs in a humid region (Sweden) and in semiarid region (Spain). annual precipitation characteristic of a semiarid region.
a
In contrast, the
annual runoffs of Vanern-Gota. Sweden, in a cool humid climate, are much less variable. 2.2.2
How temperature modifies runoff
Temperature influences runoff in two principal ways:
(1) high temperatures
increase evapotranspiration and thus reduce the amount of runoff from precipitation, and ( 2 ) freezing and thawing change the timing of runoff by delaying the response of runoff to precipitation and by modifying the flow of water already in the channel. The amount of moisture returned to the atmosphere by evaporation and by transpiration of plants depends on climate, principally temperature, sunshine, and wind, and on the supply of moisture.
Frequent rains provide a nearly
10
continuous supply of moisture, but infrequent storms leave little moisture for evapotranspiration for long periods.
Thus both potential evapotranspiration and
the difference between potential and actual evapotranspiration depend on the climate. Annual evapotranspiration, or annual water loss, can be quantified as the difference between precipitation on a basin and the resulting runoff.
Figure
2.8 shows water losses plotted against mean annual temperature for basins with
L
MEAN ANNUAL TEMPERATURE, IN " C Fig. 2.8. Annual water loss as a function of temperature, eastern USA (from Williams, 1 9 4 0 ) . mean annual precipitation greater than 500 mm.
Annual water loss is a moderate
percentage of the annual precipitation in a humid region but a very large percentage in regions of low precipitation.
Thus the annual runoff is highly
variable where precipitation is low (Red River of the North and Rio Guadalquivir in Figs. 2.6 and 2.7).
In temperate and tropical arid regions, potential evapo-
transpiration is larger than precipitation except for short periods during and following rainstorms.
Thus there are no perennial streams in such regions.
Temperature and thus evapotranspiration rates change seasonally in most parts of the world.
160
'
Figure 2.9 shows that losses during that summer are larger than
,
J F M A M J J A S O N D MONTHS 1947
Fig 2 . 9 . Seasonal relation of precipitation and runoff showing the large evapotranspiration losses in summer in North Carolina. (January precipitation probably was snow.!
11 a t o t h e r t i m e s of t h e year.
T h e p r e c i p i t a t i o n o n t h e H o mi n y C r e e k b a s i n
probably i s n o t t h e same a s a t A s h e v i l l e b u t t h e monthly t r e n d s s h o u l d be similar.
The d i f f e r e n c e b e t w e e n p r e c i p i t a t i o n and r u n o f f f o r a s i n g l e month i s
o n l y a rough a p p r o x i m a t i o n o f l o s s b e c a u s e o f t h e c a r r y o v e r of w a t e r from one month t o t h e ne xt. Diurnal v a r i a t i o n s i n e v a p o t r a n s p i r a t i o n o f t e n produce d i u r n a l f l u c t u a t i o n s i n t h e f l o w o f s m a l l s t r e a m s wh er e t h e t e m p e r a t u r e d i f f e r e n c e b e t w e e n n i g h t and a sunny day i s l a r g e .
F i g u r e 2.10 shows t h e d i s c h a r g e h y d r o g r a p h d u r i n g s u c h a
JUNE, 1941
F i g . 2.10. D i u r n a l f l u c t u a t i o n s i n s t r e a m f l o w c a u s e d by e v a p o t r a n s p i r a t i o n l o s s e s ( m o d i f i e d from Du n fo r d an d F l e t c h e r , 1 9 4 7 ) . period.
variable
The e f f e c t o f e v a p o t r a n s p i r a t i o n on s t r e a m f l o w i s s o m e t i m e s m a n i f e s t e d
i n t h e d r y i n g up o f a s m a l l s t r e a m d u r i n g summer and i t s s u b s e q u e n t r e s u m p t i o n of f l o w i n t h e a b s e n c e o f r a i n a s t e m p e r a t u r e d e c r e a s e s i n t h e f a l l months.
The
m a g n i t u d e o f e v a p o t r a n s p i r a t i o n may a l s o b e i n d i c a t e d b y a s h a r p i n c r e a s e i n s t r e a m f l o w a f t e r t h e f i r s t h a r d f r o s t o f au tumn k i l l s t h e r i p a r i a n v e g e t a t i o n . The w i t h i n - y e a r d i s t r i b u t i o n o f r u n o f f o f A r c t i c s t r e a m s i s d e t e r m i n e d by temperature, not precipitation, because the winter p r e c i p i t a t i o n remains i n s t o r a g e a s i c e o r sn o w u n t i l s u m m e r .
The mean m o n t h l y r u n o f f s o f a t y p i c a l
A r c t i c s t r e a m , Yan a R i v e r , D z a n h k y , USSR, a r e s h o w n i n F i g u r e 2.11 a l o n g w i t h t h e p r e c i p i t a t i o n and t e m p e r a t u r e a t Verhoyansk.
Imw f l o w s d u r i n g w i n t e r r e s u l t
from f r e e z i n g of n e a r l y a l l w a t e r i n t h e channel; t h e base flow of a stream draining a permafrost regime is negligible. A l e s s e x t r e m e r a n g e i n m o n t h l y f l o w s o f a n o r t h e r n s t r e a m o c c u r s on Yukon River,
Canada a nd A l a s k a , w h e r e t h e f l o w u n d e r i c e c o v e r r e c e d e s t h r o u g h o u t t h e
w i n t e r b u t i s n e v e r l e s s t h a n s e v e r a l hundreds o f c u b i c m e t e r s p e r second. Temperature i s a g a i n t h e major f a c t o r i n s e a s o n a l d i s t r i b u t i o n of fl ow a l t h o u g h t h e maximum p r e c i p i t a t i o n d o e s c o i n c i d e w i t h t h e summer h i g h f l o w .
A s h a r p r i s e in t e m p e r a t u r e f o l l o w i n g a p r o l o n g e d c o l d s p e l l w i l l r e l e a s e t h e h e a v y i c e c o v e r on a r i v e r .
The r e s u l t i n g i c e j a m s may damage s t r u c t u r e s i n and
a l o n g t h e r i v e r and c a u s e o v e r b a n k f l o o d i n g .
N o r t h w a r d f l o w i n g s t r e a m s a r e mo st
12
10,000
--
~
__
-7
YANA RIVER, DZA NG HKY, USSR
. rn
0
I
z ti
U
0
3 z
a
z
5
I
t-
MONTH
F i g . 2.11. S e a s o n a l d i s t r i b u t i o n o f r u n o f f o f a n a r c t i c s t r e a m s h o w i n g t h e e f f e c t of t e m p e r a t u r e . s u s c e p t i b l e t o i c e j a m s because t h e s o u t h e r n h e a d w a t e r s thaw b e f o r e t h e n o r t h e r l y downstream r e a c h e s of t h e channel. Small s t r e a m s i n n o r t h e r n c l i m e s f r e e z e t o t h e b o t t o m d u r i n g t h e w i n t e r .
In
c e r t a i n nonpermafrost reaches, ground w a t e r c o n t i n u e s t o f e e d t h e s t r e a m b u t b e c a u s e t h i s w a t e r c a n n o t f l o w down t h e s t r e a m c h a n n e l i t f l o w s o v e r t h e i c e u n t i l i t freezes.
T h u s , t h e i c e c o v e r on t h e s t r e a m a n d o v e r b a n k i s b u i l t u p
throughout t h e winter.
T h i s i c i n g may e n c o m p a s s r o a d s , b l o c k c u l v e r t s , and
invade b u i l d i n g s along a stream. Temperature e f f e c t s on s t r e a m f l o w where c o m p l e t e i c e c o v e r d o e s n o t o c c u r throughout t h e w i n t e r a r e somewhat d i f f e r e n t t h a n t h o s e above. l a r g e s t r e a m i s shown i n F i g u r e 2.12 (Simons. 1953).
The e f f e c t on a
Extremely c o l d w e a t h e r f o r .
a few d a y s p u t s w a t e r in s t o r a g e a s i c e i n t h e c h a n n e l a n d r e d u c e s t h e f l o w .
13 Recovery of u s u a l flow f o l l o w s an i n c r e a s e i n t e m p e r a t u r e . flow i n e a r l y F e b r u a r y was caused by above-freezing
The b i g i n c r e a s e i n
t e m p e r a t u r e s and r a i n .
PRECIPTTATION. IN MM n
Fig.
2.12.
n
D
E f f e c t of t e m p e r a t u r e on streamflow. Salmon River, Idaho.
I n more s o u t h e r l y c l i m e s ,
and g e n e r a l l y a t h i g h e l e v a t i o n s ,
t h e temperature
d u r i n g w i n t e r may r a n g e f r o m much b e l o w f r e e z i n g a t n i g h t t o a b o v e f r e e z i n g d u r i n g t h e day.
During c l e a r ,
c o l d n i g h t s anchor i c e forms on t h e r o c k s o f t h e
s t r e a m b e d b e c a u s e o f l o s s o f h e a t by r a d i a t i o n t o t h e a t m o s p h e r e . from t h e sun t h e n e x t day warms t h e r o c k s and r e l e a s e s t h e ice. n o t form under s u r f a c e i c e cover.
Radiation
Anchor i c e does
The f o r m a t i o n and s u b s e q u e n t r e l e a s e o f
anchor i c e c a u s e s s u b s t a n t i a l f l u c t u a t i o n s i n w a t e r l e v e l i n t h e s t r e a m (Fig. 2.13) and s m a l l e r f l u c t u a t i o n s i n d i s c h a r g e .
FEBRUARY. 1953
Fig. 2.13. W a t e r l e v e l f l u c t u a t i o n s i n a s m a l l s t r e a m d u e to f o r m a t i o n a n d r e l e a s e of anchor i c e (modified from Moore, 1957).
14 G l a c i e r s and s n o w f i e l d s a r e common i n mountainous r e g i o n s a t h i g h l a t i t u d e s . Runoff from t h e s e f e a t u r e s i s more c l o s e l y r e l a t e d t o t e m p e r a t u r e t h a n t o t h e previous w i n t e r p r e c i p i t a t i o n . t y p i c a l l y h i g h summer r u n o f f . i n Washington
g
State,
USA,
S t r e a m s w i t h g l a c i e r s i n t h e i r h e a d w a t e r s have Hydrographs of a g l a c i a l and a n o n g l a c i a l s t r e a m i n F i g u r e 2.14,
show t h e o p p o s i t e e f f e c t s o f
20 (Glacialin headwaters)
wl c
2 15
-~
MAY
~
JUNE
JULY
AUGUST
1962
F i g . 2.14. H y d r o g r a p h s s h o w i n g t h e o p p o s i t e e f f e c t s o f a d r y J u l y on a g l a c i a l and a n o n g l a c i a l stream. t e m p e r a t u r e on r u n o f f d u r i n g a t y p i c a l l y d r y J u l y .
High t e m p e r a t u r e i n c r e a s e s
t h e l o s s e s from both basins, but i n c r e a s e s g l a c i e r melt i n White River basin. During o t h e r s e a s o n s t h e f l o w s of t h e two s t r e a m s respond s i m i l a r l y t o temperat u r e and p r e c i p i t a t i o n . G l a c i e r s s o m e t i m e s c a u s e unusual f l o o d s by i m p o u n d i n g w a t e r a n d t h e n r e leasing i t abruptly.
From a t l e a s t 1948 t o 1962. Knik G l a c i e r , Alaska, advanced
a c r o s s Knik R i v e r each w i n t e r and t e m p o r a r i l y s t o r e d t h e s p r i n g r u n o f f .
De-
s t r u c t i o n o f t h e g l a c i e r dam e a c h summer b y m e l t i n g a n d e r o s i o n r e l e a s e d t h e s t o r e d w a t e r c a u s i n g a n o u t s t a n d i n g f l o o d on K n i k R i v e r .
F i g u r e 2.15 s h o w s
hydrographs f o r y e a r s w i t h and w i t h o u t t h e g l a c i e r e f f e c t .
Annual r u n o f f s f o r
t h e s e 2 y e a r s a r e v i r t u a l l y t h e same.
I n t e m p e r a t e r e g i o n s p r e c i p i t a t i o n may occur a s snow d u r i n g t h e w i n t e r and b e r e l e a s e d i n s p r i n g o r e a r l y summer, p a r t i c u l a r l y i f t h e s t r e a m s b e a d a t h i g h elevations.
Maximum s t r e a m f l o w s o f t e n o c c u r a s a r e s u l t of s n o w m e l t .
The
amount of r u n o f f from a snowpack depends on t h e w e a t h e r d u r i n g t h e m e l t p e r i o d .
A r a p i d m e l t w i l l produce t h e most r u n o f f .
An e x t e n d e d m e l t p e r i o d c a u s e d by
c o o l t e m p e r a t u r e s p e r m i t s more loss by a b l a t i o n and by i n f i l t r a t i o n . 2.2.3
C l i m a t i c d i f f e r e n c e s along a s t r e a m
Some s t r e a m s d r a i n a r e a s h a v i n g o n e c l i m a t i c r e g i m e i n t h e h e a d w a t e r s a'nd a n o t h e r i n t h e downstream p a r t of t h e b a s i n .
Commonly t h e p r i n c i p a l r u n o f f
is
g e n e r a t e d i n t h e h e a d w a t e r s which h a s t h e h i g h e r p r e c i p i t a t i o n ; t h e n tlx: downstream runoff c h a r a c t e r i s t i c s a r e a c o m p o s i t e .
15
z
2ooM r
i 100
-1
Fig. 2.15. Hydrographs f o r Knik River, Alaska, showing t h e e f f e c t of impoundment and r e l e a s e of w a t e r by a g l a c i e r (1961). and a y e a r w i t h no impoundment ( 1 9 6 3 ) . Two f l o o d p e r i o d s p e r y e a r a r e produced on Merced River, C a l i f o r n i a , one from l o w - e l e v a t i o n r a i n f a l l i n w i n t e r and t h e second from t h e m e l t i n g of t h e snowpack i n t h e S i e r r a Nevada i n l a t e s p r i n g .
F i g u r e 2.16
s h o w s t h e annual f l o o d -
f r e q u e n c y c u r v e s f o r t h e two t y p e s of f l o o d s (Crippen, 1978).
The s n o w m e l t
f l o o d i s t h e l a r g e r i n most y e a r s b u t t h e m a j o r f l o o d s a r e produced by r a i n f a l l . Commonly, a s t r e a m t h a t h e a d s i n t h e h i g h m o u n t a i n s w i l l r e a c h i t s a n n u a l maximum d i s c h a r g e i n i t s u p s t r e a m r e a c h e s from snowmelt w h i l e f u r t h e r downstream t h e annual maximum d i s c h a r g e may be e i t h e r from snowmelt o r from r a i n f a l l or, occasionally.
a c o m b i n a t i o n of
t h e two.
The annual r u n o f f a t a downstream s i t e
on such a s t r e a m may b e l a r g e r o r s m a l l e r t h a n t h e r u n o f f a t some p o i n t upstream
depending on t h e downstream c l i m a t e . Typically,
b u t n o t always.
t a t i o n than t h e l o w e r reaches.
t h e h e a d w a t e r s o f a s t r e a m r e c e i v e more p r e c i p i I f t h e d i s p a r i t y i n p r e c i p i t a t i o n between t h e
upper and l o w e r b a s i n s i s n o t t o o g r e a t , o r i f t h e l o w e r b a s i n i s s m a l l r e l a t i v e t o t h e upper b a s i n . then r u n o f f w i l l i n c r e a s e downstream.
no c o n t r i b u t i o n f r o m t h e l o w e r b a s i n ,
If there i s l i t t l e or
two r e s u l t s c a n occur:
(1) a l a r g e
upstream runoff w i l l be t r a n s m i t t e d through the downstream b a s i n w i t h only r e l a t i v e l y moderate l o s s e s ,
o r (2) upstream r u n o f f may be g r e a t l y ( o r e n t i r e l y )
d i s s i p a t e d by e v a p o t r a n s p i r a t i o n and by i n f i l t r a t i o n through t h e channel bed i n t h e lower basin.
The N i l e R i v e r i s an example of t h e f i r s t .
Many examples of
t h e s e c o n d a r e known i n a r i d r e g i o n s a l t h o u g h t h e f l o w i s u s u a l l y r e d u c e d by manmade d i v e r s i o n s i n a d d i t i o n t o t h e n a t u r a l l o s s e s .
Many s t r e a m s t h a t f l o w
16
50 I--
: : / P E
/ I
20-
i
0 w-
u
+
v , ?n y
5'--
RAINFALL
i
/
2t
2 5 20 50 RECURRENCE INTERVAL IN YEARS
Fig. 2.16. Flood-frequency Cal i f o r n i a .
c u r v e s of snowmelt and r a i n f a l l f l o o d s , Merced R i v e r ,
i n t o a r i d r e g i o n s t e r m i n a t e i n c l o s e d l a k e s ; G r e a t S a l ! L r k e , Dead S e a , Lake Chad, a n d C a s p i a n S e a a r e w e l l known e x a m p l e s . p l a y a s which may b e d r y f o r l o n g p e r i o d s .
Other streams t e r m i n a t e i n
S t i l l o t h e r s t r e a m s , such a s t h e many
wadis d r a i n i n g toward t h e i n t e r i o r of t h e s o u t h e r n Arabian P e n i n s u l a ,
gradually
disappear i n t o the desert.
2.3
EFFECTS OF GEOLOGY Under t h e same c l i m a t i c i n f l u e n c e s , g r e a t l y d i f f e r e n t s t r e a m f l o w r e g i m e s a r e
produced from d r a i n a g e b a s i n s h a v i n g d i f f e r e n t s o i l s and rocks.
The s o i l o r
o t h e r s u r f i c i a l m a t e r i a l d e t e r m i n e s how much and a t what r a t e t h e p r e c i p i t a t i o n w i l l i n f i l t r a t e and t h u s what p r o p o r t i o n w i l l become o v e r l a n d r u n o f f .
Some of
t h e i n f i l t r a t e d w a t e r w i l l b e e v a p o r a t e d a n d t h e r e s t w i l l move t h r o u g h t h e rocks e i t h e r t o a stream channel or, t i o n below any s t r e a m channel.
i n some a r i d r e g i o n s ,
t o a zone of s a t u r a -
The c h a r a c t e r of t h e r o c k s d e t e r m i n e s how t h e
w a t e r moves underground and a t what r a t e s . Rapid s u r f a c e r u n o f f and l i t t l e b a s e f l o w a r e a s s o c i a t e d w i t h low i n f i l t r a tion rates.
Conversely,
a high i n f i l t r a t i o n rate.
t h e s t r e a m f l o w i s much l e s s v a r i a b l e from a b a s i n w i t h The f o l l o w i n g examples d e m o n s t r a t e how geology modi-
f i e s s t r e a m f l o w ; i n most b - ; l n s
geology may be o n l y one of s e v e r a l s i g n i f i c a n t
b a s i n c h a r a c t e r i s t i c s and i t s e f f e c t on s t r e a m f l o w may n o t b e r e a d i l y a p p a r e n t .
17 Regions i n which p r a c t i c a l l y a l l t h e p r e c i p i t a t i o n s o a k s i n t o t h e ground u s u a l l y a r e d r a i n e d by s t r e a m s w i t h l i t t l e v a r i a t i o n i n flow. Nebraska i s such a region.
F i g u r e 2.17
1000,
The Sand H i l l s of
c o m p a r e s t h e m o n t h l y mean f l o w s of
-v
v)
LL
0
z
3
PONCA CREEK
750 -
-
500 -
-
9
LL
" O N D J
F
M
A
M
J
J
A
S
1978 WATER YEAR
Fig. 2.17. Monthly mean f l o w s o f two Nebraska s t r e a m s . S a n d h i l l s Region. Dismal River,
a Sand H i l l s s t r e a m ,
Dismal R i v e r i s i n t h e
w i t h Ponca Creek, which i s not.
A less
e x t r e m e d i f f e r e n c e i s shown between two North C a r o l i n a s t r e a m s , Drowning Creek w h i c h d r a i n s a s a n d y a r e a , and U w h a r r i e R i v e r whose b a s i n i s l e s s p e r m e a b l e (Fig. 2.18).
V a r i a t i o n i n d a i l y f l o w s of two g e o l o g i c a l l y - d i f f e r e n t
streams is
shown i n F i g u r e 6.3 (Chapter 6 ) . The P a h s i m e r o i R i v e r i n I d a h o f l o w s through an a l l u v i a l v a l l e y between h i g h mountains.
Snowmelt r u n o f f from t h e t r i b u t a r i e s s i n k s i n t o t h e ground b e f o r e
reaching the river.
Low-elevation s p r i n g s i n t h i s b a s i n u s u a l l y reach t h e i r
maximum d i s c h a r g e s i n August o r September.
The m o d e r a t i n g e f f e c t of t h e a l l u -
v i a l f i l l i s s o g r e a t t h a t many o f t h e a n n u a l f l o o d p e a k s o n P a h s i m e r o i R i v e r o c c u r i n November or December a l t h o u g h a l l o t h e r gaged s t r e a m s i n t h e v i c i n i t y peak i n s p r i n g o r e a r l y summer. The Yucatan P e n i n s u l a of Mexico i s a f l a t , a r e few s t r e a m channels.
l i m e s t o n e p l a t e a u i n which t h e r e
P r a c t i c a l l y a l l of t h e p r e c i p i t a t i o n i n f i l t r a t e s i n t o
t h e ground and t h e n d r a i n s d i r e c t l y t o t h e ocean.
Some sandy c o a s t a l a r e a s i n
humid p a r t s of t h e w o r l d a l s o a r e w i t h o u t s t r e a m channels. B a s i n s w i t h s i m i l a r i n f i l t r a t i o n c h a r a c t e r i s t i c s may h a v e v e r y d i f f e r e n t o u t f l o w r e g i m e s due t o d i f f e r e n c e s i n t h e r a t e of movement through t h e ground and i n t h e amount of s t o r a g e i n t h e a q u i f e r .
T r o x e l l (1953) showed t h a t a major
18
0
looo --1
1
UWHARRIE R
DROWNING CR
" J F M A M J J A S O N D MONTHS, 1957 F i g . 2.18. M o n t h l y mean f l o w s o f t w o N o r t h C a r o l i n a s t r e a m s s h o w i n g t h e d i f f e r e n c e due t o b a s i n i n f i l t r a t i o n r a t e s .
F i g . 2.19. H y d r o g r a p h f o r M i l l C r e e k , C a l i f o r n i a , s h o w i n g t h a t t h e m a j o r recharge i n 1922 contributed t o the base flow f o r the next t h r e e y e a r s ( a f t e r Troxell, 1953). r e c h a r g e of t h e s m a l l ,
s t e e p b a s i n of M i l l Creek i n s o u t h e r n C a l i f o r n i a c o n t r i -
b u t e d t o t h e b a s e flow f o r s e v e r a l s u c c e e d i n g y e a r s ( F i g u r e 2.19),
an i n d i c a t i o n
of a l a r g e ground w a t e r body t h a t d r a i n e d r e l a t i v e l y s l o w l y t o t h e s t r e a m . McDonald and L a n g b e i n ( 1 9 4 8 ) c o n c l u d e d t h a t t h e g r o u n d w a t e r s t o r a g e i n t h e b a s i n of M e t o l i u s R i v e r , Oregon was about t h r e e t i m e s t h e annual runoff.
Meto-
l i u s R i v e r d r a i n s a b a s a l t b a s i n a n d i t s f l o w i s uncommonly s t e a d y .
On t h e
o t h e r hand t h e f l o w of Drowning Creek ( F i g u r e 2.18) responds r a t h e r p r o m p t l y t o p r e c i p i t a t i o n , i n d i c a t i n g a more l i m i t e d a q u i f e r c a p a c i t y . describes t h e occurrence, origin, ex ample s
.
Meinzer (1949)
and d i s c h a r g e of ground w a t e r and g i v e s many
19 Some b a s i n s t r a n s m i t i n f i l t r a t e d w a t e r t o s t r e a m c h a n n e l s v e r y r a p i d l y through s o l u t i o n c h a n n e l s , porous l a v a , o r c o a r s e a l l u v i a l m a t e r i a l . g r a p h o f J a c k D a n i e l S p r i n g i n F i g u r e 6.2
The hydro-
( C h a p t e r 6) r e s p o n d s r a p i d l y t o
p r e c i p i t a t i o n presumably b e c a u s e t h e w a t e r i s t r a n s m i t t e d through openings i n the limestone.
R e l a t e d o c c u r r e n c e s a r e t h e d i s a p p e a r a n c e and subsequent reap-
pearance of s t r e a m c h a n n e l s i n l i m e s t o n e o r v o l c a n i c t e r r a n e s .
F i g . 2.20.
F i g u r e 2.20
Pop0 Agie River, Wyoming, where i t d i s a p p e a r s i n t o t h e ground.
s h o w s t h e Pop0 A g i e R i v e r i n Wyoming g o i n g u n d e r g r o u n d f r o m w h i c h i t e m e r g e s within a short distance. then reappears.
Rogue R i v e r i n Oregon d i s a p p e a r s i n l a v a t u b e s and
And L o s t R i v e r , i n t h e h e a d w a t e r s o f t h e P o t o m a c R i v e r , g o e s
underground n e a r W a r d e n s v i l l e , W. Va. i n a l i m e s t o n e t e r r a n e . Streams f l o w i n g i n porous m a t e r i a l may l o s e w a t e r through t h e channel bed and banks i n c e r t a i n reaches.
T h u s t h e s u r f a c e f l o w a t a p a r t i c u l a r p o i n t on t h e
channel may be o n l y a p a r t of t h e t o t a l flow p a s t t h a t s e c t i o n .
Gaging s t a t i o n s
a r e u s u a l l y l o c a t e d above o u t c r o p s which f o r c e t h e t o t a l flow t o t h e s u r f a c e . Furthermore,
d i s c h a r g e s of ground w a t e r t o a s t r e a m o f t e n a r e n o t d i s t r i b u t e d
uniformly along the channel.
Large i n c r e a s e s o r d e c r e a s e s i n ground-water
c o n t r i b u t i o n s may occur w i t h i n a s h o r t d i s t a n c e along a r e a c h a s i n d i c a t e d by t h e f l o w p r o f i l e of a s h o r t r e a c h of Spokane R i v e r ( F i g u r e 2.21).
There a r e no
a p p r e c i a b l e s u r f a c e w a t e r c o n t r i b u t i o n s i n t h i s reach. The c o n t r i b u t i o n of ground w a t e r t o a s t r e a m o f t e n i n c r e a s e s w i t h d i s t a n c e downstream a s t h e stream c u t s deeper i n t o t h e aquifer.
This e f f e c t has been
20
ui u
1600
7-1
J
I
+ z 0
0
0
4
8
12
16
20
24
28
MILES DOWNSTREAM
I
Fig. 2.21. E f f e c t of ground w a t e r on t h e f l o w of Spokane R i v e r from P o s t F a l l s , Idaho, t o mouth of L a t a h Creek i n Spokane, Washington, September 1950. observed on some Long I s l a n d , New York. s t r e a m s whose b a s e f l o w s i n c r e a s e c o n s i d e r a b l y a s t h e y approach t h e ocean.
15
1
05
F o r example s e e F i g u r e 2.22.
0
MILES ABOVE MOUTH
F i g . 2.22. B a s e f l o w o f Carman C r e e k , Long I s l a n d , New York, s h o w i n g i n c r e a s e toward mouth, 12/28/78. Basin geology may p e r m i t s u b s t a n t i a l amounts of ground w a t e r t o move a c r o s s t o p o g r a p h i c b o u n d a r i e s , c a u s i n g an unequal d i s t r i b u t i o n of r u n o f f w i t h r e s p e c t t o surface-water drainage areas.
The l a r g e d i f f e r e n c e i n y i e l d p e r s q u a r e m i l e
of two s m a l l s t r e a m s i n a l i m e s t o n e t e r r a n e i n s o u t h e a s t e r n Idaho (Fig. 2.23) i s a t t r i b u t e d t o t h i s cause.
Drainage a r e a s of Cub Creek and Bloomington Creek a r e
a r e 19.4 and 22.1 s q u a r e m i l e s r e s p e c t i v e l y .
Bloomington Creek h a s l a r g e
s p r i n g s i n i t s headwaters.
I n a r i d and s e m i a r i d r e g i o n s w h e r e t h e w a t e r t a b l e i s below s t r e a m c h ~ i n n e l s t h e p e r m e a b i l i t y of t h e s t r e a m bed d e t e r m i n e s t h e r a t e a t which s t r e a m f l o w s e e p s i n t o t h e ground.
T r a n s f e r of w a t e r between t h e s u r f a c e and t h e ground a l s o may
21
20 -
15-
CUB CREEK
10-
-
BLOOMINGTON
1947 WATER YEAR
F i g . 2.23. D i f f e r e n c e in y i e l d f r o m t w o a d j a c e n t I d a h o d r a i n a g e b a s i n s i s a t t r i b u t e d t o movement of ground w a t e r a c r o s s topographic d i v i d e s .
+ 99
30
F i g . 2.24. R e d u c t i o n i n mean f l o w s d u e t o s t r e a m s c r o s s i n g t h e B a l c o n e s F a u l t a r e a , Texas. occur a t geologic f a u l t s .
F i g u r e 2.24 shows m e a n . f l o w s a t g a g e d s i t e s i n t h e
upper b a s i n s of t h e Nueces and F r i o Rivers,
Texas.
The f l o w l o s s e s ,
indicated
by t h e mean f l o w s , occur where t h e s t r e a m s c r o s s t h e Balcones F a u l t area.
22 2.4
EFFECTS OF TOPOGRAPHY
In mountainous b a s i n s ,
l a n d s l o p e s a r e s t e e p , s t r e a m g r a d i e n t s a r e high,
p r e c i p i t a t i o n r e a c h e s t h e c h a n n e l s quickly. peaks i n c r e a s e w i t h channel slope.
and
Pany s t u d i e s have shown t h a t f l o o d
P r e c i p i t a t i o n r e a c h e s t h e c h a n n e l s more
s l o w l y where b a s i n s l o p e s a r e g e n t l e ; c o n s e q u e n t l y s t r e a m s t a k e l o n g e r t o r i s e t o a peak and t h e peaks tend t o b e f l a t t e n e d .
A f l o o d peak may move downstream
two o r t h r e e t i m e s a s f a s t on a h i g h - g i a d i e n t
s t r e a m a s on one of low g r a d i e n t .
And low g r a d i e n t c h a n n e l s tend t o b e i n wide v a l l e y s where l a r g e r i p a r i a n a r e a s a r e inundated by s i g n i f i c a n t f l o o d s ; t h e r e s a l t i n g channel s t o r a g e r e d u c e s t h e peak d i s c h a r g e a l t h o u g h much of t h e o v e r f l o w i s r e t u r n e d t o t h e s t r e a m r a t h e r promptly.
Overflows o f some c h a n n e l s i n v e r y f l a t topography may n e v e r r e t u r n
t o t h e main channel.
This n a t u r a l d i v e r s i o n r e d u c e s b o t h t h e f l o o d peak and t h e
y i e l d downstream. Lakes,
swamps, and marshes a r e common i n b a s i n s o f low r e l i e f .
The n a t u r a l
s t o r a g e i n t h e s e a r e a s g e n e r a l l y r e d u c e s t h e downstream f l o o d peaks.
Evapora-
t i o n from t h e w a t e r s u r f a c e s and e v a p o t r a n s p i r a t i o n from t h e p e r i m e t e r s o f t h e w e t l a n d a r e a s and fro m t h e s h a l l o w ground w a t e r r e d u c e b a s i n r u n o f f s n b s t a n t i a l l y a t times.
The v a r i a b i l i t y i n s t o r a g e due t o w e a t h e r p a t t e r n s r e s u l t s i n
a h i g h v a r i a b i l i t y of annual low f l o w s downstream. f l o w s o f Suwannee River, Georgia,
For example t h e annual low
which d r a i n s t h e 6 5 0 square-mile Okefenokee Swamp i n
range from about 700 c f s t o z e r o a t t h e Georgia-Florida
S t a t e line.
I n extremely f l a t regions where t h e d r a i n a g e d i v i d e s a r e n o t w e l l defined w a t e r may flow i n one o r t h e o t h e r of two d i r e c t i o n s . wetland i s t h e headwater of both streams.
U s n a l l y a s h a l l o w pond o r
An e x a m p l e i s t h e h e a d w a t e r s o f
Curlew Creek and San P o i 1 R i v e r i n e a s t e r n Washington S t a t e . Channels i n f l a t , c o a s t a l a r e a s t e n d t o be i n t e r h o n n e c t e d and t h e i r f l o w s depend on t i d a l a c t i o n and on t h e l o c a t i o n s of s t o r m s and i n f l o w s .
The f l o w i n
a p a r t i c u l a r r e a c h may b e i n one d i r e c t i o n a t o n e t i m e , and i n t h e o p p o s i t e a t another;
b e t w e e n t h o s e t i m e s t h e c h a n n e l may b e f u l l o f w a t e r t h a t i s n o t
moving. Stream p a t t e r n can be c o n s i d e r e d a topographic f e a t u r e . c h a r a c t e r i s t i c s along t h e main channel.
It a f f e c t s the flood
Tributaries entering a channel a t
r e g u l a r i n t e r v a l s o f d i s t a n c e w i l l produce a f l o o d t h a t i n c r e a s e s downstream i f t h e t r i b u t a r y peaks a r e s u b s t a n t i a l and more o r l e s s c o n c u r r e n t w i t h t h e peak on t h e main channel.
J u s t below t h e c o n f l n e n c e of two s t r e a m s of s i m i l a r s i z e and
regime, t h e combined f l o o d peak may approximate t h e sum of t h e two c o n t r i b u t i n g peaks u n l e s s t h e two peaks a r r i v e a t d i f f e r e n t times, i n which c a s e a double peak may r e s u l t .
I n a long channel r e a c h w i t h o u t t r i b u t a r i e s , o r w i t h t r i b u t a r -
i e s t h a t do n o t c o n t r i b u t e a t t h e same t i m e a s t h e headwaters, upstream w i l l be a t t e n u a t e d ; s e e F i g u r e 8.12 (Chapter 8 ) .
a flood generated
23
A common indicator of stream pattern is some index of basin shape but shape is often a poor descriptor of flood potential.
Unless the pattern is extreme,
and the basin hydrology is m o r e or less homogeneous,
the effect of pattern
probably is small and will be masked by other basin characteristics. The effect of stream pattern on mean flow or low flows is either negligible or to small to detect.
A topographic feature that affects streamflow in arid regions is the closed basin f r o m w h i c h no surface f l o w leaves. flows into a terminal lake or a sink.
W a t e r generated in a closed basin
W e l l k n o w n large closed basins are the
Great B a s i n i n w e s t e r n United States, the J o r d a n River b a s i n in the Arabian Peninsula, and t h e Caspian Lake B a s i n in Asia.
Considerable s t r e a m f l o w is
generated in these basins but none of it reaches the oceans. Small closed basins are common in semiarid regions of the world.
The contri-
buting drainage areas of some streams in western United States are less than the areas enclosed b y the topographic boundaries because of closed basins w i t h i n those boundaries. floods.
Some of these small closed basins may overflow during extreme
Basins a r e closed because of l o w precipitation: if the precipitation
were high enough the basin would become a lake and drain to an ocean. REFERENCES Crippen. J.R. 1978, Composite log-type I11 frequency-magnitude curve of annual floods: U.S. Geol. Survey Open- File Report 78-352, 5 p. Crippen, J.R., and Bue. C.D., 1977, M a x i m u m f l o o d f l o w s i n the conterminous United States: U.S. Geol. Survey Water-Supply Paper 1887, 52 p. Dunford. E.G., and Fletcher, P.W.. 1947, Effect of removal of streambank vegetation u p o n w a t e r yield: Am. Geophysical Union, Trans., Vol. 28, No. l, Feb 1947, p. 105-110. L'vovich, M.I.. 1980, World water resources and their future (translation edited 416 p. b y R.L. Nace): Am. Geophysical Union, Washington, D.C.. McDonald, C.C. and Langbein, W.B.. 1948, Trends i n runoff in t h e Northwest: Trans. Am. Geophysical Union, Vol. 29, No. 3, J u n e 1948, p. 387-397. Meinzer, O.E.,
1949, Hydrology:
New York, Dover Publications, 712 p.
Moore, A.M., 1957, Measuring s t r e a m f l o w under ice conditions: Am. SOC. Civil Engineers Proc., Jour. Hydraulics Div., v. 83, HY1, P a p e r 1162, 1 2 p. Riggs, H.C., 1980. Climatic factors of runoff, in Pollution and Water Resources: Columbia University Seminar Series, V. XIII, Part 111, Pergamon Press, p. 7383. Simons, W.D., 1953, Concept and characteristics o f base flow in t h e Columbia River basin: Western Snow Conf. Proc., 21st meeting, Boise, Idaho, p. 57-61. Troxell. H.C., 1953, The influence of ground-water storage on the runoff in the San Bernardino and eastern S a n Gabriel M o u n t a i n s of southern California: Trans. Am. Geophysical Union, Vol. 34, No. 4, p. 552-562. Williams, G.R.. 1940, Natural w a t e r loss in selected drainage basins: Geol. Survey Water-Supply Paper 846, 5 2 p.
U.S.
This Page Intentionally Left Blank
25
Chapter 3
COLLECTION OF HYDROLOGIC DATA 3.1
STREAMFLOW Continuous streamflow records a r e obtained a t a gaging s t a t i o n a t which t h e
stream stage (water-surface o r is recorded continuously.
h e i g h t above some datum) i s e i t h e r r e a d f r e q u e n t l y D i s c h a r g e i s measured,
u s u a l l y by c u r r e n t m e t e r ,
a t v a r i o u s s t a g e s f o r d e f i n i n g t h e stage-discharge r e l a t i o n ( r a t i n g curve) which
i s used t o convert the stage record t o a discharge record.
Only t h e g e n e r a l
p r o c e d u r e s a r e g i v e n h e r e ; f o r more d e t a i l s e e WMO (1980) o r Rantz (1982). 3.1.1
S t a g e measurement
Gaging s t a t i o n s a r e o f s e v e r a l t y p e s .
The s i m p l e s t c o n s i s t s o f a s e r i e s of
s t a f f g a g e s (Fig. 3.1) on w h i c h an o b s e r v e r r e a d s t h e s t a g e o n e or more t i m e s a
Fig. 3.1. day.
S t a f f g a g e s on Rio C i a , B r a z i l .
Recording g a g e s e i t h e r s e n s e t h e w a t e r s u r f a c e i n a s t i l l i n g w e l l hydraul-
i c a l l y c o n n e c t e d t o t h e s t r e a m o r by means o f a gas-purge
( b u b b l e gage) s y s t e m
w h i c h m e a s u r e s t h e p r e s s u r e on an o r o f i c e p e r m a n e n t l y m o u n t e d i n t h e s t r e a m . R e c o r d i n g g a g i n g s t a t i o n s a l s o h a v e s t a f f g a g e s ( F i g . 3.2) f o r v e r i f y i n g t h e s t a g e s b e i n g s e n s e d b y t h e equipment.
A simplified stilling-well
installation
is shown i n F i g u r e 3.3 and a g a g i n g s t a t i o n s t r u c t u r e i n F i g u r e 3.4. A bubble-gage
i n s t a l l a t i o n c o n s i s t s of an i n s t r u m e n t s h e l t e r on a c o n c r e t e
s l a b on t h e r i v e r bank. A t u b e c o n n e c t s t h e i n s t r u m e n t t o t h e o r o f i c e i n t h e stream.
N i t r o g e n gas i s bubbled t h r o u g h t h e o r o f i c e t o a c t u a t e t h e s e n s o r .
26
Fig. 3.2.
Lor-rater staff gage.
Fig. 3.3.
Simplified stilling-well installation.
Recording instruments are either analog or digital.
The latter produces a
punched-tape record for processing by digital computer; the punch interval commonly used is 15 minutes but this can be as short as 5 minutes or an hour.
as
long as
The two types of recorders are shown in Figures 3.5 and 3.6.
A gaging station should be located above a stable section of channel in order
that the relation between stage and discharge be well defined and unchanging
21
Fig. 3.4.
Gaging station.
Fig. 3.5.
Analog water-stage recorder.
with time.
T h e feature of the channel that maintains a more-or-less
stage-discharge relation is called the control.
stable
The control m a y be at a sec-
tion, such as a stable riffle ( F i g . 3.7) o r it m a y be a fairly long reach of the
28
F i g . 3.6.
D i g i t a l water-stage
F i g . 3.7.
Natural section control.
channel i t s e l f .
recorder.
A r t i f i c i a l s e c t i o n c o n t r o l s s u c h a s l o w dams a r e s o m e t i m e s
c o n s t r u c t e d where n a t u r a l channel f e a t u r e s a r e n o t s u i t a b l e . t r o l s a r e expensive,
e s p e c i a l l y f o r l a r g e streams,
A r t i f i c i a l con-
and a r e hard t o m a i n t a i n i n
e r o d i b l e c h a n n e l s c a r r y i n g heavy s e d i m e n t loads. 3.1.2
D i s c h a r g e measurement
D i s c h a r g e m e a s u r e m e n t s o f s t r e a m s a r e u s u a l l y made by currant-meter.
The
p r o c e d u r e c o n s i s t s o f (1) m e a s u r i n g t h e w i d t h , d e p t h , a n d v e l o c i t y o f f l o w i n
29
e a c h of s e v e r a l s u b s e c t i o n s of a s t r e a m c r o s s s e c t i o n , ( 2 ) c o m p u t i n g t h e d i s c h a r g e i n e a c h s u b s e c t i o n a s t h e p r o d u c t of a r e a and mean v e l o c i t y , summing t h e p a r t i a l d i s c h a r g e s t o o b t a i n t h e t o t a l .
and (3)
R e f e r r i n g t o F i g u r e 3.8.
t h e d e p t h a t e a c h of t h e s e l e c t e d v e r t i c a l s i s m e a s u r e d by s o u n d i n g and t h e width of each s u b s e c t i o n i s computed from t h e spacing of t h e v e r t i c a l s .
A t each
v e r t i c a l t h e mean v e l o c i t y i s o b t a i n e d from one or more v e l o c i t y o b s e r v a t i o n s by
Verticals
Meter locations
F i g . 3.8. S t r e a m c r o s s s e c t i o n showing m e t e r l o c a t i o n s f o r a d i s c h a r g e measurement. c u r r e n t meter.
Many s t u d i e s have demonstrated t h a t t h e mean of t h e v e l o c i t i e s
a t 0.2 and 0s of t h e d e p t h f r o h t h e w a t e r s u r f a c e i s v i r t u a l l y t h e mean velocity i n the vertical. mean i n t h e v e r t i c a l .
L i k e w i s e t h e v e l o c i t y a t 0.6 d e p t h v e r y n e a r l y e q u a l s t h e V e l o c i t y o b s e r v a t i o n s a r e u s u a l l y made a t 0.2 and 03 of
t h e depth i n each v e r t i c a l where t h e depth i s adequate. The b a s i c equipment needed f o r a d i s c h a r g e measurement c o n s i s t s of a c u r r e n t meter,
a d e v i c e f o r i n d i c a t i n g t h e r e v o l u t i o n s of t h e meter,
a s t o p watch,
and
some means of measuring d e p t h and w i d t h and of holding t h e m e t e r i n t h e proper l o c a t i o n s for v e l o c i t y observations.
In shallow s t r e a m s , measurements a r e made
by wading; t h e c u r r e n t meter i s mounted on a wading rod which i s used t o measure d e p t h and t o p o s i t i o n t h e m e t e r i n t h e v e r t i c a l .
H o r i z o n t a l c o n t r o l i s main-
t a i n e d by a t a p e or b e a d e d w i r e s t r e t c h e d a c r o s s t h e s t r e a m .
See F i g u r e 3.9.
In use, t h e number of r e v o l u t i o n s of t h e meter r o t o r i s obtained by an e l e c t r i c a l c i r c u i t w h i c h p r o d u c e s c l i c k s i n a n e a r p h o n e or r e g i s t e r s o n a c o u n t i n g device.
Elapsed t i m e i s measured by a stopwatch.
v e l o c i t y through t h e meter r a t i n g t a b l e . measurement.
These d a t a a r e t r a n s l a t e d t o
F i g u r e 3.10 shoks n o t e s of a d i s c h a r g e
30
F i g . 3.9.
Wading equipment and a measurement i n p r o g r e s s .
Deep s t r e a m s a r e m e a s u r e d f r o m a b r i d g e , c a b l e w a y , o r b o a t .
The m e t e r i s
suspended on a c a b l e above a sounding weight which i s used f o r d e p t h measurement and t o h o l d t h e c u r r e n t m e t e r a t t h e c o r r e c t p o s i t i o n i n t h e v e r t i c a l f o r Sounding w e i g h t s used range from 1 5 t o 300 pounds or more
v e l o c i t y observation.
depending on t h e d e p t h and v e l o c i t y of t h e stream. i n F i g u r e s 3.11,
3.12,
and 3.13.
Methods of gaging a r e shown
S e e Buchanan a n d S o m e r s ( 1 9 6 9 ) f o r a m o r e
complete d e s c r i p t i o n of measurement t e c h n i q u e s i n c l u d i n g measurement under i c e cover. The m o v i n g - b o a t velocity-area
method i s s i m i l a r t o t h e above method i n t h a t i t u s e s t h e
approach t o d e t e r m i n i n g d i s c h a r g e b u t i t d i f f e r s i n t h e method of
d a t a c o l l e c t i o n ; t h e de?t:..
r n d v e l o c i t i e s a t e a c h o b s e r v a t i o n p o i n t a r e ob-
tained while the boat is rapidly traversing the cross section.
Thus a measure-
ment of d i s c h a r g e by t h i s method c a n be made on wide s t r e a m s i n a few m i n u t e s a t s i t e s without fixed f a c i l i t i e s .
However,
made and t h e r e s u l t s a v e r a g e d .
The e q u i p m e n t ( F i g . 3.14) c o n s i s t s o f a s o n i c
sounder,
a vane w i t h a n g l e i n d i c a t o r ,
in practice 6 traverses usually are
a component p r o p e l l o r - t y p e
c u r r e n t meter.
and a maneuverable s m a l l boat. The t r a v e r s e o f t h e c r o s s s e c t i o n i s made w i t h o u t s t o p p i n g a n d d a t a a r e collected a t regular intervals.
The b o a t o p e r a t o r m a i n t a i n s c o u r s e by "crab-
b i n g " i n t o t h e d i r e c t i o n of f l o w s u f f i c i e n t l y t o keep on l i n e .
The f o r c e
e x e r t e d on t h e c u r r e n t m e t e r i s t h e c o m b i n a t i o n of two f o r c e s a c t i n g s i m u l t a neously,
one f o r c e d u e t o t h e movement o f t h e b o a t a n d t h e o t h e r f r o m t h e
o t r e a m f l o r normal t o t h e path.
A d d i t i o n a l i n f o r m a t i o n needed i s t h e v e r t i c a l
........................................................... qz"uan ........................................................................ ..............................................
.......
-
. . . .
..."a?3....... I
0Al"q)
...............................................
-
..................................................................... r,rmqiJ py,"s )q,", ................ p'"nu,, p , ~ , ~ n..........................
..........
-
~
.qo i+,p.J"~u
........ . . .................. .... ...... P.3 o,... a , . & ........ ~,~... . . . *y ........................................... 'WJ .......................... -* ?nj.?.... , ~ y l , ~ & ..................... &.zc J., Iu .~ ..... ............................. . . . . . . . . . . . . . "Dll,al "0'3 : N O I I ! p Y O > ~~~
'i~~LUs
yuqpJ"0 p m q
'(0'8
-
n r o ) rmd
'(Oh@) I!*)
...... .... ... ............................................. ............. .................... ........................... pYmJ 9.93 ',.q-q>q,
,.
.......................................
PY.
. 1 . *
CI '(0'5)
pms '(%Z)
>">[,a,.>
p3p,
l"?w,inrwly H 3
..
....
n 8-2
3 W Pilix"b
,
Ib!'B:./4!18.l?:!'s:l:::::::::+c:~! H
32
Fig. 3.11.
Gaging from a bridge (during a flood at left).
F i g . 3.12.
Measuring from a cableway.
the stage-discharge relation w i l l change either gradually or abruptly in response to such factors as aquatic growth, ice formation and release, erosion or deposition by floods, and other natural or man-made changes in the channel.
The
definition and application of rating curves require an understanding of stream hydraulics and considerable experience. Kennedy (1983).
S e e WYO (1980) or R a n t z
(1982). and
33
F i g . 3.13.
J e t b o a t equipped f o r gaging.
I ,Indicator
Sighting d e v i c e \
I
and dial
/"
L
L
I
F i g . 3.14. E q u i p m e n t f o r m e a s u r i n g by t h e m o v i n g - b o a t m e t h o d (From Smoot and Novak, 1969).
A stage-discharge
r e l a t i o n c a n be computed from a s u r v e y of t h e downstream
channel and e s t i m a t e s of channel roughness. backwater method,
The technique,
known a s t h e s t e p -
i s u s e f u l where t i m e does n o t p e r m i t o b t a i n i n g c u r r e n t - m e t e r
d i s c h a r g e measurements throughout t h e range of s t a g e , or where h i g h accuracy i s not required.
The method i s d e s c r i b e d i n many h y d r a u l i c t e x t s and by Davidian
(1984) and was v e r i f i e d for t h i s a p p l i c a t i o n by B a i l e y and Bay (1966).
34
Fig. 3.15
Stage-discharge relation (rating curve).
Streamflow records are sometimes needed on stream reaches affected by variable backwater.
T h e discharge past a section on such a reach is a function of
stage and the slope of the water surface through the reach.
A continuous stage
record at each end o f a reach is required to define the slope. analysis depends on the hydraulic conditions.
The method of
See W M O (1980) or Bantz (1982).
and Kennedy (1983) for rating curve theory and details of applications to various channel and flow conditions. 3.1.4
Discharge computation and the hydrograph
Given a continuous stage record or frequent stage observations, and a stagedischarge relation, the discharge can be computed for any particular time within the period of stage record.
Daily mean discharges are usually computed although
discharges at intervals of an hour or less are used to define the changes during a flood.
An annual s t r e a m f l o w record as published b y U S G S is s h o w n in F i g u r e
3.16. The daily mean discharges of Figure 3.16 the hydrograph shown in Figure 3.17. various events.
are plotted against time to produce
Hydrographs show how a stream responds to
An uncharacteristic pattern of a segment of a hydrograph may
indicate s o m e unnatural f l o w modification o r an error in the record or in t h e analysis on which the discharge record is based. Flood hydrographs are usually defined by discharges at short intervals, such as hourly, and by the peak discharge. 3.1.5
Figure 3.18
is an example.
Special gaging methods
Variable backwater due to operation of a dam or other control on a stream may result, at times, in
SO
little fall in the r a t e r surface through a reach that
35
POTOMAC RIVER BASIN
183
01600000 NORTH BRANCH POTOMAC RIVER AT PINTO, MD LOCATION.--Lat 3 9 " 3 3 ' 5 9 " , long 78'50'25''. Mineral County, W. Va., Hydrologic Unit 02070002, on right bank a r downstream side of Western Maryland Railway bridge at Pinto, 2.8 m i ( 4 . 5 km) downstream from M i l l Run, and a t mile 3 2 . 6 (52.5 km). DRAINAGE AREA:-S96
mi'
(1.544
krn'). WATER-DISCHARGE RECORDS
PERIOD OF RECORD.~-October1 9 3 8 to current year REVISED RECORDS.--WSP 1332:
1943
GAGE.--Water~stagerecorder. Datum of gage is 648.23 ft (197.581 rn) National Geodetic YeTtxCal Datum of 1 9 1 9 . P r i o r to Dec. 10, 1938, "onrecording gage at highway bridge 2 5 0 ft (76 a) downstream at same datum. REMARKS.--Water-dischargerecords good except those for winter periods. uhxch are fair. Some regulation at low flow by Stony River Reservoir, 6 6 m i (106 km) above statxon ( s e e statxon Ol59S200), and since December 1950, by Savage River Reservoir, 25 "11 ( 4 0 ke) above Station ( s e e Station 0 1 5 9 7 5 0 0 ) . AVERAGE DISCHARGE.--41 years, 886 ft'ls
(25.09 m ' l s ) ,
20.19 inlyr (513 mnlyr), unadJusred.
EXTREMES FOR PERIOD OF RECORD.--Maximum discharge, 37,000 ft'ls (1,050 " ' I s ) Oct. 16, 1954. gage height, 23.23 ft (7.081 n); minimum, 31 ft'ls (0.88 m'ls) Dec. 18, 19, 1 9 4 3 , gage height, 1.37 fr (0.418 m), result of freereup. EXTREMES OUTSIDE PERIOD OF RECORD.--Flood of Mar. 29. 1924, reached a stage of about 24 ft (7.3 m), discharge. about 5 5 , 0 0 0 ft3/s (1,560 m'/s). Flood of Mar. 17 1936. reached a stage of about 23.5 ft (7.16 m). from floodmarks, discharge, about 1 0 , 0 0 0 ft'lr ( 1 , 4 2 0 m i l s ) . EXTREMES FOR CURRENT YEAR.--Maximum discharge 1 2 800 ft'ls (362 r n ' l s ) Feb. 26. gage height, 13.28 ft ( 4 . 0 4 8 m ) ; minimum, 126 ft'ls (3.57 m'15) NO". 15. g a i e h;ight, 1.88 ft (0.573 m ) . D I S C H A R G E , I N CUSIC FEE7 PEH SECOND+ lb7ER 7 E b X OCTOBER I978 10 SEPTEUBER 1 9 7 9 UEbN VbLUES
011
OCT
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OEC
JAN
FEB
MbH
APT(
UbY
JUN
JUL
bUG
SEP
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111 170
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2410 3050
1930
318
,200 6140 6330 9570
2160 2010 2220 2650
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1030 899 710 8* 1 169
319 250 2bl 298 1140
217 188 112 161 157
564
483
169
1750 3990 3870 2700
161 165 164
2240 1500 15.0 3720 3050
1340 1230 2050 1990 1610
320 380
10400 7890
2210
3550
147
2550
6610
1170
151 159 181
1590
352 343
1560 1680 1500
631 376 286 2b3 230
152
6350 5480
I k70 1290 1130 981 893
586
36Y
LO
114 171 169 168 172
11
171
1 63 164 167 165 152
1990 2090 17.0 1260
1190
3bO 350 370 390 450
2710 2350 2010 2150
1060
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988 174 600 476 403
233 22* 206 270 260
115 406 911 $15 266
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179 184 183
250 618
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255 231 224 226 213
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209 217 463 1090 678
2330
26 21 28 29 30 31 TOT&L WEbN MAX *IN
CAL
YR I7R VR
554
165 169 235 242 20 1
_--
183
8.09 280 1090 152
5501 171 242 161 1078 1919
TOTAL l07AL
Fig. 3.16.
4BP 509
.'tP
730
3360
850 1900
2310 2100 2210
2180 5390 9280 11100 1550 5220
loso
1530 1310 1200 1010 832 969
52h7 1702 3120 514
51295 1655 3990 139
54139 1955 11100 320
2200 1610 959 1030
390628 414643
UEbN
MEAN
2410
107% 1136
_-_ ___ ---
MAX
*AX
10700 11100
3180
1810
1310 1180 1090
low
1430
1054 1044 931
1630 1160 853
'. Dz o1 e0
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15.
1010 Y36 819 1160 2720
111
631
663 660 895 753
625 1210 3080
1150 1580
TO,
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2200 2040 1830 1530 968 817
746 1530
---
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99270 3202
39624 1321 26511 660
43416 1k01 3090 595
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333
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---
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---
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669
IN 24.38 I N 25.88
Published annual streamflow r e c o r d .
the f a l l cannot be measured c l o s e l y enough ( o r i s a f f e c t e d by wind) for use i n a stage-f a l l - d i s c h a r g e
relation.
Several a l t e r n a t i v e s a r e a v a i l a b l e .
36
Fig. 3.17.
I:
Hydrograph of daily discharges of Figure 3.16.
20,000
I
10,ooo
-
I
z W'
U [r
40
1 m -
cn n
10050 50 21
lqIl Fig. 3.18. (i)
I
t
'I
23
"I
"
,
l
25
27
1
JUNE 1972
Flood hydrograph.
Deflection meter.
The simplest alternative is use of a deflection vane
set at a fixed position below the minimum stage and at a right angle to the current (Fig. 3.19).
The angular deflection of the vane is a function of the
velocity in the cross section, and the stream stage is related to the cross sectional area.
Deflection and stage are measured at the gage site and the
relation with discharge is based on current-meter measurements. The deflection vane is used in small channels having little change in stage. Both downstream and upstream flow can be measured so it is suitable for tidal
37
High tide7
Low tidei
River bottom-
F i g . 3.19
Deflection-meter vanes.
channels.
D i s c h a r g e s c o m p u t e d by t h i s m e t h o d a r e g e n e r a l l y of low a c c u r a c y ,
e s p e c i a l l y t h o s e n e a r zero. ( i i ) A c o u s t i c method.
V e l o c i t y a t some f i x e d l e v e l i n t h e s t r e a m i s ob-
t a i n e d by d e t e r m i n i n g t h e t r a v e l t i m e s of sound i m p u l s e s moving i n b o t h d i r e c t i o n s along a d i a g o n a l p a t h between t r a n s d u c e r s (sound g e n e r a t o r s o r r e c e i v e r s ) mounted n e a r e a c h bank. shown i n F i g u r e 3.20.
The l a y o u t of a n o p e r a t i n g s y s t e m on Columbia River i s The i n s t a l l a t i o n a n d o p e r a t i o n o f t h a t s y s t e m i s deC a l i b r a t i o n i s by c u r r e n t meter.
s c r i b e d b y S m i t h and o t h e r s (1971).
Laenen
and S m i t h ( 1 9 8 2 ) h a v e a s s e m b l e d p u b l i s h e d and u n p u b l i s h e d i n f o r m a t i o n on t h e o p e r a t i o n , a p p l i c a t i o n s , performance, and l i m i t a t i o n s of a c o u s t i c v e l o c i t y measurement s y s t e m s w i t h s p e c i f i c a p p l i c a t i o n s t o measurement of streamflow. ( i i i ) E l e c t r o m a g n e t i c method.
tromagnetic meter.
P o i n t v e l o c i t y can b e measured by a n elec-
Continuous r e c o r d s of v e l o c i t y a t one p o i n t i n a c r o s s
s e c t i o n and of t h e s t a g e can b e t r a n s f o r m e d i n t o a continuous d i s c h a r g e r e c o r d a f t e r c a l i b r a t i o n w i t h c u r r e n t - m e t e r measurements.
The r e l i a b i l i t y of t h e
computed d i s c h a r g e depends on how c l o s e l y t h e v e l o c i t y a t t h e one p o i n t repres e n t s mean v e l o c i t y through t h e range of d i s c h a r g e experienced a s w e l l as on t h e r e l i a b i l i t y of t h e p o i n t v e l o c i t i e s .
Such a n i n s t a l l a t i o n s h o u l d b e o f r e l a -
t i v e l y low c o s t b u t t h e e l e c t r o m a g n e t i c m e t e r i s a l w a y s s u b j e c t t o damage from
38
Fig. 3.20. 1971).
Layout o f an a c o u s t i c v e l o c i t y measuring system (Smith and o t h e r s ,
d e b r i s i f i t i s s u i t a b l y located.
Lack of s t a b i l i t y of t h e m e t e r c a l i b r a t i o n i s
a l s o a problem. Green and Herschy (1978) d e s c r i b e an e l e c t r o m a g n e t i c g a g i i g s t a t i o n based on t h e total-flow
e l e c t r o m a g n e t i c method.
T h i s a p p l i c a t i o n i s s t i l l under develop-
ment. (iv)
D i l u t i o n methods.
D i l u t i o n methods o f measuring s t r e a m d i s c h a r g e a r e
u s e f u l under flow c o n d i t i o n s t h a t e x i s t i n s h a l l o w , Current-meter
e x t r e m e l y rough channels.
measurements a r e g e n e r a l l y q u i c k e r and more r e l i a b l e a t a l l b u t
extremely unfavorable s i t e s . The f i e l d p r o c e d u r e i n v o l v e s i n j e c t i n g a t r a c e r of g i v e n c o n c e n t r a t i o n i n t o a s t r e a m and sampling t h e c o n c e n t r a t i o n downstream where t h e t r a c e r i s c o m p l e t e l y mixed w i t h t h e w a t e r .
The t r a c e r may b e i n j e c t e d a s a s l u g o r a t a c o n s t a n t
rate.
U s e f u l t r a c e r s i n c l u d e s a l t s , r a d i o a c t i v e m a t e r i a l s , and f l u o r e s c e n t
dyes.
The method r e q u i r e s s k i l l e d o p e r a t o r s , c o n s i d e r a b l e t i m e ,
and a c o n s t a n t
discharge. Stream d i s c h a r g e for c o n s t a n t - r a t e Q =
injection is
c1 - c2 c -cb
2 where q i s t h e t r a c e r i n j e c t i o n r a t e and cb,
c1
and C2 a r e c o n c e n t r a t i o n s of t h e
39 stream a t t h e i n j e c t i o n p o i n t , of t h e i n j e c t e d t r a c e r , and of t h e s t r e a m a t t h e downstream c r o s s s e c t i o n r e s p e c t i v e l y .
See White (1978) or K i l p a t r i c k and Cobb
(1984) f o r d e t a i l s . 3.1.6
I n d i r e c t measurements
I t i s o f t e n i m p o s s i b l e t o measure f l o o d d i s c h a r g e s a t p a r t i c u l a r t i m e s because o f l a c k of a c c e s s t o t h e s i t e , s h o r t a g e of manpower, o r i n a d e q u a t e advance n o t i c e of t h e flood.
Engineers have t h e r e f o r e d e v i s e d methods of computing peak
d i s c h a r g e a f t e r t h e passage of t h e f l o o d : t h e common ones a r e slope-area, tracted-opening,
flow-over-dam,
and fl o w -t h r ongh- cul ver t .
con-
These methods a r e
b a s e d on h y d r a u l i c e q u a t i o n s t h a t r e l a t e t h e d i s c h a r g e t o t h e w a t e r - s u r f a c e p r o f i l e , t h e geometry of t h e channel, and t h e channel roughness.
These measure-
ments may be e x p e n s i v e and t h e y a r e l e s s a c c u r a t e t h a n c u r r e n t - m e t e r
measure-
ment s. The s l o p e - a r e a m e t h o d i s t h e m o s t w i d e l y u s e d .
An i d e a l s i t e i s a r e a c h o f
u n i f o r m c h a n n e l on w h i c h t h e f l o o d p e a k p r o f i l e i s d e f i n e d on b o t h b a n k s by high-water
marks.
Surveys o f t h e s e p r o f i l e s and o f channel c r o s s s e c t i o n s ,
and
e s t i m a t e s o f t h e r o u g h n e s s c o e f f i c i e n t i n t h e Manning e q u a t i o n a r e r e q u i r e d . F i e l d e x p e r i e n c e i n s e l e c t i n g roughness c o e f f i c i e n t s i s d e s i r a b l e b u t guidance can be o b t a i n e d from t h e photographs i n t h e r e p o r t by Barnes (1967). I n d i r e c t methods a r e d e s c r i b e d by Barnes and Davidian (1978).
Users g u i d e s
t o t h e v a r i o u s t e c h n i q u e s a r e g i v e n by D a l r y m p l e and Benson (1967). B o d h a i n e (1968).
M a t t h a i (1968).
and Hulsing (1968).
Common t o a l l t h e s e methods i s t h e need t o s e l e c t t h e roughness c o e f f i c i e n t subjectively.
The roughness c o e f f i c i e n t o f a n a t u r a l channel i s a f u n c t i o n of
bed roughness,
bank i r r e g u l a r i t y ,
e f f e c t of v e g e t a t i o n ( i f any), d e p t h o f w a t e r ,
c h a n n e l s l o p e , and o t h e r f a c t o r s .
No o b j e c t i v e way o f c o m b i n i n g a l l t h e s e
e f f e c t s i n t o one c o e f f i c i e n t i s a v a i l a b l e .
F u r t h e r m o r e t h e v e r i f i e d v a l u e of a
roughness c o e f f i c i e n t f o r a p a r t i c u l a r channel r e a c h and f l o o d i s a f f e c t e d by i n a c c u r a c i e s i n measuring o t h e r v a r i a b l e s i n t h e Manning e q u a t i o n ; t h i s r e s u l t s i n some a p p a r e n t i n c o n s i s t e n c i e s among v e r i f i e d r o u g h n e s s c o e f f i c i e n t s . avoid t h i s s u b j e c t i v i t y .
Riggs (1976) developed a s i m p l i f i e d s l o p e - a r e a
To
method
i n w h i c h d i s c h a r g e i s r e l a t e d t o c r o s s - s e c t i o n a l a r e a and t o w a t e r - s u r f a c e slope.
A roughness c o e f f i c i e n t i s n o t used because, i n n a t u r a l channels, roughThe e q u a t i o n i s
n e s s and s l o p e a r e r e l a t e d . l o g Q = 0.366
+
1.33 log A
+
0.05 l o g S
-
0.056 ( l o g S ) *
w h e r e Q i s i n c f s , A i s a v e r a g e c r o s s s e c t i o n a l a r e a i n s q u a r e f e e t , and S i s d i m e n s i o n l e s s s l o p e of t h e w a t e r s u r f a c e through t h e reach. Mud f l o w s or d e b r i s f l o w s i n s m a l l ,
steep-gradient
channels leave physical
e v i d e n c e t h a t may b e m i s i n t e r p r e t e d a s i n d i c a t i n g t h e p a s s a g e o f a f l o o d .
A
40
flood-peak d i s c h a r g e computed f r o m s u c h e v i d e n c e m i g h t b e e x t r e m e l y l a r g e , p o s s i b l y g r e a t e r t h a n t h e p o t e n t i a l f o r t h e b a s i n o r region.
Costa and J a r r e t t
(1981) d e s c r i b e how t o make t h e p r o p e r i n t e r p r e t a t i o n of t h e evidence. 3.1.7
Crest-stage
gaging s t a t i o n s
A c r e s t - s t a g e gaging s t a t i o n p r o v i d e s a r e c o r d of peak s t a g e s and t h e c o r r e s I t s purpose i s t o p r o v i d e d a t a f o r d e f i n i n g t h e
ponding d i s c h a r g e s a t a s i t e . flood-peak
f r e q u e n c y c h a r a c t e r i s t i c s where t h e c o s t o f c o l l e c t i n g a c o n t i n u o u s
s t r e a m f l o w r e c o r d cannot b e j u s t i f i e d .
A crest-stage
gage u s u a l l y c o n s i s t s of a 2-inch
t h e s t r e a m bank.
p i p e mounted v e r t i c a l l y on
The p i p e i s c a p p e d a t b o t h e n d s and c o n t a i n s a wooden s t a f f .
and i n t h e bottom cap, some ground cork.
I n t a k e h o l e s i n t h e bottom cap, and an
a i r h o l e i n t h e top cap, p e r m i t w a t e r t o e n t e r t h e p i p e a s t h e s t r e a m r i s e s . The c o r k f l o a t s on t h e w a t e r and some o f i t s t i c k s t o t h e s t a f f a t t h e c r e s t stage.
The gage i s i n s p e c t e d p e r i o d i c a l l y t o r e c o r d t h e c r e s t s t a g e ,
the staff,
t o clean
and t o r e p l e n i s h t h e cork.
Crest-stage
gages a r e u s u a l l y l o c a t e d where a s t a g e - d i s c h a r g e
computed from channel c h a r a c t e r i s t i c s , a r e a c h s u i t a b l e f o r step-backwater
r e l a t i o n can be
u s u a l l y above a b r i d g e o r c u l v e r t ,
analysis.
F i g u r e 3.21
o r on
shows a c r e s t - s t a g e
gage i n s t a l l a t i o n on a n ephemeral s t r e a m i n South Dakota. Data produced by c r e s t - s t a g e
gaging s t a t i o n s u s u a l l y a r e l i m i t e d t o t h e
maximum s t a g e and d i s c h a r g e e a c h y e a r , a l t h o u g h a d d i t i o n a l p e a k s may b e r e corded. 3.1.8
Time of t r a v e l
Time of t r a v e l i s u s u a l l y c o n s i d e r e d t h e mean t r a v e l t i m e of w a t e r p a r t i c l e s f l o w i n g from one c r o s s s e c t i o n t o a n o t h e r , a t a g i v e n d i s c h a r g e .
I t i s much
l o n g e r t h a n t h e t i m e r e q u i r e d f o r a f l o o d wave t o p a s s t h r o u g h t h e same reach. E s t i m a t e s o f t h e r a t e o f movement o f w a t e r b o r n e p a r t i c l e s i n s t r e a m s a r e needed f o r d e f i n i n g t h e w a s t e - a s s i m i l a t i v e
c a p a c i t i e s of s t r e a m s and t o f o r e c a s t
t h e movement of a s l u g of contaminant such a s might r e s u l t from a n a c c i d e n t a l spill. Various h y d r o l o g i c t r a c e r s such a s s a l t , have been used.
radioisotopes,
and f l u o r e s c e n t d y e s
The d y e Rhodamine WT i s a p o p u l a r t r a c e r .
It is injected
i n s t a n t a n e o u s l y a t a s t r e a m c r o s s s e c t i o n and t h e dye c o n c e n t r a t i o n is m o n i t o r e d a s t h e dye c l o u d p a s s e s each of a s e r i e s of c r o s s s e c t i o n s .
Dye c o n c e n t r a t i o n
i s measured by a f l u o r o m e t e r which i s s e n s i t i v e t o c o n c e n t r a t i o n s a s low a s 0.05 p a r t s per billion.
F i g u r e 3.22
shows t h e measured c o n c e n t r a t i o n a t f o u r p o i p t s
on t h e M i s s i s s i p p i R i v e r r e s u l t i n g f r o m t h e i n j e c t i o n o f d y e a t B a t o n Rouge. The maximum c o n c e n t r a t i o n d e c r e a s e s and t h e l o n g i t u d i n a l d i s p e r s i o n i n c r e a s e s w i t h d i s t a n c e downstream. l e a d i n g edge,
Time o f t r a v e l c a n b e e x p r e s s e d a s t i m e f o r t h e
t h e peak c o n c e n t r a t i o n , o r t h e l a s t d e t e c t a b l e dye t o p a s s a g i v e n
41
Fig. 3.21.
Crest-stage gage installation.
r B A T O N ROUGE
k
Q: 6700 M3/5EC.
I00 KM 147
20
KM
40 60 80 HOURS AFTER DYE RELEASE
202 KM (NEW ORLfANS)
100
I
Fig. 3.22. Distribution of dye concentration with time at midstream sampling points, Mississippi River, Louisiana, September, 1965 (From Wilson, 1968).
42 point.
A l l t h r e e t i m e s may b e n e e d e d f o r some p r o b l e m s .
D e t a i l s of time-of-
t r a v e l m e a s u r e m e n t s a r e g i v e n b y Hubbard a n d o t h e r s (1982).
See a l s o White
(1978) on d i l u t i o n gauging. t r a v e l i s g r e a t l y increased a s stream discharge i s decreased.
Time o f
Buchanan (1964) showed t h a t t r i p l i n g t h e d i s c h a r g e of Swatara Creek, Pa. reduced t h e t r a v e l t i m e about h a l f . r e a c h of S t .
Mary's
River,
T a b l e 3.1 s h o w s t r a v e l t i m e s t h r o u g h a 14.4 m i Indiana f o r a range i n discharge,
a s given by
Eikenberry and Davis (1976). TABLE 3 . l T r a v e l time v e r s u s d i s c h a r g e Discharge
T r a v e l time ( h o u r s )
cfs
% mean
22 120 620 810 1220
4.6 25 130 170 255
3.1.9
l e a d i n g edge
peak
105 33 .o 13.8 12.0 10.8
1 30 40 .O 16.8 14.8 12 .o
Sediment t r a n s p o r t
Sediment-laden
w a t e r i s n o t o n l y u n s u i t a b l e f o r many u s e s w i t h o u t t r e a t m e n t ,
b u t i t a l s o d e p o s i t s s e d i m e n t i n c h a n n e l s , c a n a l s , and r e s e r v o i r s .
Thus, de-
s i g n e r s and o p e r a t o r s of w a t e r p r o j e c t s need i n f o r m a t i o n on t h e amounts and t i m e d i s t r i b u t i o n of sediment t r a n s p o r t e d so a s t o minimize t h e d e t r i m e n t a l e f f e c t s . Sediment i s t r a n s p o r t e d by a s t r e a m a s suspended sediment, which i s c o n t i n u a l l y i n suspension, and a s bed l o a d which moves by r o l l i n g , ing along t h e bottom.
sliding,
or bound-
The a m o u n t o f s e d i m e n t b e i n g t r a n s p o r t e d i s h i g h e s t
d u r i n g a p e r i o d of f l o o d r u n o f f because of t h e e r o s i o n produced by t h e c a u s a t i v e r a i n f a l l and because of t h e h i g h e r v e l o c i t i e s and t u r b u l e n c e i n t h e channels.
A sediment-discharge
measurement,
and a c o n c u r r e n t w a t e r - d i s c h a r g e
ment, p r o d u c e d a t a from w h ich t h e f o l l o w i n g c a n be o b t a i n e d :
measure-
mean s u s p e n d e d
s e d i m e n t c o n c e n t r a t i o n , p a r t i c l e s i z e d i s t r i b u t i o n , s p e c i f i c g r a v i t y of t h e suspended sediment, t e m p e r a t u r e of t h e sediment-water m i x t u r e , w a t e r d i s c h a r g e , and t h e d i s t r i b u t i o n of flow i n t h e s t r e a m c r o s s s e c t i o n .
In a sediment-discharge
measurement water-sediment
selected v e r t i c a l s i n the cross section.
samples a r e c o l l e c t e d a t
The s a m p l e a t e a c h v e r t i c a l i s ob-
t a i n e d a s t h e s a m p l e r (Fig. 3.23) i s lowered t o t h e streambed and r a i s e d t o t h e s u r f a c e a t a uniform r a t e or, a l t e r n a t i v e l y , by c o l l e c t i n g samples a t s e l e c t e d points in the vertical. water-discharge
Laboratory analyses of t h e samples a r e used w i t h t h e
measurement t o p r o d u c e t h e d e s i r e d i n f o r m a t i o n .
g i v e n by Vanoni (1975, p. 317-349)
On s m a l l ,
Details are
and by Guy and Norman (1976)
f l a s h y streams n e a r l y a l l t h e sediment i s transported during t h e
s h o r t p e r i o d s of h i g h d i s c h a r g e .
Because t h e s e f l o o d p e r i o d s a r e r a r e l y known
43
F i g . 3.23.
Sediment sampler.
i n advance, a u t o m a t i c sampling equipment h a s been developed.
T h i s may b e a
s e r i e s of c o n t a i n e r s a t d i f f e r e n t e l e v a t i o n s f o r c a t c h i n g samples a s t h e s t r e a m r i s e s , or a pumping s a m p l e r p r o g r a m m e d t o t a k e s a m p l e s a t s e l e c t e d i n t e r v a l s according t o stream stage. Records o f sediment d i s c h a r g e o v e r a c o n s i d e r a b l e p e r i o d o f t i m e a r e needed t o d e f i n e i t s v a r i a t i o n w i t h s t r e a m f l o w and w i t h seasons, and t o d e f i n e t h e mean annual l o a d of sediment t r a n s p o r t e d .
If a d a i l y r e c o r d i s d e s i r e d , one or more d e p t h - i n t e g r a t e d
samples a r e t a k e n
e a c h d a y a t one v e r t i c a l : t n e s e a r e s u p p l e m e n t e d by p e r i o d i c , m o r e - d e t a i l e d suspended-sediment
measurements.
The d a i l y measured c o n c e n t r a t i o n s a r e p l o t t e d
on a c h a r t of gage h e i g h t a g a i n s t t i m e ( u s u a l l y t h e one from t h e analog r e c o r d e r a t t h e stream-gaging
s t a t i o n ) and t h e graph of s e d i m e n t c o n c e n t r a t i o n i s drawn
between observed p o i n t s u s i n g t h e s t a g e graph a s a guide. t i o n graph and t h e s t r e a m f l o w record, ( P o r t e r f i e l d , 1972).
From t h e concentra-
t h e d a i l y sediment l o a d can be computed
P a r t o f a p u b l i s h e d s e d i m e n t r e c o r d i s shown i n F i g u r e
3.24. The t o t a l suspended sediment l o a d f o r a y e a r c a n be approximated from occas i o n a l s e d i m e n t measurements by u s e of a s e d i m e n t - t r a n s p o r t d u r a t i o n curve.
curve and a flow-
The f o r m e r i s a p l o t o f s e d i m e n t d i s c h a r g e a g a i n s t s t r e a m
d i s c h a r g e ( F i g . 3.25) and t h e l a t t e r s h o w s t h e d i s t r i b u t i o n o f d a i l y s t r e a m d i s c h a r g e s during t h e y e a r (Chapter 5 ) .
The d u r a t i o n c u r v e i s d i v i d e d i n t o
i n t e r v a l s of t i m e and t h e mean d i s c h a r g e f o r e a c h i n t e r v a l i s determined.
This
d i s c h a r g e i s used t o d e f i n e t h e sediment t r a n s p o r t f o r t h a t i n t e r v a l of time. The a n n u a l s e d i m e n t d i s c h a r g e i s t h e sum f o r a l l o f t h e i n t e r v a l s . (1963) and,
f o r a n example,
See C o l b y
Simmons (1976).
The m e a s u r e m e n t s and t h e c o m p u t e d s e d i m e n t l o a d s d e s c r i b e d a b o v e a r e o f suspended sediment.
T o t a l sediment l o a d i n c l u d e s t h e bed l o a d which i s u s u a l l y
44
11477000 SUSPENDED-SEDIMENT
EEL RIVER AT SCOTIA, CA--Continued
OlSCtlAHGE ITONS/OAY), WATER YEAR 0CTlJt)ER 1979 TO SCPTEM~CF? 1980
OCTOBER
NOVEMBER
ME.M MEAN
COiCENTRATlDN IYGILJ
DISCHARGE DAY
ICFSL
I
106
L
100 96 91 93
3 4
5 b
7 8
9 10
11
12 1>
ZY
30 31 TOTAL
-26
I
.25 .50
2
3 3 3 3 3
133 156 169 348 984
26 27 28
1
98 96 99
16 17 18 19
21 22 23 24 25
.29 .27
2 2
123
20
I 1
93 94 94 V6 96
1* 15
.50 .5L -76 .78 .7e
3 3 3
I21
1
2 2 5 20
2400 2540 2e20
85 68 125 234 1740
472U
23000 20600 6580 3700 2540 1930
1150 220
1610
16
75726
---
10
35 16
Fig. 3.24. computed,
SEDIMENT DISCHARGE ITDNSIDAY)
.18 .18
.no
1.0 .9e -36 .e4 .91 4.7 53
MEAN DISCHARGE ICFSJ
MEAN CONCEN-
TRATION
1370 1340 SO50 11200 9270 14000
29000 15700 8960 6130
IMGILl
12100 6010
646 1260 340 I40 10
33509 10400U 116U
3150 2900 2600 2500 2310
4s 24 16
563 237 131
2150 2020 1910
11 LO
7s 6L
ieoo
1730
5
6890 lO8OOU 2140U 5230 2050
1 b50
4 5 4
5220
271 1160
20300
6460
55
b66
7340 z&eoo 19500 25500
910 502 560
196743.1
359090
I2
400 240
34700
--_
52 55 30 22 17
6510
12100 e440
3910 699 240 83 70
6180 5290 4550 3940 3440
30
4630 3660 3040 2610 22eo
26800 19000 12800 9510 7+m0
tCF5l
MEAN CONCENIRATION IMGILL
9 196
624
64000
DISCHAHGE ITONS/UAV)
MEAN DISCHARGE
e
390 160 90
952 3630 122000
DtCEMBER
SCDIMLNT
33
14400
339u
95Y 5370 67800 28000
174
e6e 786 369 234
158 102 7s 101
10
54 62
e
46
6
33 31 39 23
b
e
10
38
in 21 I7 52 293
inso
4540 8290 7980 30300 37600
220
518U
25700 15900 11300
355 215 105
24IU
8680
60
lllU
9660 38300
218
1410 7070
1310
144000
m600
643
6ezou
295 150 94 55
151ou
_--
--_-_
ITON51DAY)
10 14
e
1580 1540 1920 2860
StO 1MEN1 DISCHARGE
536503
I27 320 916 741
---
254350
7160 4740 14500
iseoo
24600 9230 3100
366945
Published sediment record. o r i s e s t i m a t e d a s a p e r c e n t a g e of t h e suspended load.
of bed load g e n e r a l l y a r e n o t r e l i a b l e .
Measurements
See Vanoni (1975).
I f a stseam f l o w s through a r e s e r v o i r most of t h e sediment w i l l b e t r a p p e d i n the reservoir.
The volume of m a t e r i a l d e p o s i t e d and i t s volume-weight
d e t e r m i n e d b y s u r v e y s a t i n t e r v a l s of s e v e r a l y e a r s.
can be
Of c o u r s e t h e r e s e r v o i r
outflow w i l l c o n t a i n some suspended m a t e r i a l ; t h u s t h e t o t a l i n f l o w load w i l l b e somewhat g r e a t e r than t h a t measured i n t h e r e s e r v o i r .
F i e l d measurement tech-
n i q u e s t o d e t e r m i n e t h e volume occupied by s e d i m e n t s d e p o s i t e d i n a r e s e r v o i r a r e d e s c r i b e d i n Vanoni (1975, p. 349-382).
Runoff and sediment y i e l d of ephe-
m e r a l s t r e a m s c a n b e o b t a i n e d f r o m d a t a c o l l e c t e d a t s m a l l r e s e r v o i r s a s des c r i b e d by P e t e r s o n (1962). 3.1.10
Chemical and b i o l o g i c a l q u a l i t y
Whether w a t e r i s c o n s i d e r e d of good or poor q u a l i t y depends on t h e use t o be made of it.
Drinking w a t e r should n o t c o n t a i n b a c t e r i a .
c e r t a i n m i n e r a l s , or d i s s o l v e d gases.
suspended m a t e r i a l s ,
Water f o r i r r i g a t i o n should c o n t a i n o n l y
45
100,000
I
I
I
40,000
10,000
4000
300 L 5000
I
10,000
I
I
20,000
50,000 100,000
DAILY MEAN WATER DISCHARGE, IN CFS
F i g . 3.25. Sediment-transport c u r v e f o r Sacramento R i v e r a t Sacramento. C a l i f o r n i a (From P o r t e r f i e l d , 1980). a l i m i t e d amount o f sodium and o f some o t h e r elements; and suspended sediment i s u n d e s i r a b l e because i t c l o g s t h e p i p e s and d i t c h e s . r e q u i r e w a t e r s o f v e r y s p e c i f i c c h e m i c a l content.
Some i n d u s t r i a l p r o c e s s e s Esthetically,
w a t e r i s con-
s i d e r e d good i f i t i s c l e a r ( h a s l i t t l e or no suspended or f l o a t i n g m a t e r i a l ) , h a s no c o l o r or odor, and s u p p o r t s f i s h and o t h e r b i o t a . Water q u a l i t y c a n be d e s c r i b e d i n two ways,
by i d e n t i f y i n g and q u a n t i f y i n g
the i n o r g a n i c and t h e o r g a n i c m a t e r i a l s i n t h e w a t e r , or by some measures o f t h e e f f e c t s of t h e s e m a t e r i a l s .
F o r example.
t h e c o n c e n t r a t i o n of d i s s o l v e d s o l i d s
is r e l a t e d t o t h e e l e c t r i c a l conductance: t h e t y p e s o f d i s s o l v e d s o l i d s d e t e r mine t h e pH,
a measure of hydrogen-ion
a c t i v i t y ; and t h e c o n c e n t r a t i o n of d i s -
s o l v e d oxygen is an i n d i c a t i o n of t h e b i o c h e m i c a l c o n d i t i o n of t h e water.
These
t h r e e i n d i c a t o r s p l u s t e m p e r a t u r e c a n b e m e a s u r e d i n t h e f i e l d a n d a r e good g e n e r a l measures o f w a t e r q u a l i t y .
But f o r c e r t a i n u s e s one needs t o know t h e
k i n d s a n d c o n c e n t r a t i o n s of t h e v a r i o u s d i s s o l v e d e l e m e n t s in t h e r a t e r . and
46
whether dangerous b a c t e r i a l or c h e m i c a l p o l l u t a n t s a r e p r e s e n t .
This informa-
t i o n i s o b t a i n e d by l a b o r a t o r y a n a l y s e s of samples o f w a t e r from t h e stream. D e t e r m i n a t i o n of w a t e r q u a l i t y i s a d e t a i l e d and s p e c i a l i z e d o p e r a t i o n a s i n d i c a t e d by t h e wide range of p h y s i c a l , chemical, b i o l o g i c a l , and r a d i o c h e m i c a l i n f o r m a t i o n p u b l i s h e d i n t h e a n n u a l w a t e r - d a t a r e p o r t s of t h e USGS f o r t h e
A purpose of t h e s e
N a t i o n a l S t r e a m - Q u a l i t y A c c o u n t i n g (NASQUAN) s t a t i o n s . NASQUAN s t a t i o n s i s t o m o n i t o r changes i n w a t e r q u a l i t y ,
consequently s p e c i f i c
conductance,
concentration a r e re-
pH.
water temperature,
corded continuously.
and dissolved-oxygen
T h i s d e t a i l i s n o t n e c e s s a r y on n a t u r a l ( u n p o l l u t e d )
w a t e r s whose c h a r a c t e r d o e s n o t c h a n g e a p p r e c i a b l y f r o m y e a r t o y e a r .
Hem
(1972. p. 40-50) d e s c r i b e s how e n v i r o n m e n t a l i n f l u e n c e s a f f e c t n a t u r a l w a t e r qua1 i ty. Methods f o r c o l l e c t i n g and a n a l y z i n g w a t e r - q u a l i t y o f t h i s book.
d a t a a r e beyond t h e scope
S e e Hem ( 1 9 7 2 , p. 60-68) f o r g u i d e l i n e s o f s a m p l i n g ; S k o u g s t a d
(1979) f o r d e t e r m i n a t i o n of i n o r g a n i c s u b s t a n c e s : B a r n e t t and M a l l o r y (1971) f o r d e t e r m i n a t i o n o f m i n o r e l e m e n t s ; G o e r l i t z and Brown ( 1 9 7 2 ) f o r m e t h o d s f o r a n a l y s i s o f o r g a n i c s u b s t a n c e s ; Greeson and o t h e r s (1977) for methods f o r coll e c t i o n and a n a l y s i s of a q u a t i c b i o l o g i c a l Thatcher, J a n z e r .
and m i c r o b i o l o g i c a l s a m p l e s ;
and Edwards (1977) f o r methods f o r d e t e r m i n a t i o n of r a d i o a c -
t i v e s u b s t a n c e s i n w a t e r ; and Stevens,
Picke,
and Smoot (1975) f o r measurement
of water temperature.
WEATHER OBSERVATIONS
3.2
The p r i n c i p a l w e a t h e r o b s e r v a t i o n s o f concern t o h y d r o l o g i s t s a r e p r e c i p i t a t i o n , t e m p e r a t u r e . and e v a p o r a t i o n from w a t e r s u r f a c e s . 3.2.1
.
Precipitation
A t most m e t e o r o l o g i c a l s t a t i o n s , t h e p r e c i p i t a t i o n i s caught i n a can and t h e c a t c h measured d a i l y .
The N a t i o n a l Weather S e r v i c e 8-inch nonrecording gage i s
shown i n F i g u r e 3.26.
D e t a i l s o f t h e gage and i n s t r u c t i o n s f o r making observa-
t i o n s a r e g i v e n by t h e N a t i o n a l Weather S e r v i c e (NWS, 1972). t a t i o n i s snow, t h e gage c a t c h may n o t be r e p r e s e n t a t i v e .
When t h e p r e c i p i -
Then a sample of snow
o n t h e g r o u n d i s o b t a i n e d b y i n v e r t i n g t h e c a n and c u t t i n g a v e r t i c a l s a m p l e which i s m e l t e d t o d e t e r m i n e t h e w a t e r c o n t e n t . Recording p r e c i p i t a t i o n gages commonly weigh t h e c a t c h and r e c o r d t h e cumulat i v e c a t c h on a n a n a l o g c h a r t or a s p u n c h e s a t s e l e c t e d i n t e r v a l s on a p a p e r tape. Data from t h e s e gages a r e commonly t a b u l a t e d a t h o u r l y i n t e r v a l s ; c a t c h e s a t s h o r t e r i n t e r v a l s c a n be o b t a i n e d most r e a d i l y from t h e d i g i t a l t a p e , l i m i t e d of c o u r s e by t h e punch i n t e r v a l . The t i p p i n g - b u c k e t r a i n g a g e , commonly u s e d i n h y d r o l o g i c s t u d i e s , i s a c t u a t e d by s m a l l i n c r e m e n t s o f r a i n ( u s u a l l y 0.01 i n c h e s i n U.S.). ments a r e r e c o r d e d on an analog c h a r t .
The i n c r e -
41
F i g . 3.26.
N a t i o n a l Weather S e r v i c e n o n r e c o r d i n g r a i n gage.
I n remote areas, p r e c i p i t a t i o n i s caught i n s t o r a g e gages, 8-inch cans of c o n s i d e r a b l e depth.
The c a n s a r e charged w i t h c a l c i u m c h l o r i d e t o m e l t snow and
t o prevent severe freezing of the catch.
O i l i s sometimes used t o reduce
The c a n i s u s u a l l y e l e v a t e d on a tower and
e v a p o r a t i o n between o b s e r v a t i o n s .
e q u i p p e d w i t h a s h i e l d to r e d u c e w i n d v e l o c i t y ( F i g . 3 . 2 7 ) . serviced a t i r r e g u l a r intervals,
Storage gages a r e
sometimes o n l y 3 o r 4 t i m e s a year.
Generally
o n l y s e a s o n a l o r annual p r e c i p i t a t i o n i s o b t a i n e d . The c a t c h o f a p r e c i p i t a t i o n g a g e d e p e n d s on i t s l o c a t i o n w i t h r e s p e c t t o trees, buildings,
and o t h e r o b s t r u c t i o n s .
A l o c a t i o n i s considered s a t i s f a c t o r y
i f t h e r e a r e no o b s t r u c t i o n s w i t h i n a n i n v e r t e d 45-degree However,
cone above t h e gage.
a gage l o c a t i o n may become u n s u i t a b l e because of t r e e growth o r b u i l d -
ing construction.
Gages on windy,
open a r e a s tend t o c a t c h t o o l i t t l e p r e c i p i -
tation. A l t h o u g h a p r e c i p i t a t i o n g a g e may c o l l e c t s a m p l e s r e p r e s e n t a t i v e o f t h e immediate l o c a l i t y ,
t h e r e c o r d a t t h e s i t e may n o t d e s c r i b e t h e p r e c i p i t a t i o n
p a t t e r n some d i s t a n c e away, e s p e c i a l l y i n mountainous country. N a t u r a l p r e c i p i t a t i o n may be a f f e c t e d by man's a c t i v i t i e s .
Smoke and o t h e r
a i r b o r n e e f f l u e n t s from i n d u s t r i a l a r e a s t e n d t o i n c r e a s e p r e c i p i t a t i o n downwind, and l a r g e urban a r e a s become h o t t e r than undeveloped a r e a s and induce more thunderstorms.
I n addition t o inadvertent modifications.
enhance p r e c i p i t a t i o n i n some regions.
3.2.2
c l o u d s a r e seeded t o
See Chapter .lo.
Evaporation from w a t e r s u r f a c e s
E v a p o r a t i o n i s commonly m e a s u r e d i n a n o p e n pan.
The w i d e l y - u s e d W e a t h e r
B u r e a u C l a s s A p a n i s 4 f t i n d i a m e t e r and 1 0 i n c h e s d e e p ( F i g . 3 . 2 8 ) .
It i s
48
Fig. 3 . 2 1 .
S t o r a g e r a i n gage w i t h s h i e l d .
F i g . 3.28.
Evaporation pan.
f i l l e d t o a d e p t h of 8 inches and t h e d e p t h i s measured d a i l y w i t h a hook gage. Evaporation i s t h e d i f f e r e n c e between r e a d i n g s , during the interval. refilled.
a d j u s t e d f o r any p r e c i p i t a t i o n
When t h e w a t e r l e v e l h a s r e c e d e d a n i n c h ,
t h e pan i s
An e v a p o r a t i o n s t a t i o n i n c l u d e s r a i n a n d t e m p e r a t u r e g a g e s . a n d
sometimes a n anemometer f o r measuring r i n d .
49 The r a t e o f e v a p o r a t i o n f r o m a p a n i s g r e a t e r t h a n t h a t f r o m a l a k e o r r e s e r v o i r because of t h e h e a t t r a n s f e r r e d t h r o u g h t h e pan w a l l s .
Although t h e
"pan c o e f f i c i e n t " t o a d j u s t annual pan e v a p o r a t i o n t o annual l a k e e v a p o r a t i o n i s c o n s i d e r e d t o b e a b o u t 0.7,
f o r s h o r t e r p e r i o d s i t v a r i e s c o n s i d e r a b l y and
cannot b e d e f i n e d re1 iably. O t h e r ways o f m e a s u r i n g w a t e r - s u r f a c e e n e r g y b u d g e t , and m a s s t r a n s f e r .
evaporation include w a t e r budget,
These methods r e q u i r e c o n s i d e r a b l e d a t a
c o l l e c t e d on a r e s e r v o i r f o r a y e a r or more. Water budget i s t h e s i m p l e s t . s t o r a g e a r e measured.
Inflow, outflow,
Water-surface
the o n l y unknown i n t h e water-budget
rainfall,
and change i n
e v a p o r a t i o n c a n be computed because i t i s equation.
R e l i a b i l i t y of t h e r e s u l t de-
p e n d s on t h e m a g n i t u d e of t h e e v a p o r a t i o n r e l a t i v e t o t h e m a g n i t u d e s o f t h e o t h e r e l e m e n t s : a s m a l l d i f f e r e n c e between two l a r g e numbers, some e r r o r ,
each s u b j e c t t o
tends t o be unreliable.
The e n e r g y - b u d g e t e q u a t i o n i n c l u d e s t h e e n e r g y i n p u t s a n d o u t p u t s , a l l o f which,
except evaporation,
c a n b e measured.
Data c o l l e c t i o n and a n a l y s i s a r e
d e s c r i b e d i n a c o m p r e h e n s i v e i n t e r a g e n c y p r o j e c t r e p o r t (U.S. Geol. S u r v e y , 1954). The m a s s - t r a n s f e r
E = Np ( e o
-
equation is
e,)
where E i s e v a p o r a t i o n , N i s t h e mass t r a n s f e r c o e f f i c i e n t .
p i s wind speed, and
eo and ea a r e s a t u r a t i o n vapor p r e s s u r e and a c t u a l vapor p r e s s u r e r e s p e c t i v e l y . M e a s u r e m e n t s o f w i n d s p e e d , and w a t e r and a i r t e m p e r a t u r e a r e r e q u i r e d .
The
c o e f f i c i e n t , N, m u s t b e d e r i v e d f r o m e v a p o r a t i o n m e a s u r e d b y a n o t h e r m e t h o d (See T u r n e r , 1966). 3.2.3
Temperature
D a i l y maximum and minimum a i r t e m p e r a t u r e s a r e o b t a i n e d a t many l o c a t i o n s by t h e N a t i o n a l Weather Service.
D e t a i l s of c o l l e c t i o n a r e g i v e n i n t h e i r Observ-
i n g Handbook No. 2 (NWS, 1 9 7 2 ) . 3.2.4
Snow accumulation
Snow f a l l i s r e p o r t e d a t w e a t h e r s t a t i o n s b u t t h e a c c u m u l a t i o n of snow on t h e ground o r d i n a r i l y is not.
Snow on t h e ground i s p o t e n t i a l r u n o f f which can be
f o r e c a s t i f t h e amount and c h a r a c t e r of t h e snowpack a r e known. t h e snowpack,
Measurement of
c a l l e d snow surveying, c o n s i s t s of measuring t h e d e p t h and w a t e r
c o n t e n t a t snow c o u r s e s ( F i g . 3.29).
A t u b e i s u s e d . t o e x t r a c t c o r e s of snow
f r o m t h e p a c k a t d e s i g n a t e d d i s t a n c e s a l o n g t h e l i n e m a r k i n g t h e snow c o u r s e . D e p t h is r e c o r d e d a t e a c h s a m p l i n g p o i n t and t h e c o r e i s w e i g h e d t o d e t e r m i n e t h e w a t e r c o n t e n t ( F i g . 3.30). D e p t h s and w a t e r c o n t e n t s a r e a v e r a g e d o v e r a l l
F i g . 3.29. Snow s u r v e y o r s a t a marker d e s i g n a t i n g o n e end o f a snow c o u r s e ( U . S . S o i l Conservation S e r v i c e ) .
Snow surveying: I n s e r t i n g t h e tube, reading t h e depth. and weighing F i g . 3.30. the tube w i t h the snow c o r e i n i t (U.S. S o i l Conservation S e r v i c e ) .
51 the sampling points to give the result.
Snow surveys are usually made near the
first of each of the spring months. In mountainous regions travel to a snow course by skis or snowshoes is time consuming;
if by helicopter the travel is expensive.
The number of visits can
be reduced by using a snow pressure pillow which is a flat flexible container filled with anti-freeze.
The pillow indicates the snow-water equivalent by the
pressure of the snow pack on the pillow.
Pressure readings are transmitted by
radio or satellite and transformed to water content by a previous calibration of the pillow (Ballison, 1981).
Soil Conservation Service (1972) describes snow-
surveying procedures in detail.
Use of snow survey results is described in
Chapter 11. 3.3
BASIN CHARACTERISTICS Knowledge of drainage basin characteristics is useful in understanding a
streamflow record and is a requirement in some methods of estimating flow c h a r acteristics at nngaged sites. Size of drainage area is the most common basin characteristic. basin is delineated on topographic maps and its area measured.
The drainage
In arid or
semiarid regions a major drainage basin may encompass an area which has no surface drainage; the contributing drainage area excludes that interior area. Drainage area may not be a good indicator of streamflow if the topographic and the ground-water divides are not coincident.
This disparity cannot be
easily quantified but its recognition will help to understand the measured flows or to estimate flows at ungaged sites. Basin topography influences runoff in several ways
-
steep slopes concentrate
the rainfall quickly and result in high flood discharges; flat slopes result in slow runoff, increased gronnd-water recharge, increased evapotranspiration, and consequently in decreased total runoff.
Basin topography is commonly quantified
by some approximation of the slope of the main channel.
An additional index is
the percentage of lakes and swamps in the basin. Vegetative cover can sometimes be quantified as the percentage of the area forested, or under cultivation.
In a natural basin, the vegetative cover de-
pends on climate and on soil characteristics. Soil characteristics determine the rate of infiltration of rainfall to the soil and thus affect the rate and amount of runoff.
The Soil Conservation
Service (1971) classifies each soil into one of four ranges according to infiltration rate. The geology of a basin affects the rate of runoff',
the losses or gains along
the channels, and especially the low-flow characteristics. Knowledge of the geology as i t affects the water resource may be very useful even though i t is only qualitative.
52 P r e c i p i t a t i o n usually i s considered a basin characteristic. p r e s s e d a s mean annual p r e c i p i t a t i o n ,
t h e 12-hour s t o r m p r e c i p i t a t i o n a t 50-year a p p r o p r i a t e t o a p a r t i c u l a r problem.
I t c a n b e ex-
some measure of s t o r m i n t e n s i t y such a s r e c u r r e n c e i n t e r v a l , or i n o t h e r ways
Likewise,
monthly mean t e m p e r a t u r e s a r e
b a s i n c h a r a c t e r i s t i c s in t h a t t h e y a r e i n d i c a t o r s of p o t e n t i a l e v a p o r a t i o n and t r a n s p i r a t i o n r a t e s and of whether p r e c i p i t a t i o n w i l l be snow and whether i c e w i l l form i n s t r e a m s .
Stream channel geometry,
esthetic character,
stability,
and s u i t a b i l i t y f o r
f i s h a n d w i l d l i f e h a b i t a t a r e useful d e s c r i p t o r s a l t h o u g h q u a n t i f i c a t i o n i s somewhat s u b j e c t i v e . 3.4
TRANSMISSION OF HYDROLOGIC DATA Conventionally, t h e s t a g e d a t a observed o r recorded a t a gaging s t a t i o n i s
o b t a i n e d when t h e hydrographer v i s i t s t h e s t a t i o n , a t monthly or l o n g e r i n t e r vals.
T h i s frequency of c o l l e c t i o n i s adequate i f t h e d a t a a r e t o be used f o r
w a t e r r e s o u r c e s t u d i e s or f o r p r o j e c t design.
But f o r w a t e r management p u r p o s e s
t h e d a t a may be needed immediately, or i n s o - c a l l e d " r e a l time."
B a s i c e l e m e n t s f o r a s a t e l l i t e d a t a - c o l l e c t i o n s y s t e m (From U.S. F i g . 3.31. Geological Survey). V a r i o u s s y s t e m s f o r t r a n s m i t t i n g d a t a d a i l y or m o r e f r e q u e n t l y u t i l i z e phone l i n e s o r r a d i o s .
Xn t h e l a s t few y e a r s automated s a t e l l i t e t e l e m e t r y h a s
become a p r a c t i c a l means of p r o v i d i n g water-data t i o n w i t h i n t h e t i m e frame needed.
u s e r s w i t h h y d r o l o g i c informa-
S a t e l l i t e data-collection
s y s t e m s use e a r t h -
o r b i t i n g s a t e l l i t e s t o r e l a y d a t a from c o l l e c t i o n s i t e s t o r e c e i v i n g s t a t i o n s . The system c o n s i s t s of s e n s o r s ,
small radios called data-collection
platforms.
53 satellites, earth receiving sites, and a data processing and distribution system.
See Shope and P a u l s o n (1981) and F l a n d e r s (1981).
T h e system is illus-
trated in Figure 3.31. REFERENCES Bailey, J.F. and Ray, H.A., 1966, Definition of stage-discharge relation in natural channels by step-backwater analysis: U.S. Geol. Survey Watersupply Paper 1869-A, 24 p. Barnes, H.H., Jr., 1967, Roughness characteristics of natural channels: Geol. Survey Water-Supply Paper 1849, 213 p. Barnes, H.H., Jr. and Davidian. J., 1978, Indirect methods Herschy, ed., New York. John Wiley and Sons.
U.S.
Hydrometry, R.W.
Barnett, P.R. and Mallory, E.C., Jr., 1971, D e t e r m i n a t i o n of m i n o r elements in w a t e r b y e m i s s i o n spectroscopy: U.S. Geol. Survey Techniques of WaterResources Investigations, Book 5, Chapter A2, 31 p. Bodhaine, G.L., 1968, M e a s u r e m e n t of p e a k discharge at culverts b y indirect methods: U.S. Geol. Survey Techniques of Water-Resources Investigations, B o o k 3, Chapter A3. 60 p. Buchanan, T.J., 1964, Time of travel of soluble contaminants in streams: of Sanitary Engineering Division, ASCE, Vol. 90. No. SA3, 12 p.
Jour.
Buchanan, T.J. and Somers, W.P., 1969, Discharge m e a s u r e m e n t s at gaging stations: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A8, 6 5 p. Colby. B.R., 1963, P l u v i a l s e d i m e n t s - A s u m m a r y of source, transportation, deposition, and m e a s u r e m e n t of sediment discharge: U.S. Geol. Survey Bull e t i n 1181-A, 4 7 p. 1981, Debris f l o w s i n s m a l l m o u n t a i n stream Costa, J.E. and Jarrett, R.D., channels of Colorado and their hydrologic implications: Bulletin of the Assoc. of Engineering Geologists, Vol. xviii, No. 3, August 1981. Dalrymple, T. and Benson, M.A., 1967, M e a s u r e m e n t of p e a k discharge b y the slope-area method: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A2, 12 p. Davidian, J., 1984, C o m p u t a t i o n of water-surface profiles: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapt. Al5. 1976, A technique for estimating t i m e of Eikenberry, S.E. and Davis, L.G., travel of water in Indiana streams: U.S. Geol. Survey Water Resources Investigations 9-76. 3 9 p. Flanders, A.F., 1981, Hydrological data transmission: W o r l d Meteorological Organization, Operational Hydrology Report No. 14, WMO-No. 559, 3 4 p., Geneva, Switzerland. Goerlitz, D.F. and Brown, E., 1972, M e t h o d s for analysis of organic substances in water: U.S. Geol. Survey Techniques of Water-Resources Investigations, B o o k 5, Chapter A3, 40 p. Green, M.J. and Herschy, R.W.. 1978, N e w methods & J Hydrometry, R.W. ed., Chichester, W, John Wiley and Sons.
Herschy,
Greeson, P.E.. Elke, T,A., Irwin. G.A., Lium, B.W., and Slack, K.V., 1977, Methods for collection and analysis of aquatic biological and microbiological samples: U.S. Geol. Survey Techniques o f W a t e r Resources Investigations, B o o k 5, Chapter A4, 3 3 2 p.
54 Guy, H.P. and Norman, V.W.. 1976, Field methods for measurement of fluvial sediment: U.S. Geol. Survey Techniques of Wa t er-Resources Investigations, Book 3. Chapter C2, 5 9 p. Hem. J.D.. 1972. Study and interpretation of the chemical characteristics of natural water: U.S. Geol. Survey Water-Supply Paper 1473, Second Edition, 363 p. Hubbard. E.F.. Kilpatrick, F.A., Martens, L.A.. and Wilson, J.F.. Jr., 1982, Measurement of time of travel and dispersion in streams by dye tracing: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3. Chapt. A9. 44 p. Hulsing. H., 1968, Measurement of peak discharge at dams by indirect methods: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A5. 29 p. Kennedy, E.J., 1983. Discharge ratings at gaging stations: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapt. A10. Kilpatrick. F.A. and Cobb. E.D.. 1984. Measurement of discharge using tracers: U . S . Geol. Survey Open-File Rept. 84-136, 73 p. Laenen, A. and Smith, W., 1982. Acoustic systems for the measurement of streamflow: U.S. Geol. Survey Open-File Rept. 82-329, 45 p. Matthai. H.F.. 1968, Measurement of peak discharge a t width contractions by indirect methods: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A4. 44 p. NWS,
1972, Substation observations, National Weather Service Observing Handbook No. 2: National Weather Service, Data Aquisition Division, Office of Meteorological Operations, Silver Spring, Md.
Peterson, H.V.. 1962. Hydrology of small watersheds in western States: Geol. Survey Water Supply Paper 1475-1, 137 p.
U.S.
Porterfield, G., 1972. Computation of fluvial-sediment discharge: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3 . Chapter C3. 66 P. Rallison. R.E.. 1981, Automated system for collecting snow and related hydrological data in mountains of western United States: Hydrological Sciences Bulletin, Vol. 26, No. 1, March 1981, p 83-89. Rantz, S.E.. 1982. Measurement and computation of streamflow: U.S. Water-Supply Paper 2175. 631 p.
Geol. Survey
Riggs. H.C., 1976, A simplified slope-area method for estimating flood discharges in natural channels: U.S. Geol. Survey Jour. of Research, 4 (3). p 285-291. Shope. W.G. and Paulson, R.W., 1981, Data collection via satellite for water management: Transportation Engineering Journal, ASCE, Vol. 107, No. TE4, July 1981. p 445-455. Simmons, C.E., 1976. Sediment characteristics of streams in the eastern Piedmont and western Coastal Plain regions of North Carolina: U.S. Geol. Survey Water-Supply Paper 1798-0. p 10-14. Skougstad. M.W.. Ed., 1979, Methods for determination of inorganic substances in water and fluvial sediments: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 5 . Chapter Al. 626 p. Smith, W., Hubbard, L.L.. and Laenen. A., 1971, The acoustic streamflow-measuring system on Columbia River at The Dalles. Oregon: U.S. Geol. Survey OpenFile Report, Portland, Oregon.
55 Smoot, G.F. and Novak, C.E.. 1969, M e a s u r e m e n t of discharge b y the moving-boat method: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter All, 2 2 p. Soil Conservation Service, 1971, Hydrology, SCS National Engineering Handbook, Section 4: Soil Conservation Service, U.S. Dept. of Agriculture, Washington, D.C. Soil Conservation Service, 1972, Snow survey and water-supply forecasting: SCS National Engineering Handbook., Section 22, Soil Conservation Service. U.S. Dept. of Agriculture, Washington. D.C. Stevens. H.H.. Jr., Ficke, J.F., and Smoot. G.F., 1975. W a t e r temperature influential factors, field measurement. and data presentation: U.S. Geol. 65 Survey Techniques of Water-Resources Investigations, Book 1, Chapter D1, P. Janzer, V.J., and Edwards. K.W.. 1977. Methods for determination Thatcher. L.L., of radioactive substances in water and fluvial sediments: U.S. Geol. Survey 95 p. Techniques of Water-Resources Investigations, Book 5. Chapter AS, Turner, J.F., Jr., 1966, Evaporation study i n a h u m i d region, Lake Michie, North Carolina: U.S. Geol. Survey Prof. Paper 272-6. U.S.
Geological Survey, 1954. W a t e t l o s s investigations Volume 1 - Lake Hefner studies: U.S. Geol. Survey Prof. P a p e r 269.
Ed., 1975, Sedimentation engineering: Vanoni, V.A.. Practice, 745 p.
ASCE Manual of Engineering
White, K.E., 1978, Dilution methods & H y d r o m e t r y by R.W. Pork, John Wiley and Sons.
Herschy, Ed.:
New
Wilson, J.F., Jr.. 1968, Time of travel measurements and other applications of dye tracing: International Assoc. of Scientific Hydrology Publ. NO. 76, Bern. p 252-262. WMO, 1980, Manual on stream gauging: World Meteorological Organization Operational Hydrology Report No. 13. W M O - No. 519. Vol. 2, Geneva. Switzerland.
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51
Chapter 4
STAT1STICS 4.1
INTRODUCTION Some u n d e r s t a n d i n g o f t h e p r i n c i p l e s of s t a t i s t i c s i s needed t o a n a l y z e and
i n t e r p r e t hydrologic d a t a properly.
I n t h i s chapter p r i n c i p l e s a r e described
without use of h i g h e r m a t h e m a t i c s b u t w i t h t h e a s s u m p t i o n t h a t t h e r e a d e r h a s some f a m i l i a r i t y w i t h s t a t i s t i c s terminology, mentary p r o b a b i l i t y . inference,
c o m p u t a t i o n procedures,
and e l e -
Coverage i s l i m i t e d t o f r e q u e n c y c u r v e s , s t a t i s t i c a l
and r e g r e s s i o n and c o r r e l a t i o n .
S t a t i s t i c a l i n t e r p r e t a t i o n s a r e v a l i d o n l y t o t h e e x t e n t t h a t t h e d a t a and the p h y s i c a l c o n d i t i o n s conform t o t h e a s s u m p t i o n s r e q u i r e d by t h e s t a t i s t i c a l method used.
Many s t a t i s t i c a l p r o c e d u r e s r e q u i r e t h e assumption t h a t t h e d a t a
a r e n o r m a l l y d i s t r i b u t e d , b u t t h e t y p e s of d a t a used i n hydrology commonly a r e n o t n o r m a l l y d i s t r i b u t e d , and some have no p r o b a b i l i t y d i s t r i b u t i o n a t a l l .
The
h y d r o l o g i s t must s e l e c t p r o c e d u r e s most n e a r l y s u i t a b l e t o t h e c h a r a c t e r of h i s d a t a and must i n t e r p r e t t h e r e s u l t s a c c o r d i n g l y . This c h a p t e r p r o v i d e s t h e b a s i c s t a t i s t i c a l t o o l s , b o t h a n a l y t i c a l and graphical,
and c o n c l u d e s w i t h a d i s c u s s i o n of t h e c h a r a c t e r i s t i c s of h y d r o l o g i c d a t a .
Applications t o s p e c i f i c problems a r e given i n l a t e r chapters.
Most o f t h e
m a t e r i a l i n t h i s c h a p t e r i s t a k e n from USGS p u b l i c a t i o n s a u t h o r e d by Riggs. 4.2
FREQUFNCY CURVES
4.2.1
Distributions
T h e concept of a p o p u l a t i o n of o b j e c t s having a d i s t r i b u t i o n of s i z e s (or of some o t h e r c h a r a c t e r i s t i c ) i s b a s i c t o t h e s t a t i s t i c a l method.
It i s n o t p o s s i -
b l e t o c o l l e c t enough d a t a t o d e f i n e a f r e q u e n c y d i s t r i b u t i o n e x a c t l y , b u t t h e e x i s t e n c e of a p a r t i c u l a r one can be proven t o t h e d e s i r e d degree of c o n f i d e n c e by r e p e a t i n g an experiment many times. K e n d a l l ( 1 9 5 2 , p. 2 3 ) r e p o r t e d t h e r e s u l t s o f a d i c e - t o s s i n g e x p e r i m e n t i n which 1 2 d i c e w e r e t o s s e d s i m u l t a n e o u s l y and t h e number of s i x e s was r e c o r d e d f o r each t o s s . 4.1.
The d i c e were t o s s e d 4,096 t i m e s w i t h t h e r e s u l t s shown i n Table
A l s o shown a r e t h e r e l a t i v e f r e q u e n c i e s c o m p u t e d f r o m t h e e x p e r i m e n t a l
r e s u l t s and t h e t h e o r e t i c a l r e l a t i v e f r e q u e n c i e s c o m p u t e d f r o m t h e b i n o m i a l distribution.
The c l o s e a g r e e m e n t b e t w e e n t h e t h e o r e t i c a l a n d e x p e r i m e n t a l
frequencies indicates t h a t the binomial d i s t r i b u t i o n i s applicable t o t h i s problem. The b i n o m i a l d i s t r i b u t i o n i s a d i s c r e t e d i s t r i b u t i o n , t h a t i s , i t c a n t a k e v a l u e s o n l y a t s p e c i f i c p o i n t s along a s c a l e .
In t h e d i c e - t o s s i n g experiment,
58
TABLE 4.1 R e s u l t s of d i c e - t o s s i n g
experiment ( A f t e r Kendall,
No. of sixes
Belat ive f requency
Frequency
441 1,145 1.181 796 380 115 24 8 4,096
0 1
2 3 4 5 6
I and over Total
0.109 .280 .288 .194
.093 .028 .006 .002
1.oo
1952)
Theoretical relative frequency
0.112 .269 .296 .197 -08 9 .029
.001
.001 1.oo
i t i s p o s s i b l e t o o b t a i n an i n t e g e r number of s i x e s o n l y ; t h e r e i s no such t h i n g
a s 5.5
o r 3.2 s i x e s .
More commonly,
a v a r i a b l e may t a k e any v a l u e along a s c a l e .
and i t s d i s t r i b u t i o n a r e known a s continuous.
Such a v a r i a b l e
A v a r i a b l e may be c l a s s i f i e d a s
continuous i f i t can t a k e any v a l u e along a s c a l e even though t h e l i m i t a t i o n s of measurement r e s t r i c t t h e o b s e r v a t i o n s t o d i s c r e t e values.
This condition e x i s t s
w i t h most n a t u r a l phenomena.
To a i d i n u n d e r s t a n d i n g a d i s t r i b u t i o n , c o n s i d e r 1,000 t r e e - r i n g ranging in s i z e from 2 t o 240. a histogram,
size,
0
60
i n c r e m e n t s of
o r frequency d i s t r i b u t i o n , i s o b t a i n e d (Fig. 4.1.
120 WIDTH INDEX
F i g . 4.1.
I f t h e s e a r e grouped by s i x - u n i t
180
indices
left).
The
240 WIDTH INDEX
Histogram and p r o b a b i l i t y - d e n s i t y c u r v e of 1000 t r e e - r i n g
indices.
i r r e g u l a r i t y of t h e p r o f i l e of t h i s d i s t r i b u t i o n i s due t o t h e s m a l l ( i n a s t a t i s t i c a l s e n s e ) number of i n d i c e s used i n i t s p r e p a r a t i o n . number used,
The g r e a t e r t h e
t h e smoother would be t h e p r o f i l e of t h e frequency d i s t r i b u t i o n .
I f t h e number of o b s e r v a t i o n s a p p r o a c h e s i n f i n i t y a n d t h e s i z e i n c r e m e n t approaches zero, t h e enveloping l i n e of t h e frequency d i s t r i b u t i o n w i l l approach a smooth curve.
Then i f t h e o r d i n a t e v a l u e s a r e d i v i d e d by a number such t h a t t h e
59
area under the curve becomes one, the resulting curve is a probability density curve. or probability distribution, as shown on the right of Figure 4.1.
The
process just described requires the additional assumption that the variable can take any value within the range, that the variable is continuous, not discrete. A theoretical probability distribution describes the relation between size
(or some other characteristic) and probability.
For this relation to be valid,
the individuals must occur randomly or be drawn randomly.
The size of any
individual drawn should not depend on the size of any one previously drawn. Probability. in the concept of frequency distributions, is defined as relative frequency.
The distribution of the number of sixes obtained from repeated
tosses of 12 dice could be illustrated by plotting the theoretical relative frequencies of Table 4.1.
The relative frequencies of each of the 6-unit incre-
ments in Figure 4.1 could likewise be computed.
In the first of these examples,
a probability is associated with each possible outcome.
In the second, a proba-
bility is associated with each increment of size; here the probability is of obtaining not a specific individual but any individual within the increment of size.
This interpretation is required for continuous distributions because
there is an infinite number of possible values and, thus, no probability of occirrence of a particular individual.
Referring to the right curve of Figure
4.1, probability is related to the continuous distribution in the following way: The area under the curve represents the sum of all probabilities and therefore must equal one. Because every item was used in defining the distribution for which the total area is one, then the probability that any item will fall in the distribution is one and the probability that an item will fall in any segment of the distribution is the ratio of the area of that segment to the total area. The distributions just described, both discrete and continuous. are called relative-frequency distributions, probability distributions, or just distributions.
However, the probability interpretation is valid only if the data used
are random.
For example, the daily mean flow of a stream is closely related to
the flows of previous days, s o the distribution of daily means is not one to which the probability interpretation strictly applies. approximate
a
It is possible also to
distribution which merely describes the sample.
For instance, the
distribution of grain sizes of a sample of a streambed is measured to characterize the material; there is no interest in the probability of obtaining a grain in a particular size range by additional sampling.
Here the sample is not the
individual grain but an aggregate of grains of various sizes. Only a few standard theoretical distributions are widely used.
Sampling
theory and inference are based largely on the normal distribution with which the reader is assumed to be familiar. introduced as appropriate.
Other theoretical distributions will be
60
4.2.2
Cumulative distributions
Suppose w e know the probability density curve (probability distribution) for a variable and are interested in the probability of a random event being greater than some particular value E.
This probability can be obtained by measuring or
computing the proportion of the total area above the base value.
For instance,
the left curve of F i g u r e 4.2 s h o w s an area under the c u r v e to the right of E of
0.1, that is, P = 0.1.
Thus the probability of a r a n d o m event exceeding E is
0.1.
-E
0.I PROBABILITY OF EXCEEDANCE
MAGNITUDE
F i g . 4.2.
Probability density curve (left) and its cumulative form (right).
Another f o r m of the probability curve can be prepared by c u m u l a t i n g the probabilities f r o m one end o f the curve and plotting each of these c u m u l a t e d probabilities against the magnitude of its appropriate event. right-hand curve of Figure 4.2.
The result is the
Cumulative distributions are commonly plotted
to a probability scale such that the theoretical curve is a straight line. a scale can be devised for any two-parameter distribution. plotting paper is widely known and used. hydrologic frequency analyses.
Such
Normal probability
Gumbel plotting paper is used in many
(Although the Gumbel extreme-value distribution
is a three-parameter distribution.
one parameter, the skew, is constant for the
form used and permits the construction of a scale which gives a straight-line plot).
B o t h the n o r m a l and G u m b e l probability plotting papers are available
with either arithmetic or logarithmic ordinate scales. four distributions
-
Thus plotting papers for
normal, log-normal, Gumbel, and log-Gumbel
-
are available.
W h e n the probability density curve is c u m u l a t e d f r o m the right end, the probabilities of exceeding the various magnitudes are obtained.
If cumulated
from the left, probabilities of being less than those magnitudes are obtained. The appropriate cumulative curve, commonly called a frequency curve in hydrology. depends on the desired use.
61 A more detailed examination of the relation between a
curve and its cumulative form (the frequency curve) follows. two normal distributions shown in Figure 4.3.
20
14
26
MAGNITUDE
Fig. 4.3.
32
0.9
We begin with the
Their cumulative forms can be
I 8
probability density
I
0.8 0.7
I 0.5
1
1
1
0.3 0.2
01
PROBABILITY THAT A RANDOMLY-DRAWN INDIVIDUAL WILL EXCEED THE INDICATED MAGNITUDE
Two normal distributions and their cumulative forms.
expressed as straight lines by use of the special abscissa scale which is derived from the characteristics of the normal distribution.
Both distributions
have the same median value, 20. and these medians plot at 0.5 probability on the cumulative graph.
The variability of a distribution is indicated by the slope
of the cumulative distribution; that is, the greater the variability, the greater the slope.
The standard deviation is half the difference between magnitudes
at probabilities of 0.16 and 0.84; (See a table of the cumulative normal distribution). Many frequency distributions are nonsymmetrical. For such distributions, the mean, median. and mode have different values which consequently correspond to different probabilities on the cumulative graph. is classified as skewed.
A nonsymmetrical distribution
Skewness may be shown graphically as right or left; it
may be described mathematically by a number, either positive or negative.
Two
skewed distributions and a symmetrical distribution are shown in Figure 4.4, which also shows the corresponding cumulative distributions (frequency curves). For a normal. or any symmetrical. distribution the mean and median are the same value.
Thus, the value corresponding to the probability of 0.5 on the
Cumulative frequency curve is the mean as well as the median for such distributions.
The relative positions of the mean, median, and mode for skewed
62
I
30 r
10
IS
20
30
MAGNITUDE A - Right s k e w e d B - Normal C - Left skewed
0 0.9
0.80.7
0.5
0.30.2
0.1
PROBABILITY T H A T A RANDOMLY-DRAWN INDIVIDUAL W I L L EXCEED THE I N D I C A T E D M A G N I T U D E
F i g . 4.4. Normal and s k e w e d d i s t r i b u t i o n s a n d t h e i r c u m u l a t i v e f o r m s on a normal-probabil i t y p l o t . d i s t r i b u t i o n s a r e shown i n F i g u r e 4.5. from t h e c u m u l a t i v e p l o t .
Only t h e median v a l u e can be d e t e r m i n e d
The p o s i t i o n of t h e mean w i t h r e s p e c t t o t h e median
R e l a t i v e p o s i t i o n s o f t h e mean, m e d i a n , a n d mode f o r p o s i t i v e or F i g . 4.5. r i g h t - s k e w e d ( l e f t g r a p h ) a n d f o r n e g a t i v e or l e f t - s k e w e d ( r i g h t g r a p h ) distributions.
on t h e c u m u l a t i v e p l o t d e p e n d s on t h e d e g r e e o f s k e w n e s s , skewness,
t h e d i r e c t i o n of
and t h e d i r e c t i o n i n which t h e frequency d i s t r i b u t i o n i s cumulated.
F o r e x a m p l e , 43 p e r c e n t o f t h e s a m p l e s d r a w n f r o m a p a r t i c u l a r r i g h t - s k e w e d d i s t r i b u t i o n w i l l e x c e e d t h e mean and 5 7 p e r c e n t w i l l b e l e s s t h a n t h e mean. Thus,
i f t h e d i s t r i b u t i o n i s c u m u l a t e d f r o m t h e h i g h end.
t h e mean i s t o t h e
r i g h t of t h e m e d i a n ; i f c u m u l a t e d f r o m t h e l o w end. t h e mean i s t o t h e l e f t o f t h e median. 4.6
These r e l a t i o n s a r e r e v e r s e d for left-skewed d i s t r i b u t i o n s .
illustrates the relations.
Figure
The p r o b a b i l i t y s c a l e s o f t h e t w o p l o t s of
63
n
I\
/ A
I
LEFT SKEW
MEDIAN
-
0.5
B
0.5
PROBABILITY OF EXCEEDANCE (A) OR OF BEING LESS THAN (B)
Fig. 4.6. Frequency c u r v e s showing e f f e c t of d i r e c t i o n of skew and d i r e c t i o n of cumulation on p o s i t i o n of t h e mean w i t h r e s p e c t t o t h e median. F i g u r e 4.6
a r e d i f f e r e n t : each i s designed f o r t h e p a r t i c u l a r d i s t r i b u t i o n
plotted. 4.2.3
Recurrence i n t e r v a l
Frequency c u r v e s of h y d r o l o g i c d a t a commonly r e l a t e magnitude t o r e c u r r e n c e i n t e r v a l o r r e t u r n p e r i o d i n s t e a d of t o p r o b a b i l i t y .
Recurrence i n t e r v a l i s t h e
r e c i p r o c a l of p r o b a b i l i t y when t h e p o p u l a t i o n c o n s i s t s o f annual events.
Thus
t h e r e c u r r e n c e i n t e r v a l o f a p a r t i c u l a r v a l u e i s t h e a v e r a g e number o f y e a r s between o c c u r r e n c e s g r e a t e r t h a n (or l e s s t h a n ) t h a t value. 4.2.4
GraDhical f i t t i n e
A f r e q u e n c y c u r v e can be d e f i n e d g r a p h i c a l l y from a l i s t of items. method, interval.
In t h i s
e a c h i n d i v i d u a l i n t h e sample i s a s s i g n e d a p r o b a b i l i t y or r e c u r r e n c e Then magnitudes of t h e i n d i v i d u a l s a r e p l o t t e d a g a i n s t t h e s e proba-
b i l i t i e s or recurrence intervals,
and a l i n e i s drawn t o p r o p e r l y i n t e r p r e t t h e
points. A s s i g n m e n t o f p r o b a b i l i t i e s i s by means o f a p l o t t i n g - p o s i t i o n
formula.
V a r i o u s f o r m u l a s may b e u s e d , e a c h b a s e d on a d i f f e r e n t a s s u m p t i o n a s t o t h e c h a r a c t e r i s t i c s of ting-position
t h e sample.
Langbein (1960) r e l a t e s t h e better-known
f o r m u l a s t o t h e i r u n d e r l y i n g assumptions.
plot-
Benson (1962b) compares
t h e r e s u l t s o f u s i n g v a r i o u s p l o t t i n g p o s i t i o n s on t h e economics o f e n g i n e e r i n g planning.
RI
A widely-used f o r m u l a i s t h e Weibull
= 1 / p = (n+l)/m
where R I i s r e c u r r e n c e i n t e r v a l i n y e a r s ,
p i s p r o b a b i l i t y of an erceedence i n
any one y e a r , n i s t h e number of i t e m s i n t h e sample, and m i s t h e o r d e r number of t h e i n d i v i d u a l i n t h e sample a r r a y (Dalrymple,
1960).
Although Beran (1981,
p 26) j u s t i f i e s use of t h e G r i n g o r t e n formula,
t h e Weibull i s used i n t h i s book
because o f i t s wide use i n t h e United S t a t e s .
The sample d a t a may be a r r a y e d
-
64 arranged in order of magnitude
-
beginning w i t h the largest as No. 1, or w i t h
the smallest as No. 1, according to whether the frequency curve is to describe the probability of exceedence or of being less than.
A distribution curve can
be cumulated from either end, and in the graphical method this effect is accomplished by selecting the direction in which the data are arrayed. The next step is plotting magnitude against recurrence interval (or probability) on a graph. results.
I f arithmetic coordinates are used, an S-curve usually
It is difficult to define such a curve by the few observations; it is
customary, therefore, to use a graph sheet having the abscissa graduated in such a w a y that a particular theoretical frequency curve w i l l plot as a straight
line.
Such g r a p h sheets are available for the normal, log-normal, and G u m b e l
Type I distributions.
It is possible to prepare such a scale for any two-
parameter dis tribut ion. A l t h o u g h sets o f data of the s a m e type m a y not appear to lie on straight lines on a particular plotting paper, the lines of good fit usually are only slightly curved i n one direction.
An additional advantage of the probability
graph appears when a straight line is a reasonable interpretation of the plotted points; then the straight line is a frequency curve of the theoretical type on w h i c h the plotting paper is based.
It should be clearly understood that a
frequency curve is not necessarily normal just because the points are plotted on normal-probability paper (or has a Gumbel distribution because the points are plotted on G u m b e l probability paper); only w h e n the frequency curve is a straight line is this true. T h e m e a n of a n o r m a l distribution corresponds to the 0.5 probability or to the %-year recurrence interval.
But a curved line on normal-probability paper
represents a siewed distribution whose mean is not at 2-year recurrence interval.
T h e effect of a s k e w on the relation of m e a n to recurrence interval is
easily demonstrated by use of the Gumbel Type I distribution which has a fixed positive skew. rence interval.
As used for flood analyses, the mean occurs at 2.33-year
recur-
But if the s a m e G u m b e l distribution is used to represent t h e
frequency of floods less than. the positions of the m e a n and m e d i a n are reversed, and the mean plots at about 1.59 years. 4.5 and 4.6.
This effect is shown by Figures
The discharge corresponding to the 2.33-year
recurrence interval
as obtained from a curved line on Gumbel probability paper is not the mean.
It
can, however, be used as a characteristic discharge as could the 2-year value or any other near the central part of the distribution. The annual discharges for the years 1915-50 inclusive in Table 4.2, can be used to define a frequency curve.
column 2.
T h e curve can be cumulated from the
65 TABLE 4.2 Computation of p l o t t i n g p o s i t i o n s Water year
Discharge
Order number, m; highest a s No. 1
Plotting position (n+l)/m
Order number, m ; lowest a s No. 1
Plotting p o s i t ion (n+l)/m,
1915 16 17 ia 19
264 374 332 346 359
34 11 19 16 13
1.09 3.37 1.95 2.31 2.85
3 26 ia 21 24
11.2 1.43 2.06 1.76 1.54
1920 21 22 23 24
333 483 417 346 320
ia 3 5 17 21
2.06 11.2 7.40 2.18 1.76
19 34 32 20 16
1.95 1.09 1.16 1 .a5 2.31
1925 26 27 28 29
271 214 530 304 271
31 36 2 25 32
1.19 1.03 i a .5 1.48 1.16
6 1 35 12 5
6.16 37.0 1.06 3.09 7.40
1930 31 32 33 34
27 1 304 400 327 415
33 26 9 20 6
1.12 1.43 4.11 1 .a5 6.16
4 11 28 17 31
9.25 3.37 1.32 2.18 1.19
1935 36 37 3a 39
402 362 320 272 244
a 12 22 30 35
4.62 3.09 1.68 1.23 1.06
29 25 15 7 2
1.28 1.48 2.47 5.30 ia .5
1940 41 42 43 44
279 303 3 10 27 5 317
28 27 24 29 23
1.32 1.37 1.54 1.28 1.61
9 10 13 14
4 .ll 3.70 2 .a5 4.62 2.65
1945 46 47 4a 49
350 387 359 449 406
15 10 14 4 7
2.47 3.70 2.65 9.25 5.30
22 27 23 33 30
1.68 1.37 1.61 1.12 1.23
1950
570
1
36
1.03
37 .O
a
h i g h end o r from t h e low end, depending on whether t h e d a t a a r e a r r a y e d from t h e high end or from t h e low end. Arraying 20 or 25 items,
Both a r r a y s a r e g i v e n i n t h e t a b l e . t h a t is.
a r r a n g i n g them i n o r d e r of magnitude, and
a s s i g n i n g o r d e r numbers, can be done r e a d i l y by o b s e r v a t i o n .
For a larger
number of items, v a r i o u s schemes may be used. The p l o t t i n g p o s i t i o n s g i v e n in Table 4.2 a r e p r e l i m i n a r y r e c u r r e n c e v a l s ; p r o b a b i l i t i e s would be t h e i r r e c i p r o c a l s ; n i s t h e number of i t e m s
- 1915 + 1 = 36). a n d m i s t h e o r d e r number.
inter-
(1950
66 Discharge i s p l o t t e d a g a i n s t r e c u r r e n c e i n t e r v a l on a p l o t t i n g p a p e r having e i t h e r a n a r i t h m e t i c or l o g a r i t h m i c o r d i n a t e s c a l e and a n a b s c i s s a s c a l e based
on t h e normal o r some o t h e r 2-parameter p l o t t e d f r o m T a b l e 4.2 d a t a .
distribution.
F i g u r e s 4.7 and 4 8 a r e
S e l e c t i o n of t h e o r d i n a t e s c a l e was a r b i t r a r y ;
b o t h a b s c i s s a s c a l e s a r e based on t h e Gumbel Type I d i s t r i b u t i o n .
The l i n e s
N e i t h e r of t h e s e c u r v e s r e p r e s e n t Gumbel
are graphical interpretations.
d i s t r i b u t i o n s because t h e y a r e n o t s t r a i g h t l i n e s .
v)
500.
Z
I
W'
9
400
0
v,
0
I
I
200
l
l
1.3 1.6 2
1.1
I
I
I
3
5
10
1
1
20 30
J 50
RECURRENCE INTERVAL, IN YEARS
F i g . 4.7. F r e q u e n c y c u r v e b a s e d on d a t a f r o m T a b l e 4.2 a s s u m i n g t h a t d a t a a r e annual maximums.
!K
I
:
l0O0
I
I
I
I
I
I
Z
@z
4
1
1
-
. -1-
300-
200
I
-
0
v, 0
100
I
I
I
t
I
I
I
I
I
F i g . 4.8. F r e q u e n c y c u r v e b a s e d on d a t a f r o m T a b l e 4.2 a s s u m i n g t h a t d a t a a r e annual minimums.
61 4.2.5
Fitting theoretical distributions
T h e first step is to decide w h i c h distribution w o u l d be most appropriate. The ones most commonly used in hydrology are normal, lognormal. and log Pearson Type 3.
(Gumbel and Weibull), ble.
extreme value
Selection depends on the varia-
Previous analyses may be used as a guide.
(i)
T h e n o r m a l distribution h a s o n l y 2 parameters,
N o r m a l distribution.
m e a n and standard deviation.
E s t i m a t e s of these are c o m p u t e d f r o m the dis-
charges of Table 4.2 by
Mean =
6
= ZQIN = 12,486136 = 341
ZQZ
Variance
=
-
tZQ)Z/N
Sz =
-
4,542,500
N-1
-
155,900,196136 =
6055
35
Standard deviation = S = 11.8 Using these, the detailed characteristics of the distribution can be extracted from a table of the cumulative normal distribution, which is available in many statistics texts.
In a table of the cumulative normal distribution, magnitude
is expressed as the mean plus or minus some multiple of the standard deviation. We assume that
a
and S are equal to their respective population parameters p and
Then for selected values of magnitude in terms of p and a we determine the
a.
probabilities f r o m the table at enough points to define the frequency curve. Results using a mean of 341 and a standard deviation of 11.0 are shown in Table
4.3. TABLE 4.3 Frequency characteristics of data from Table 4.2 assuming a normal distribution
xa p - 2.0a p - 1.5~ p - 1.0~ p - .8a
-
.5a .2a
p + p +
.2a .5a
p p
P(X<Xa)
Recurrence Interval of Exceedance
= = = =
191 230 269 285
0.02 01 .16 .21
0.98 .93 .8 4 .I9
1.02 1.08 1.19 1.21
=
308
.31 .42 .50 .58 .69
.69 .58 .50 .42 .31
1.45 1 .I2 2 .oo 2.38 3.22
.I9 .8 4 .93 .98
.21 .16 01 .02
4.16 6.25 14.4 50 .O
= 331 =
p + .8a p + 1.00 p + 1.5~ II + 2.0~
P(X>X,)
341
= 363 = 386 = 409 = 425 = 464 =
503
.
.
68 The same r e s u l t s c o u l d have been o b t a i n e d from a p l o t on normal p r o b a b i l i t y The mean i s p l o t t e d a t 0.5 p r o b a b i l i t y .
paper.
the standard d e v i a t i o n i s plot-
t e d p l u s and minus from t h e mean a t p r o b a b i l i t i e s o f 0.16
and 084, r e s p e c t i v e -
ly, a s t r a i g h t l i n e i s drawn through t h e p l o t t e d p o i n t s , and p r o b a b i l i t i e s a t s e l e c t e d l e v e l s a r e r e a d from t h e l i n e . The lognormal d i s t r i b u t i o n i s a normal d i s t r i b u t i o n of t h e l o g a r i t h m s o f t h e data.
E i t h e r Naperian o r common l o g a r i t h m s can b e used b u t common l o g a r i t h m s
a r e most w i d e l y u s e d i n h y d r o l o g y .
I n terms of the untransformed data the
lognormal d i s t r i b u t i o n h a s a r a n g e from z e r o t o p l u s i n f i n i t y and t h u s i s positively
skewed.
The lognormal d i s t r i b u t i o n i s u s u a l l y t r e a t e d s i m p l y a s a
n o r m a l d i s t r i b u t i o n of l o g a r i t h m s a n d c a n b e f i t t e d t o d a t a a s shown i n t h e above example by s u b s t i t u t i n g l o g Q f o r Q i n T a b l e 4.2. Type I E x t r e m e - v a l u e d i s t r i b u t i o n (Gumbel).
(ii)
d i s t r i b u t i o n having a c o n s t a n t skew of 1.139.
-
u = X
-
J.N /a
This i s a 2-parameter
The p a r a m e t e r s a r e
l/a = S/aN
and
w h e r e u i s t h e mode, l/a i s a s c a l e p a r a m e t e r , standard d e v i a t i o n respectively, i t e m s i n t h e sample.
Values o f
Gumbel (1958, p. 228).
x and S a r e
t h e s a m p l e mean a n d
and TN and aN a r e f u n c t i o n s o f yN and aN f o r N from 8 t o 1,000
N.
t h e number of
a r e t a b u l a t e d by
P a r t o f Gumbel's t a b l e i s g i v e n i n T a b l e 4.4.
TABLE 4.4 Means and s t a n d a r d d e v i a t i o n s of reduced extremes (from Gumbel. 1958)
YN
N
10 12 14 16 18 20 25 30 40 50 60 80 100 200 500 1000
UN
0 -4952
,5035 -5100 .5157 .5202 .52355 .53086 .53622 .54362 .54854 .55208 .55688 .56002 .56715 .57240 .51450
0.9497 .9833 1.0095 1.0316 1.0493 1.06283 1.09145 1.11238 1.14132 1.16066 1.17467 1.19382 1.20649 1.23598 1.25880 1.26851
The mean a n d s t a n d a r d d e v i a t i o n o f t h e s a m p l e a r e c o m p u t e d ,
yN a n d
aNa r e
r e a d f r o m t h e t a b l e , u a n d l/a a r e c o m p u t e d f r o m t h e a b o v e f o r m u l a s . a n d t h e straight line
69
is determined.
On Gumbel probability graph the mean is plotted
at 2.33 years
and the approximate relation y = In RI can be used to locate another point on the straight line. Following is a sample computation for annual floods on Columbia River near Data are from USGS WSP 1080.
The Dalles, Oregon for 1858-1946. Mean flood is 606,200 cfs = Standard deviation, S
=
f
d(ZX2
- *;)IN
-
1 = 175,200.
From Table 4 . 4 for N = 89,
YN
= ,558 and uN = 1.20
then l/a = SluN = 175,200l1.20 = 146,000 and u =
x - 7Nla = 606,200
-
(.558)(146.000)
= 524.100.
The equation of the straight line is
X = u + y/a = 524,700 + 1 4 6 . 0 0 0 ~ . The relation y = In T may be used to define plotting points for large recurrence intervals. y = In T = 2.303 log T.
For T = 50 years, X = 524,700
y = 3.91,
i146,000(3.91)
and = 1,096.000
cfs.
The straight line is defined on the graph of Figure 4.9 by the points X = 606,200 cfs at 2.33 years and 1,096,000
cfs at 50 years.
The plotted points for
the period 1858-1948 are shown to indicate the fit of the computed line. Several analysts have concluded that the above fitting procedure recommended by Gumbel ( 1 9 5 8 ) may produce biased estimates.
See
Lettenmaier and Burges
(1982) and references given in their paper.
(iii) Pearson Type 3 distribution.
The Pearson Type 3 distribution is a
70 flexible distribution in three parameters with a limited range to the left and unlimited range to the right.
Plotting paper is not available for this distri-
bution because s k e w n e s s varies.
This distribution is c o m m o n l y fitted to the
1200
800
r
400
0 1 .01
Fig. 4.9.
1.2
5 10 20 RECURRENCE INTERVAL, IN YEARS 2
50
100
Gumbel frequency curve.
common logarithms of flood magnitudes because this results in a smaller skew. The Pearson T y p e 3 distribution w i t h zero s k e w is identical to the n o r m a l distribution. Fitting a 3-parameter distribution starts w i t h c o m p u t a t i o n of the mean, standard deviation, and coefficient of skew.
The mean and standard deviation
(347 and 77.8) o f the discharges o f T a b l e 4.2 normal distribution.
cs
were c o m p u t e d for fitting t h e
The coefficient of skew is
(36)a(1,738,665.756)
-
3(36)(12,486)(4,542,500) + 2(12,486)'
=
(36)(35)(34)(6055)(77.8)
Cs = 1.04. These data parameters may be used to fit any 3-parameter distribution but the procedure is indirect because the probability density function cannot be integrated directly and thus there is no formula for the cumulative distribution. The relation between magnitude and probability of being larger than (or smaller than) is commonly determined from a table of frequency factors for the chosen distribution.
Frequency factors for the P e a r s o n T y p e 3 distribution, adapted
71 f r o m a m o r e extensive table b y W a t e r Resources Council (1982), are given in Specific points on the fitted distribution are computed by
Table 4.5.
where X
is the variable
probability),
-X
at
a selected
recurrence
interval
(or
is the mean, K is the frequency factor for the same recurrence
interval, and S is the standard deviation. Using the above value of mean. standard deviation, and skew, and T a b l e 4.5, the discharge at 20-year recurrence interval would be
X = 341
+
1.88
(71.8) = 493 c f s
Additional points would be computed as needed to define the curve. T h e log P e a r s o n T y p e 3 distribution is fitted s i m i l a r l y except that the c o m m o n l o g a r i t h m s of the discharges are used i n c o m p u t i n g t h e three parameters. Frequency curve fitting is usually done by digital computer. 4.2.6
Evaluation of fitting methods
Fitting to theoretical distributions has the following advantages: 1.
For the same theoretical distribution. every analyst using a given set of data would get the same answer.
2.
Fitting can be done quickly by use of computer programs.
3.
The curve can be completely described by 2 or 3 parameters and the name of the distribution.
and the following disadvantages:
1.
Selection of the theoretical distribution is arbitrary.
2.
No one theoretical distribution will adequately fit a11 hydrologic data of one type such as flood peaks.
3.
Some data cannot be fitted by a distribution with only 3 parameters.
4.
T h e highest and l o w e s t data points m a y b e given too m u c h weight (the objective i n hydrology is to best define o n e end o f a frequency curve, not to define the best fit throughout the range).
Graphical fitting has the following advantages: 1.
Procedure is simple and can be done quickly.
2.
No assumption as to the type of distribution need be made.
3.
Analyst can use other information in interpreting the plotted points.
4.
Historical data may be readily incorporated.
and these disadvantages: 1.
Even though the same plotting position formula is used, different analysts will draw somewhat different frequency curves.
2.
A graphical curve cannot be described by 2 or 3 parameters.
72 TABLE 4.5 Frequency factors for Pearson Type 3 distributions Recurrence Interval, in Years
CS
100
20
2.0 1.8 1.6 1.4 1.2
3.61 3.50 3.39 3.27 3.15
2.00 1.98 1.96 1.94 1.91
1.30 1.32 1.33 1.34 1.34
1.0
1.88 1.84 1.80 1.75 1.70
1.34 1.34 1.33 1.32 1.30
.38 .41
.6 -4 .2
3.02 2.89 2.76 2.62 2.47
0
2.33
1.64
1.28
-52
0
2.18 2.03 1.88 1.73 1.59
1.59 1.52 1.46 1.39 1.32
1.26 1.23 1.20 1.17 1.13
.55 .57 .59 .60 .62
.8
- -2 - -4 - .6 - .8 -1.0 4.2.7
10
3.33 .20
.24 .28 .31 .35
.44 .47 .50
2
1.43
1.11
-.64
-
-.64
- .94
-.64 -.64
1.05
-
.99 -1.04 -1.09
- .95 -1.02 -1.09 -1.17 -1.24
-.55
-1.13 -1.17 -1.20 -1.23 -1.26
-1.32 -1.39 -1.47 -1.52 -1.59
-.52
-1.28
-1.64
-03
-.SO
.07 .10 .13 .16
-.41
-1.30 -1.32 -1.33 -1.34 -1.34
-1.70 -1.75 -1.80 -1.84 -1.88
-.31 -.28 -.25 -.23 -.20 -.16 -.13 -.lo -.07 -.03
-.63 -.62 -.60 -.59 -.57
-.44 -.41 -.38
.89
Interpretation of frequency curves
A frequency curve based on random homogeneous data is an estimate of the cumulative probability distribution of the population from which the sample was drawn.
The following interpretations of the frequency curve require the assump-
tion that the curve is a good representation of the population distribution. Referring to the graphical curve of Figure 4.7, the recurrence interval of 500 cfs is 16 years.
This means that the annual maximum will exceed 500 cfs at
intervals averaging 16 years in length, or that the probability of the annual maximum exceeding 500 cfs in any one year is 1/16. From Figure 4%
the recurrence interval of 2 5 0 cfs is 13 years.
Thus, the
annual m i n i m u m discharge will be less than 2 5 0 cfs at intervals averaging 13 years in length, and the probability that the minimum discharge in any one year will be less than 250 cfs is 1/13. Many interpretations of frequency curves in hydrology have been stated in terms of the probability "of equaling or exceeding" a selected value.
Most
variables in hydrology, notably streamflow, are continuous - but reported as discrete
-
and the theoretical probability of occurrence of any particular value
in a continuous distribution is zero.
Therefore it seems desirable to delete
"of equaling." The interpretations of frequency curves given above will not answer questions such as the probability of an event o f 10-year recurrence interval being exceeded in a 10-year period.
Intuitively, one might expect that probability to
13
be 0 . 5 , but it is not.
The correct probability can be computed a s follows.
Since the probability of exceeding the 10-year event in 1 year is 0.1, the probability of not exceeding it in 1 year is 0.9.
Then, the probability of not
exceeding it in 10 years is, by the multiplicative law of probabilities ( 0 . 9 ) l o = 0.35 and the probability of one or more events exceeding the 10-year event in 10
years is 0.65.
A more complete interpretation of a frequency curve is given by
Riggs (1961). Although frequency curves are used a s though they were accurate representations of the population distribution, w e know that they may not be.
Benson
(1960) sampled from a known distribution and showed a wide range in shape and position of frequency curves defined by different samples of the same size. Another way of assessing the reliability of a frequency curve is by computing the confidence limits.
Chow (1964, p. 8-31) describes a method.
These compu-
tations indicate that the frequency curve is most reliable in the vicinity of the mean.
4.2.8
Describing frequency characteristics
A mathematically-fitted frequency curve can be described by the name of the
distribution and the mean, standard deviation, and skew.
For use in hydrologic
analyses, or for quantifying a regulatory flow, the discharge at some point on the frequency curve is used; for example the 100-year (0.01 probability) flood and the 10-year low flow are commonly used indices.
The measure of central
tendency commonly used is the median which is the discharge at 2-year recurrence interval or at 0.5 probability. Variability of a distribution is described by its standard deviation, S.
For
comparison of variabilities among frequency curves the dimensionless ratio of standard deviation to the mean is used.
This is called the coefficient of
variation
cv
=
Sli
If logarithms of the data are used to define the frequency curve, the standard deviation of the logarithms is called the index of variation, I,;
unlike S,
I,
is already dimensionless and need not (and should not) be divided by the mean. The mean and standard deviation of graphically-fitted frequency curves are readily obtained from the graph if the frequency curve is a straight line on normal or lognormal probability paper.
But the usual graphically-fitted fre-
quency curve is not a straight line on the plotting paper used; consequently, the mean is not at a known probability or recurrence interval, the standard deviation cannot be accurately determined, and the curvature indicates the
14 existence of skewness.
For such curves it is customary to use the median flow
as the characteristic of central tendency.
Discharges at selected recurrence
intervals also are readily obtained but an index of variability can only be approximated from the graphically-defined curve. 4.3
STATISTICAL INFERENCE
W e have 5 4 years of record on the Rappahannock River of Virginia and might ask two questions about the mean flow. First, what is the mean flow for the period of record?
This is a unique value which can easily be computed.
The
second question, what is the mean flow of the stream?, cannot be answered
W e can only assume that the mean of the 54-year sample is an
definitely.
estimate of the true (population) mean.
In other words, we infer the population
characteristics from those of a sample from that population. Statistical inference is based on the theory of sampling.
From a population
of known characteristics many samples are drawn (either actually or conceptually), and the relation of the sample characteristics to the population characteristics is defined. Sampling theory requires use of the concept of a probability distribution. Assume that the distribution of some random variable is normal with mean, p, and standard deviation, u, a s shown in Figure 4.10.
(The term "random", a s used
here, means that the probability of drawing any one item of the population is the same a s for any other).
Fig. 4.10.
Normal distribution.
Now suppose we take many samples of size N from this distribution, compute the mean of each of these samples, and compute the mean and variance of these sample means.
The distribution of the means of samples of size N is superposed
on the original distribution in Figure 4.11.
It can be shown that the distriba-
tion of the means is centered at p and that the standard deviation of the distribution of means is u / a .
Therefore, the mean of the means of samples of
DISTRIBUTION OF MEANS OF SIZE N
ORIGINAL DISTRIBUTION
F i g . 4.11.
D i s t r i b u t i o n o f means o f s a m p l e s from a n o r m a l d i s t r i b u t i o n .
s i z e N i s a n u n b i a s e d e s t i m a t e o f p.
Furthermore,
Consequently,
u n b i a s e d e s t i m a t e o f p.
e s t i m a t e o f t h e p o p u l a t i o n mean.
t h e mean o f o n e s a m p l e i s an
we i n f e r t h a t t h e s a m p l e mean,
Obviously,
X, i s a n
i f we u s e d o t h e r s a m p l e s we would
o b t a i n d i f f e r e n t e s t i m a t e s o f t h e p o p u l a t i o n mean. From a s i n g l e s a m p l e , we c a n a p p r a i s e t h e r e l i a b i l i t y of t h e e s t i m a t e , t h e p o p u l a t i o n mean.
Consequently,
two-thirds
of t h e v a l u e s s h o u l d f a l l
w i t h i n o n e s t a n d a r d d e v i a t i o n (u/fi) o n e a c h s i d e o f t h e mean. IJ
of
The d i s t r i b u t i o n o f means o f v a l u e s d r a w n f r o m a n o r m a l
d i s t r i b u t i o n i s normal.
n o t know
%,
H o w e v e r , we d o
so we h a v e t o s u b s t i t u t e S f o r i t ( w h e r e S i s t h e s t a n d a r d d e v i a t i o n
computed from t h e sample).
The d i s t r i b u t i o n o f
x
having a s t a n d a r d d e v i a t i o n of
S/fi i s known a s t h e S t u d e n t ’ s t d i s t r i b u t i o n , v a l u e s o f w h i c h a r e t a b u l a t e d i n s t a t i s t i c s t e x t s f o r v a r i o u s s i z e s o f N. S u p p o s e now t h a t we h a v e K s a m p l e s o f s i z e N a n d h a v e d e f i n e d K d i f f e r e n t s a m p l i n g d i s t r i b u t i o n s o f t h e mean o f s i z e N.
For each sampling d i s t r i b u t i o n ,
we c a n d e f i n e a m e a n a n d a r a n g e o f r e l i a b i l i t y , w h e t h e r s u c h a r a n g e i n c l u d e s t h e t r u e m e a n p.
a n d we a r e i n t e r e s t e d i n
Considering the range a s a
we may s t a t e t h a t t h e p r o b a b i l i t y ( P ) t h a t t h e random i n t e r v a l
random i n t e r v a l , i n c l u d e s p i s 1-e.
where e i s t h e l e v e l of s i g n i f i c a n c e .
Mathematically,
for e
= 0.32.
P[x - u/\TN)
; W 2 U
O
N
D
J
F
M
A
M
J
J
A
S
MONTH
F i g . 5.1. 5.3
Mean monthly d i s c h a r g e s , E.F.
J a r b i d g e R i v e r , Idaho.
FREQUENCY CHARACTERISTICS V a r i a b i l i t y of f l o w can b e d e s c r i b e d by t h e c o e f f i c i e n t of v a r i a t i o n or t h e
i n d e x o f v a r i a t i o n , b o t h of w h i c h c a n b e c o m p u t e d r e a d i l y ; s e e S e c t i o n 4.2.8. More commonly f l o w v a r i a b i l i t y i s d e s c r i b e d b y a f r e q u e n c y c u r v e f r o m w h i c h
108 s e l e c t e d p o i n t s a r e used a s d e s c r i p t o r s . data a r e asymmetrically distributed,
Furthermore,
because most h y d r o l o g i c
t h e median f l o w ( a t 0.5 p r o b a b i l i t y o r 2-
y e a r r e c u r r e n c e i n t e r v a l ) i s o f t e n used a s t h e index o f c e n t r a l tendency r a t h e r t h a n t h e mean.
The f r e q u e n c y c u r v e o f a n n u a l mean d i s c h a r g e s o f F i g u r e 5.2
shows t h e p r o b a b i l i t i e s t h a t a n annual mean f l o w w i l l be l e s s t h a n v a r i o u s c u r v e values.
F o r e x a m p l e , t h e p r o b a b i l i t y i s 1 0 p e r c e n t t h a t a f u t u r e a n n u a l mean
flow w i l l b e l e s s t h a n about 450 c f s .
1
3000
z
w-
1000
2a
I
?L! n
500
200 99
90
50
10
1
DEFlClE.NCY PROBABILITY, IN PERCENT
Fig. 5.2.
Frequency c u r v e of annual mean d i s c h a r g e s f o r Red River, Tennessee.
Flood-frequency
c n r v e s and low-flow
frequency c u r v e s a r e u s u a l l y d e f i n e d i n
t e r m s o f r e c u r r e n c e i n t e r v a l ; c h a r a c t e r i s t i c s such as t h e 100-year
f l o o d and t h e
l o - y e a r l o w f l o w a r e common d e s c r i p t o r s t a k e n f r o m t h e s e c u r v e s .
Methods o f
p r e p a r i n g frequency c u r v e s a r e g i v e n i n Chapter 4 and o t h e r examples a r e g i v e n i n C h a p t e r s 8 a n d 9. The r e l i a b i l i t y of a frequency c u r v e depends on t h e number of y e a r s o f d a t a on w h i c h i t i s b a s e d , on t h e v a r i a b i l i t y o f s t r e a m f l o w , and on w h e t h e r o r n o t t h e f l o w r e g i m e was changed d u r i n g or s u b s e q u e n t t o t h e p e r i o d of r ecor d.
A
r e q u i r e m e n t f o r v a l i d i t y of a f r e q u e n c y c u r v e i s t h a t t h e d a t a a r e a l l drawn from t h e same p o p u l a t i o n ;
t h i s i s u s u a l l y met by f l o w s which a r e averaged o v e r
some p e r i o d o f t i m e - s u c h a s m o n t h l y o r a n n u a l means; i t may n o t b e m e t b y f l o o d p e a k s on e p h e m e r a l s t r e a m s o r b y a n n u a l l o w f l o w s i n h u m i d r e g i o n s . f u r t h e r r e q u i r e m e n t i s t h a t t h e d a t a n o t be s e r i a l l y c o r r e l a t e d .
A
Thus an under-
s t a n d i n g of t h e b a s i n h y d ro lo g y i s needed f o r p r o p e r i n t e r p r e t a t i o n of a f r e quency curve. low-flow
The v a r i o u s f a c t o r s t h a t i n f l u e n c e f l o o d - f r e q u e n c y
c u r v e s and
frequency c u r v e s a r e d i s c u s s e d i n t h e c h a p t e r s on t h o s e s u b j e c t s .
109 JBTWDING STREAMFLOW RECORDS I N TIME
5.4
A frequency c u r v e b a s e d on 1 0 or 15 y e a r s of r e c o r d may n o t be v e r y r e l i a b l e . E s t i m a t e s for a d d i t i o n a l y e a r s can b e made by r e g r e s s i o n s on p r e c i p i t a t i o n or on a longer s t r e a m f l o w r e c o r d c o n c u r r e n t w i t h t h e one f o r t h e s i t e t o be e s t i m a t e d .
These e s t i m a t e s a r e t h e n combined w i t h t h e f l o w s of r e c o r d t o d e f i n e a n o t h e r . and p r e s u m a b l y b e t t e r , f r e q u e n c y c u r v e . t r a t e t h e procedure.
D a t a i n T a b l e 5.1 a r e u s e d t o i l l u s -
Assume t h a t annual f l o o d peaks f o r B l a c k w a t e r River a r e
a v a i l a b l e o n l y 1951-60.
The r e g r e s s i o n r e l a t i o n between f l o o d peaks f o r t h e two
streams f o r t h a t period i s log B = 1.035 + 0.676 l o g L and t h e c o r r e l a t i o n c o e f f i c i e n t i s 085.
T h i s r e l a t i o n i s used t o e s t i m a t e
B l a c k w a t e r f l o o d p e a k s f o r 1922-50; t h e e s t i m a t e s a n d t h o s e f o r 1951-60 a r e shown i n Table 5.1.
F i g u r e 5.3
shows f r e q u e n c y c u r v e s f o r B l a c k w a t e r based on
1951-60; on t h e a c t u a l r e c o r d ; and on t h e c o m b i n a t i o n of e s t i m a t e s f o r 1922-50 and a c t u a l f o r 1951-60.
I n t h i s example, t h e f r e q u e n c y curve d e f i n e d p a r t l y by
e s t i m a t e s i s p o o r e r t h a n t h e one b a s e d on o n l y t h e 1 0 y e a r s of record. TABLE 5.1 Annual f l o o d s , i n c f s , on two M i s s o u r i s t r e a m s . Year
Lamine R. Record
1922 3 4 1925 6 7 8 9 1930 1 2 3 4 1935 6
7 8 9 1940
15200 9300 7640 10100 11300 25000 7620 33000 7260 8500 11200 17800 5190 25000 13200 22200 16600 40200 4280
Blackwater R. Record
9280 10800 7060 10000 17400 21800 54000 7990 3200 9680 6900
9810 5300
Year
From Regression
7280 5230 4580 5530 5 960 10200 4570 12300 4420 4920 5930 8110 3520 10200 6620 9410 7730 14100 3090
1941 2 3 4 1945 6 7 8 9 1950 1 2 3 4 1955 6 7 8 9 1960
Lamine R.
Blackwater R.
Record
Record
18600 21400 60000 32500 12200 14500 14300 32500 12400 12200 65500 9750 5360 3830 8260 14000 6740 25 500 9980 28700
3890 13400 27900 32400 12600 11300 12900 15600 9760 13200 23900 7100 5880 3290 5170 3960 3150 8100 3570 16200
From Regression 83 50 9180 18400 12200 6280 7060 6990 12200 6350 6280 19600 5 400 3600 2870 4820 6890 4200 10300 5480 11200
F i e r i n g (1963) h a s shown t h a t u n l e s s t h e c o r r e l a t i o n c o e f f i c i e n t i s g r e a t e r t h a n a b o u t 0.8, u s e o f r e g r e s s i o n e s t i m a t e s w i l l n o t i m p r o v e t h e e s t i m a t e of variance.
The e x a m p l e r e g r e s s i o n h a s a n r o f 0.85; and F i g u r e 5.3 s h o w s t h a t
t h e v a r i a n c e ( s l o p e of t h e l i n e ) i s i m p r o v e d by u s e o f e s t i m a t e s , b u t t h a t t h e
110 mean i s n o t .
Apparently t h e r e l a t i o n between f l o o d peaks of t h e two s t r e a m s
d u r i n g 1951-60 i s c o n s i d e r a b l y d i f f e r e n t t h a n f o r o t h e r p e r i o d s .
In g e n e r a l ,
u s e of r e g r e s s i o n e s t i m a t e s produces a n improved frequency c u r v e o n l y when t h e two v a r i a b l e s a r e v e r y h i g h l y c o r r e l a t e d .
I
100,000,
uU
1922-33 1939-60
/
(r
4V
E Q Y
20,000
-
10,000
-
-
$ Q
3 Z
PLUS 23 ESTIMATES
-
Z Q
5000 _ _ _ .
1.5
-4
2
3 '
5
10
20
30
50
RECURRENCE INTERVAL, IN YEARS
F i g . 5.3. R e s u l t of a t t e m p t t o improve a flood-frequency regression estimates.
c u r v e by u s e of
Streamflow r e c o r d s may be extended i n t i m e f o r purposes o t h e r t h a n frequency curve improvement.
A mean f o r some s p e c i f i c p a s t month o r y e a r may be needed.
T h i s c a n b e o b t a i n e d by s i m p l e r e g r e s s i o n o r by r e g r e s s i o n m o d e l s w i t h b o t h s t r e a m f l o w and p r e c i p i t a t i o n a s independent v a r i a b l e s .
S c h n e i d e r (1961), Riggs
(1964a) and M a r t i n (1964) proposed and e v a l u a t e d s e v e r a l models f o r e s t i m a t i n g monthly mean d i s c h a r g e s f o r months o u t s i d e t h e p e r i o d of r e c o r d from d i s c h a r g e a t a n e a r b y g a g e d s i t e and f r o m t h e m o n t h l y p r e c i p i t a t i o n t o t a l s on t h e t w o sites.
Carroon (1970) extended monthly flow r e c o r d s a t many s i t e s in t h e upper
Colorado R i v e r b a s i n by a g r a p h i c a l method.
The r e l i a b i l i t y of such a r e g r e s -
s i o n e s t i m a t e i s i n d i c a t e d by t h e s t a n d a r d e r r o r . Rainfall-runoff
models which account f o r t h e d e t a i l e d d i s p o s i t i o n of r a i n f a l l
may b e u s e d t o e x t e n d s t r e a m f l o w r e c o r d s .
T h e s e may b e r e g r e s s i o n m o d e l s i n
w h i c h r u n o f f i s r e l a t e d t o s t o r m m a g n i t u d e , s t o r m d u r a t i o n , and a n i n d e x o f a n t e c e d e n t s o i l m o i s t u r e ; o r d i g i t a l computer models which model t h e l a n d phase of t h e h y d r o l o g i c cycle.
Both t y p e s of models r e q u i r e s e v e r a l y e a r s of concur-
r e n t s t r e a m f l o w and h o u r l y p r e c i p i t a t i o n r e c o r d s f o r c a l i b r a t i o n ;
t h e i r output
111
i s continuous d a i l y s t r e a m f l o w , record. (1969).
l i m i t e d i n t i m e by t h e a v a i l a b l e p r e c i p i t a t i o n
R e g r e s s i o n m o d e l s a r e d e s c r i b e d by Moore ( 1 9 6 8 ) and S i t t n e r , e t a 1 There a r e many d i g i t a l computer models f o r producing a c o n t i n u o u s flow
record from p r e c i p i t a t i o n ; most a r e some m o d i f i c a t i o n o f t h e S t a n f o r d Watershed Model (Crawford and L i n s l e y , 1966).
Rainfall-runoff
models produce s y n t h e t i c
s t r e a m f l o w r e c o r d s t h a t a r e a d e q u a t e f o r many p u r p o s e s i f t h e p r e c i p i t a t i o n r e c o r d i s r e p r e s e n t a t i v e o f p r e c i p i t a t i o n on t h e b a s i n .
But t h e s y n t h e t i c
record i s n o t r e l i a b l e enough t o improve f r e q u e n c y c u r v e s of d a i l y extremes.
A
r a i n f a l l - r u n o f f model t h a t s y n t h e s i z e s s t o r m h y d r o g r a p h s f o r t h e p u r p o s e o f extending a f l o o d r e c o r d i s d e s c r i b e d i n s e c t i o n 8.7. 5.5
FLOW-DURATION CURVES The f l o w - d u r a t i o n
c u r v e i s a c u m u l a t i v e f r e q u e n c y c u r v e based on d a i l y d i s -
charges f o r one or many complete y e a r s of record.
The u s u a l g r a p h i c a l method o f
d e f i n i n g a frequency c u r v e by p l o t t i n g each p o i n t i s n o t f e a s i b l e when t h e r e a r e many p o i n t s :
i n t h i s a p p l i c a t i o n t h e r e a r e 365 f o r each year.
Consequently,
the
numbers of d a y s h av in g d i s c h a r g e s w i t h i n ea ch o f 20 o r 30 r a n g e s of d i s c h a r g e a r e determined, u s u a l l y by computer. of t h e t o t a l ,
These numbers a r e c o n v e r t e d t o p e r c e n t a g e s
t h e p e r c e n t a g e s a r e cumulated from t h e upper end (of d i s c h a r g e ) .
and t h e cumulated v a l u e s a r e p l o t t e d a g a i n s t t h e a p p r o p r i a t e d i s c h a r g e s on a l o g normal graph. cumulated
F i g u r e 5.4 i s a n e x a m p l e .
from t h e high-discharge
end,
Because t h e p e r c e n t a g e s of d a y s a r e any p o i n t on t h e d u r a t i o n c u r v e shows
t h e p e r c e n t o f d a y s ( d u r i n g t h e p e r i o d u s e d ) t h a t had d i s c h a r g e s g r e a t e r t h a n t h e i n d i c a t e d value. Although t h e d u r a t i o n c u r v e i s a c u m u l a t i v e frequency curve i t should be i n t e r p r e t e d m e r e l y a s an e x p r e s s i o n o f what happened i n a p a r t i c u l a r t i m e p e r i o d , n o t a s a p r o b a b i l i t y c u r v e because d a i l y d i s c h a r g e s a r e n o t o n l y s e r i a l l y c o r r e l a t e d b u t t h e i r c h a r a c t e r i s t i c s change throughout t h e year.
Consequent-
l y t h e p r o b a b i l i t y of a d a i l y d i s c h a r g e b e i n g g r e a t e r t h a n some s p e c i f i e d v a l u e d i f f e r s f r o m t h a t g i v e n b y t h e d u r a t i o n c u r v e b e c a u s e i t d e p e n d s b o t h on t h e p r e c e d i n g f l o w s and on t h e t i m e of year. The d u r a t i o n c u r v e c a n b e i n t e r p r e t e d a s f o l l o w s :
a d a i l y f l o w may b e
e x p e c t e d t o e q u a l or e x c e e d Q c f s P p e r c e n t o f t h e t o t a l t i m e i n a p e r i o d of y e a r s e q u a l t o t h e p e r i o d used i n d e f i n i n g t h e d u r a t i o n curve.
This i n t e r p r e t a -
t i o n would b e r e a s o n a b l e o n l y i f t h e d u r a t i o n c u r v e is based on t e n s of y e a r s of record.
D u r a t i o n c u r v e s based on one or o n l y a few y e a r s of r e c o r d may d e v i a t e
g r e a t l y from t h e curve based on a long record. D u r a t i o n c u r v e s may be used t o d i s p l a y g r a p h i c a l l y t h e v a r i a b i l i t y of flow, a change due t o s t r e a m r e g u l a t i o n ,
or t h e d e p e n d a b i l i t y of low flows.
d u r a t i o n c u r v e may be used w i t h a s e d i m e n t - r a t i n g sediment load.
An annual
c u r v e t o compute t o t a l annual
D i s c h a r g e s a t 95 p e r c e n t on t h e l o n g - t e r m d u r a t i o n c u r v e a r e
112
Fig. 5.4.
Flow-duration
c u r v e f o r James R i v e r a t Buchanan. V i r g i n i a .
r e l a t e d t o p o i n t s on t h e l o w - f l o w
frequency curve b u t t h e s e r e l a t i o n s change
geographically. 5.6
BASE-FLOW RECESSION CURVES Streamflow v a r i e s n o t o n l y because t h e c a u s a t i v e s t o r m s a r e random i n t h e i r
o c c u r r e n c e , g e o g r a p h i c a l e x t e n t , d u r a t i o n , and i n t e n s i t y b u t a l s o b e c a u s e v a r i o u s p o r t i o n s of t h e p r e c i p i t a t i o n a p p e a r a s measured s t r e a m f l o w a t d i f f e r e n t times.
The l a g between p r e c i p i t a t i o n and r u n o f f depends on t h e p a t h which t h e
w a t e r f o l l o w s from t h e s u r f a c e of t h e ground t o t h e stream.
That p o r t i o n which
f l o w s on t h e s u r f a c e of t h e ground t o t h e s t r e a m channel i s most c l o s e l y r e l a t e d in time t o precipitation.
Another p o r t i o n may t r a v e l through t h e upper l a y e r s
of t h e s o i l and a r r i v e a t t h e s t r e a m c h a n n e l s r a t h e r promptly b u t somewhat l a t e r t h a n s u r f a c e runoff.
The s u r f a c e flow and t h e s h a l l o w s u b s u r f a c e f l o w a r e o f t e n
c o n s i d e r e d t o g e t h e r under t h e t i t l e of d i r e c t r u n o f f , of s t r e a m f l o w d u r i n g f l o o d s . ward i n t o t h e ground-water
which i s t h e major p o r t i o n
A t h i r d p o r t i o n of t h e p r e c i p i t a t i o n s e e p s down-
a q u i f e r t h a t f e e d s t h e stream.
This t h i r d p o r t i o n i s
t h e l a s t t o r e a c h t h e s t r e a m and i s t h e p o r t i o n t h a t m a i n t a i n s s t r e a m f l o w d u r i n g p e r i o d s of no r a i n .
I t i s commonly c a l l e d t h e b a s e flow of t h e stream.
113
The h y d r o g r a p h o f s t r e a m f l o w d u r i n g p e r i o d s when a l l d i s c h a r g e i s d e r i v e d f r o m g r o u n d w a t e r s o u r c e s i s known a s a b a s e - f l o w a v e r a g e s t h e s e r e c e s s i o n s i s t h e base-flow 5.6.1
recession.
A curve which
r e c e s s i o n curve.
Theory
T h e o r e t i c a l e q u a t i o n s f o r f l o w i n an a q u i f e r a r e t h e b a s i s f o r e q u a t i o n s d e s c r i b i n g a s t r e a m f l o w r e c e s s i o n c u r v e ( H a l l , 1968).
These e q u a t i o n s a r e
g e n e r a l l y of t h e form
Qt
= Qo
K-t
w h e r e Q t i s t h e d i s c h a r g e a t a n y i n s t a n t , Qo i s t h e d i s c h a r g e a t some i n i t i a l time, K i s t h e r e c e s s i o n c o n s t a n t , and t i s t h e t i m e i n t e r v a l between Qo and Q,. The p l o t o f l o g Q t a g a i n s t t i s a s t r a i g h t l i n e on s e m i l o g p a p e r .
Rorabaugh
(1964) showed t h a t e q u a t i o n 1 i s n o t c o r r e c t s h o r t l y a f t e r a r echar ge. e q u a t i o n f o r t h e movement of ground w a t e r , h a s many t e r m s ,
adapted from a heat-flow
Eis
equation,
a l l b u t t h e f i r s t of which become v e r y s m a l l a f t e r s u f f i c i e n t
time has elapsed.
A f t e r t h a t c r i t i c a l t i m e , w h i c h may b e w e e k s o r m o n t h s
d e p e n d i n g on t h e a q u i f e r c h a r a c t e r i s t i c s , R o r a b a u g h ' s e q u a t i o n g i v e s r e s u l t s comparable t o e q u a t i o n 1.
The Rorabaugh e q u a t i o n a p p l i e s t o one a q u i f e r t h a t i s
u n i f o r m , i s o t r o p i c , and h o m o g e n e o u s ; h a s a h o r i z o n t a l w a t e r s u r f a c e ; and h a s o t h e r s p e c i f i c boundary r e s t r i c t i o n s . restrictions.
N a t u r a l a q u i f e r s do n o t conform t o t h e s e
In a d d i t i o n , a s t r e a m may be f e d by s e v e r a l a q u i f e r s , each having
d i f f e r e n t d i s c h a r g e c h a r a c t e r i s t i c s and d i f f e r e n t r a t e s and t i m e s of recharge. Furthermore,
t h e a q u i f e r or a q u i f e r s may l o s e w a t e r through e v a p o t r a n s p i r a t i o n ,
and t h e w a t e r d i s c h a r g e d t o t h e s t r e a m i s s u b j e c t t o v a r i a b l e e v a p o t r a n s p i r a t i o n w i t h d r a w a l s d a i l y and s e a s o n a l l y s o t h a t t h e r e c e s s i o n o f s t r e a m f l o w i s n o t n e c e s s a r i l y a t t h e same r a t e a s t h e r e c e s s i o n of a q u i f e r outflow.
Other f a c t o r s
such as changes i n channel s t o r a g e f u r t h e r modify t h e streamflow recession. Consequently,
the theoretical straight-line
semilog recession curve i s not
a p p l i c a b l e t o many s t r e a m f l o w r e c e s s i o n s . Suppose a b a s i n h a s a l a r g e - c a p a c i t y
a r t e s i a n a q u i f e r which r e l e a s e s w a t e r
s l o w l y t o t h e s t r e a m and which i s recharged o n l y i n u n u s u a l l y wet years. pose t h i s b a s i n a l s o h a s a w a t e r - t a b l e
Sup-
a q u i f e r which i s r e c h a r g e d s e a s o n a l l y .
Assume i n i t i a l l y t h a t b o t h a q u i f e r s a r e r e c h a r g e d t o c a p a c i t y a t t h e same t i m e and t h a t t h e i n d i v i d u a l r e c e s s i o n s a r e r e p r e s e n t e d by t h e s o l i d l i n e s beginning a t z e r o days i n F i g u r e 5.5.
Then t h e t o t a l b a s e flow of t h e s t r e a m w i l l be t h e
sum of t h e two r e c e s s i o n curves.
T h i s i s r e p r e s e n t e d by t h e dashed l i n e which
becomes t a n g e n t t o t h e s o l i d l i n e of f l a t t e r s l o p e a s t h e c o n t r i b u t i o n from t h e o t h e r a q u i f e r approaches zero.
A s u b s e q u e n t r e c h a r g e o n l y of t h e w a t e r t a b l e
a q u i f e r a t 60 days w i l l produce a combined r e c e s s i o n c u r v e of d i f f e r e n t s l o p e
114 and shape.
Thus, b a s e flow r e c e s s i o n s of s t r e a m s f e d by more t h a n one a q u i f e r
may t a k e a v a r i e t y of shapes and s l o p e s a t d i f f e r e n t times.
0
120
60
180
240
DAYS
Fig. 5.5. Assumed r e c e s s i o n c u r v e s ( s o l i d l i n e s ) f r o m t w o a q u i f e r s a n d t h e streamflow r e c e s s i o n s (dashed l i n e s ) which a r e t h e sums. 5.6.2
Derivation
Base-flow
r e c e s s i o n c u r v e s a r e commonly d e r i v e d from segments of d i s c h a r g e
hydrographs when t h e r e i s no s u r f a c e r u n o f f
i n t h e channels.
Weather r e c o r d s
should be u t i l i z e d i n j u d g i n g which segments a r e u n a f f e c t e d by p r e c i p i t a t i o n . A f t e r t h e end of a s t o r m s u f f i c i e n t t i m e i s a l l o w e d f o r t h e d i r e c t r u n o f f a n d d r a i n a g e from channel s t o r a g e t o have passed t h e gage.
T h i s t i m e may range from
a few d a y s f o r a s m a l l s t r e a m t o s e v e r a l weeks f o r a l a r g e one.
Ordinarily the
segment s e l e c t e d should be a t l e a s t 10 d a y s long because s h o r t e r segments may n o t be r e p r e s e n t a t i v e .
And a segment should be s t e e p enough so t h a t subsequent
d i s c h a r g e s do n o t f a l l below an e x t e n s i o n o f t h a t segment.
Usually several
y e a r s of h y d r o g r a p h s a r e needed t o i d e n t i f y an a d e q u a t e number of r e c e s s i o n segments. These s e l e c t e d segments c a n b e s y n t h e s i z e d i n t o a f u l l r e c e s s i o n c u r v e on a p i e c e o f t r a c i n g p a p e r h a v i n g d i s c h a r g e and t i m e s c a l e s i d e n t i c a l t o t h o s e o f t h e hydrographs.
A f t e r t h e f i r s t segment i s t r a c e d ,
i z o n t a l l y so t h a t t h e o t h e r s e g m e n t s f a l l alignment.
t h e s h e e t i s s h i f t e d hor-
i n t o a common a n d c o n t i n u o u s
F i g u r e 5.6 shows t h e segments t r a c e d on the s h e e t .
A mean r e c e s s i o n
curve c a n be drawn through these. S t r e a m f l o w may r e c e d e a t d i f f e r e n t r a t e s i n d i f f e r e n t s e a s o n s b e c a u s e o f changes i n e v a p o t r a n s p i r a t i o n .
The g r a p h i c a l s y n t h e s i s d e s c r i b e d a b o v e w i l l
produce s e a s o n a l l y d i f f e r e n t r e c e s s i o n curves o n l y i f t h e y e a r i s d i v i d e d a priori.
A method w i t h o u t t h i s l i m i t a t i o n b e g i n s w i t h s e l e c t i o n ,
from t h e iden-
t i f i e d r e c e s s i o n s , o f s e g m e n t s o f a common l e n g t h , s u c h a s 10 d a y s .
For each
115
200
'
0
I
I
I
I
20
40
60
80
100
DAYS
F i g . 5.6. S e g m e n t s o f h y d r o g r a p h r e c e s s i o n s t r a c e d on a s h e e t t o d e f i n e t h e r e c e s s i o n c u r v e , James R i v e r , V i r g i n i a . segment, t h e d i s c h a r g e s o f t h e b e g i n n i n g day and t h e t e n t h day f o l l o w i n g a r e p l o t t e d a s shown on t h e l e f t g r a p h of F i g u r e 5.7.
The p o i n t s c a n b e i d e n t i f i e d
cn LL
0
z
cn LL
Ir
0
t-
4 cn
w
2
I
W
a
t
2
w 2
4 0
1OoL100 200
1 0 0 500
1000
2000
0
20
DISCHARGE A T BEGINNING DAY, IN CFS
40
60
80
100
DAYS
F i g . 5.7. S y n t h e s i s o f a b a s e - f l o w r e c e s s i o n c u r v e f r o m s e l e c t e d 10-day g r a p h segments, B u f f a l o R i v e r n e a r L o b e l v i l l e , Tennessee.
hydro-
b y month so t h a t mean r e l a t i o n s by s e a s o n s c a n b e d r a w n i f s i g n i f i c a n t d i f f e r e n c e s a r e found ( t h e y were n o t found i n t h e s e d a t a ) .
The mean l i n e of f i g u r e
5.7 was t r a n s f o r m e d t o t h e r e c e s s i o n c u r v e b y b e g i n n i n g a t 1 0 0 0 c f s p l o t t e d a t z e r o days.
T h e n t h e d i s c h a r g e 1 0 d a y s l a t e r i s p l o t t e d a t d a y 10.
Nest, t h e
d a y 1 0 d i s c h a r g e i s u s e d a s b e g i n n i n g d i s c h a r g e t o d e t e r m i n e t h e d i s c h a r g e 10
116 This process i s repeated u n t i l the complete
days l a t e r ( t o be p l o t t e d a t 2 0 ) .
r e c e s s i o n c u r v e ( t h e r i g h t c u r v e of F i g u r e 5.7) 5.6.3
i s defined.
Assumptions a s t o r e c h a r g e
Most s u b s t a n t i a l r i s e s i n s t r e a m f l o w a r e accompanied by an a p p a r e n t i n c r e a s e
i n base f l o w which may be drainage from bank storage rather than from a recharge t o the aquifer.
The a s s u m p t i o n s made a s t o r e c h a r g e , or l a c k o f i t , f r o m a
p a r t i c u l a r s t o r m i n a p a r t i c u l a r season g r e a t l y i n f l u e n c e t h e c h a r a c t e r i s t i c s of t h e d e r i v e d r e c e s s i o n c u r v e and c o n s e q u e n t l y i t s r e l i a b i l i t y and meaning.
The
a p p r o p r i a t e assumption a s t o r e c h a r g e depends on t h e b a s i n and channel characteristics,
t h e magnitude of t h e p r e c i p i t a t i o n ,
t i m e o f year.
antecedent conditions,
and t h e
Knowledge of t h e b a s i n and s t u d y of t h e hydrograph i n c o n j u n c t i o n
w i t h w e a t h e r r e c o r d s s h o u l d l e a d t o a r e a s o n a b l e concept f o r a p a r t i c u l a r s t r e a m site. 5.6.4
Seasonal v a r i a b i l i t y
E v a p o t r a n s p i r a t i o n l o s s e s from t h e a q u i f e r and from t h e channel v a r y g r e a t l y w i t h t i m e o f y e a r and may v a r y w i t h e l e v a t i o n of t h e w a t e r t a b l e and w i t h s t r e a m discharge.
Consequently,
i t h a s been t h e p r a c t i c e t o d e f i n e s e p a r a t e r e c e s s i o n
c u r v e s f o r summer a n d f o r w i n t e r p e r i o d s .
The w i n t e r r e c e s s i o n c u r v e s h o u l d
more c l o s e l y r e p r e s e n t t h e d i s c h a r g e f r o m g r o u n d - w a t e r s o u r c e s b e c a u s e t h e l o s s e s t o t h e atmosphere a r e minor d u r i n g w i n t e r .
Unfortunately,
t h e frequency
o f p r e c i p i t a t i o n d u r i n g w i n t e r and t h e f l u c t u a t i o n s o f t e m p e r a t u r e a b o v e and below f r e e z i n g produce s u c h f l u c t u a t i o n s i n s t r e a m f l o w t h a t i t becomes n e a r l y i m p o s s i b l e t o d i s c r i m i n a t e p e r i o d s o f b a s e f l o w f o r many streams. m o s t r e c e s s i o n c u r v e s a r e d e f i n e d f o r summer c o n d i t i o n s .
Consequently,
Data a v a i l a b l e f o r
B r a n d y w i n e C r e e k a t Chadds F o r d , Pa. p e r m i t t h e d e f i n i t i o n o f c u r v e s f o r b o t h summer and w i n t e r ( s e e F i g u r e 5.8).
Obviously, t h e r e c e s s i o n r a t e does n o t
change a b r u p t l y from one c u r v e t o t h e o t h e r ; t h e r e f o r e t h e s e c u r v e s do n o t a p p l y t o s p r i n g and f a l l c o n d i t i o n s .
Other f a c t o r s t h a t cause v a r i a b l e recession
r a t e s a r e d e s c r i b e d by Riggs (1964b). 5.7
WATER QUALITY CHARACTEBISTICS The g r e a t many c o n s t i t u e n t s and c h a r a c t e r i s t i c s of a n a t u r a l w a t e r r u l e o u t
any s i m p l e d e s c r i p t i o n of t h e q u a l i t y of a water.
But some g e n e r a l i z a t i o n s a r e
u s e f u l a s i n d i c a t o r s of whether a w a t e r i s l i k e l y t o be s u i t a b l e f o r a p a r t i c u l a r purpose.
The s i g n i f i c a n t c h a r a c t e r i s t i c s of w a t e r and i t s i m p u r i t i e s t h a t
a f f e c t q u a l i t y f o r v a r i o u s u s e s a r e d i s c u s s e d by Camp (1963) and by Hem (1972, p. 320-336).
T h e s e c h a r a c t e r i s t i c s i n c l u d e t e m p e r a t u r e and t h e a m o u n t s o f
suspended sediment, d i s s o l v e d s o l i d s , and b i o l o g i c a l m a t e r i a l i n t h e water. Water t e m p e r a t u r e changes s e a s o n a l l y ; i t may even change throughout a day on s m a l l streams.
The v a r i a t i o n o f weekly or monthly mean t e m p e r a t u r e s throughout
117 t h e y e a r p r o v i d e s i n f o r m a t i o n n e e d e d f o r many u s e s .
F i g u r e 5.9
shows t h e
s e a s o n a l c y c l e s o f w a t e r t e m p e r a t u r e i n a n o r t h e r n and a s o u t h e r n S t a t e .
0
60
30
90
120
DAYS
F i g . 5.8. W i n t e r ( u p p e r ) a n d summer ( l o w e r ) b a s e - f l o w Brandywine Creek n e a r Chadds Ford, Pennsylvania.
recession curves f o r
The s e d i m e n t t r a n s p o r t e d by a s t r e a m i s a measure o f w a t e r q u a l i t y , and i t i s t h e b a s i s f o r c o m p u t a t i o n of t h e sediment d e p o s i t i o n t o be expected i n r e s e r voirs,
downstream channels,
or e s t u a r i e s .
Sediment c o n c e n t r a t i o n i s needed i n
t h e d e s i g n and management of w a t e r - t r e a t m e n t
facilities; it
ized by t h e frequency d i s t r i b u t i o n of d a i l y means.
can be c h a r a c t e r -
Where only o c c a s i o n a l s e d i -
ment measurements a r e a v a i l a b l e t h e d i s t r i b u t i o n of d a i l y mean c o n c e n t r a t i o n s c a n b e a p p r o x i m a t e d f r o m a s e d i m e n t - r a t i n g c u r v e ( S e c t i o n 3.1.9) a n d a f l o w d u r a t i o n curve. The mean annual sediment l o a d i s t h e a p p r o p r i a t e c h a r a c t e r i s t i c f o r use in
A
e s t i m a t i n g t h e amount o f s e d i m e n t t h a t w i l l b e d e p o s i t e d i n a r e s e r v o i r .
s h o r t r e c o r d o f annual sediment l o a d may be extended by u s e of a long s t r e a m f l o w r e c o r d and a s e d i m e n t r a t i n g curve. Chemical q u a l i t y of a w a t e r depends on t h e amounts of each of many c o n s t i t u e n t s (Swenson and Baldwin,
1965).
The w a t e r may c o n t a i n m i n e r a l s and o r g a n i c
compounds t h a t a r e u n d e s i r a b l e f o r c e r t a i n uses.
Mineral c o n t e n t also d e t e r -
mines whether t h e w a t e r i s hard or s o f t and a c i d or a l k a l i n e . S p e c i f i c c o n d u c t a n c e i s an i n d i c a t i o n o f t o t a l d i s s o l v e d s o l i d s .
Waters
having s p e c i f i c conductances o f l e s s than a few hundred micromhos p e r c e n t i m e t e r g e n e r a l l y a r e c o n s i d e r e d good.
But t h e c o n c e n t r a t i o n of d i s s o l v e d s o l i d s ,
t h u s t h e conductance, changes w i t h d i s c h a r g e .
and
A more i n f o r m a t i v e c h a r a c t e r i s t i c
t h a n t h e maximum or t h e average conductance would be t h e frequency d i s t r i b u t i o n of d a i l y mean conductances or t h e r e l a t i o n of conductance t o s t r e a m d i s c h a r g e .
*
118
LL v)
W
U
30
J
I
F
I
1
M
A
I M
I J
I
I
I
1
I
J
A
S
O
N
D
MONTHS
Fig. 5.9.
Variation in mean monthly water temperatures.
Various methods of graphically representing the concentrations of the principal dissolved constituents are described by Hem (1972). Such graphs permit ready comparisons among waters. Hardness is indicated by the concentration of calcium carbonate or its equivalent: water with less than 60 mg/l of hardness is considered soft.
The pH is
the characteristic that indicates whether the water is acid or alkaline and to what degree. The biological content of a water is usually the result of pollution and cannot be simply characterized quantitatively, although the dissolved oxygen content is an indicator. Simplistic indicators of chemical quality are useful for preliminary studies and evaluations but more detailed information is usually required in planning a specific use of a water. REFERENCES Camp, T.R, 1963, Water and its impurities: New York, Reinhold Publ. Corp., 355 P. Carroon, L.E., 1970, Correlative estimates of streamflow in the upper Colorado River basin: U.S. Geol. Survey Water-Supply Paper 1875, 145 p. and Linsley, RK., 1966, Digital simulation in hydrology: StanCrawford, N.& ford Watershed Model IV: Dept. of Civil Engineering, Stanford University, Tech. Rept. No. 39, 210 p.
119 Piering, M.B., 1963. Use of correlation to improve e s t i m a t e s of the m e a n and variance: U.S. Geol. Survey Prof. Paper 434-c. Hall, P.R., 1968, Base-flow recessions - a review: Vol. 4. NO. 5, p. 973-983.
W a t e r Resources Research.
Hem. J.D., 1972, Study and interpretation of the c h e m i c a l characteristics of natural water: U.S. Geol. Survey W a t e r S u p p l y Paper, 1473. Second Edition. 3 6 3 p. 1964, Use of precipitation records in the correlation of streamMartin, R.O.R., flow records: International Assoc. of Scientific Hydrology Boll., Vol. IX. NO. 4. p. 24-31. 1968, Synthesizing daily discharge from rainfall records: Journal Moore, D.O.. o f Hydraulics Division, ASCE, Vol. 94, No. HYS, Proc. P a p e r 6119, p. 12831298. 19641. Stream discharge regressions using precipitation: Riggs. H.C., Geol. Survey Prof. P a p e r 501-C, p. 185-187.
U.S.
Riggs. H.C., 1964b, T h e base-flow recession c u r v e a s a n indicator of ground water: International Assoc. of Scientific Hydrology Pnbl. 63. Berkeley. p. 352-363. Rorabaugh, M.I., 1964. Estimating changes in b a n k storage and ground-water contribution to streamflow: International Assoc. of Scientific Hydrology Publ. 63. Berkeley, p. 432-441. Schneider, W.J.. 1961, Precipitation as a variable in the correlation of runoff data: U.S. Geol. Survey Prof. P a p e r 424-B, Article 9. Schauss, C.E., and Monro. J.C., 1969. Continuous hydrograph Sittner. W.T.. synthesis w i t h a n API-type hydrologic model: W a t e r Resources Research, Vol. 5, NO. 8, p. 1007-1022. Swenson, H.A. and Baldwin, H.L., Survey, 2 7 p.
1965. A p r i m e r on w a t e r quality:
U.S.
Geol.
This Page Intentionally Left Blank
121
Chapter 6
RFLATXON OF GROUND WATER M STREAMFLOW 6.1
INTRODUCTION Ground w a t e r and s u r f a c e w a t e r a r e o f t e n s t u d i e d i n d e p e n d e n t l y b u t a p a r t i c -
u l a r p a r t i c l e o f w a t e r may b e c o n s i d e r e d ground w a t e r a t one t i m e and s u r f a c e w a t e r a t a n o t h e r i n i t s t r a n s i t of t h e land.
A p r o p e r i n t e r p r e t a t i o n of stream-
flow c h a r a c t e r i s t i c s r e q u i r e s an u n d e r s t a n d i n g of how ground w a t e r i s r e p l e n i s h ed and d e p l e t e d and how t h e s e changes r e l a t e t o streamflow. Ground w a t e r f i l l s t h e pore s p a c e s and f r a c t u r e s i n t h e e a r t h m a t e r i a l s t o a l e v e l known a s t h e w a t e r t a b l e . c a l l e d an aquifer.
The p o r o u s m a t e r i a l t h a t c o n t a i n s w a t e r i s
I f t h e porous m a t e r i a l e x t e n d s t o t h e ground s u r f a c e ,
SO
t h a t t h e w a t e r t a b l e i s f r e e t o move v e r t i c a l l y i n response t o changes i n volume of w a t e r i n storage, the a q u i f e r i s c a l l e d a water-table
aquifer.
I f t h e upper
p a r t i s c o n f i n e d by a n i m p e r m e a b l e or s e m i p e r m e a b l e r o c k f o r m a t i o n , and t h e ground w a t e r i s under p r e s s u r e ,
the aquifer i s artesian.
Many a q u i f e r s i n humid r e g i o n s d i s c h a r g e a t l e a s t f o r p a r t o f t h e y e a r t o t h e ground s u r f a c e e i t h e r through s p r i n g s or d i r e c t l y t o a s t r e a m channel a s shown i n F i g u r e 6.1.
K i l p a t r i c k (1964) showed t h a t t h e low flow of a s m a l l s t r e a m i n
Georgia was d e r i v e d from d i s c h a r g e s of a w a t e r - t a b l e leakage from an a r t e s i a n a q u i f e r .
a q u i f e r and from upward
A q u i f e r s i n a r i d r e g i o n s may d i s c h a r g e o n l y
by e v a p o t r a n s p i r a t i o n .
Fig. 6.1. V a l l e y c r o s s s e c t i o n showing how a q u i f e r s d i s c h a r g e t o a s t r e a m and t o a spring. The r a t e of movement of ground w a t e r depends on t h e h y d r a u l i c g r a d i e n t and t h e t r a n s m i s s i v i t y of t h e a q u i f e r m a t e r i a l . t h a n 2 o r d e r s o f magnitude.
T r a n s m i s s i v i t y may range o v e r more
Consequently t h e v e l o c i t y of ground w a t e r may range
122 f r o m a f e w f e e t p e r y e a r i n c l a y t o many f e e t p e r d a y t h r o u g h v e r y p o r o u s material.
Soluble rocks, such a s limestone, o f t e n c o n t a i n s o l u t i o n channels
t h r o u g h w h i c h g r o u n d w a t e r moves r a p i d l y .
F i g u r e 6.2 s h o w s h y d r o g r a p h s o f 2
s p r i n g s which i l l u s t r a t e t h e d i f f e r e n t r a t e s o f g r o u n d - w a t e r Daniel Spring d r a i n s a l i m e s t o n e a r e a ;
movement.
Jack
i t s r a p i d response t o r a i n f a l l i n d i c a t e s
t h e p r o b a b l e e x i s t e n c e o f s i n k s and s o l u t i o n c h a n n e l s i n t h e b a s i n .
The more
t y p i c a l hydrograph of I n d i a n Ford S p r i n g r e f l e c t s slow i n f i l t r a t i o n through t h e s o i l and slow movement through t h e a q u i f e r ; i t does n o t f o l l o w t h e hydrograph of t h e nearby stream.
50
500
20
10
5
2
1
x
\I,
200
100
50
20 I
I
OCTOBER 1975
10
SPRING
I
1
OCTOBER 1947
Fig. 6.2. Eydrographs of two s p r i n g s , and of a s t r e a m n e a r one of them, t h e d i f f e r e n c e s i n flow v a r i a b i l i t y .
showing
Spring flow i s l e s s v a r i a b l e i f t h e recharge a r e a i s d i s t a n t from t h e d i s c h a r g e p o i n t and i f t h e a q u i f e r i s n o t s u b j e c t t o e v a p o t r a n s p i r a t i o n . s p r i n g s a r e b e t t e r i n d i c a t o r s of ground-water
Such
d i s c h a r g e t h a n a r e t h e low f l o w s
of streams. AQUIFER RECHARGE
6.2
Ground w a t e r i s r e p l e n i s h e d b y r a i n or m e l t i n g snow w h i c h i n f i l t r a t e s t h e soil.
In t e m p e r a t e , humid c l i m a t e s t h e major r e p l e n i s h m e n t or r e c h a r g e o c c u r s
d u r i n g t h e w i n t e r and s p r i n g months when p r e c i p i t a t i o n i s p l e n t i f u l , evapotransp i r a t i o n i s low,
and s o i l m o i s t u r e i s high.
During t h e growing s e a s o n a l a r g e
p a r t of t h e p r e c i p i t a t i o n i s h e l d i n t h e s o i l u n t i l i t i s r e t u r n e d t o t h e atmosphere by e v a p o t r a n s p i r a t i o n .
Thus t h e c o n t r i b u t i o n of a s u b s t a n t i a l r a i n
123 t o t h e ground w a t e r body r a n g e s from a maximum i n w i n t e r o r e a r l y s p r i n g t o v e r y l i t t l e f o l l o w i n g a l o n g d r y p e r i o d i n summer.
In m o s t a r i d r e g i o n s t h e w a t e r t a b l e i s b e l o w t h e s t r e a m b e d s and t h u s t h e s t r e a m s a r e ephemeral.
Here a s u b s t a n t i a l s t o r m w i l l produce s t r e a m f l o w and
some i n f i l t r a t i o n over t h e b a s i n b u t l i t t l e of t h a t i n f i l t r a t e d w a t e r g e t s below plant roots.
Recharge,
i f any,
o c c u r s a s l e a k a g e through t h e s t r e a m b e d s whose
p e r m e a b i l i t y may be i n c r e a s e d t e m p o r a r i l y by t h e f a s t ,
t u r b u l e n t flows.
Jordan
(1977) r e p o r t e d s u b s t a n t i a l t r a n s m i s s i o n l o s s e s i n s t r e a m s i n w e s t e r n Kansas; most of t h e w a t e r l o s t from t h e s e c h a n n e l s i s a c c r e t i o n t o ground water. The amount o f r e c h a r g e t o a n a q u i f e r f r o m a s t o r m may b e c o m p u t e d f r o m t h e r i s e i n t h e w a t e r t a b l e a s measured i n w e l l s , t h e e s t i m a t e d p o r o s i t y of t h e aquifer material.
and t h e e x t e n t of t h e a q u i f e r .
P o r o s i t y i s t h e p e r c e n t a g e of
void s p a c e r e l a t i v e t o t h e t o t a l volume of t h e mass. 6 .3
HYDROGRAPH INTERPRETATION The s t r e a m f l o w hydrograph c o n t a i n s c o n s i d e r a b l e i n f o r m a t i o n about t h e hydrol-
ogy o f a b a s i n .
Highly-variable
d a i l y d i s c h a r g e s i n d i c a t e r a p i d r u n o f f and
l i t t l e i n f i l t r a t i o n , e s p e c i a l l y i f t h e mimimum f l o w s a r e p a r t i c u l a r l y low.
Very
uniform f l o w s throughout t h e y e a r a r e produced by b a s i n s on which much of t h e p r e c i p i t a t i o n r e a c h e s t h e w a t e r t a b l e on i t s way t o t h e stream. The hydrographs of F i g u r e 6.3 c o n t r a s t t h e r u n o f f p a t t e r n s of d r a i n a g e b a s i n s o n l y 50 m i l e s a p a r t .
R u n o f f s i n i n c h e s a r e a b o u t t h e same b u t t h e a n n u a l
Pig. 6.3. C o n t r a s t i n r u n o f f p a t t e r n s of s t r e a m s d r a i n i n g b a s i n s of d i f f e r e n t p e r m e a b i l i t y (From McGuinness, 1963).
124 v a r i a b i l i t y a s w e l l a s t h e d a i l y v a r i a b i l i t y i s much g r e a t e r on W i l d c a t Creek. According t o YcGuinness (1963) W i l d c a t Creek f l o w s f r om a b a s i n f l o o r e d w i t h clayey till.
The c r e e k r e s p o n d s q u i c k l y t o p r e c i p i t a t i o n a n d t h e n f a l l s o f f
r a p i d l y t o a low b a s e flow.
T i p p e c a n o e R i v e r d r a i n s a b a s i n i n much o f w h i c h
permeable sandy g r a v e l l y g l a c i a l outwash l i e s a t t h e s u r f a c e . a b s o r b s much of t h e p r e c i p i t a t i o n ,
This outwash
p r e v e n t i n g s h a r p f l o o d peaks and r e l e a s i n g
w a t e r s l o w l y t o m a i n t a i n a l a r g e r b a s e flow. The r e l a t i o n o f g r o u n d w a t e r t o s t r e a m f l o w c a n b e i m p l i e d b y s t u d y o f t h e s t r e a m hydrograph.
A t t h e end o f a l o n g p e r i o d o f f a i r w e a t h e r t h e f l o w i n a
s t r e a m u s u a l l y w i l l b e from ground w a t e r ( b u t i t w i l l b e l e s s t h a n t h e d i s c h a r g e from t h e ground-water body because o f e v a p o t r a n s p i r a t i o n ) .
Overland f l o w from a
heavy r a i n w i l l i n c r e a s e t h e f l o w i n t h e s t r e a m channel a s shown i n F i g u r e 6.4.
Fig. 6.4. Streamflow hydrograph showing t h e i n c r e a s e i n b a s e flow (Ground w a t e r d i s c h a r g e ) r e s u l t i n g from a storm. Some o f t h e w a t e r t h a t a r r i v e s r a t h e r q u i c k l y i n t h e c h a n n e l t r a v e l s by a s h a l l o w s u b s u r f a c e course:
i t may be r e g a r d e d a s ground w a t e r a l t h o u g h i t be-
longs i n a d i f f e r e n t c a t e g o r y than w a t e r i n t h e f o r m a t i o n s below t h e w a t e r table.
A n o t h e r p o r t i o n o f t h e r a i n f a l l i n f i l t r a t e s t o t h e g r o u n d w a t e r body,
r a i s i n g t h e w a t e r t a b l e , i n c r e a s i n g t h e head t o w a r d t h e s t r e a m , and t h u s i n c r e a s i n g t h e b a s e f l o w r a t e o v e r t h a t p r i o r t o t h e s t o r m a s shown i n F i g u r e 6.4. The p o r t i o n of s t r e a m f l o w d e r i v e d from ground w a t e r d u r i n g o r c l o s e l y f o l l o w ing a p e r i o d of overland runoff cannot b e e s t i m a t e d c l o s e l y .
However w a t e r -
t a b l e p r o f i l e s n e a r a s t r e a m d u r i n g changes i n s t r e a m s t a g e i n d i c a t e t h e d i r e c t i o n of ground-water
flow a t various times.
A s shown i n F i g u r e 6.5, t h e g r a -
d i e n t of t h e w a t e r t a b l e i s towards t h e s t r e a m when t h e s t r e a m s t a g e i s low. the stage r i s e s , the water-table
As
g r a d i e n t d e c r e a s e s and f i n a l l y r e v e r s e s , a t
which t i m e w a t e r from t h e s t r e a m f l o w s i n t o t h e banks.
A t t h e same t i m e ground
w a t e r t h a t o t h e r w i s e would have gone t o t h e s t r e a m i s b e i n g s t o r e d f u r t h e r inland.
As the stream s t ag e recedes t h e water t a b l e gr adi ent begins i t s r e t u r n
t o normal.
125
W
U
Q
13LAND SURFACE
0
11
-
-
9-
7-
51 I
I
I
I
HORIZONTAL DISTANCE, FEET
Ground w a t e r l e v e l s and flow d i r e c t i o n s d u r i n g t h e r i s i n g and f a l l i n g Fig. 6.5. s t a g e s of a s t r e a m ( A f t e r D a n i e l and o t h e r s , 1970). Two c o n c l u s i o n s can be drawn from t h i s .
F i r s t , t h e ground-water c o n t r i b u t i o n
t o s t r e a m f l o w d u r i n g a f l o o d r u n o f f becomes n e g a t i v e d u r i n g t h e r i s i n g s t a g e and l a t e r i n c r e a s e s above t h e p r e v i o u s b a s e flow a s t h e s t a g e d e c r e a s e s (Fig. 6.6). Second, t h e w a t e r s t o r e d n e a r t h e c h a n n e l d u r i n g t h e r i s e t a k e s some t i m e t o d r a i n away,
thus,
f o r some t i m e a f t e r t h e flood.
t h e s t r e a m f l o w r e c e s s i o n in-
c l u d e s d r a i n a g e b o t h from bank s t o r a g e and channel s t o r a g e i n a d d i t i o n t o aquif e r drainage.
In t h e e x a m p l e o f F i g u r e 6.5, t h e s t r e a m s t a g e w a s n o t h i g h e n o u g h t o i n u n da te the adjacent land surface. t h e i r channels,
When m a j o r f l o o d s i n u n d a t e l a r g e a r e a s along
t h e v e r t i c a l i n f i l t r a t i o n i s l a r g e and t h e r e s u l t a n t s t o r a g e in
t h e f l o o d p l a i n may c o n t r i b u t e t o s t r e a m f l o w f o r a long period.
126
Hydrograph showing ground w a t e r c o n t r i b u t i o n t o a s t r e a m d u r i n g a F i g . 6.6. r i s e i n streamflow. The above i n t e r p r e t a t i o n of t h e s t r e a m f l o w hydrograph d u r i n g and f o l l o w i n g a f l o o d i s h e l p f u l i n i d e n t i f y i n g t h o s e segments of a hydrograph which r e p r e s e n t only b a s e flow.
Such s e g m e n t s a r e u s e d t o d e f i n e b a s e - f l o w r e c e s s i o n c u r v e s
( S e c t i o n 5.6) and t o e s t i m a t e t h e ground-water
y i e l d t o a s t r e a m (Riggs,
1963).
O b v i o u s l y t h e r e c e s s i o n s h o r t l y a f t e r a h y d r o g r a p h r i s e may i n c l u d e d r a i n a g e from bank s t o r a g e b u t whether a r e c h a r g e of t h e p r i n c i p a l a q u i f e d s ) was assoc i a t e d w i t h a r i s e may be l e s s c l e a r .
A hydrograph l i k e t h a t of F i g u r e 6.4 d o e s
n o t always i n d i c a t e t h a t a r e c h a r g e occurred.
In F i g u r e 6.7,
t h e hydrograph f o r
t h e l a t t e r p a r t o f J u l y and t h e f i r s t h a l f o f A u g u s t d e f i n e s t h e s l o p e o f t h e base-flow
r e c e s s i o n curve.
An e x t e n s i o n of t h a t curve through September would
b e v e r y c l o s e t o t h e h y d r o g r a p h f o r m o s t o f t h a t month, i n d i c a t i n g t h a t t h e storm of l a t e August d i d n o t r e c h a r g e t h e a q u i f e r a p p r e c i a b l y .
v)
;f
500
z
JULY
AUG
SEPT
Fig. 6.7. Hydrograph f o r N.F. Obion River, b l e r e c h a r g e from t h e l a t e August storm.
Tennessee,
which i n d i c a t e s n e g l i g i -
The assumption t h a t r e c h a r g e o c c u r r e d from a s t o r m t h a t produced a p p r e c i a b l e d i r e c t r u n o f f c a n b e checked.
C o n s i d e r F i g u r e 6.8
(dashed) i n d i c a t e a p p r e c i a b l e r e c h a r g e i n May and June.
i n which t h e r e c e s s i o n s The volume of r e c h a r g e
i s t h e d i f f e r e n c e i n t h e volumes under t h e two r e c e s s i o n c u r v e s from some common d a t e t o such t i m e a s t h e curves reach n e g l i g i b l e discharges.
The Red R i v e r
127
5000 !
I
I
.
100
I
I
I
MAY
JUNE
I
I
i
JULY
Fig. 6.8. Hydrograph f o r Red River, Tennessee, 1955, which i n d i c a t e recharge from May and June storms.
showing r e c e s s i o n curves
r e c e s s i o n curve would drop from 500 c f s t o 1 c f s i n about 150 days. d i f f e r e n c e can be d e f i n e d g r a p h i c a l l y recession curve i s defined. respect t o the rainfall, i t i s not,
- or
The volume
m a t h e m a t i c a l l y i f t h e equation of t h e
The computed r e c h a r g e s h o u l d b e r e a s o n a b l e w i t h
t h e measured runoff, and t h e e s t i m a t e d evaporation.
If
t h e e s t i m a t e of t h e amount of base flow f o l l o w i n g ( o r preceding) t h e
r i s e i s incorrect.
I n t h e a b s e n c e of r a i n f a l l r e c o r d s one m i g h t a p p r a i s e
w h e t h e r t h e computed r e c h a r g e i s r e a s o n a b l e f o r t h e m a g n i t u d e of t h e r i s e i n streamflow.
Data f o r o t h e r r i s e s would be needed f o r t h i s t e s t :
see references
i n s e c t i o n 11.5.3.
A word o f w a r n i n g : t h e s t o r m h y d r o g r a p h o f a n e p h e m e r a l s t r e a m may l o o k s i m i l a r t o one f o r a s t r e a m w i t h a dependable ground-water c o n t r i b u t i o n .
Study
o f s u c h a h y d r o g r a p h f o r a few months w i l l show t h a t t h e a p p a r e n t i n c r e a s e i n b a s e f l o w f o l l o w i n g a p e a k i s n o t due t o r e c h a r g e o f a g r o u n d - w a t e r body: i t probably r e f l e c t s t h e d r a i n a g e from channel and bank storage. 6.4
BANK STORAGE IN SURFACE RESERVOIRS .The s t o r a g e c a p a c i t i e s of s u r f a c e r e s e r v o i r s a t v a r i o u s l e v e l s a r e defined by
topographic surveys. operations.
The r e s u l t i n g stage-capacity
curves a r e used i n r e s e r v o i r
But when some r e s e r v o i r s a r e f i l l e d f o r t h e f i r s t t i m e t h e y t a k e
c o n s i d e r a b l y more w a t e r t h a n i s i n d i c a t e d b y t h e s t a g e - c a p a c i t y later,
curve.
a r e d u c t i o n i n r e s e r v o i r s t a g e produces more w a t e r than expected.
And These
e f f e c t s a r e d u e t o t h e i n f i l t r a t i o n o f w a t e r i n t o t h e b a n k s of t h e r e s e r v o i r ( p r e s u m a b l y t h e p r o j e c t i n v e s t i g a t i o n a s s u r e d t h a t t h e g e o l o g i c s e t t i n g cont a i n e d nothing t h a t would p e r m i t s t o r e d w a t e r t o bypass t h e dam). Bank s t o r a g e below t h e o p e r a t i n g s t a g e of a r e s e r v o i r i s merely an a d d i t i o n t o dead sto r a g e .
B u t w i t h i n t h e o p e r a t i n g r a n g e bank s t o r a g e i s i n c r e a s e d
128 d u r i n g r i s i n g s t a g e s and i s d e c r e a s e d d u r i n g f a l l i n g s t a g e s .
The magnitude of
bank s t o r a g e changes may b e l a r g e enough t o b e taken i n t o account i n r e s e r v o i r operation.
F o r e x a m p l e , Simons a n d R o r a b a u g h (1971) c o m p u t e d t h e d e a d or i n -
a c t i v e a q u i f e r - s t o r a g e c a p a c i t y o f Hungry H o r s e R e s e r v o i r , Montana a s a b o u t 50.000
cfs-days.
and t h e a c t i v e c a p a c i t y about 100,000 cfs-days.
However,
the
a v a i l a b l e w a t e r f r o m a q u i f e r s t o r a g e d e p e n d s on t h e m a g n i t u d e of t h e s t a g e r e d u c t i o n and on t h e t i m e t h e s t a g e i s h e l d a t t h e l o w e r l e v e l :
complete d r a i n -
age from a bank a q u i f e r may t a k e months. 6.5
THE WATER RESOURCE Although t h e r e a r e many r e a s o n s f o r s t u d y i n g ground w a t e r and s u r f a c e w a t e r
separately,
one should r e c o g n i z e t h a t t h e t o t a l renewable w a t e r r e s o u r c e of a
b a s i n i n t h e flow of t h e s t r e a m a s i t l e a v e s t h e bazin.
The g r o u n d - w a t e r
r e s o u r c e i s i n c l u d e d i n t h e s t r e a m f l o w : any w i t h d r a w a l of ground w a t e r w i l l reduce streamflow.
B u t t h e two r e s o u r c e s a r e i n d e p e n d e n t , o r n e a r l y so, i n
r e g i o n s where t h e w a t e r t a b l e i s below s t r e a m c h a n n e l s and i s n o t a f f e c t e d by i n f i l t r a t i o n from t h e streams. able:
Here o n l y t h e s u r f a c e w a t e r r e s o u r c e i s renew-
t h e ground w a t e r r e s o u r c e i s not.
Within a b a s i n i t i s p o s s i b l e t o p r o v i d e a more dependable s u p p l y by u t i l i z i n g s t o r a g e o f w a t e r i n t h e g r o u n d i f t h e s t o r a g e a q u i f e r i s n o t c l o s e l y conn e c t e d ( i n t i m e ) t o a stream.
Then w i t h d r a w a l s of ground w a t e r w i l l n o t reduce
streamflow d u r i n g t h e low-water period. supplement low s t r e a m f l o w s ;
Conjunctive u s e i s a management t o o l t o
i t does n o t change t h e t o t a l supply.
O t h e r a c t i v i t i e s o f man i n w h i c h g r o u n d w a t e r n e e d s t o b e c o n s i d e r e d a r e channel deepening,
which may provide a b e t t e r c o n n e c t i o n t o an a q u i f e r :
raising
a r i v e r l e v e l b y dams, w h i c h r a i s e s t h e l e v e l of t h e a d j a c e n t w a t e r t a b l e : d i v e r s i o n of s t r e a m f l o w from a l o s i n g stream, ground-water
recharge:
which may reduce t h e downstream
and r o u t i n g o f r e s e r v o i r r e l e a s e s down a channel where
the w a t e r t a b l e i s i n c o n t i n u i t y w i t h the stream.
Moench. S a n e r a n d J e n n i n g s
(1974) f o u n d t h a t r e s u l t s o f r o u t i n g r e s e r v o i r r e l e a s e s w e r e a p p r e c i a b l y i m proved by i n c l u s i o n of a gross s i m p l i f i c a t i o n of t h e ground-water
system.
RPPERENCES D a n i e l , J.F., C a b l e , L.W., and Wolf, R.J., 1 9 7 0 , Ground w a t e r - s u r f a c e w a t e r r e l a t i o n d u r i n g p e r i o d s o f o v e r l a n d f l o w : U.S. Geol. S u r v e y P r o f . P a p e r 700-B, p. 219-223. 1977. Streamflow t r a n s m i s s i o n l o s s e s i n w e s t e r n Kansas: Jordan, P.R., t h e H y d r a u l i c s D i v i s i o n , ASCE, Vol. 1 0 3 , No. HY8, p. 905-919.
Jour. of
K i l p a t r i c k , F.A., 1964, Source of base flow of s t r e a m s : I n t e r n a t i o n a l Assoc. of S c i e n t i f i c Hydrology Publ. No. 63, Berkeley, p. 329-339. McGuinness, C.L., 1 9 6 3 , The r o l e o f g r o u n d w a t e r i n t h e n a t i o n a l w a t e r s i t u a tion: U.S. Geol. Survey Water-Supply 1800, 1121 p.
-
129 Moench, A.P., S a n e r , V.B., and J e n n i n g s , M.E., s t r e a m f l o w by channel loss and base flow: 10, No. 5, p. 963-968.
1974, M o d i f i c a t i o n o f r o u t e d Water Resources Research, Vol.
R i g g s , H.C., 1963, The b a s e - f l o w r e c e s s i o n c u r v e a s a n i n d i c a t o r o f ground water: I n t e r n a t i o n a l Assoc. of S c i e n t i f i c Hydrology P u b l . NO. 63, Berkeley, p. 352-363.
Simons, W.D. and Rorabaugh, M.I., 1971, Hydrology of Hungry Horse R e s e r v o i r , n o r t h w e s t e r n Montana: U.S. Geol. Survey Prof. Paper 682.
This Page Intentionally Left Blank
131
Chapter 7
FLOW CHARACTERISTICS AT UNGAGED SITES
7.1
INTRODUCTION Although hydrologic data have b e e n collected at thousands o f sites, those
sites constitute only a small sample of the sites where flow characteristics may be needed.
The information at gaged sites permits the calibration of various
procedures for transferring flow characteristics to ungaged sites or estimating them from rainfall.
Methods are categorized into ones that require drainage-
basin and climatic characteristics obtainable from maps and climatic records, and those that require a s m a l l amount of data to be collected at the site of interest.
I .2
NO DATA AT SITE
I .2.1
Regression analysis
Regional analysis of streamflow characteristics is a widely applicable and fairly simple method.
Using data at gaging stations, a flow characteristic is
related to basin and climatic characteristics, usually by multiple regression. An example is log Q25 = -2.07 + 0.97 log A + 2.11
log P
(1)
where Q25 is the 25-year flood in cfs in the Snohomish River basin, Washington:
A is drainage area in square miles; .and P is m e a n annual precipitation in inches.
The equation is in a linear form, a requirement of the usual regression
method.
It may be transformed to
QZ5 = 0.0085
AoSg1 P2*11
(2)
F o r a stream site in the S n o h o m i s h River b a s i n QZ5 can be e s t i m a t e d f r o m the equation using drainage area measured above the site, and the mean annual rainfall on that drainage area from an isohyetal map.
The reliability of the result
is indicated by the standard error of the regression, 0.14 log units, w h i c h corresponds to +38 and -28 percent. Multiple regression is directly useful as a regionalization tool because the discharge for a given frequency level can be related to basin characteristics, leaving residuals that may be considered as due to chance. averages these residuals.
The regression line
Thus, in one operation, the effects of differing
basin characteristics are preserved and the chance variation is averaged.
132 The r e g r e s s i o n model used s h o u l d a p p r o x i m a t e t h e p h y s i c a l p r o c e s s a s c l o s e l y a s p o s s i b l e and i t must be i n a l i n e a r form.
The l o g - l i n e a r f o r m i s s u i t a b l e
f o r many h y d r o l o g i c r e l a t i o n s b u t i t s h o u l d n o t be a c c e p t e d b l i n d l y .
Graphical
m u l t i p l e r e g r e s s i o n i s a good way t o d e f i n e t h e s u i t a b l e m o d e l ; a g r a p h i c a l s o l u t i o n need n o t b e l i n e a r ,
F i g u r e 7.1
however.
u s i n g t h e d a t a on which eq. 1 was based.
shows t h e g r a p h i c a l s o l u t i o n
This confirms t h a t the r e l a t i o n s with
A and P a r e l o g l i n e a r and t h a t t h e form of eq. 1 i s a p p r o p r i a t e € o r t h e s e data. The e q u a t i o n o f t h e g r a p h i c a l r e l a t i o n o f F i g u r e 7.1- i s v i r t u a l l y t h e s a m e a s e q u a t i o n 1.
100,000
1
-
10
n
Z
0 U
"/
I
Y
m p:
u a
=;
10,000-
LL Y
vm 3 U
? a O
9
1000-
'
Y
-i
0
25
EXPLANATION o Plotted point
0 47
50
100
300
M E A N ANNUAL
i
053
,
IL
1
PRECIPITATION, I N INCHES
'
Point a d j u s t e d I
for P 100' 1
1
1
10
100
i
1 1000
D R A I N A G E AREA, IN SQUARE M I L E S
Fig. 7 . 1
G r a p h i c a l a n a l y s i s of d a t a used t o d e f i n e e q u a t i o n 1.
I f a g r a p h i c a l m u l t i p l e r e g r e s s i o n i s developed on a r i t h m e t i c g r a p h p a p e r , r a t h e r than on l o g paper, and i s found t o be l i n e a r t h e model i s Y = a
+ blXl + b2X2
(3)
and t h e s t a n d a r d e r r o r i s i n u n i t s o f Y. sometimes s t a t e d i n p e r c e n t of mean Y ; from t h e mean.
S t a n d a r d e r r o r u s i n g t h i s model i s
the percentage increases w i t h d i s t a n c e
See s e c t i o n 4.4.1.
I n model e q u a t i o n 3 t h e e f f e c t s of t h e v a r i a b l e s a r e a d d i t i v e whereas i n t h e model used i n e q u a t i o n 1 t h e e f f e c t s a r e m u l t i p l i c a t i v e .
I f a v a r i a b l e can t a k e
a v a l u e of z e r o t h e n t h e l o g - l i n e a r model c a n n o t be used w i t h t h a t v a r i a b l e because z e r o does n o t have a r e a l l o g a r i t h m .
T h i s l i m i t a t i o n can be overcome by
133 adding a small constant, commonly 1 or 0.1, using the variable in regression.
to all values of the variable before
Before doing this the analyst should assure
himself that the addition will not violate the concepts used. The independent variables selecred for use in the regression analysis should be ones that can be readily quantified at ungaged sites and that are postulated to have a particular effect on the dependent variable (the flow characteristic). Selection of independent variables is often made on a statistical basis;
that
is, m a n y variables are used in p r e l i m i n a r y regressions and those that l a c k statistical significance are discarded.
This approach occasionally results in
retention of a variable whose effect on the dependent variable does not conform to hydrologic principles.
Usually the effect of such a variable is trivial.
It
s e e m s better to select in advance those variables w h i c h are expected to h a v e practical significance tical selection.
-
to rely on hydrologic judgment rather than on statis-
However, a variable that is known to affect a flow character-
istic in a particular way may not be statistically significant in a regression if the range of that variable in the s a m p l e is small.
Channel slope as a n
estimator of flood characteristics is an example of a variable that has little range in some regions. Some variables such as basin storage, channel slope, and storm magnitudes are appropriate for estimating flood characteristics but have little effect on mean flow.
Mean flow in humid regions of homogeneous geology is closely related to
drainage area and mean annual precipitation. Not all important variables c a n be quantified f r o m maps. desirable or necessary to use surrogates.
It is s o m e t i m e s
Occasionally the regression coeff i-
cient of a variable selected on a hydrologic basis appears to represent something other than that intended.
For example, consider the relation of 50-year
flood to drainage area and percent of area forested, P50 = 6.03 for California mountain streams.
For this region of large topographic relief
the regression indicates that an increase in percent area forested will produce an increase in 50-year flood, contrary to expectation.
But examination of maps
shows that forest cover increases with elevation, and presumably with precipitation.
Thus forest cover may be a surrogate for precipitation.
Although surro-
gate variables are useful, extrapolation of a regression equation which includes surrogates may produce questionable results.
The applicability of a regression equation to ungaged streams in the region for w h i c h it w a s derived depends on h o w w e l l the data used i n its derivation cover the ranges of variables in the region, and whether the variables used are adequate descriptors of the flow characteristic at all of the streams to which the regression equation might be applied.
134 If more than one regression equation is derived for a single flow characteristic, the equation with the smallest standard error is commonly used.
However,
one with fewer variables or with only those variables that are easy to quantify at an ungaged site may be selected if its standard error is not appreciably greater than the smallest standard error obtained.
There lray be no practical
difference in the results from two equations whose standard errors differ considerably. Only equations in which all the regression constants are statistically significant should be considered.
Computer programs for regression analysis either
produce regression equations which include only those variables whose effects or they show
are statistically significant at the specified level (usually 95%). the statistical significance of each variable in the equation.
Regression on basin characteristics produces best results in humid regions of fairly uniform terrain and gradual areal changes in precipitation.
The method
is not generally useful for estimating low flows because of the large influences of basin geology and evapotranspiration on those flows.
Among the factors that
limit the method are (1) large interchanges of surface and ground water due to geologic conditions, ( 2 ) large ranges in elevation in the basins, and the corresponding large range in basin precipitation, (3) poor definition of precipitation in arid regions, and (4) flow modification due to man's activities. Regression equations and their standard errors are given for many flow characteristics in four regions of the United States by Thomas and Benson (1970). 7.2.2
From rainfall
Techniques for estimating flood-peak characteristics from rainfall are discussed in Chapter 8 . Rainfall ordinarily is not a major indicator of low-flow characteristics. Mean flows of ungaged streams may be approximated from an isohyetal map if
(1) flow records from some basins in the region are available to develop a calibration, (2) the isohyetal map is based on precipitation records (someisohyetal maps are based partly on streamflow records) and (3) the geology of the region is more or less homogeneous.
In regions of high relief and the
consequent high range in precipitation from the upper to the lower part of the basin,
a
runoff-altitude relation can be developed by trial-and-error from gaged
records, even in the absence of precipitation records (Riggs
6
Moore, 1965).
This relation can be used to estimate mean flow from the measured areas in each of several elevation ranges of an ungaged basin; the sum of these partial runoffs is the runoff from the ungaged basin. 7.2.3
Interpolation along a channel
Interpolation of flow characteristics between gaged points on a stream usually produces more reliable results than regression on basin characteristics.
The
13 5 flow characteristics a r e plotted against channel length (Fig. 7.2); points of interest c a n be readily identified on the g r a p h by their relation to a gaged point.
A method of interpolating low flows is given in Chapter 9.
See Chapter
8 for another example of the method applied to floods.
I
200,000 -
1
I
I
I
1
I
I
1
I
I
100.000 50,000 -
10,000 -
5000 2000 1000
Fig. 7.2. 7.3
Flow characteristics along the main stem of James River, Virginia.
SOME DATA AT SITE
F l o w characteristics in s o m e regions are not closely related to variables that can be obtained from maps, the usual variables cannot be quantified reliably, or a s i m p l e regression m o d e l does not explain t h e relation.
In arid and
semarid regions precipitation is highly variable in time and space, extent of s t o r m s is o f t e n limited, and w e a t h e r records are few.
the areal
In basins of
large topographic relief, precipitation in the headwaters may be 4 or 5 times that in the l o w e r reaches; a b a s i n average w o u l d be a poor indicator of flow characteristics.
When topographic and ground-water divides are not coincident
the runoff f r o m a b a s i n m a y be more, or less, than that indicated by basin precipitation.
For example,
the annual runoffs of two adjacent streams in the
h e a d w a t e r s of U m p q u a River, Oregon, are 3 3 and 5 4 inches; the difference is largely due to interbasin movement of ground water.
Some drainage basins in-
clude areas that do not contribute surface runoff or that contribute only occasionally. reliably.
The contributing drainage area for such a basin cannot be defined And the efficiency with which a stream system transmits water depends
136 b o t h on geology and on topography n e i t h e r of which c a n be a d e q u a t e l y e x p r e s s e d by s i m p l e v a r i a b l e s i n some regions.
A consequence of one o r more of t h e s e c o n d i t i o n s i s t h a t mean f l o w or f l o o d p e a k s on some s t r e a m s d e c r e a s e w i t h i n c r e a s i n g d r a i n a g e a r e a .
A regression
model c a n n o t b e d e v i s e d t h a t w i l l a p p l y t o a r e g i o n i n w h i c h some s t r e a m s e x h i b i t t h i s anomalous c h a r a c t e r i s t i c . Flow c h a r a c t e r i s t i c s of s t r e a m s i n t h e s e t t i n g s d e s c r i b e d above u s u a l l y c a n be e s t i m a t e d more r e l i a b l y from some i n f o r m a t i o n a t t h e s i t e t h a n from informat i o n t a k e n f r o m maps or c l i m a t o l o g i c a l r e c o r d s .
D i s c h a r g e m e a s u r e m e n t s and
measurements of channel geometry a r e t h e most u s e f u l s i t e d a t a . 7.3.1
Mean flow from monthly measurements
Where mean f l o w i s n o t c l o s e l y r e l a t e d t o d r a i n a g e a r e a , B i g g s ( 1 9 6 9 ) h a s shown t h a t r e l i a b l e e s t i m a t e s i n some r e g i o n s can be made from monthly d i s c h a r g e measurements f o r a year. F i g u r e 7.3.
The prooedure i s d e m o n s t r a t e d i n t h e r e g i o n shown i n
The p l o t o f F i g u r e 7.4
establishes that drainage area is not a
u s e f u l e s t i m a t o r of mean f l o w i n t h i s region.
49"
--------I---
I
ALBERTA
MONTANA /---
0~
/
...
-
0
46" 113"
F i g . 7.3.
I
20
40
6 0 MILES
t-
109"
P a r t o f M i s s o u r i River b a s i n showing l o c a t i o n s of gaging s t a t i o n s .
lo00
/// I
I
5
1
li
13
F i g . 7.4.
137
R e l a t i o n o f mean flow t o d r a i n a g e a r e a a t gages shown i n F i g u r e 7.3.
B o t h a n e x p l a n a t i o n a n d a v e r i f i c a t i o n o f t h e m e t h o d a r e p r o v i d e d by u s i n g d a t a f r o m two g a g e d s t r e a m s , o n e o f w h i c h , Two M e d i c i n e C r e e k (number 7) i s c o n s i d e r e d ungaged.
C u t Bank C r e e k (number 9 ) i s u s e d a s t h e i n d e x s t a t i o n .
Assume t h a t t h e d i s c h a r g e s of Two Medicine Creek on t h e 1 5 t h of each month a r e e q u i v a l e n t t o what would have been measured on t h o s e days.
The c o n c u r r e n t d a i l y
d i s c h a r g e s and t h e monthly means of Cut Bank Creek would be a v a i l a b l e from t h e record.
T h e s e t h r e e i t e m s o f d a t a a r e l i s t e d i n T a b l e 7.1.
Although t h e
o b j e c t i v e o f t h i s t e c h n i q u e i s t o e s t i m a t e a n n u a l f l o w , t h i s i s o b t a i n e d by e s t i m a t i n g and summing monthly d i s c h a r g e s . The p l o t o f c o n c u r r e n t midmonth d i s c h a r g e s o f t h e two s t r e a m s shows t h a t t h e r e l a t i o n ch an g es a t l e a s t monthly.
i n F i g u r e 7.5
These changes a r e due t o
d i f f e r e n c e s i n t h e t i m i n g o f snowmelt and t o a p a t t e r n of m ont hl y d i v e r s i o n s from Two Medicine Creek,
ranging from z e r o t o o v e r 10,000 a c r e - f e e t ,
r e a s o n a b l y c o n s i s t e n t from y e a r t o year.
which i s
Obviously a l i n e a v e r a g i n g t h e p o i n t s
of F i g u r e 7.5 would n o t be a r e a s o n a b l e b a s i s f o r e s t i m a t i o n . The Riggs method u s e s a d i f f e r e n t r e l a t i o n o f u n i t s l o p e f o r each month, p o s i t i o n d e t e r m i n e d by t h e p l o t t e d point.
its
The dashed l i n e through p o i n t 10 on
F i g u r e 7.5 i s t h e r e l a t i o n used f o r t r a n s f e r r i n g t h e October monthly mean of Cut Bank C r e e k t o g e t t h e Two M e d i c i n e C r e e k e s t i m a t e . necessary:
Graphical t r a n s f e r is not
t h e monthly mean flow of Two Medicine Creek u s u a l l y i s o b t a i n e d by
m u l t i p l y i n g t h e measured monthly mean flow of Cut Bank Creek by t h e r a t i o of t h e midmonth d i s c h a r g e s .
R e s u l t s a r e shown i n T a b l e 7.1 a l o n g w i t h t h e m e a s u r e d
v a l u e s f o r comparison.
Some of t h e monthly e s t i m a t e s a r e c o n s i d e r a b l y i n e r r o r
b u t t h e annual mean i s l e s s t h a n 6 p e r c e n t from t h a t measured.
138 TABLE 7.1
Data and results of computing annual mean flow from monthly measurements
Date
Daily mean discharge. cfs
~~
Two Medicine Creek
Month
~
~~
Monthly mean discharge, cfs
Cut Bank Creek
Cut Bank Creek
Two Medicine Creek Computed Measured
lO/l5/60 11/15 12/15 11 15/61 2/15 3/15 4/15 51 15 6/15 7/15 8/15 9/15
36 26 44 30 65 72 82 332 470 164 74 42
244 56 50 40 50 156 175 978 8 50 82 50 85
10 11 12 1 2 3 4 5 6 7 8 9
32.6 28.5 26 .O 23.9 48.3 67 .O 94.2 47 1 509 148 58.6 40.7
Annual mean, 1961 water year
129
220 61 30 32 37 140 200 1040 920 74 40 82
55.3 58.2 36.1 29.5 82.2 128 23 1 1211 1010 114 22.6
240
254
60.5
1000
300
100
30
20
I
I
I
I
50
100
200
500
CUT BANK CREEK
Fig. 7.5.
Concurrent mid-month discharges, in cfs, from Table 7.1.
The final step in this procedure is to relate annual means for 1961 to means of record for s t r e a m s i n the area, to define a m e a n relation line (Figure 7.6) and to transfer the estimated 1961 mean of 240 through that relation to get an
139 e s t i m a t e of t h e long-term
mean f o r Two Medicine Creek.
The long-term
mean of
430 c f s , a s e s t i m a t e d by t h i s method, compares f a v o r a b l y w i t h 385 c f s based on 31 y e a r s of record. T h i s m e t h o d is a p p l i c a b l e t o s t r e a m s i n r e g i o n s w h e r e f l o w i s p r i n c i p a l l y from snowmelt o r from ground w a t e r , o r where s t o r m s c o v e r l a r g e a r e a s .
1000 I
I
I
lool
1
1
P/
1
10 4
1
10
100
1000
MEAN FLOW, 1961 WATER YEAR
Fig. 7.6. R e l a t i o n of 1961 mean f l o w s t o mean f l o w s of r e c o r d i n c f s . a t gaging s t a t i o n s i n F i g u r e 7.3 ( e x c e p t gage 7). 7.3.2
Low-flow c h a r a c t e r i s t i c s from base-flow
measurements
The p r o c e d u r e i s d e s c r i b e d i n Chapter 9. 7.3.3
Flow c h a r a c t e r i s t i c s from channel s i z e
Channel morphology s t u d i e s have shown c o n s i s t e n t r e l a t i o n s between d i s c h a r g e and t h e c o r r e s p o n d i n g width,
depth,
and v e l o c i t y i n n a t u r a l channels,
partic-
u l a r l y a t or n e a r b a n k f u l l s t a g e ( L e o p o l d , Wolman, a n d M i l l e r , 1 9 6 4 ) .
The
g e o m e t r y o f t h e c h a n n e l o f a n a t u r a l s t r e a m i s t h o u g h t t o b e d e v e l o p e d by discharges near bankfull. geometry,
Thus b a n k f u l l d i s c h a r g e should b e r e l a t e d t o channel
s u b j e c t o f c o u r s e t o v a r i a t i o n s d u e t o t h e t y p e s o f bed and b a n k
m a t e r i a l i n which t h e channel i s formed and t o t h e s e d i m e n t load. Flood c h a r a c t e r i s t i c d i s c h a r g e s a t v a r i o u s r e c u r r e n c e i n t e r v a l s have been shown t o be r e l a t e d t o channel width.
A common r e l a t i o n is
Q=aWn w h e r e Q i s a f l o o d c h a r a c t e r i s t i c , W is c h a n n e l w i d t h , and a and n a r e c o e f f i cients.
140 Channel geometry representative of flood characteristics occurs only in certain stream reaches. A straight, narrow reach is best.
The bed and banks
should be stable but should be of a material that has permitted the channel to develop to a size just adequate to handle the flow regimen.
Most reaches
suitable for slope-area measurements would be suitable for channel-geometry measurements.
Proper selection of the cross section and of the level within the
cross section at which the width is measured is critical to success.
In
meandering channels the most restricted section is just downstream from a bend. The level at which the width is measured is defined by channel features. Two levels are widely used; they identify the active-channel section and the wholechannel section (Fig. 7.7).
The width of the active-channel section is a
within-channel dimension represented by (1) the width of the low-water channel, ( 2 ) the distance between within-channel bars, or ( 3 ) the distance between annual
vegetation lines.
FLOOD
WHOLE-CHANNEL WIDTH ACTIVE-CHANNEL
Fig. 7.7.
Idealized stream cross section showing two width measurements.
The reference level for the whole-channel section is variously defined by breaks in bank slope, by the edg,es of the flood plain or by the lower limits of permanent vegetation. In perennial streams the whole-channel width is the width at bankfull stage.
In ephemeral streams a flood plain may not exist.
Width
measurements are shown in Figures 7 8 and 7.9. To define a calibration, flood characteristics from gaging-station or creststage-gage records are plotted on log paper against the corresponding channel widths measured near the gaged sites a s in Figure 7.10.
Relations of 10-year
flood to width generally differ for perennial and for ephemeral streams because of the differing channel shapes.
And even among perennial streams the channel
shapes differ according to the material in which the channels have developed.
An index of channel shape such a s some function of depth may appreciably improve the calibration if a wide range of shapes are included in the sample. Channel shape is also a function of bed and bank material, and indices of these may be used (Osterkamp, 1977). Channel geometry has also been used for estimating mean streamflow (Hedman,
1970).
A relation between channel size and mean flow presumably exists because
141
Fig. 7.8.
Whole-channel width of a perennial stream is shown by the tape.
Fig. 7 . 9 .
Measuring active-channel width of an ephemeral stream.
of a relation of mean flow to flood Characteristics; such a relation for perennial streams obviously would not hold for ephemeral streams. graphical area of applicability of
a
Thus, the geo-
relation for estimating mean flow from
channel width would be much more limited than one for estimating flood-peak characteristics.
142
20 z d
1000 i
0 0 _1
U
100
:
W
t
10
1
100
1000
WHOLE-CHANNEL WIDTH, IN FEET
F i g . 7.10. R e l a t i o n o f 1 0 - y e a r f l o o d t o c h a n n e l w i d t h f o r s t r e a m s i n Owyhee County, Idaho (From Riggs and Harenberg, 1976). The r e l i a b i l i t y of a f l o o d e s t i m a t e made by t h e channel-geometry
method a t an
ungaged s i t e depends p r i n c i p a l l y on t h e s t a n d a r d e r r o r of t h e c a l i b r a t i o n and on t h e r e l i a b i l i t y of t h e w i d t h measurement a t t h e s i t e .
Wahl (1977) d e s c r i b e d a
t e s t t o d e t e r m i n e t h e r e l i a b i l i t y of measurements o f channel w i d t h ;
seven i n d i -
v i d u a l s i n d e p e n d e n t l y v i s i t e d 22 s i t e s and measured c h a n n e l d i m e n s i o n s f o r 3 d i f f e r e n t r e f e r e n c e l e v e l s i n s e c t i o n s o f t h e i r own choosing.
Wahl a t t r i b u t e d
an a v e r a g e s t a n d a r d e r r o r f o r d i s c h a r g e o f a b o u t 30 p e r c e n t t o d i f f e r e n c e s i n w i d t h measurements alone.
Combining t h a t w i t h an assumed 40 p e r c e n t c a l i b r a t i o n
s t a n d a r d e r r o r ( l o w e r t h a n m o s t ) g i v e s a 50 p e r c e n t s t a n d a r d e r r o r of t h e discharge estimate. E s t i m a t i n g r e l a t i o n s a p p l i c a b l e t o many r e g i o n s of w e s t e r n United S t a t e s have been p u b l i s h e d ,
f o r example s e e Hedman and Osterkamp (1982).
In g e n e r a l t h e s e
r e l a t i o n s a r e f o r r e g i o n s i n which f l o w c h a r a c t e r i s t i c s a r e n o t c l o s e l y r e l a t e d t o d r a i n a g e area.
The channel-geometry method i s a p p l i c a b l e t o most s t r e a m s b u t
i t s u s e i s recommended o n l y w h e r e b a s i n c h a r a c t e r i s t i c s a r e p o o r i n d i c a t o r s . B e t t e r e s t i m a t e s of flood c h a r a c t e r i s t i c s u s u a l l y can be obtained from b a s i n c h a r a c t e r i s t i c s i n humid r e g i o n s .
A d i s a d v a n t a g e of t h e channel-geometry
method
i s t h e need f o r a channel measurement n e a r t h e s i t e where t h e f l o w c h a r a c t e r i s t i c i s needed.
See s e c t i o n 8.10.3
f o r a way of reducing t h e f i e l d work r e q u i r e d
t o apply t h e technique. A p p l i c a t i o n s and l i m i t a t i o n s of t h e channel-geometry p u b l i s h e d r e p o r t s a r e g i v e n by Riggs (1978).
method and r e f e r e n c e s t o
See a l s o Wahl (1984).
143 REFERENCES Hedman, E.R. 1970. Mean annual runoff as related to channel geometry in selected streams in California: U.S. Geol. Survey Water-Supply Paper 1999-E. Bedman, E.R. and Osterkamp, W.R., 1982, Streamflow characteristics related to channel geometry of streams in western United States: U.S. Geol. Survey Water-Supply Paper 2193, 17 p. Leopold, L.B., Wolman, M.G., and Miller, J.P., morphology: San Francisco, W.E. Freeman
1964, Fluvial processes in geoCo., 522 p.
6
Osterkamp, W.R., 1977, Effect of channel sediment on width-discharge relations. with emphasis on streams in Kansas: Kansas Water Resources Board Bull. NO. 21, 25 p. Riggs, EC.. 1969, Mean streamflow from discharge measurements: Bull. of International Assoc. of Scientific Hydrology, Vol. XIV, No. 4, p. 95-110. Riggs, H.C., 1978, Streamflow characteristics from channel size: Journal Of Hydraulics Division, ASCE, Vol. 104, No. E l , January 1978, p. 87-96. Riggs, E.C. and Moore, D.O., 1965, A method of estimating mean runoff from ungaged basins in mountainous regions: U.S. Geol. Survey Prof. Paper 525D, p. 199-202. Thomas. D.M. and Benson, M.A., 1970, Generalization of streamflow characteristics from basin characteristics: U.S. Geol. Survey Water-Supply Paper 1975. 55 p. Wahl, K.L., 1977, Accuracy of channel measurements and the implications o n estimating streamflow characteristics: Jour. Research, U.S. Geol. Survey, Vol. 5, NO. 6, p. 811-814. Wahl, K.L., 1984, Evaluation of the use of channel cross section properties for estimating s treamflow characteristics: U.S. Geol. Survey Water-Supply Paper 2262, p. 53-66.
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145
Chapter 8
FLOOD-FREQUENCY ANALYSES
8.1
INTRODUCTION The p r i n c i p l e s g i v e n i n s e c t i o n s 4. 5 , a n d
I
f o r d e f i n i n g t h e magnitude-
frequency r e l a t i o n s of streamflow c h a r a c t e r i s t i c s . i l l u s t r a t e d by a p p l i c a t i o n s t o f l o o d s .
b o t h gaged and ungaged.
were
But t h e v a l u e of r e l i a b l e f l o o d informa-
t i o n and t h e r a n g e of problems a s s o c i a t e d w i t h g e t t i n g t h a t i n f o r m a t i o n j u s t i f y a more d e t a i l e d d i s c u s s i o n . 8 .2
ANNUAL FLOODS An a n n u a l f l o o d i s t h e h i g h e s t p e a k d i s c h a r g e d u r i n g a y e a r .
Most f l o o d -
f r e q u e n c y a n a l y s e s a r e concerned w i t h e s t i m a t i n g t h e c h a r a c t e r i s t i c s of a n n u a l floods.
I n d i v i d u a l s t h a t make up a p o p u l a t i o n s h o u l d b e i n d e p e n d e n t o f e a c h
o t h e r and s h o u l d o c c u r randomly i f a sample from t h a t p o p u l a t i o n i s t o p r o v i d e a r e a s o n a b l e e s t i m a t e of t h e frequency c h a r a c t e r i s t i c s .
Annual f l o o d s u s u a l l y
m e e t t h e f i r s t r e q u i r e m e n t , b u t s h o r t r e c o r d s o f f l o o d s t e n d t o b e made up of nonrandom e v e n t s b e c a u s e t h e c a u s a t i v e m a j o r s t o r m s a r e n o t randomly d i s t r i b u t e d i n time.
8.3
FLOODS ABOVE A BASE
An o b j e c t i o n t o t h e use o f t h e annual f l o o d s e r i e s i s t h a t t h e second h i g h e s t f l o o d i n some y e a r s i s h i g h e r t h a n t h e a n n u a l f l o o d s f o r o t h e r y e a r s b u t i t i s n o t c o n s i d e r e d ’ i n d e f i n i n g t h e frequency curve.
l l i s o b j e c t i o n can be r e s o l v e d
by u s i n g a l l i n d e p e n d e n t f l o o d s a b o v e a n a r b i t r a r y b a s e d i s c h a r g e d u r i n g t h e p e r i o d of record. partial-flood
These f l o o d s a r e c a l l e d t h e p a r t i a l - d u r a t i o n
series,
o r f l o o d s above t h r e s h o l d .
series, the
The b a s e d i s c h a r g e i s s e l e c t e d
so t h a t s e v e r a l p e a k s w i l l q u a l i f y i n most y e a r s .
Only t h o s e p e a k s t h a t a r e
r e a s o n a b l y independent of each o t h e r s h o u l d b e i n c l u d e d ; i n d e p e n d e w e i s assumed i f t h e p e a k s a r e w i d e l y s e p a r a t e d i n t i m e and by a s u b s t a n t i a l r e c e s s i o n i n discharge.
8.4
ANNUAL AND PARTIAL-DURATION FREQUENCY CURVES F r e q u e n c y c u r v e s b a s e d on t h e a n n u a l s e r i e s a n d on t h e p a r t i a l - d u r a t i o n
s e r i e s a r e s i m i l a r a b o v e a r e c u r r e n c e i n t e r v a l o f a b o u t 10 y e a r s ( F i g . 8.1). The t h e o r e t i c a l r e l a t i o n between t h e two f r e q u e n c y c u r v e s wns d e m o n s t r a t e d b y Langbein (1949).
E m p i r i c a l r e l a t i o n s a p p r o x i m a t e t h e t h e o r e t i c a l one b u t i n d i -
c a t e some g e o g r a p h i c v a r i a t i o n . The f r e q u e n c y c u r v e of
annual f l o o d s i s used f o r d e f i n i n g t h e p r o b a b i l i t i e s
of f l o o d s t h a t a r e exceeded i n f r e q u e n t l y .
F o r p r o b a b i l i t i e s o f l e s s t h a n 0.10
146 ( r e c u r r e n c e i n t e r v a l s g r e a t e r t h a n 1 0 y e a r s ) e i t h e r t h e annual or t h e p a r t i a l d u r a t i o n f r e q u e n c y c u r v e c o u l d b e used b u t a n n u a l f l o o d s a r e more r e a d i l y a v a i l a b l e t h a n f l o o d s above a b a s e so t h e annual c u r v e i s more w i d e l y used.
1.1
2
5
10
50
100
RECURRENCE INTERVAL, IN YEARS
F i g . 8.1. Annual a n d p a r t i a l - d u r a t i o n f l o o d - f r e q u e n c y n e a r St. Regis, Montana. The p a r t i a l - d u r a t i o n
c u r v e s f o r C l a r k Fork
f r e q u e n c y c u r v e i s used f o r e v a l u a t i n g r i s k f o r a p e r i o d
of a few y e a r s or where a l l ex ceed an ces a r e of i n t e r e s t , n o t j u s t t h e l a r g e s t one o f t h e y e a r . FITTING ANNUAL FREQUENCY CURVES
8.5
G r a p h i c a l f r e q u e n c y a n a l y s i s i s d e s c r i b e d i n s e c t i o n 4.
I n t e r p r e t a t i o n of
t h e p l o t t e d p o i n t s by drawing a mean l i n e i s somewhat s u b j e c t i v e , p a r t i c u l a r l y a t the high recurrence i n t erv als .
RI
=
The Weibull p l o t t i n g formula,
(n+l)/m.
commonly used f o r t h e annual s e r i e s a l s o h a s been used f o r t h e p a r t i a l - d u r a t i o n series.
The n u m b e r o f y e a r s o f r e c o r d , n, i s t h e same f o r b o t h s e r i e s .
a n n u a l s e r i e s t h e o r d e r n u m b e r , m. r a n g e s f r o m one t o n. duration series,
In t h e
But i n t h e p a r t i a l -
m w i l l t a k e v a l u e s much g r e a t e r t h a n n ; t h u s t h e f o r m u l a
produces some r e c u r r e n c e i n t e r v a l s l e s s t h a n one which cannot b e i n t e r p r e t e d a s t h e r e c i p r o c a l of p r o b a b i l i t y .
The a b s c i s s a s c a l e f o r a p a r t i a l - d u r a t i o n
fre-
q u e n c y c u r v e s h o u l d b e p r o b a b i l i t y o f e x c e e d a n c e or n u m b e r o f f l o o d s p e r 1 0 0 y e a r s exceeding a g i v e n value. Mathematical f i t t i n g o f flood-frequency c u r v e s e l i m i n a t e s t h e s u b j e c t i v i t y of g r a p h i c a l f i t t i n g a l t h o u g h t h e s e l e c t i o n of a s u i t a b l e d i s t r i b u t i o n r e m a i n s subjective.
The m o s t common t h e o r e t i c a l d i s t r i b u t i o n s now u s e d f o r a n n u a l
147 floods are log Pearson Type 3 , log normal, and the extreme-value (Gumbel).
The
log-normal distribution is the same a s the log Pearson Type 3 with zero skew. Methods of fitting are given in section 4.
Digital computer programs are
commonly used. Mathematical methods of defining flood-frequency characteristics are not suitable without modification if some of the annual floods are unusually small. In Figure 8.2 the one extremely small annual flood introduces so much curvature (negative skew) into the fitted curve that the upward, extrapolation of that curve is unrealistic.
Hydrologically the occurrence of an unusually low annual
flood should be unrelated to the flood potential of the stream, and consequently it should not influence the upper end of the flood distribution.
Such reasoning
is the basis for modifying the purely statistical fitting process.
2
50,000
I
.
I
I
I
I
I
I
I
I
V W-
U IT
4u
10,000 -
v,
Q Y
a
W
a
1000
0 1
Fig. 8.2 Frequency curve for Platte River, Missouri, showing how a low outlier distorts the upper end of the frequency curve. Deletion of the unusually low annual flood or floods before fitting the distribution mathematically is a common practice.
If the lowest peak discharge
in Figure 8.2 had not been used in the curve fitting, the SO-year flood would have been 40 percent greater than that shown.
This is still well below the SO-
year floods obtained by a graphical interpretation or by a Gumbel fit, both of which are confirmed by the subsequent record which includes 2 peaks over 50.000 cfs. The flexibility of the log Pearson Type 3 distribution is sometimes a disadvantage; for the record in Figure 8.2 it gives too much weight to peaks on both ends of the array.
Objective methods for identifying low "outliers" and for
148 e l i m i n a t i n g them from t h e f i t t i n g p r o c e s s a r e given by Water Resources Council (1981). Some annual f l o o d r e c o r d s of s m a l l , ephemeral s t r e a m s i n c l u d e z e r o f l o w s f o r s e v e r a l years.
In o t h e r r e c o r d s t h e annual peaks a r e a v a i l a b l e o n l y f o r t h o s e
y e a r s i n w h i c h t h e p e a k was a b o v e some b a s e ; s u c h a r e c o r d m i g h t b e o b t a i n e d from a c r e s t - s t a g e a n n u a l peaks. Montana.
g a g e w h i c h was n o t low enough t o r e c o r d t h e s t a g e s o f a l l
A r e c o r d c o n t a i n i n g z e r o s i s t h a t of T u s l e r C r e e k t r i b u t a r y ,
f o r 1957-73;
t h e a n n u a l p e a k s a r e 1.71.
45.2, 0.03, 0. 0. 0. 0 . 0 8 , 1.12, 1.00.
4.20.
0, 1.04,
a n d 0.17 m ’ l s .
2.38,
0. 0 . 0.84.
The f r e q u e n c y c u r v e
can be d e f i n e d g r a p h i c a l l y from t h e 8 h i g h e s t d i s c h a r g e s i n 17 y e a r s ; t h e r e s t of t h e a n n u a l p e a k s need n o t b e p l o t t e d ( F i g . 8.3).
DO
I
W
a 0.41 1.5
I
1
,
3
I
I
,/Ill
1
5 10 20 RECURRENCE INTERVAL. IN YEARS
2
Fig. 8.3. Graphically-defined Montana, 1957-73.
f l o o d frequency c u r v e for T u s l e r Creek T r i b u t a r y .
Frequency c u r v e s c a n be d e f i n e d m a t h e m a t i c a l l y from r e c o r d s c o n t a i n i n g some a n n u a l f l o o d s whose m a g n i t u d e s a r e o n l y known t o b e l e s s t h a n some b a s e .
The
frequency curve f o r T u s l e r could b e computed by f i t t i n g t h e l o g Pearson Type 3 d i s t r i b u t i o n t o t h e 8 h i k h e s t d i s c h a r g e s and then a d j u s t i n g t h a t d i s t r i b u t i o n t o a c c o u n t f o r t h e a d d i t i o n a l y e a r s of r e c o r d ( J e n n i n g s a n d Benson. 1 9 6 9 ) .
An
example of t h i s type of computation i s given by Water Resources Council (1981, p. 12-32). F l o o d i n f o r m a t i o n a t a g a g e d s i t e may i n c l u d e s t a g e s o f m a j o r f l o o d s t h a t o c c u r r e d p r i o r t o t h e gaged period.
E s t i m a t e s of d i s c h a r g e s of t h e s e h i s t o r i c
f l o o d s may be i n c o r p o r a t e d i n a g r a p h i c a l frequency a n a l y s i s by a s s i g n i n g approp r i a t e recurrence intervals.
For example.
given a flood-peak
r e c o r d from 1940
t o 1980 and an e s t i m a t e of t h e d i s c h a r g e of t h e 1916 f l o o d which i s known t o be l a r g e r than any subsequent one a t t h e s i t e , a t 65 y e a r s on t h e graph. h i s t o r i e s and w i t h i n - r e c o r d
t h e 1916 e s t i m a t e would b e p l o t t e d
Dalrymple (1960) d e s c r i b e s how o t h e r combinations of f l o o d s can b e analyzed g r a p h i c a l l y .
The g u i d e l i n e s
149 recommended b y the W a t e r Resources Council (1981) for determining flood frequency curves m a t h e m a t i c a l l y include procedures for incorporating historic flood information. 8.6
A UNIFORM METHOD Flood characteristics are used for various purposes a n d b y various people.
Conflicts or inconsistencies may arise if different flood frequency curves are derived from the same data.
Uniform methods of analysis reduce such problems.
Bulletin No. 15, "A uniform technique for determining flood flow frequencies",
issued by the Hydrology Committee of the United States Water Resources
Council in 1967. recommended use of the log-Pearson Type 3 distribution as the base method but allowed for other m e t h o d s of analysis if justification w e r e provided.
Guidelines in subsequent Bulletins in 1976, 1979, and 1 9 8 1 specify
use of the log Pearson Type 3 distribution and provide specific procedures for using historic data, for identifying and adjusting for the effects of high and low "outliers", and for weighting skew coefficients computed from a flood record with generalized mapped skew coefficients (Water Resources Council, 1981). The weighting of the skew coefficient computed f r o m the s a m p l e w i t h an average skew coefficient for the geographic area was recommended because a skew coefficient computed f r o m a s a m p l e of a f e w tens of y e a r s is k n o w n to have a large error.
This procedure is based on the assumption that the skewness varies
geographically.
The adjustments for low and high "outliers" are also intended
to make the sample more representative. The decision to use the log-Pearson Type 3 distribution for flood peaks was based on comparisons of frequency curves fitted by various statistical distributions to the graphically-defined frequency curves.
F l o o d records for many
streams encompassing a wide range of sizes and characteristics were used in the tests. T h e s a m e m e t h o d o f testing also w a s used on floods of streams in Great Britain.
That investigation plus other statistical considerations led to the
conclusion that the Gumbel extreme-value
distribution was appropriate for the
majority of British streams although the conclusion was qualified by "Statistics do not point to a single distribution being certainly the correct o n e and therefore a choice must involve an element of subjectivity."
(National Environ-
ment Research Council (1975, p. 241, 155-160). T h e guidelines o f the W a t e r Resources Council for c o m p u t a t i o n of floodfrequency curves at gaging stations are not widely supported by the profession. Some hydrologists question the validity of a map of generalized skew and consequently its use in modifying the frequency curve at a gaged site.
B u t the
principal objection is that no single nonsubjective statistical method w i l l
150 produce t h e b e s t e s t i m a t e s under a l l c o n d i t i o n s . provided by P a t t i s o n (1977).
Support f o r t h a t o b j e c t i o n i s
commenting on A u s t r a l i a n experience:
"The purpose of t h e p r e v i o u s e d i t i o n s of A u s t r a l i a n R a i n f a l l and Runo f f was t o p r o v i d e an u n o f f i c i a l code of recommended p r a c t i c e i n t h e s e l e c t i o n and a p p l i c a t i o n of methods of d e s i g n f o r v a r i o u s t y p e s of hydrologic problems.
The work was taken by many p r a c t i c i n g e n g i n e e r s ,
and o f t e n by t h e Courts, a s a guide t o s t a n d a r d p r a c t i c e . "
"It i s t h e view of t h e N a t i o n a l Committee on Hydrology t h a t t h e r o l e of A u s t r a l i a n R a i n f a l l and Runoff (1958 e d i t i o n ) a s a code of pract i c e h a s been abused.
There a r e , f o r example.
i n s t a n c e s of t h e hy-
d r o l o g i c d e s i g n of i m p o r t a n t f a c i l i t i e s i n which t h e r e q u i r e m e n t s of good e n g i n e e r i n g p r a c t i c e have been ignored, t o some e x t e n t , when r e l e v a n t assumptions have been drawn u n c r i t i c a l l y from g u i d e l i n e s s e t o u t i n A u s t r a l i a n R a i n f a l l and Runoff.
Also i t i s a p p a r e n t
t h a t some e n g i n e e r i n g and l e g a l b o d i e s view any h y d r o l o g i c d e s i g n procedure which d e p a r t s from t h a t recommended i n A u s t r a l i a n R a i n f a l l and Runoff a s b e i n g unacceptable.
T h i s i s t h e approach t r a d i t i o n a l l y
taken w i t h codes of p r a c t i c e , and tends t o i n h i b i t i n n o v a t i v e d e s i g n based on l o c a l knowledge, customs, and e s t a b l i s h e d c r i t e r i a .
Insis-
t e n c e t h a t h y d r o l o g i c d e s i g n f o r a l l p a r t s of A u s t r a l i a f o l l o w a p a t t e r n u s i n g a methodology p r e s c r i b e d i n a s i n g l e compendium w i l l , in many i n s t a n c e s .
l e a d t o d e s i g n s which a r e t e c h n o l o g i c a l l y i n f e r i o r
and economioally unsound." 8.7
RECORD EXTWSION
Annual f l o o d s o u t s i d e t h e p e r i o d o f r e c o r d may b e e s t i m a t e d f r o m a l o n g e r f l o o d r e c o r d o r from p r e c i p i t a t i o n .
Except f o r s t a t i o n s on t h e same stream, t h e
f i r s t technique i s r a r e l y u s e f u l f o r improving t h e frequency curve; f l o o d peaks a r e so h i g h l y i n f l u e n c e d by a r e a l v a r i a t i o n s i n p r e c i p i t a t i o n and by topography t h a t peaks from nearby s t r e a m s a r e n o t c l o s e l y c o r r e l a t e d . Rainfall-runoff o r volumes,
See s e c t i o n 5.4.
models may be used t o s y n t h e s i z e long r e c o r d s of f l o o d peaks,
from r a i n f a l l .
Continuous-flow
models such a s t h e S t a n f o r d Water-
shed Model (Crawford and L i n s l e y , 1966) o r ones t h a t model o n l y t h e storm r u n o f f (Dawdy and o t h e r s , 1 9 7 2 ) a r e e x a m p l e s .
F o r s m a l l s t r e a m s , r a i n f a l l and d i s -
charge a t 15-minute o r s h o r t e r i n t e r v a l s a r e n e e d e d f o r a d e q u a t e c a l i b r a t i o n . The o n l y o t h e r i n p u t t o t h e model developed i n Dawdy and o t h e r s (1972) is d a i l y pan evaporation.
O r d i n a r i l y 8 t o 1 0 y e a r s of r e c o r d a r e n e e d e d t o d e f i n e a n
adequate c a l i b r a t i o n ; s h o r t e r r e c o r d s u s u a l l y include o n l y s m a l l floods.
Figure
8.4 shows t h e r e s u l t s o f c a l i b r a t i n g on 1 6 f l o o d e v e n t s i n 1936-46 on B e e t r e e Creek,
North Carolina.
a 5.41 s q u a r e - m i l e
basin.
An a d e q u a t e c a l i b r a t i o n
151 u s u a l l y r e q u i r e s t h a t a r a i n gage be i n t h e basin.
I f basin r a i n f a l l i s not
uniform, more t h a n one r a i n gage r i l l be needed.
OBSERVED PEAK DISCHARGE, IN CFS
F i g . 8.4. R e s u l t s of c a l i b r a t i n g a r a i n f a l l - r u n o f f o t h e r s , 1972).
m o d e l ( A f t e r Dandy and
The f l o o d r e c o r d i s extended by a p p l y i n g a long r e c o r d i n g r a i n f a l l r e c o r d t o t h e c a l i b r a t i o n and s e l e c t i n g t h e a n n u a l f l o o d s f r o m t h e s y n t h e s i z e d peaks. Whether t h e f r e q u e n c y c u r v e based on t h e extended r e c o r d i s an improvement o v e r t h e one based on t h e gage r e c o r d depends on t h e q u a l i t y of t h e c a l i b r a t i o n and
on t h e r e p r e s e n t a t i v e n e s s o f t h e long r a i n f a l l r e c o r d a s w e l l as on t h e repres e n t a t i v e n e s s of t h e o r i g i n a l gage reco rd .
I t h a s b e e n o b s e r v e d t h a t some
r a i n f a l l r e c o r d s o f 6 0 or more y e a r s d o n o t c o n t a i n s t o r m s a s l a r g e a s o t h e r s which have been o b t a i n e d i n t h e v i c i n i t y i n much s h o r t e r p e r i o d s .
An a d d i t i o n a l
u n c e r t a i n t y i s i n t r o d u c e d when t h e l o n g r a i n f a l l r e c o r d i s a p p l i e d t o a b a s i n d i s t a n t from where t h e r a i n f a l l was observed. 8.8
RELATION TO BASIN CHARACTERISTICS Flood-frequency
c h a r a c t e r i s t i c s depend on basin and c l i m a t i c c h a r a c t e r i s t i c s .
I f t h e geology and topography of a b a s i n a r e more o r l e s s homogeneous and major storms cover l a r g e a r e a s , then t h e flood-frequency
curve can be r e p r e s e n t e d
a d e q u a t e l y by a log-Pearson Type 3 d i s t r i b u t i o n w i t h a s m a l l skew.
But suppose
t h e b a s i n e n c o m p a s s e s a l a r g e r a n g e i n e l e v a t i o n s o t h a t f l o o d s may r e s u l t e i t h e r from snowmelt or r a i n f a l l as i n t h e Merced River b a s i n ,
California.
The
Merced R i v e r frequency c u r v e (Fig. 8.5) h a s a shape t h a t cannot be approximated by any 3-parameter
distribution.
The r a i n f a l l peaks and t h e snowmelt peaks of
M e r c e d R i v e r a r e s e p a r a t e d by s e v e r a l m o n t h s i n m o s t y e a r s .
Thus d a t a a r e
152 a v a i l a b l e f o r d e f i n i n g s e p a r a t e f r e q u e n c y c u r v e s o f a n n u a l r a i n f a l l a n d of snowmelt peaks.
These c u r v e s , shown i n F i g u r e 2.16 (Chapter 2)
c o u l d have been
f i t t e d t o l o g P e a r s o n Type 3 d i s t r i b u t i o n s and t h e two d i s t r i b u t i o n s c o u l d have been combined on t h e b a s i s of p r o b a b i l i t i e s t o g e t t h e f r e q u e n c y c u r v e of annual floods.
500
The a l t e r n a t i v e i s a g r a p h i c a l f i t t o t h e annual f l o o d s .
I
I
I
I
I
I
I
I
v)
:: z
zu’
200
L3 U
6
3
100
2 cl ?L
$
50
a
30
I
I
I
1
1.01
1.11
2
5
20 5c
RECURRENCE INTERVAL, IN YEARS Fig. 8.5. Frequency c u r v e of annual f l o o d s f o r Merced River, Crippen, 1978 )
.
California (After
More commonly, some o f t h e f l o o d p e a k s f r o m b a s i n s o f l a r g e r e l i e f a r e n o t e n t i r e l y f r o m r a i n f a l l or f r o m s n o w m e l t a n d i t i s n o t f e a s i b l e t o d e v e l o p s e p a r a t e f r e q u e n c y curves.
Nor h a s i t proved f e a s i b l e t o d e f i n e s e p a r a t e f r e -
quency c u r v e s f o r f l o o d s caused by f r o n t a l s t o r m s and by h u r r i c a n e s b e c a u s e t h e r e a r e t o o few of t h e l a t t e r t o d e f i n e a f r e q u e n c y c u r v e a t a s i t e and b e c a u s e t h e c l a s s i f i c a t i o n of some of t h e c a u s a t i v e s t o r m s must b e a r b i t r a r y . Under t h e s e c o n d i t i o n s o n l y a s i n g l e f r e q u e n c y c u r v e can be defined.
Whether a
s i n g l e m a t h e m a t i c a l l y - f i t t e d c u r v e i s r e a s o n a b l e can b e judged from a computer p l o t of t h e c u r v e and of t h e d a t a p o i n t s .
An u n d e r s t a n d i n g o f t h e b a s i n hy-
d r o l o g y and of t h e f l o o d r e c o r d w i l l h e l p i n d e c i d i n g w h e t h e r t h e c u r v e i s t o b e a c c e p t e d o r m o d i f i e d , and i f so, how. The s l o p e s a n d s h a p e s o f f l o o d - f r e q u e n c y c u r v e s may c h a n g e f r o m p o i n t t o p o i n t a l o n g t h e same s t r e a m .
I n r e g i o n s s u c h a s t h e e a s t e r n s l o p e s of t h e
Colorado Rocky Mountains, f l o o d s i n t h e h e a d w a t e r s a r e from snowmelt, t h o s e i n t h e m i d d l e r e a c h e s may b e f r o m r a i n a s w e l l a s s n o w m e l t , a n d t h o s e n e a r t h e Plains, p a r t i c u l a r l y the major floods,
a r e from t h u n d e r s t o r m . r a i n f a l 1 .
I f such
a s t r e a m i s gaged a t s e v e r a l p o i n t s , t h e s t a n d a r d d e v i a t i o n and t h e skew of t h e annual f l o o d s w i l l i n c r e a s e downstream.
153 8.9
RELIABILITY OF FLOOD-FREQUPNCY CURVES The nonrandomness o f w e a t h e r c o n d i t i o n s f a v o r a b l e t o major f l o o d s i n d i c a t e s
t h a t a long f l o o d r e c o r d s h o u l d p r o v i d e t h e b e s t e s t i m a t e of t h e f r e q u e n c y curve.
R e l i a b i l i t y of t h e l a r g e r annual discharges,
i f d e f i n e d by i n d i r e c t
measurement, w i l l a l s o a f f e c t t h e f r e q u e n c y c u r v e r e l i a b i l i t y b u t o n l y moderately unless the discharges a r e g r e a t l y i n error. s a m p l e i s t h e m a j o r unknown.
The l a c k o f r a n d o m n e s s i n t h e
For t h i s reason, s t a t i s t i c a l confidence l i m i t s
about a frequency c u r v e a r e n o t n e c e s s a r i l y dependable i n d i c a t o r s o f t h e r e l i a b i l i t y of a frequency curve, p a r t i c u l a r l y i f t h e r e c o r d i s s h o r t . The upper end of a flood-frequency c u r v e may be e v a l u a t e d by comparing i t t o the maximum f l o o d s of r e c o r d i n t h e region.
I f a f r e q u e n c y c u r v e shows a 100-
y e a r f l o o d i n e x c e s s o f a n y t h i n g e x p e r i e n c e d i n t h e r e g i o n , and t h e f r e q u e n c y curve i s n o t s u p p o r t e d by d a t a n e a r t h a t l e v e l ,
is q u e s t i o n a b l e .
t h e n t h e upper end of t h e c u r v e
Crippen and Bue (1977) compiled maximum f l o o d s i n t h e United
S t a t e s and p l o t t e d envelope c u r v e s of peak d i s c h a r g e v e r s u s d r a i n a g e a r e a f o r each of 17 r e g i o n s of t h e conterminous United S t a t e s .
T h e i r n a t i o n w i d e envelope
c u r v e i s i n F i g u r e 8.6.
1,000,000 m
LL 0
z
w' 100,000 0 n
4 0
v,
0
10,000
Y
a W a
A--
1000 0.1
1 10 100 1000 DRAINAGE AREA, IN SQUARE MILES
10,000
Fig. 8.6. Envelope c u r v e of maximum f l o o d s i n conterminous U n i t e Crippen and Bue, 1977).
S t a t e s (After
Under c e r t a i n c o n d i t i o n s h i s t o r i c f l o o d s t a g e s c a n be e s t i m a t e d from geologi c a l and b o t a n i c a l e v i d e n c e .
S e e S t e w a r t a n d B o d h a i n e (1961).
LaMarche (19731, C o s t a ( 1 9 7 8 ) . and B a k e r and K o c h e l ( 1 9 7 9 ) .
B e l l e y and
These h i s t o r i c
s t a g e s , when t r a n s l a t e d t o d i s c h a r g e , may p e r m i t r e a l i s t i c e x t r a p o l a t i o n s o f f r e q u e n c y c u r v e s b a s e d on s h o r t r e c o r d s .
On t h e o t h e r hand, J a h n s ( 1 9 4 7 ) con-
cluded "Because t h e C o n n e c t i c u t River h a s been engaged i n l o w e r i n g i t s bottom s i n c e t h e d r a i n i n g of t h e l a t e g l a c i a l v a l l e y l a k e , d i s c u s s i o n of s o - c a l l e d
154 1000-year
f l o o d s on t h e b a s i s of t h e i r c r e s t h e i g h t s a s r e f e r r e d t o p o i n t s along
t h e v a l l e y i s o f no v a l u e . " E r t r a p o l a t i o n s of f r e q u e n c y c u r v e s t o r e c u r r e n c e i n t e r v a l s g r e a t e r t h a n 100 years generally are not reliable. mathematically derived,
Most f r e q u e n c y c u r v e s ,
graphically or
a r e unbounded a t t h e upper end a l t h o u g h t h e r e must be
some p h y s i c a l l i m i t t o t h e f l o o d p o t e n t i a l on any stream. h a s n o t b e e n shown b y f l o o d r e c o r d s ,
Such a p h y s i c a l l i m i t
e i t h e r b e c a u s e t h e y a r e t o o s h o r t or
because t h e r e c o r d s a r e nonhomogeneous due t o changes i n t h e b a s i n s a l t h o u g h a n u p p e r l e v e l s e e m s i n d i c a t e d by e s t i m a t e s o f m a j o r f l o o d s on Han R i v e r , C h i n a , f r o m s t a g e i n f o r m a t i o n ; Chen C h i a - c h i and o t h e r s f r o m t h e M i n i s t r y o f W a t e r Conservancy and E l e c t r i c Power i n Peking r e p o r t e d i n 1974 t h a t t h e maximum f l o o d
on Han R i v e r o c c u r r e d in 1583 and a p p a r e n t l y was t h e h i g h e s t i n t h e l a s t 1000 years. Another approach t o d e f i n i n g t h e p r o b a b l e maximum f l o o d i s through e s t i m a t e s of t h e maximum p r o b a b l e p r e c i p i t a t i o n on t h e basin.
See s e c t i o n 112.7.
E v a l u a t i o n o f f r e q u e n c y c u r v e s i n t h e range below 100-year r e c u r r e n c e i n t e r v a l may be done s u b j e c t i v e l y by comparison among s e v e r a l i n a region.
I f flood
r e c o r d s a r e a v a i l a b l e a t s e v e r a l s i t e s on t h e s a m e s t r e a m a p l o t o f p e a k d i s c h a r g e s f o r s e v e r a l r e c u r r e n c e i n t e r v a l s a g a i n s t channel d i s t a n c e , a r e a , may b e u s e d t o i d e n t i f y i n c o n s i s t e n c i e s . i n f o r m a t i o n a t one s i t e .
500,00(
100,00(
1O,OO(
500(
I
'I 00
1000
I
10.oO0
DRAINAGE AREA, IN SQUARE MILES
Fig. 8 . 7 .
or drainage
F i g u r e 8.7 s h o w s q u e s t i o n a b l e
Flood c h a r a c t e r i s t i c s a t gaging s t a t i o n s on Potomac River.
155
FLOOD CEARACTEBISTICS AT UNGAGED SITES
8.10
Regression on basin characteristics
8.10.1
Refer to Chapter 4 for description of regression analysis and to Chapter 7 for its use in estimating flow characteristics of ungaged streams.
The method
is widely used to develop equations for estimating flood-frequency characteristics f r o m b a s i n characteristics.
Applications of the derived relations to
ungaged sites usually require only site data that are readily available f r o m maps or w e a t h e r records.
T h e equations developed b y T h o m a s and Corley (1977)
for Oklahoma streams are typical:
P1*92
Q2 = 0.111 = 1.00
QS
~ 0 . 6 7 ~0.26 p1.45
SE = 48% 40
Q~~
= 2.99
~ 0 . 6 8 ~ 0 . 2 8 p1.22
39
%s
=
9.49
~ 0 . 6 9 ~ 0 . 3 0 p0.97
4m
= 20.0
~ 0 . 6 9 ~ 0 . 3 1 p0.81
Q
S
~
QIOO
=:
38.6
Ao*7O
poe67
42 45
where Q is the annual flood peak in cfs at the indicated recurrence interval, A is drainage area in square miles, S is an index of main-channel slope, and P is mean annual basin precipitation in inches. sion is given.
The standard error of each regres-
The above equations are transformed from the log-linear form
in which they were solved by multiple regression. log Q = log a + bl log A + b2 log S
+ b3 log P
Various other basin characteristics have been used in regressions for estimating flood-peak characteristics.
The appropriate characteristics depend on
the hydrology of the region and the availability of data.
Rarely are more than
three basin characteristics b o t h statistically and practically significant. Although a fourth characteristic may be statistically significant and its inclusion m a y reduce the standard error a f e w percent, the results obtained b y the equations with and without this characteristics usually do not differ appreciably.
A regression on basin characteristics is defined by data from some region. and the results are considered applicable to that region.
The applicability to
all parts of the region can be appraised subjectively by plotting on a m a p at each data site the ratio of the discharge b y regression equation to the k n o w n discharge.
T h e geographic distribution of these residuals s h o u l d b e m o r e or
less random. T h e above test is l i m i t e d to sites used in defining the relation.
If these
sites do not represent the range of hydrologic conditions in the region then the
156
A regional
relation may not apply to some ungaged streams in that region. relation is commonly qualified a s to its applicability; 8.10.2
Index-flood method
The index-flood method was used for most of the regional flood-frequency analyses made by the U.S. Geological Survey prior to 1965 and is used in England (National Environment Research Council, 1975).
It consists of two parts.
The first part graphically relates mean annual flood to drainage area, and sometimes to other variables.
The mean annual flood was defined a s the 2.33
year recurrence interval flood, based on the Gumbel distribution. plotted points define several different relations.
Usually the
On the basis of these pre-
liminary relations, the geographic area being studied is divided into subareas such that a single relation of mean annual flood to drcinage area applies to each.
Thus the regionalization of the mean annual flood is attained.
The second part of the regionalization process averages the individual frequency curves to provide a regional curve.
This is accomplished after expres-
sing the flood magnitudes a t selected recurrence intervals for each curve a s ratios to the mean annual flood (the index flood).
If some of the dimensionless
individual curves are greatly different from others, the geographic area is subdivided so that each subdivision contains curves of similar shape. curves in each subdivision are averaged.
Then the
The subdivisions for this purpose are
usually not coincident with the subareas defining the various relationships of mean annual flood to drainage area.
.
Figure 8.8 shows the two parts of the
analysis
The index-flood method thus accomplishes the general purposes of a regionalization by relating the position of the frequency curve on the discharge scale to basin size, and by averaging the shapes of the individual curves. The method provides satisfactory results in many regions and is fairly simple to perform. The results are easy to apply to ungaged areas because usually only drainage area need be measured. Application of the method requires arbitrary decisions
as
to the boundaries
of subareas considered homogeneous with respect to mean annual flood or to shape of frequency curve.
No subarea should be represented by fewer frequency curves
than needed to define a meaningful regionalization, even though a close agreement among frequency characteristics in the subarea is not attained. An evaluation of the index-flood method is described by Benson (1962).
A
detailed discussion of the preparation of regional frequency curves is given by National Environment Research Council (1975, p. 170-185).
8.10.3
From channel geometry
In arid and semiarid regions and in ones with heterogeneous geology, channel geometry is
a
better indicator of flood-peak characteristics than basin
157
10
20
50
100 200
500 1000
DRAINAGE AREA, IN SQUARE MILES
1.1
1.52
5
10
20
50
100
RECURRENCE INTERVAL. IN YEARS F i g . 8.8. Relations developed by t h e index-flood Golden, 1 9 6 6 ) . characteristics.
The method,
m e t h o d ( A f t e r B a r n e s and
d e s c r i b e d i n Chapter 7,
r e q u i r e s f i e l d measure-
ments o f c h a n n e l s f o r c a l i b r a t i o n and f o r a p p l i c a t i o n t o ungaged s i t e s :
these
measurements s h o u l d b e made by p e o p l e w i t h some e x p e r i e n c e w i t h t h e technique. P r i m a r y c a l i b r a t i o n s a r e u s u a l l y made w i t h t h e 10-year f l o o d because t h a t f l o o d
is d e f i n e d a t many more s i t e s t h a n f l o o d s of h i g h e r r e c u r r e n c e i n t e r v a l .
In r e -
g i o n s where f l o o d r e c o r d s a r e long, u s u a l l y f o r t h e l a r g e r s t r e a m s , o t h e r f l o o d c h a r a c t e r i s t i c s may b e r e l a t e d t o c h a n n e l width.
F i g u r e 8.9
r e l a t i n g 50-year
158 f l o o d t o channel width, Nevada,
i s d e f i n e d by d a t a from mountain s t r e a m s i n Colorado.
Northwestern United S t a t e s ,
and Alaska.
40 10,000
t 10
5
X P
10
0
coIoraao a n d Nevada
100
1 1000
W H O L E C H A N N E L WIDTH, IN M E T E R S
Fig. 8.9.
p e l a t i o n of 50-year f l o o d t o channel width (From Riggs. 1 9 7 8 ) .
V a r i a t i o n s i n t h e r e l a t i o n s of flood peak c h a r a c t e r i s t i c s t o w i d t h occur because of d i f f e r e n c e s i n channel shapes. i n which t h e channel i s formed,
Channel shape depends on t h e m a t e r i a l
t h e amount of sediment c a r r i e d ,
r e g i m e , p a r t i c u l a r l y w h e t h e r i t i s p e r e n n i a l or ephemeral.
and on t h e f l o w Some d i f f e r e n c e s
among c a l i b r a t i o n s o n w i d t h a r e shown i n F i g u r e 8.10; t h e K a n s a s c h a n n e l s a r e deep and narrow,
t h e w e s t e r n mountain c h a n n e l s tend t o b e wide and s h a l l o w , and
t h e Kentucky c h a n n e l s a r e i n t e r m e d i a t e . Some a d d i t i o n a l measure of channel geometry i s needed f o r c a l i b r a t i o n i n a r e g i o n which c o n t a i n s c h a n n e l s o f v a r i o u s types.
Using d a t a f o r 42 c h a n n e l s of
v e r y d i f f e r e n t shapes and s i z e s i n Kansas, Alaska, Northern Canada,
and Wyoming
t h e s t a n d a r d e r r o r o f r e g r e s s i o n of t h e 1 0 - y e a r f l o o d on w i d t h a n d mean d e p t h
159
6000
1000
100
10
t 1 c
2
10
100
WHOLE-CHANNEL WIDTH, IN METERS
F i g . 8.10.
V a r i a t i o n s due t o d i f f e r e n t channel shapes (From Riggs. 1978).
was 0.22 l o g u n i t s c o m p a r e d t o 0.45 alone.
l o g u n i t s f o r a r e g r e s s i o n b a s e d on w i d t h
Even though mean d e p t h was a h i g h l y s i g n i f i c a n t and u s e f u l v a r i a b l e i n
t h i s example.
t h e s t a n d a r d e r r o r i s u n a c c e p t a b l y large.
C a l i b r a t i o n on s t r e a m s
i n a s m a l l e r r e g i o n u s u a l l y w i l l produce b e t t e r r e s u l t s .
A d i s a d v a n t a g e of t h e channel-geometry method i s t h e need f o r f i e l d measurem e n t s a t t h e s i t e s of a p p l i c a t i o n .
The u s e r n o t o n l y n e e d s t o v i s i t e a c h s i t e
where he w a n t s a f l o o d e s t i m a t e b u t he a l s o s h o u l d have some u n d e r s t a n d i n g of channel morphology i n o r d e r t o g e t a p p r o p r i a t e measurements. berg (1976) c a l i b r a t e d 10-year channel width;
Riggs and Haren-
f l o o d s a t gaged s i t e s i n Owyhee County,
Idaho on
t h e n t h e y measured channel w i d t h s a t many ungaged s i t e s ,
mined t h e 1 0 - y e a r f l o o d s a t t h e s e s i t e s , a n d p l o t t e d them on a map.
deter-
The u s e r
c a n e s t i m a t e t h e 1 0 - y e a r f l o o d s a t o t h e r s i t e s a n d on o t h e r s t r e a m s by i n t e r p o l a t i o n o r , b y u s i n g t h i s map i n c o n j u n c t i o n w i t h a t o p o g r a p h i c map, h e c a n i d e n t i f y a measured s t r e a m s i m i l a r t o t h e one f o r which a n e s t i m a t e i s wanted. I f a c a l i b r a t i o n i s a v a i l a b l e o n l y f o r t h e 10-year f l o o d , f l o o d s of l a r g e r recurrence
i n t e r v a l s may be approximated by m u l t i p l y i n g t h e e s t i m a t e d 10-year
f l o o d b y f a c t o r s b a s e d on f r e q u e n c y c u r v e s f o r t h e r e g i o n ; t h i s i s s i m i l a r t o t h e procedure used i n t h e index-flood
method.
160
8.10.4
From precipitation
Methods of estimating flood-peak characteristics directly from precipitation include the so-called Rational Method and procedures developed by the U.S. Conservation Service (SCS)
and by the U.S.
Soil
Corps of Engineers Hydrologic
Engineering Center (HEC). The Rational Method, widely used for design of storm drainage facilities, gives peak runoff rate, Q, in cubic feet per second, by Q = C I A where C is a dimensionless runoff coefficient; I is rainfall intensity in inches per hour for a period of time equal to the time of concentration of the basin, and for the s a m e recurrence interval as the discharge; and A is the drainage area in acres.
Time of concentration is usually defined as the estimated time
required for runoff to flow from the farthest point in the drainage area. The coefficient C depends on the permeability of the basin soils and other surfaces.
Its value ranges from about 0.10 for sandy soil to 0.95 for imper-
vious pavement; it is generally above 0.50 for urbanized areas.
Rainfall inten-
sity, I is obtained from an intensity-duration-frequency relation derived from precipitation records.
The duration used is the time of concentration which
must b e estimated at ungaged sites.
Anderson (1970) shows lag time (time of
concentration) as a function of basin length divided by the square root of hasin slope for natural and for fully urbanized basins. The Rational Method usually is applied only to small drainage areas. Schaake, Geyer. and Knapp (1967) examined the method and compared runoff estimates with those from runoff frequency curves for urban drainage areas.
They
found that for every five Rational Method estimates made by storm drain designers in the Baltimore, Md. area, one of them, on the average, may b e in error by more than 25%.
Ardis, Dueker. and L e n z (1969) reported a w i d e variation in
procedures used by practicing engineers for applying the Rational Method, and a consequent lack of consistency among results. Both the Hydrologic Engineering Center (HEC) of the Corps of Engineers and the Soil Conservation Service (SCS) have computer programs for estimating flood peaks of various recurrence intervals from precipitation.
These programs are
applicable to drainage areas ranging from a few to several thousand square miles. The SCS TR-55 graphical method of estimating flood-peak characteristics begins with classification of all soil units in the basin as to infiltration capacity.
This classification is used with adjustment for soil cover to define
a curve number (CN) for each.
These are area weighted and the result is used
with storm rainfall to get direct runoff in inches, usually by a graphical solution of a runoff equation.
Peak discharge is computed from direct runoff
161 computed a s above; d r a i n a g e a r e a ; t i m e of c o n c e n t r a t i o n from channel l e n g t h and slope:
a n d a c o n s t a n t (U.S.
S o i l C o n s e r v a t i o n S e r v i c e , 1 9 7 1 ) . and (McCuen.
1982). Methods f o r e s t i m a t i n g f l o o d p e a k s f r o m p r e c i p i t a t i o n u s u a l l y r e q u i r e t h e assumption t h a t t h e r e c u r r e n c e i n t e r v a l of t h e computed f l o o d i s t h e same a s t h e r e c u r r e n c e i n t e r v a l of t h e c a u s a t i v e r a i n f a l l . drainage basins.
a q u e s t i o n a b l e assumption i n some
The m e t h o d s a l s o r e q u i r e i n p u t d a t a t h a t o f t e n a r e e i t h e r
u n a v a i l a b l e or t h a t must be d e f i n e d somewhat s u b j e c t i v e l y . 8.10.5
I n t e r p o l a t i o n along channel
S t r e a m f l o w r e c o r d s and t h u s flood-peak c h a r a c t e r i s t i c s a r e a v a i l a b l e a t i n t e r v a l s along the l a r g e r streams i n t h e United States.
Better estimates
between t h e gaged s i t e s can be made by i n t e r p o l a t i o n t h a n by any of t h e methods d e s c r i b e d above, p a r t i c u l a r l y i f t h e f l o o d c h a r a c t e r i s t i c s do not change consist e n t l y along t h e channel.
The i n t e r p o l a t i o n shown i n F i g u r e 8.11 i s b a s e d on
10-year f l o o d s d e f i n e d a t 3 s i t e s on t h e main s t r e a m and on 5 t r i b u t a r i e s i n t h e
i;
20,000
2 0
g 10,000
d
0
::
L
+ 4
0
2 iooo~ n
?
e
iL tf r a W
2000
0
4
9 z
I
I
I
I
10
20
30
40
MILES ALONG CHANNEL
Fig. 8.11. Ten-year f l o o d s i n t e r p o l a t e d between gaged s i t e s , New Hampshire. F i g u r e s a r e 10-year f l o o d s a t t r i b u t a r i e s . reach.
The a b s c i s s a i s d i s t a n c e along t h e channel.
t e d and t h e mouths of major t r i b u t a r i e s a r e located.
Contocook River,
The gaged p o i n t s a r e p l o t I n t e r p o l a t i o n i s by t r i a l ,
based on t h e assumption t h a t a p p r e c i a b l e i n c r e a s e s occur o n l y where t r i b u t a r i e s enter.
The c o n t r i b u t i o n o f a g a g e d t r i b u t a r y s h o u l d b e n o t more t h a n i t s 10-
y e a r f l o o d b u t i t may be much l e s s i f t h e t r i b u t a r y f l o o d i s u s u a l l y n o t concurr e n t w i t h t h e f l o o d on t h e main stream.
162
I
I
cn
z
::
5-
I
W W
2000-
100-YR e
W'
0
5
1000-
50-YR
Y
g 2
I
-
10-YR
I
I
300
Fig. 8.12.
+ W
fi
P
0,
O
Q
0
9
0
$ v 3 a
o - lm m 1
4a
:s
>