Ladoga and Onego - Great European Lakes: Observations and Modeling

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Ladoga and Onego - Great European Lakes Observations and Modelling

Leonid Rukhovets and Nikolai Filatov (Editors)

Ladoga and Onego - Great European Lakes Observations and Modelling

~ Springer

Published in association with

Praxis Publishing Chichester, UK

Editors Professor Leonid Rukhovets Institute for Economics and Mathematics at St. Petersburg Russian Academy of Sciences St Petersburg Russia

Professor Nikolai Filatov Institute of Northern Water Problems Karelian Research Centre Russian Academy of Sciences Petrozavodsk Russia

SPRINGER-PRAXIS BOOKS IN ENVIRONMENTAL SCIENCES SUBJECT ADVISORY EDITOR: John Mason, M.B.E., B.Sc., M.Sc., Ph.D.

ISBN 978-3-540-68144-1 Springer is part of Springer-Science + Business Media (springer.com) Library of Congress Control Number: 2009924722 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers.

© Copyright, 2010 Praxis Publishing Ltd. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cover design: Jim Wilkie Project copy editor: Mike Shardlow Typesetting: Aarontype Limited Printed in Germany on acid-free paper

Contents

List of contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

IX

Preface

Xl

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 The Great European lakes: state of the art. . . . . . . . . . . . . . . . . . . . . . . .. 1 1.1 Physiographic features and history of the formation of the lakes and their catchments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 1.2 History of research of the lakes. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9 1.3 Characteristics of temperature and currents 14 1.3.1 The thermal regime and limnic zones 14 1.3.2 Currents and circulations 23 1.4 The cycle of substances in Lake Ladoga and the dynamics of its warer~osy~em 31 1.4.1 Lake ecosystem phosphorus supply. . . . . . . . . . . . . . . . . . . . . 31 1.4.2 Phytoplankton in the Lake Ladoga ecosystem 33 1.4.3 Bacterioplankton, water fungi and destruction processes 39 1.4.4 Zooplankton..................................... 41 1.4.5 The role of the zoobenthos in the ecosystem 42 1.4.6 Dissolved organic matter 44 1.4.7 The role of seston and bottom sediments in the lake phosphorus cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.5 The cycle of substances in Lake Onego and its water ecosystem 47 1.5.1 Phosphorus supply to the Lake Onego ecosystem 48 1.5.2 Biological communities in the Lake Onego eutrophication state 51

vi

Contents

1.6

1.5.3 Relation between the primary production and the destruction of organic matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59 1.5.4 Peculiarities of Lake Onego eutrophication . . . . . . . . . . . . .. 60 The main tendencies in the evolution of large, deep, stratified lakes. . .. 61

2 Hydrothermodynamics of large stratified lakes 2.1 Ensemble of thermo- and hydrodynamical processes and phenomena in lakes 2.2 Lake models: state of the art. Problem formulation for the simulation of lake hydrothermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.2.1 Introduction.................................... 2.2.2 Equations of geophysical hydrodynamics. . . . . . . . . . . . . . .. 2.3 A climatic circulation model for large stratified lakes . . . . . . . . . . . .. 2.3.1 General comments 2.3.2 Mathematical formulation. . . . . . . . . . . . . . . . . . . . . . . . . .. 2.3.3 Realization of the model. . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.3.4 Generalized formulations of the mathematical model . . . . . .. 2.3.5 About the discrete model . . . . . . . . . . . . . . . . . . . . . . . . . .. 3

67 67 69 69 70 73 73 76 80 80 83

Climatic circulation and the thermal regime of the lakes . . . . . . . . . . . . . .. 85 3.1 The climatic circulation in Lakes Ladoga and Onego from observational data and estimates. . . . . . . . . . . . . . . . . . . . . . . . . . .. 85 3.2 On the problem of simulating climatic circulation . . . . . . . . . . . . . . .. 87 3.3 Setting of external forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91 3.4 Simulation of the Lake Ladoga climatic circulation. . . . . . . . . . . . . .. 97 3.4.1 Computational procedure. . . . . . . . . . . . . . . . . . . . . . . . . .. 97 3.4.2 Description and analysis of thermal regime calculation results.. 99 3.4.3 Description and analysis of current calculation results. . . . .. 112 3.5 Simulation of the Lake Onego climatic circulation . . . . . . . . . . . . .. 122 3.5.1 Computational procedure. . . . . . . . . . . . . . . . . . . . . . . . .. 122 3.5.2 The results of thermal regime modelling. . . . . . . . . . . . . . .. 122 3.5.3 The results of currents simulations. . . . . . . . . . . . . . . . . . .. 129

4 Estimation of the lakes' thermohydrodynamic changes under the impact of regional climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.1 Climate change over the lakes' catchments. . . . . . . . . . . . . . . . . . .. 4.1.1 Climatic features and their variability . . . . . . . . . . . . . . . .. 4.1.2 Probable climate changes over the lakes' catchments. . . . . .. 4.1.3 Estimates of potential changes in the thermal regime of the lakes by 2050. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.2 Modelling the thermohydrodynamics of the lakes under different climatic conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.2.1 Modelling thermohydrodynamics: statement of the problem and numerical experiments. . . . . . . . . . . . . . . . . . . . . . . .. 4.2.2 Analysis of the results of simulations. . . . . . . . . . . . . . . . ..

134 134 134 138 143 150 150 155

5

6

7

Contents

vii

Three-dimensional ecosystem model of a large stratified lake . . . . . . . . . . . 5.1 Modelling the functioning of the lake ecosystems: state of the art 5.2 Aquatic ecosystem mathematical model 5.3 Discrete models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Discretization of the solution domain 5.3.2 Reconstruction of transport, turbulent diffusion and the sedimentation of substances in the model . . . . . . . . . . . . . . . 5.3.3 Reconstruction of the transformation of substances. . . . . . . . 5.3.4 Total variation of the concentration of substances in additional division cells 5.3.5 Discrete analogue of the total substances content variation law in lake waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Changes in the discrete model with coarsening of the domain decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163 163 165 168 169

Ecosystem models of Lakes Ladoga and Onego . . . . . . . . . . . . . . . . . . . 6.1 The history of the ecosystem modelling of Lakes Ladoga and Onego. 6.2 Complex of Lake Ladoga ecosystem models . . . . . . . . . . . . . . . . . . 6.3 Ecosystem model for Lake Onego, based on the turnover of biogens nitrogen and phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Ecological formulation of the model 6.3.2 Mathematical formulation of the model 6.3.3 The discrete model 6.3.4 Reproduction of Lake Onego annual ecosystem functioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Lake Ladoga phytoplankton succession ecosystem model . . . . . . . . . 6.4.1 Formulation of the model 6.4.2 The discrete model 6.4.3 Model verification, computation experiments 6.4.4 Reproduction of phytoplankton succession

171 173 173 173 175

. 179 . 179 . 182 . 186 186 188 192 . 197 . 206 208 212 217 219

Estimating potential changes in Lakes Ladoga and Onego under human and climatic impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Modelling changes in the Lake Ladoga ecosystem under different scenarios of climate change and anthropogenic loading . . . . . . . . . . . . 7.1.1 Modelling changes in the ecosystem under different scenarios of climate change 7.1.2 Modelling changes in the ecosystem under different scenarios of climate change and changes in the level of anthropogenic loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Modelling changes in the Lake Onego ecosystem under different scenarios of climate change and anthropogenic loading . . . . . . . . . . . .

227 228 228

232 238

viii

Contents

8 Lake Ladoga and Lake Onego models of fish communities . . . . . . . . . . .. 8.1 Introduction......................................... 8.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8.3 The models study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9 Natural resources of Lakes Ladoga and Onego and sustainable development of the region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9.1 Water supply and management in the catchments. Legal and regulatory aspects of water use. . . . . . . . . . . . . . . . . . . . . . . . . . .. 9.2 Assimilation potential of lake ecosystems and sustainable development of the region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9.2.1 Introduction................................... 9.2.2 Assimilation potential of the natural environment. . . . . . . .. 9.2.3 Quantification of the assimilation potential of the ecosystems of Lakes Ladoga and Onego . . . . . . . . . . . . . .. 9.2.4 Economic quantification of assimilation potential. . . . . . . .. 9.2.5 Mathematical economic model . . . . . . . . . . . . . . . . . . . . .. 9.2.6 Computational experiments. . . . . . . . . . . . . . . . . . . . . . . .. 9.2.7 Conclusions....................................

247 247 249 354 261 261 268 268 271 271 273 274 276 280

Afterword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 281 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 283 Index

The colour plate section appears between pages 144 and 145.

299

List of contributors

G. P. Astrakhantsev N. N. Filatov A. V. Litvinenko V. V. Menshutkin T. R. Minina L. E. Nazarova N. A. Petrova V. N. Poloskov L. A. Rukhovets A. V. Sabilina Ju. A. Salo A. Yu. Terzhevik T. M. Timakova

Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Institute of Limnology, Russian Academy of Sciences, S1. Petersburg Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk

Preface

Problems of environment pollution and depletion of natural resources have become global. One such problem is the shortage of potable water in many parts of the world. Although Russia is one of the world's richest countries in terms of water resources, some problems with public potable water supply do exist here too. The region of the Great European Lakes is very rich in surface and ground waters, and the water factor does not limit economic development of northwest Russia. The Great European Lakes - Ladoga and Onego - attract the continuously increasing attention of both researchers and end-users. The importance of the Great European Lakes proper, to drinking purposes, recreation, transport, and energy, together with the use of bioresources and the impacts of the pulp-and-paper industry and the discharge of waste from cities and towns located on the shores and in the catchment areas, will require the working out of scientifically substantiated recommendations for the rational use and the protection of the resources. A serious problem for the Great Lakes of Europe, as for the other very large lakes of the world, is anthropogenic eutrophication. The necessity of minimizing the impact of anthropogenic eutrophication and water pollution, which have reached a global scale and jeopardize the quality of already limited freshwater resources, has triggered quite a number and variety of studies in limnology, mathematical modelling, and economics, with view to the conservation, restoration, and efficient use of the resources of large stratified lakes. The authors undertook to develop a set of mathematical models that help to rework available knowledge about hydrophysical, chemical and biological processes in large stratified lakes into adequate reconstructions of circulation, temperature regime and function of the ecosystems. This set of models is meant to be a tool for handling the tasks of managing water use and conservation of the natural resources of large stratified lakes, the prime consideration being water quality. This monograph is based on the authors' work in the development of mathematical models of the hydrothermodynamics of deep stratified lakes and ecosystem

xii

Preface

models, as well as in the application of the models to reproducing circulation, temperature regime and function of the lake ecosystems. An equally important component of the book is the description of the results of long-term limnological studies of Lakes Ladoga and Onego implemented by researchers from the Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, and Institute of Limnology, RAS, and development of mathematical models in the Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, including the authors of this monograph. This book Ladoga and Onego - Great European Lakes: Observations and Modelling addresses the contemporary state of the largest lakes of Europe and their catchment under anthropogenic and climate changes, with special emphasis placed on feedforward and feedback interactions between aquatic ecosystems, watershed hydrology and the economy of the region. To investigate the responsiveness of both environments to the respective counter-impacts, as well as to regional and global climate change, data analysis of multi-year field observation numerical modelling are exploited. This book is a first attempt to apply a quantitative approach to the assessment of changes occurring at present and anticipated in the future to dynamic relationships between the anthropogenic impacts, climate change and water ecosystems of both of the largest lakes of Europe. Thus, the book is primarily a synthesis of multifaceted interdisciplinary studies conducted by a team of experts working in a wide spectrum of natural and human sciences. Indeed, it is a synthesis of limnology, mathematics, hydrobiology, hydrochemistry, thermohydrodynamics , aquatic ecology, and economics. The book consists of nine chapters. Chapter 1 addresses a wide range of issues related to the geographical position, origin and palaeogeological background of Lakes Ladoga and Onego catchments. The knowledge of the physical geography of the catchments is essential for understanding the fundamental features of the lacustrine environments. Discussed here are the most reliable and recently updated data on the hydrodynamics of the lakes. The dynamics of human impact on the lakes and their catchments is analysed. Special attention is paid to investigations of material cycles in Lakes Ladoga and Onego and dynamics of the ecosystems. The chapter contains detailed information on the chemistry and biology of the lakes. The last paragraph of the chapter is devoted to the main tendencies in the evolution of great deep lakes Ladoga and Onego. Chapter 2 discusses the range of water movements in the lakes, circulation patterns and currents, as they are influenced by atmospheric forcing. The approaches to choosing the hydro thermodynamic model are explained. The state of the art of the lake models is reported. Geophysical hydrodynamics equations and their applications for description and simulation of lake hydrothermal dynamics are presented. The main objective of modelling the dynamic hydrothermal regime in our monograph is to offer ecological models with information on abiotic environment factors, first of all hydrophysical processes, which to a large extent control the functioning of aquatic ecosystems. Chapter 3 is devoted to the reproduction of climatic circulations in lakes. The problem statement is given, and the issues of setting the external parameters

Preface

xiii

are discussed. The central issue in the chapter is the results of modelling water dynamics in the lakes. Chapter 4 is dedicated to data analysis of long-term observations of the hydrometeorological regime in the catchment. Estimates of regional climate changes are made, climatic data are put together and analysed to reveal tendencies in climate change in the lakes' catchment. Climatic fluctuations in the region evidence ongoing warming. Possible climate scenarios are estimated using global climate models (ECHAM-4) and IPCC scenarios for Lake Ladoga and Onego basins. Based on these analyses, numerical simulations were performed in order to explore the options of future alterations to the regional climate against the background of global climate change scenarios. In the second part of the chapter, the hydro thermodynamic model for large stratified lakes is applied to estimate potential changes in the lakes' temperature regime and currents until the year 2050. Chapter 5 formulates the 3D mathematical model of the aquatic ecosystem of an abstract waterbody, represented as a system of nonlinear differential equations in partial derivatives. The chapter postulates requirements to the structure of the descriptors of the processes of biochemical transformation of matter in lake ecosystems. If these requirements are satisfied, long-term (many-year) calculations can be performed by the models. The ecosystem model for Onego is an adaptation of the model produced for Ladoga (Astrakhantsev et al., 2003). The biotic part of the model is based on the model developed by Menshutkin and Vorobyova (1987). The model of Lake Ladoga ecosystem is the phytoplankton succession model the most advanced one of all the ecosystems models developed for Ladoga. Chapter 6 focuses on the development of ecosystem models. The history of Ladoga and Onego ecosystem modelling is briefly described in this chapter. Also, the models of the lakes' ecosystems developed by the authors in recent years and representing, in fact, an integrated complex, are reviewed. Major attention in this chapter is paid to two models, that is, the Lake Onego ecosystem model, based on the nitrogen and phosphorus cycles, and the latest one developed by the authors: the model of phytoplankton succession in Lake Ladoga. The coupled thermohydrodynamic and ecosystem models for Lakes Ladoga and Onego have been developed to study the contemporary situation, to understand the main mechanisms of the ecosystem transformation, and to learn what may happen in future under the varying anthropogenic impact and climate change. Models are developed that enable simulation of hydrodynamics, phytoplankton, zooplankton communities, distribution and transformation of dissolved oxygen, distribution and transformation of substances/pollutants, evolution of the lakes' ecosystems, and reliable quantitative estimation of eutrophication in Lakes Ladoga and Onego. Descriptions of the models are followed by examples of their application for the present day and for hind- and forecasting. Chapter 7 analyses the dynamics of the lakes' water ecosystems under climate change (warming and cooling) and anthropogenic impacts relying on observed and modelled data. The advanced mathematical model of phytoplankton succession including nine species of phytoplankton was developed. Special attention here is given to the feedforward and feedback interactions in these lakes and the

xiv

Preface

catchment under various scenarios of regional climate change and anthropogenic nutrient loading. The results of analysis of observed data and numerical experiments are presented. Chapter 8 tells about the state of the art in modelling fish populations and their variability. In fish community models, active migration plays a dominant role in fish movements from one region to another within Lakes Ladoga and Onego. The main idea of constructing fish community models consists in separate description of trophic, population, and fishery processes that take place in the fish community. This study deals with the succession of the fish community species composition under eutrophication. Chapter 9 is devoted to the analysis of water supply problems, economy of the regions of the Great European Lakes, and their sustainable development. It describes modern systems of water management for the large lakes of the Russian Federation. The environment assimilation potential (EAP) is the ability of an environment to restore itself with regard to matter and energy loading as the result of economic activities. The authors suggest that economic estimates of EAP are obtained using the iterative procedure based on the 'trial and error method'. We combined ecosystem models with economic and mathematical models of the enterprises that use water resources in the catchment areas of the lakes. The main goal of economic estimation of EAP is definition of the fees for discharges of nutrients and pollutants to ensure conservation of the resources and aquatic ecosystems of the largest lakes of Europe. The book offers useful answers and tools for decision-makers. In the Afterword the authors show that the important feature of this book devoted to the study of the Great European Lakes is a combination of traditional limnological research with numerical modelling. A satisfactory correspondence between the results of numerical modelling and observational data collected in Lakes Ladoga and Onego, especially well-reproduced successive stages of the lake ecosystem transformation, allows us to conclude that the main patterns of ecosystem functioning are reliably described by numerical models. This means that it is possible to use the models developed as a powerful tool in decision-making on the management of water use of the great lakes, and also for cognitive purposes. This book was written by the team of authors under the editing professors L. A. Rukhovets and N. N. Filatov. G. P. Astrakhantsev took part in Chapters 2 to 7; N. N. Filatovin the Preface, the Afterword, Chapters 3,4 and 9 and sections 1.1,1.6, 2.1, 6.1 and 7.2; A. V. Litvinenko in section 9.1; V. V. Menshutkin in Chapters 6 and 8; T. R. Minina in Chapters 6 and 7; L. E. Nazarova in section 4.1; N. A. Petrova in Chapters 6 and 7 and sections 1.4 and 1.6; V. N. Poloskov in Chapters 3, 4, 6 and 7; L. A. Rukhovets in the Preface, the Afterword, Chapters 2 to 7 and 9 and sections 1.1 and 1.6; A. V. Sabilina in section 1.5; Ju. A. Salo in section 4.1; A. Yu. Terzhevik in Chapter 4 and sections 1.3, 2.1, 3.1 and 6.3; T. M. Timakova in sections 1.5 and 1.6.

Acknowledgements

This book is based on the results of the cooperations of the authors during the teamwork at the Institute of Limnology, Russian Academy of Science and those under realization of joint projects of the Russian Fund for Basic Research (RFBR) by the teamwork of the Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, and Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences. We involved some research results obtained by the Northern Water Problems Institute (NWPI), Karelian Research Centre, Russian Academy of Sciences, and the Institute of Limnology, Russian Academy of Sciences, and some published data of the Hydrometeorological Service. The authors of the book thank the projects of Basic Research supported by the Department of Earth Sciences of the Russian Academy of Sciences. The authors of the book thank their colleagues from NWPI, Drs N. Kalinkina, N. Belkina, P. Lozovik, M. Sjarki , T. Tekanova and Dr G. Raspletina from the Institute of Limnology, for kindly provided data analysis and useful recommendations and Dr R. Zdorovennov from NWPI for help. The authors also express their gratitude to Dr V. Podsechin for very important help, Mrs M. Bogdanova for preparing and redrawing figures for the present book. Special thanks go to academician S. Inge-Vechtomov and academician O. Vasiliev and Dr T. Florinskaja for support of our work. The authors extend their sincere gratitude to Dr T. Podsechina and O. Kislova for the translation of the book. The authors thank Mr I. Georgievsky for fine pictures of Lakes Ladoga and Onego.

1 The Great European Lakes: state of the art

1.1 PHYSIOGRAPIDC FEATURES AND IDSTORY OF THE FORMATION OF THE LAKES AND THEIR CATCHMENTS Lake Ladozhskoe and Lake Onezhskoe (Ladoga and Onego respectively) are the greatest lakes in Europe. Another geographical object in Northern Russia has a similar name: the Onega River. At first the definition for the Great European Lakes (GEL) like Ladoga and Onego by analogy with the Great American Lakes (GAL) was used in a book written by Gusakov and Petrova, In front of the Great Lakes (1987). The authors called these European lakes 'Great', because of their size, their dimensions are larger than those of any other lake in Europe (Fig. 1.1, Table 1.1). From the point of view of geophysical hydrodynamics the Large Lakes of Europe (Ladoga and Onego) are the largest because the baroclinic Rossby radius of deformation is too small RR < L if compared with the lakes' horizontal dimensions. RR = Cdfwhere C, is the phase speed andfis the Coriolis parameter. In these lakes, the baroclinic Rossby radius of deformation RR during summer stratification is several kilometres, i.e, smaller by several orders than the lakes' horizontal dimension (RR < L); epilimnion thickness (hI) is much smaller than hypolimnion thickness (h2), hI < h2. That is why the effect of the Earth's rotation on water hydrodynamics is so essential. The Burger number Si, is defined as the ratio of the internal (baroclinic) Rossby radius deformation, RR' to a length scale, L, that characterizes the basin dimension. In the large lakes of Europe and North America this parameter in summer time is about 0.03-0.05 and in other large European lakes - Vennern, Geneva, Saimaa, Constance and others - this parameter is about 0.2-0.6. GEL as GAL represents system of a unified lake. Lake Ladoga is connected with Lake Onego via River Svir, which is 224 km in length, with Lake Saimaa via River Vuoksa (Burnaya) and Lake Ilmen via River Volkhov (Fig. 1.I(b)). Lake system is linked with the Gulf of Finland in the Baltic Sea via River Neva. The surface area of Lake Ladoga is 17 891 km 2 and volume is 902 krrr', it ranks among the top fifteen world's freshwater lakes and is comparable with surface area

2

The Great European Lakes: state of the art

[Ch. I

... ......"""-.-

,.

. . . ----.-..J---

~r lIt.

I. ~ ·

I'

- -- - ...

r'

. .. "':-

Russi

- - .... . . ;. ... r~

Germ n

r'

- -- """

-'

. ' • .,..... ..J'

•......, --~...

.., '....

•

r- J

.... ~.

,-

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I

(a)

Fig. 1.1. Largest lakes on European map (a) and catchment of Lake Ladoga (b).

of Lake Ontario (Figs. 1.2 and 1.3; Table 1.1). Lake Onego's surface area is 9600 km 2 and its volume is 292 krrr' (Chernyaeva, 1966).1 The water renewal time is 11 years for Lake Ladoga and 14 years for Lake Onego and indicates that the lake ecosystems are rather conservative. The catchment of the Great European Lakes is 258 000 km 2 and extends through northwestern European Russia and the eastern part of Finland, including the large lakes Onego, lImen and Saimaa (see Fig . 1.1). Lakes Ladoga and Onego are 1 Other dimensions of the lakes are published in a paper by M. A. Naumenko in Lake Ladoga. At/as , St. Petersburg, Nauka, 2002.

Sec. 1.1]

Physiographic features and history of the formation of the lakes

3

(b) Fig. l.l(h).

an important link in the Caspian-Baltic-White Sea waterway system. Ladoga and Onego are also a key section in the drainage basin of the Baltic Sea, which at present is receiving very deep interest from the research, monitoring and protection communities. Both systems of Great Lakes in North America and Northern Europe have certain common features due to a similar genesis and the similar geological evolution of their hollows and catchments. They both were generated between contrasting crystalline shields (the Canadian in North America and the Fennoscandian (Baltic) in Europe) and plates: North American and Russian respectively, composed of Palaeozoic rocks. In the area of crystalline shields the ancient Earth rocks - granites

4


[Ch. I

Table 1.1. Physiographic parameters of the largest European Lakes. Lake

Ladoga Onego Vennem Pskovsko-Chudskoe (Peipsi) Yettem Saimaa

Square, km 2

Above sea level m

Maximum depth, m

Average depth, m

Volume, km 3

18000 9840 5648 3558

4 33 44 30

230 120 106 15

51 30 27 7

910.0 295.0 152.5 24.9

1856 1800

89 76

128 58

40 20

74.2 36.0

:ero I

:i ~~

,>;,1 © .I

""'1

91 Q,~

a) ~~,t

= l :co J

"J. -.__ .~-:::_~_. ~-~--~ ..__.-/ ! ;: 3 z '5 E:

,....-----------------, '

Fig. 1.2. Volume in km? (a) and area in km2 (b) of the large lakes of Europe: I, Ladoga; 2, Onego ; 3, Vennem; 4, Pskovsko-Chudskoe (peipsi); 5, Yettem; 6, Saimaa.

and gneisses - are found at the surface with an age up to 2 billion years. The regions of neighbouring plates are presented mainly by limesstone, dolomites and sandstones with an age of less than 570 million years. The northern parts of the basins and catchments of Lakes Ladoga and Onego, as well as Lakes Superior and Huron, were formed on crystalline shields in places of ancient tectonic cracks, and the southern parts of these lakes, as basins of Lakes Michigan , Erie and Ontario were formed in

Sec. 1.1]


5

La

On

Fig. 1.3. Bathymetry of Lakes Ladoga and Onego.

sediments during the last glacial period. The last Ice Age of the Quaternary period, at a maximum approximately 25-10 thousand years ago , was the most important factor affecting the basins and catchments of both lake systems. At their maximum stage glaciers completely covered the northern parts of North America and Europe, including the regions occupied by the modern Great American and European Lakes. The highest degree of glacial erosion took place in the boundary shield regions , where vast systems of near-glacial lakes were formed (Kvasov, 1975; Gusakov and Petrova, 1987; The History of Ladoga and Onego ... , 1990). The history of the development of Lakes Ladoga and Onego is linked with the initial stage of the formation of the Baltic Sea - the Baltic system of near-glacial lakes. The territories of Lakes Ladoga and Onego were covered with ice at that time (Kvasov, 1975). About 11.8 thousand years ago with regression of the ice the Baltic glacial lake was formed, which occupied the major part of the modern Baltic Sea basin. At that time the near-glacial lakes system was generated. The main waterbody of this system was the Southern Baltic glacial lake, which existed approximately 12-13 thousand years ago. This lake water level was higher than the ocean level and saline water did not penetrate into it. At that time Lake Ladoga was a bay of the Baltic Lake, connected with it via a narrow strait in the northern part of the Karelian

6


[Ch.l

Isthmus. About the same time the southern and the eastern part of pre-Onego Lake basin were released from ice. As a result the Vytegorskoye and Vodlinskoye nearglacial lakes were formed. Later these lakes were connected, forming the Southern Onego glacial lake, which was not then a connected system with Lake Ladoga with outflow towards the basin of the White Sea. Only after glacier regression, did the River Svir carry its waters to Ladoga Bay of the Baltic glacial lake. Nearly 10 thousand years ago the Baltic Sea water level dropped by more than 20 m and equalled the ocean level. Oceanic waters penetrated into the Baltic Sea and created a waterbody, which was named the Ioldy Sea. The consequence of declination of the Baltic glacial lake level was that Lake Ladoga was no longer a bay and for the first time became a separate waterbody. The river appeared where the strait was, which carried its waters from Lake Ladoga to the Ioldy Sea. Since the Lake Ladoga level was at that time considerably higher that the Ioldy Sea level, brackish sea waters did not penetrate into the lake, where water remained fresh. During the same years which saw regression and melting of the ice, the formation of Lake Onego continued, of which the northern part was much larger than it is nowadays. After complete release from glacial cover about 4.5 thousand years ago, the northern shores of the lake underwent an isostatic rise, which has continued at a low rate up to the present day, and Lake Onego acquired something close to its modern shape. During the isostatic rise of Scandinavia the level of the ancient Baltic waterbody started to grow again and a freshwater body was formed out of the brackish water of the Ioldy Sea, named Lake Antsylovoye. At its maximum the water level of this lake exceeded the threshold magnitude for Lake Ladoga inflow and, as a result, in the northern part a shallow strait was formed. Lake Ladoga became a bay, this time of Lake Anstylovoye. About 8.4 thousand years ago Lake Antsylovoye formed a new threshold flow mark in the region of the modern Danish straits and, under the influence of erosion processes, the flow threshold mark decreased and the level of Lake Antsylovoye declined by 12m. Sea waters later penetrated into the ancient Baltic waterbody and for some time the Littorinovoye Sea existed there but, even at the stage of its maximal development, the level of Lake Ladoga was always higher, which prevented the spreading of saline sea waters. During the whole formation period Lakes Ladoga and Onego remained freshwater bodies. Thawing glacial waters brought to forming lakes a large amount of coarse and fine mineral particles and dissolved substances, including biogens that were stocked earlier in the glacier. These waters, comprising the basis of income water balance, were relatively rich in biogens; the lakes ecosystem productivity was low for several reasons: first, incoming glacial waters had low transparency and light was one of the limiting factors for phytoplankton development, and, second, low temperatures and a short vegetation period, typical for the late post-glacial period, influenced biota development (Davidova and Subetto, 2000). Thus, at the end of the Pleistocene, preLadoga and pre-Onego were oligotrophic cold water bodies. Lake ecosystems were formed under the influence of gradual climate warming. The beginning of the Boreal period and climate warming resulted in further development of forest vegetation on the lakes' catchments and was characterized by deposition in the deep lakes of

Sec. 1.1]


7

homogeneous clays with high biogenic concentrations. The climate warming and high humidity over the territory led to growth on the catchments of mixed conifer and broadleaved forests with an admixture of oak, lime, elm, and maple, which provided the growth of the organic component in bottom sediments (Davidova and Subetto, 2000) and higher accumulation rates of sludge. Approximately 4-5 thousand years ago the formation of the modern Baltic Sea was practically complete. By this time Lake Onego had reached its modern shape, while the Lake Ladoga basin continued to transform. About 5 thousand years ago (Saarnisto et al., 1995) on the edge of atlantic and sub-boreal periods, the isostatic rise in the near-Ladoga region modified the hydrographic network, redirecting flows and turning the flow of the Saimaa lake system through River Vuoksi to Lake Ladoga, which increased by approximately one-third the income component of the lake water balance. The northern coast of Lake Ladoga experienced considerable isostatic rise and, as a result, the outflow from the lake to the northern part of the Karelian Isthmus nearly stopped. The lake level started to rise, and that affected mostly the southern coastal part. The highest lake water level was reached about 2 thousand years ago. When the lake water level reached the height of the watershed dividing the Mga River, inflowing to Lake Ladoga, from the Tosna River, inflowing to Gulf of Finland, Lake Ladoga waters washed away the narrow isthmus of the watershed and the Neva River was formed. After the generation of the new threshold flow value, the level of Lake Ladoga started to decline. The northern flow had stopped completely and the relatively short, 74 km long, Neva River became the only outflow from Lake Ladoga to the Baltic Sea. Its average discharge equalled 2500 m 3/s, and it has not changed in fact since that time. The final formation of the Neva River and the whole system of Great European Lakes took place less than 2 thousand years ago. By this time the level of Lake Ladoga had attained its modern magnitude (about 4-5 m above sea level). At the same time erosion processes were intensified on the catchment, which created favourable conditions for natural but fairly gradual lake ecosystem eutrophication processes. The peculiarities of the Ladoga and Onego lake basin and catchment generation and evolution had created such specific features of the coastline as its high embayment in the north and its regular smoothness in the southern, southeastern and southwestern parts. A high degree of similarity is observed in the northern parts of the lakes' coasts - a large amount of narrow long coves, bays and fiords, elongated from north to south or from northwest to southeast, and the existence of skerries. Lakes Ladoga and Onego in general are very similar to the Great American Lakes in their origin, coast types, and bottom relief and in the contrast between the northern and the southern parts of their basins. Lake Onego is the upper one in the system of Great European Lakes. Comparing the two largest lake systems of the North American and European continents, it could be mentioned that they are relatively young by origin and reached their modern shapes only a few thousand years ago. The ecosystem dynamics of the Great Lakes in Europe and America have a lot in common, but there also exist some individual features specific to each.


[Ch.l

(a)

(b)

(c)

Fig. 1.4. Satellite images of the lakes in winter. Ladoga: (a) satellite 'Resource 01'; Onego (b) cold year, 04 FEB 2005, and (c) warm year 05 FEB 2007, satellite 'Terra'.

Sec. 1.2]

History of research of the lakes

9

Summing up, it is possible to point out that, regardless of the initial similarity in the limnological characteristics of GAL and GEL, the contemporary evolution of these lake ecosystems over recent centuries has proceeded differently. Moreover, even within each lake system the processes of eutrophication and toxic contamination differ quite distinctively. These differences are promoted by specificity in limnogenesis, in morphometry, in thermohydrodynamic processes and in catchment changes, as well as in legislation, practical water resources management and investments in nature preservation. Current and future tendencies in climate change are allegedly bound to drive the evolutionary paths of the lake systems even further apart. Though Lakes Ladoga and Onego are located more towards the north than American lakes, climatic peculiarities of their catchments are to a certain degree similar. Air masses of a different origin collide there and unstable climatic conditions develop with frequent changes of weather conditions. Air masses, coming from the Atlantic Ocean over the catchments of Lakes Ladoga and Onego, bring intensive snowfalls and thaws in winter, and in summer rainy and windy weather. The intrusion of arctic air masses causes abrupt cooling, sometimes below -40°C. The invasion of continental air masses from the east and southeast leads to dry and hot weather in summer and to clear and frosty weather in winter over the lakes' catchments. The Great American Lakes never freeze completely, while Lakes Ladoga and Onego are completely covered with ice during cold winters; in warm winters the ice covers only part of lakes (Fig. 1.4). Ice cover thickness on Lake Ladoga and Lake Onego may reach 1m and even more in some years. On Lake Ladoga during the winter period quasi-steady polynyas exist, dividing the ice cover of the coastal area (fast ice) from that of the central part of the lake. In years when the lake is not completely covered with ice, the ice mass in the central part drifts, depending on prevailing wind direction. This ice mass is usually fractured (Tikhomirov, 1982). Ice cover destruction usually takes place in May, but in a cold spring floating ice may be observed in June. The same origin of the Great American and Great European Lakes basins and the geological peculiarities of their catchment are revealed in their similarity of morphometric features and thermal regime formation. Lakes Ladoga and Onego belong to the so-called dimictic lake type (Ryanzhin, 1994). 1.2 HISTORY OF RESEARCH OF THE LAKES Lakes Ladoga and Onego have been studied during the last hundred years, both before the pronounced influence of human activities and during the period of catastrophic ecosystem change under increased anthropogenic pressure in 1970s and 1980s. Taking into consideration the common features of the abovementioned lakes, we will show in this work that mathematical models developed and tested for Lakes Ladoga and Onego, contain formulations of the problems and algorithms suitable for the ecosystem modelling of other large lakes located in temperate latitudes. Lakes Ladoga and Onego, located between 59°54' Nand 62°55' N are among the northernmost of the world's great lakes. The tremendous catchment area of Lake


[Ch.l

Ladoga, located in different landscapes, determines the wide diversity of natural and anthropogenic factors affecting the lake ecosystem dynamics. The considerable size of the lake and the slow water exchange (the ratio of the lake volume to annual inflow, that is the conventional water exchange coefficient, equals 0.08) are the reasons for ecosystem conservativity. The complicated morphometry of the lake basin and its large proportions account for heterogeneity of hydrophysical, hydrochemical and hydrobiological processes in different parts of the waterbody. The variability of limnetic parameters, typical for deep, large lakes, is especially intensified under the heavy and essentially always non-uniform anthropogenic impact. The studies of this waterbody are typical, since all changes that take place in Lake Ladoga are reflected in the water quality of the Neva river, and thus in the water supply of St. Petersburg, and influence the water quality of the Neva Bay of the Gulf of Finland. The initial studies of Lake Ladoga date back to the end of the nineteenth and the beginning of the twentieth centuries (Andreev, 1875; Molchanov, 1945). The significant results of that period are generalized in the monograph written by I. V. Molchanov (1945). Knowledge of the ice regime helped in the building and maintaining of a temporary road (the so-called 'road of life') over the ice cover across the southern part of Lake Ladoga during the Second World War. This road provided a connection with Leningrad city during the blockade period. It helped to maintain a temporary road on the ice which was used to evacuate refugees and to organize the delivery of supplies to Leningrad city. The bibliography of Lake Ladoga studies includes several hundreds of titles (Bibliography . . . , 1997). Comprehensive investigations of the limnological processes in Lake Ladoga were conducted by the specialists of the Laboratory of Limnology of the USSR Academy of Sciences (now the Institute of Limnology of the Russian Academy of Sciences) in 1956-1963. The results of these studies were published in eight monographs from 1961 to 1968 (Hydrological Regime ... , 1966). In this period of time, precise spatial and seasonal characteristics of the main hydrochemical and hydrobiological processes, which appeared as a result of increasing anthropogenic loading, were obtained. Until the mid-1960s industrial activities in the catchment had very little influence on the state of the ecosystem and the water quality in Lake Ladoga. The lake preserved its status as an oligotrophic waterbody, as it had at the beginning of the century. Insignificant bacterial pollution was registered only in the vicinity of the wastewater outlets of the paper mill establishments. Noticeable changes in the lake ecosystem were related to increasing phosphorus loading in the waterbody, mainly from the wastewaters of the Volkhov aluminium plant and agricultural activities. The increase of phosphorus loading led to the development of the process of anthropogenic eutrophication. The first step in studying this process, which nowadays has the central role in the evolution of the ecosystem of Lake Ladoga, is related to the period 1975-1980. The research was carried out by the Limnological Institute of the Russian Academy of Science and the results were published in the monograph of Petrova (1982). The main features of the anthropogenic eutrophication were described and the reasons for its existence were

Sec. 1.2]


11

established. The next step in this research, dating from 1981 to 1990, made it possible to formulate a series of theoretical concepts, necessary for understanding and forecasting the tendencies of waterbody development (Lake Ladoga. Atlas, 2002). Estimates were made of the principal difference of anthropogenic eutrophication in large deep lakes compared with its natural evolution, of the effect of morphological homogeneity in the lake basin on the formation of limnological processes, and of the dangerous consequence of eutrophication - the decrease of oxygen content in water. An important result of these studies was the comparison of alteration scales in the ecosystem under the influence of anthropogenic activities with the natural diversity, and the selection of an optimal number of parameters - ecological criteria - which can be used during analysis, modelling and forecasting of the state of the lake. The beginning of the development of a mathematical ecosystem model dates to this period In all studies attention was mainly paid to the interaction of phosphorus with the carbon cycle in the lake ecosystem, which defines production-destruction relations, and as a result the rate of its destabilization (Modern states . . . , 1987; Lake Ladoga ... , 1992). It was pointed out that anthropogenic eutrophication is a phenomenon comparable to the scale of natural processes. Furthermore a number of approaches for the estimation of the degree of pollution and the potential for such pollution in different parts of the waterbody was developed. The starting point was the analysis of the lake processes which determined the development of significant consequences of anthropogenic impact. Unfortunately the studies carried out in the 1990s were less regular and were limited mainly to the summer periods. Let us mention the international research on the lake which was conducted in these years (Viljanen and Drabkova, 2000). The monitoring of the main lake processes was carried on and the results could be found in the proceedings of three international Lake Ladoga symposiums and in the collective monographs (Lake Ladoga, 2000; Lake Ladoga. Atlas, 2002; Rumyantsev and Drabkova, 2006). In these years a number of substantial studies, started earlier, were fulfilled: the conclusions of the long-term analyses of the generation of lake organic substances pool were drawn (Kulish, 1996), and the phosphorus fluxes at the water-bottom interface were estimated (Ignatieva, 1997). There were studies of the role of humic complexes in lake organic substances during the accumulation process, conservation and recirculation in the lake phosphorus cycle. This analysis made it possible to understand the mechanism of lake ecosystem stability and the reasons for its transformation during long-term anthropogenic pressure (Korkishko et al., 2002). During the period 19962005 the phosphorus loading on Lake Ladoga noticeably decreased. Its mean value during this period did not exceed 4000 tons of phosphorus per year. Such low levels of phosphorus loading on the lake had not been registered in more than 20 years, from 1975 until 1995. The following publications devoted to the analysis of the process of anthropogenic eutrophication from the 1960s until 2005: Petrova et al. (2005) and Rumyantsev and Drabkova (2006). Generalizations of the data obtained over several decades are presented in Lake Ladoga. Atlas (2002). Geographical descriptions of Lake Onego, performed by travellers and researchers were rare and incomplete before the nineteenth century. In ancient times Lake Onego was called Anizskoye (from Finnish Aiininen jdrvi; iiiini means


[Ch.1

voice, sound) and later Onego. Academician Ozeretskovky, who visited Lake Onego in 1785, first published a review about the lake at the end of the eighteenth century (1792). In the nineteenth century several expeditions were organized there to study water level, thermal regime and sediments; a general geographic description of the lake was prepared by Bergshtresser, Stabrovsky, Keppen, Andreev and Drizhenko, Sovetov (see in Molchanov (1946) and in Lake Onego. Atlas (2009)). From the 1870s, water level recording and collecting observation data was organized at meteorological stations on Lake Onego and its catchment. Beginning from the end of the nineteenth century Russian Geographical Society initiated systematic investigations on Lake Onego. The first water-temperature data recordings on the lake were obtained in 1903 by N. A. Pushkarev. In 1914 the expedition under the leadership of S. A. Sovetov measured water temperature and transparency at 15 deepwater stations from a steamboat, and took sediment samples to fulfil mechanical, chemical and biological analyses. During the period 1924-1933 the complex Onezhskaya expedition of the State Hydrological Institute under the guidance of S. A. Sovetov conducted studies on the lake; the results were generalized in monograph by Molchanov (1946). Since 1933, after the construction of Belomorsko-Baltyisk Canal, the lake has been connected with the White Sea and joined the united system, linking the White, the Baltic and the Caspian seas. In 1953 on the River Svir, connecting Lake Ladoga and Lake Onego, an Upper Svir (Verhnesvirskaya) hydropower station was constructed, since then the lake water regime was regulated and the Upper Svir reservoir was formed. In 1964 the complex Onezhskaya expedition was organized to study the lake pollution problems and their influence on water quality and biological productivity (Ecosystem of Lake Onego ... , 1990). The expedition combined the Limnological Institute of the USSR Academy of Sciences, the Department of Water Problems of the Karelian Branch of the USSR Academy of Sciences, SevNIORH and the Petrozavodsk hydrometeorological observatory of UGMS. The studies were organized according to a special programme in the areas of the highest pollution. In 1970-1971 real-time measurements were conducted on a hydrophysical polygon in Bolshoye Onego Bay with different biotopes. Investigations were carried out by specialists of the Department of Water Problems of the Karelian Branch of the USSR Academy of Sciences, the Institute of Zoology of the USSR AS, and the Computing Centre of the USSR AS (Limnological Investigations ... , 1982). In 1981-1985 the Department of Water Problems of the Karelian Branch of the USSR AS performed complex studies of the lake all over the waterbody including measurements at 200 stations in connection with possible redistribution of water resources on the European territory of the USSR starting from the White Sea, via the lake system of Arkhangelsk and Vologodsky regions, through Lakes Ladoga and Onego to the south of the USSR (Ecosystem of Lake Onego ... , 1990). But the diversion of river flow from the north to the south with abstraction of the waters of Lakes Ladoga and Onego was not realized. At the end of the 1980s and the beginning of the 1990s the Limnological Institute of the USSR AS and the Department of Water Problems of the Karelian Branch of the USSR AS conducted a unique hydrophysical experiment 'Onego-89' using three

Sec. 1.2]


13

research vessels, autonomous buoy stations, an airborne laboratory and three satellites. The aim of this experiment was the development of operational methods for checking water quality parameters (Lake Onego ... , 1999; Filatov, 1991). In the volume and spread of its observations it could be compared with the International Field Year of Great Lakes (IFYGL) on the Great American Lakes (Mortimer, 1974). In 1991 the Department of Water Problems was reorganized into the Northern Water Problems Institute of the Karelian Research Centre of the RAS. Since 1992 NWPI Karelian RC RAS has started regular observations on Lake Onego in accordance with a programme of complex monitoring (Ecosystem of Lake Onego ... , 1990). Since 1991 the Hydrometeorological Service of the RF has started to diminish the observation network and meteorological stations, so, the measurements of hydrophysical parameters of Lake Onego using research vessels and an airborne laboratory were stopped. At the present time, monitoring on the lake and its catchment are performed by the NWPI and the Karelian Hydrometeocentre of Roshydromet. All information about the origin of the lake and its hydrophysical, hydrobiological and hydrochemical processes, collected during the last 50 years, are generalized in Lake Onego. Atlas (2009). Appreciating the results for Lakes Ladoga and Onego of all researches mentioned above, it is worth mentioning that as a rule obtaining generalized conceptions about the processes in ecosystems and its quantitative estimates were conducted without using mathematical models of waterbody ecosystems. The application of mathematical models for quantitative estimates of phosphorus fluxes and of the input of different hydrobiotic complexes in the regulation of matter and energy exchange in the ecosystem, of matter fluxes in the water/atmosphere and water/ bottom interfaces and for forecasting calculations appears to be not only useful but necessary. The main reasons for that were on the one hand the absence of relative mathematical models and on the other hand the lack of cooperation between specialists in ecological modelling and so-called naturalists (limnologists, biologists, ecologists, hydrologists etc.). The first mathematical model of the Lake Ladoga ecosystem, developed by V.V. Menshutkin and O.N. Vorobjova (1987) for the study of Lake Ladoga ecosystem response to the increase of phosphorus loading, is exclusion. Regarding the research into the hydrothermal regime of Lakes Ladoga and Onego, its development and its model applications, it started quite a long time ago (Okhlopkova, 1966; Tikhomirov, 1982; Akopyan et al., 1984; Astrakhantsev et al., 1987; Beletsky et al., 1994; Podsetchin et al., 1995). Reviews of studies devoted to the problem of modelling lake dynamics can be found in Filatov's books (1983, 1991) and in Kondratyev and Filatov (1999). Lake Ladoga and Lake Onego research results based on mathematical model applications carried out during the last two decades by the authors are presented in this monograph. It is worth mentioning that this monograph presents the development of conceptions expressed in the previous monograph, where were reflected mainly the studies of Lake Ladoga (Astrakhantsev et al., 2003). For the first time the results of Lake Onego studies applying mathematical modelling are presented in this monograph.


[Ch.1

A brief description of the evolution of Lakes Ladoga and Onego ecosystems in the process of anthropogenic eutrophication and of observation data is presented below. The focus is on the main processes causing ecosystem destabilization and the new trophic state of the lake. Wide national and international experience within scientific programmes concerning the problem of lake ecosystem anthropogenic eutrophication shows that many processes in these lakes are similar to those which took place, or have been observed at the present time, in other lakes of the temperate zone. Furthermore, according to all their characteristics, Lakes Ladoga and Onego provide classical examples of large stratified lakes in the temperate zone. 1.3 CHARACTERISTICS OF TEMPERATURE AND CURRENTS 1.3.1 The thermal regime and limnic zones The complicated morphometry of Lake Ladoga basin determines the spatial heterogeneity of processes in the Lakes Ladoga and Onego waterbodies. So, the difference in depths within the waterbody leads to significant inhomogeneity in the heating and cooling of water masses. According to the Hutchinson classification (Hutchinson, 1975), Lakes Ladoga and Onego belong to the dimictic type of lake, where the complete mixture of the waterbody takes place twice a year - in spring and in autumn. The thermal cycle is divided into two periods: heating (hydrological spring and summer) and cooling (autumn and winter). Long spring and winter seasons strongly affect variations of limnetic processes. Due to specific freshwater density distribution, spring and autumn thermal heterogeneity initiates the formation of a unique phenomenon: the so-called 'thermal bar' (Tikhomirov, 1982). The early studies of the thermal bar in Lake Ladoga and Lake Onego by Tikhomirov (1963) along with Rodgers (1971) publications on the Great American Lakes are the classical studies on this subject. The thermal bar is a zone of intensive lake water mixing; the resulting effect is that water temperature in this zone reaches the temperature of maximal density +4°C all through the waterbody. This frontal zone, extending along the coastal line, divides the lake into two regions: the warmer coastal and the deep, colder central one. In the frontal zone, from both warm and cold directions, appear steady vertical downwelling movements (Fig. 1.5). In the bottom layer water starts moving aside from the thermal bar: in the coastal zone to the shore, in the central zone towards the open parts of the lake. Besides vertical downwelling water movements, density flows along the thermal bar front are formed. Circulation density flow in the coastal region is of a cyclone type (oriented anti-clockwise); in the central part it is of anticyclone type. This flow pattern along the thermal bar additionally supports its sustainable state. Due to cyclonic coastal flow, tributary waters are spread far away from the mouth, not mixing with the lake waters of the central region. This phenomenon is especially significant for Lake Ladoga: the chemical compound of the Volkhov river water flowing into the southeastern part of the lake differs considerably and it spreads along the eastern coast far away to the north. The Volkhov waters are formed within the Lake Ilmen

Characteristics of temperature and currents

Sec. 1.3]

':IV

15

I

'j)

.....

-, r'

"I-

l...... . . W~

M'

~-

~5

\

, u

\

r." ... i

....,

-

)

-....,

j .u

Fig. 1.5. Mean perennial location of the spring thermal bar in Lake Ladoga (Lake Ladoga. Atlas, 2002).

catchment where sedimentary rocks prevail. Those waters are the main source of biogenic elements in Lake Ladoga, phosphorus in particular. As the lake waters warm up, the thermal bar moves towards the deeper regions (Naumenko, 1994; Zilitinkevich et al., 1992). When water temperature exceeds +4 °C (exactly 3.98°C) all through the waterbody the thermal bar completely disappears . The thermal bar horizontal mixing speed in Lake Ladoga at the end of May is nearly 150m S-I, sometimes reaching 600m S-1 (Tikhomirov, 1982). The disappearance of the thermal bar occurs usually at the end of June - beginning of July, within 50-60m depth, and defines the end of the spring period of the lake hydrological cycle. In the late 1980s-early 1990s, the theoretical, laboratory, and field studies of the thermal bar phenomenon in Lake Ladoga were continued. First, a theoretical model taking into account the horizontal heat transport from the warm to the cold zone was proposed (Zilitinkevich and Terzhevik, 1989), which was further developed in (Zilitinkevich et al., 1992).


[Ch.1

In the years 1991-1992, the joint Soviet-Swedish field study of the thermal bar in Lake Ladoga was initiated to validate the theoretical parameterizations received. The surveys along two cross-sections with different bottom slopes perpendicular to the southern and western shores were performed in the spring 1991 and 1992 two and three times, respectively, to collect data on the vertical distribution of water temperature and currents. The results of the 1991 (Malm et al., 1993) and 1992 (Malm et al., 1994) field campaigns can be summarized as follows. The measured current velocity distributions were found to be strongly dependent on wind conditions. The density-induced currents seemed to be of secondary importance compared to the observed currents, even during calm conditions. Estimates of the heat content change along crosssections revealed the presence of horizontal heat transport from the nearshore warm zones to the thermal bar. The estimates of the thermal bar propagation rates based on observational data were compared with those received from the theoretical models. The model accounting for the horizontal heat transfer (Zilitinkevich et al., 1992) was found to better predict the propagation rate compared to earlier models (e.g. Elliot and Elliot (1970), and similar). The depth-integrated advective flux calculated from the temperature distribution observed and the along-section velocity component computed with a one-dimensional k-c model was found to be 100 times smaller than that estimated from heat content change calculations. The analysis of the satellite images (Kondratyev et al., 1988) clearly demonstrated the presence of the warm-water vortex trails on the cold side of a thermal bar, which should accelerate the front propagation. The mechanism of these intrusions is not clear yet, but Zilitinkevich has suggested that such a phenomenon can occur due to baroclinic instability of the currents on the warm side of the thermal bar. As surface water warming proceeds, the horizontal thermal heterogeneity near the coasts becomes the vertical thermal stratification. Along with disappearance of the thermal bar the vertical stratification is formed in the deep regions, marking the beginning of the hydrological summer. The isotherm +4°C in every vertical cross-section defines the lower boundary of the heated layer, dividing it from the waterbody thickness, forming the cold water dome in the deep water part of the lake. By the moment of dense water dome formation the difference in the surface water temperature over the lake exceeds the maximal annual value and the cyclone circulation its utmost development. The drift flows start to lie over the cyclone circulation. The surface temperature over the whole lake gradually becomes even, under the influence of convective-wave mixing. The water dome and the limiting layer of rapid temperature decrease, the so-called thermocline or depth of metalimnion, drops down. The upper layer of the lake becomes isothermal, forming a sustained epilimnion (the upper quasi-homogeneous layer). The water temperature in the lake exceeds its maximal value. The thicknesses of epi- and hypolimnion gradually increase and in the deep layers (hypolimnion) the water temperatures remain nearly +4°C. According to Tikhomirov (1982) classification Lakes Ladoga and Onego belong to the classification: hypothermal lakes - those lakes where, during the period of summer warming, the main water mass forms the hypolimnion.

Sec. 1.3]


17

By the beginning of the hydrological autumn the dense water dome is observed at depths of more than 100m. Starting with water cooling in the coastal regions, the autumn horizontal thermal heterogeneity becomes settled. This phase is characterized by the coming into existence of the thermal bar, intensive water cooling in shallow coastal waters, ice cover formation and the long-term preservation (until December-January) of a water temperature of nearly +4°C in the deep parts of the lake. Complete ice cover of the lake occurs during cold winters only. Over the deepest regions ice cover is observed for short periods of time: 10-15 days. The deep part of the lake is not covered with ice during warm winters (Fig. 1.4(a)). Ice cover disappears in AprilMay (Tikhomirov, 1982). Water masses the thermal heterogeneity of water masses is responsible for the variation in most limnological features within the waterbody. Of greatest significance during the period of the hydrological spring is the horizontal thermal heterogeneity. The existence of the frontal thermal bar zone defines the accumulation of the initial water masses, the lake tributary waters, preserving their specific chemical, physical and other features. That is to say, the biogenic elements of the epilimnion mainly participate in the consumption cycle during the summer period - regeneration related to biological processes. That is why only here is recorded the reduction of dissolved mineral phosphorus and nitrogen concentrations, whereas in the hypolimnion its storage is preserved at the winter-spring level. Equally all changes of hydrophysical and hydrochemical indicators caused by the photosynthetic activities of phytoplankton (high values of pH, reduction of transparency, the increase of water oxygen concentration) are revealed in the epilimnion. The hypolimnion mainly is the zone of the development of destruction processes - the tropholytic area of the lake. The main process leading to essential changes of limnetic parameters in the hypolimnion is the decrease of oxygen concentration in water. The mixing of the whole water column during the periods of spring and autumn homothermy provides the equalizing of hydrophysical and hydrochemical parameters. As a result of long-term Lake Ladoga studies the lake was divided into four limnetic zones (Lake Ladoga ... , 1992) each of which plays a special role in ecosystem functioning and in general has its value from the point of water supply (Fig. 1.6). In Lake Ladoga the coastal zone I, where the depths are the shallowest and less than 15m, is subjected to the maximum influence of its catchment processes including anthropogenic impact. It is here that tributary waters, industrial and agricultural wastewaters, surface runoff, drainage waters of land reclamation systems and so on enter the lake. At the same time only in the coastal zone are located industrial and municipal water intakes, recreational areas and the most of the spawning-grounds. In spring and autumn months the thermal bar front prevents free water exchange with the deep central part of the waterbody. The flood waters of tributaries enriched with biogenic elements and allochthonous organic matter are retained in the near-shore zone for a long time. In summer time in the well-heated coastal zone the composition of water organisms is diverse and their production


[Ch.l

Fig. 1.6. Limnetic zones of Lake Ladoga.

rate is high. During the summer stratification period the coastal zone, due to its shallowness, generally is well mixed. The declinal zone II, with depths in the range 15-52 m, is typically characterized by the existence of the stable thermal bar front which is clearly pronounced during the spring period. As the thermal bar passes through downwelling water movements, the suspended solids of autochthonous and allochthonous origin penetrate to the near-bottom layers. At the same time, in the larger part of the declinal zone, formation of autochthonous organic matter takes place due to the high productivity of spring phytoplankton and the spreading into this area of coastal water masses enriched with allochthonous organic matter. Thus the tremendous amount of organic matter, both of allochthonous and autochthonous origin is accumulated in the near-bottom layers of the declinal zone. During the summer stratification period the hypolimnion has a relatively small thickness, being the peripheral part of the lake hypolimnion. Consequently, in the minimal hypolimnial volume the considerable share of organic matter annually incoming to the lake, spring phytoplankton production and flood organic matter is gathered . The declinal zone is the place of the

Sec. 1.3]


19

primary accumulation and mineralization of organic matter in the hypolimnion. This is the place where the considerable consumption of dissolved oxygen initially occurs during destruction processes and, as a consequence, the near-bottom oxygen deficit might develop. Two other areas, the profundal zone III (52-89 m) and the ultraprofundal zone IV (more than 89m) are the most conservative parts of the lake. All limnetic processes are slowed down in these two zones, the largest by their volumes and the least heated. This is the accumulating and generating area of organic matter in the water column and in the silts on the bottom. Thus the two shallower zones are the areas of primary accumulation and the deep water zones are the regions where the accumulated substances are transformed, entrained in the inner waterbody cycles or conserved. The thermal regime and currents in Lake Onego were studied in detail by Tikhomirov (1982), Okhlopkova (1972), Boyarinov et al. (1994), and Filatov (1991). To derive average perennial characteristics of the Lake Onego thermal regime, the observation data of the Karelian Republic Centre on hydrometeorology and monitoring of the environment for the period 1958-1989, both from research vessels and an airborne laboratory were used. Observations performed by the Northern Water Problems Institute from 1992 to 2007 were used as well. The measurements were made during a navigation period on a fixed stations grid at offshore verticals with a temporal resolution of 10-30 days. The unique survey of currents and water temperatures was conducted during experiment 'Onego'; later these data were used for numerical computations of currents in Lake Onego on the basis of mathematical models (Filatov, 1991; Beletsky et al., 1994). For calibration and verification of models described in this monograph, both 'Onego' experimental data and averaged data on the thermal regime, is included in the Lake Onezhskoe Atlas (T. V. Efremova; see Lake Onego. Atlas, 2009). To calculate the mean perennial variations of water temperatures at different layers the continuous-in-time approximation parametric function was used, making it possible to obtain daily mean water temperature values at standard depths in different parts of Lake Onego. On the basis of modelled curves, the monthly maps/ diagrams of water temperature distribution from 1 June till 1 November, at different depths, were produced and limnetic zones were contoured (Fig. 1.7). Data analysis of the lake thermal regime has showed that seasonal variations of water temperature are influenced by peculiarities of the lake basin, its dimensions, coast line unevenness and, mainly, by depth. That is why seasonal changes of water temperature in different parts of the lake are clearly distinguished. Ice destruction in Lake Onego usually happens at the beginning of May, and its complete disappearance is observed in average on 18 May. With ice destruction and ice melting, the amount of heat penetrating into the water column increases essentially. In May the thermal bar formation starts; it divides the lake into two regions: the coastal stratified region and the deepwater homogeneous one. The 4°C isotherm on 1 June contours the lake and it is located at 20-25 m depth. The thermal bar phenomenon results in heat redistribution and water masses mixing in Lake Onego for rather a long period of time. According to mean perennial data it disappears in

20


(I

[Ch. I

N

6'

...

m

m

....

\"

Fig. 1.7. Mean perennial location of the spring thermal bar front in Lake Onego (Lake Onego. Atlas, 2009).

the third decade of June, and a direct thermal stratification is established, when the summer heating period starts. During summer heating the lake becomes steadily stratified in the vertical direction with an upper warm homogeneous layer (the epilimnion), a layer with a high temperature gradient (the thermocline) and a bottom cold layer (the hypolimnion). The transition layer with high vertical temperature gradients prevents penetration of heat flux from the upper layer towards the bottom. After thermal bar front destruction, in the deep central part of the lake the temperature growth rate in June in the near-surface layer (0-5 m) increases by 3.5-4 times and equals approximately 0.35-0AO°C day" , At a depth of 20m it is close to its spring value of O.l oC day:", and at a depth of more than 40 m it is less than 0.03°C day", Starting from 1 July the minimum temperature in the nearsurface layer is observed in the deep central part of the lake, and the maximum temperature in coves and bays. At this time the seasonal thermocline layer in the deepwater area is at a depth of 5-IOm. The dome of cold water is formed over the deepwater part at a depth of more than 50 m, where water temperature is less

Sec. 1.3]


21

than 4°C. From the beginning of July the gradual smoothing of temperature over the whole of the lake and a reduction of horizontal inhomogeneity is observed. According to average perennial data, at this time the transition of water temperature in the surface layer over 10°C takes place all over the lake; the so-called 'biological summer' begins. The biological summer is a period when surface water temperature steadily exceeds 10°C. On the basis of available data on surface-water temperature the 'biological summer' begins earlier in the shallow Zaonezhsky Bay, in early June. The delay period for biological summer in the deep central part of the lake is on average 30 days. The end of July-beginning of August is characterized by the greatest warming of the surface 5 m water layer. Mean surface water temperature reaches its maximum value; its distribution over the waterbody becomes rather homogeneous; the seasonal thermocline deepens to the depth of 15-25 m, depending on the lake region. In the first decade of August the autumn cooling starts, i.e, in the lake heat balance, losses prevail over heat income. In the near-surface layer the temperature inversion is formed, and that creates gravitational instability, destruction of stratification and formation of the surface quasi-homogeneous layer. The deepening rate of the mixed layer from August to October increases from 0.3 to 3.0mday-l. The thickness of the quasi-homogeneous layer with a temperature of 13°C equals 10m on 1 September. By 1 October this value increases to 20m, and water temperature decreases to 9.5°C. Maximum water temperature is registered at a depth of 0.1 m at the beginning of July-beginning of August, at a depth of 10m at the beginning of September, at a depth of 20m in the middle of September, at a depth of 50m in the first half of October; at a depth of 80m the maximum temperature, 6.6°C, is registered after 20 October. So the time delay of maximum temperature between the bottom layers and the surface layer in Lake Onego reaches 3 months. In the second half of October homothermy is established in the lake with a temperature of 6-8°C. The lake water cooling at this time happens gradually: the decrease of temperature throughout the water column occurs at a rate of about 0.1°C day ": On 1 November in the central part of the lake, homothermy with a temperature higher than 6°C is observed. In the coastal regions with depths up to 20 m, water temperature is, as a rule, below 5°C. In shallow near-coast areas, water cools at this time to 4°C, the temperature of maximum density. The 4°C isotherm slowly moves with water cooling to deepwater areas, leaving behind the regions with inverse temperature stratification, where water temperature is less than 4°C. The 4°C isotherm disappears on 22-25 of November. By 1 December in the surface layer of coastal regions the water temperature is 1.9-2.2°C; in the central part it is higher than 3°C. The ice appears on the lake on average between the second decade of November and the middle of December after a steady decrease of water temperature below 0.2°C and cooling of the surface layer down to freezing point. In some years, autumn ice phenomena are observed as early as the second half of October (1945, 1946, 1959, and 1968). Sometimes, for example in 1960-1961, complete ice cover is not formed, and wide polynyas to the south of the island of Mayachny and in Bolshoye Onego are observed (Fig. 1.4(c)). The maximum thickness of white ice at the end of the ice

22


[Ch. I

cover period exceeded one metre (104cm) near the village of Longasy in the third decade of April, 1956. The initial ice erosion stage on the lake is observed in the first decade of May (in the southern part of the lake, in the third decade of April), and at the latest by the middle of May; and ice destruction starts in narrow bays and skerries. Mean dates of ice clearance correspond to the second decade of May; in skerries and in the southern part of the lake it is the third decade of May. For the whole observation period, starting from 1884 and up to the present time, the tendency of the ice cover period to reduce has been registered at certain observation stations and all over the lake. For the ice-free period a positive trend has been observed (the coefficient of the linear trend is about 7 days per 100 years). Schematic zoning of depths in Lake Onego was carried out using statistical approach, suggested by Gusakov and Terzhevik (1992) for limnetic zoning of Lake Ladoga. According to this method, boundaries between limnetic zones are marked along isobaths with values of mean lake depth (15) and depths: (15 - So) and (15 + So), where So is the mean square-root deviation of the depth field. The

Fig. 1.8. Limnetic zones of Lake Onego (Lake Onego. At/as, 2009).

Sec. 1.3]


23

statistical calculations for Lake Onego zoning were based on the grid (with a resolution of approximately one kilometre) built by S. F . Rudnev. As a result, the following values of statistical parameters were obtained: 15 = 30m and So = 20m. Thus, Lake Onego was divided into four depth zones: coastal, declinal (or slope), profundal (or deepwater) and ultraprofundal, morphometric feaures of which represent the most essential morphological peculiarities of the lake basin (Fig. 1.8).

1.3.2 Currents and circulations While the first long-term measurements of currents in Lakes Ladoga were made in the 1940s by specialists from Finland, the systematic study of thermal structure and circulation in Lakes Ladoga and Onego began only in the late 1950s (Tikhomirov, 1982). Shipborne observations of currents were realized by Okhlopkova (1966, 1972). The first moorings with current-meters were deployed in the middle of the 1960s, in Lakes Ladoga and Onego, and the results of numerous observations of currents and temperature variability were summarized by Boyarinov et ai. (1994) and Filatov (1983). The first maps of water mass circulations of Lakes Ladoga and Onego were presented by Okhlopkova (1972) Fig. 1.9.

Fig. 1.9. Geostrophic currents in the summer period: Lake Ladoga (a) and Onego (b) (Okhlopkova, 1966, 1972)

24


[Ch.l

Complex hydrological and meteorological data were collected in Lakes Ladoga and Onego during the last two decades and created a database for physical analysis and modelling experiments (Filatov, 1991; Beletsky et ai., 1994). Synoptic ship surveys were conducted during the periods of spring and autumn thermal bar formation and the full stratification period too. Long-term currents and temperature data were recorded using a network of buoys (ABS). The primary emphasis is given to the temporal and spatial variability of currents and temperature, numerical modelling of hydrophysical fields and model verification. The data on water temperature obtained during the 'Onego' experiment (Filatov et ai., 1990) have the best temporal and space resolution, compared with data collected on other large

II

..,

13

-(f-' /

it

I "

Fig. 1.10(a). Long-term observations of currents in Lake Ladoga averaged for all periods of observations 1969-1975. On the scheme is shown the number of ABS, the distributions of directions (a), the speed of currents (b) and the vector of the currents in ems"! (from Kondratyev and Filatov, 1999)

Sec. 1.3]


25

lakes of the world. The synchronic ship surveys for Lake Onego were conducted during the period of one day and were repeated three times by three research vessels of the NWPI and the Institute of Limnology of RAS (Beletsky et ai., 1994). At the same time data were recorded using a network of buoy stations with currents and temperature measurements on several horizons (in the epi-, meta- and hypolimnion) together with remote sensing infrated airborne and satellite observations. These data were used for calibration, parameterization and 3D verification diagnostic and prognostic models for the Great European Lakes (Filatov, 1991; Beletsky et ai., 1994). The long-term multi-year observations of currents and water temperature on Lakes Ladoga and Onego were made at the end of the 1960s and in the early 1970s

[r

(b) Fig. 1.10(b). Water circulations in Lake Onego calculated from multi-year observations of currents averaged for the period 1969-1990 on 5-7m horizons . On the scheme is shown regions of the lake (1,2,3) and the number of observations (a), the distributions of directions (b) and the vector of the currents in cm S-1 (c) (Boyarinov and Rudnev, 1990).

26


[Ch.l

and the 1980s. The maximum length of the time series was up to 5 months with the time-step ranging from 10 to 30 minutes. These data allowed us to study the variability of currents and water temperature with characteristic timescales from several hours to 15 days. The data were averaged for all periods of observations (May-November) and showed that there exists a tendency to anticlockwise circulation in Lake Ladoga (Fig. 1.10(a)) and Lake Onego; but in Lake Onego integral circulation is more complicated them in Llake Ladoga due to complicated morphometry (Fig. 1.1O(b)). This kind of circulation in large lakes is characterized by the so-called 'climate' of currents. The spectra of currents for all points of measurement on anchored stations were calculated using the tensor analysis technique (Filatov, 1991). The frequencytemporal spectrum (linear-invariant) and bi-spectral of currents in Lake Ladoga illustrates the non-stationary character of the current variability (Kondratyev and Filatov, 1999). Analysis of currents showed spectrum transformations from nearshore to offshore regions and from depth of measurements. In Lakes Ladoga and Onego (Fig. 1.11), the spectral constituents with frequencies of 0.02 rad h- I (correspond to a timescale of about 2 weeks), 0.06-0.12 rad h- I (2-4 days), 0.24 rad h- I (1 day) and close to the inertial frequency corresponding to the latitude 61 N is 0.45 rad h- I (13.5 h) stand out more clearly. There are several peaks corresponding to the frequencies which are lower than the local inertial oscillations (period of about 13.5h). In the offshore regions, lowfrequency oscillations with periods from days to weeks are usually caused by largescale synoptic wind variations. In the coastal zone some low-frequency waves should also be taken into consideration; for example, it may be the manifestation of internal Kelvin waves and topographic waves which can be generated by wind and can persist long after the decrease of the initial wind impulse, causing the characteristic increase of the current velocity (Filatov et al., 2009). There is a pronounced peak in the 0

--

I

I}

Fig. 1.11. Spectrum of currents (I I-linear-invariant of tensor), (a) in the offshore zone of Lake Ladoga at metalimnion (1), at epilimnion (2), and at depths of 30 (3), 50 (4) and 70 (5) m and (b) spectrum of currents in the near-shore zone at horizons 10m (1) and 20m (2).

Sec. 1.3]


27

current spectrum which corresponds to the frequency of the Poincare waves with local inertial oscillations (Fig. 1.11). This peak may be caused by the inertial oscillation of currents provoked by spatially inhomogeneous winds and also by the internal Poincare waves which dominate in large lakes at distances exceeding the internal Rossby radius of deformation (about 3-5 km from a shore). Maxima of energy of Poincare waves observed at the metalimnion (Fig. 1.II(a)). In Lakes Ladoga and Onego the lifetime of these motions does not exceed the duration of two or three inertial periods. The data of observations reveal large-scale current and temperature variability in both lakes with several energy peaks reflecting the lake's response to the atmospheric forcing and the lake's own system movements. This is the so-called 'weather' of hydrodynamical processes which follows atmospheric weather changes. The wind-induced coastal upwelling is among the main components of the mentioned hydrological weather in a lake. In response to the wind, coastal upwelling continually changes its strength and location, which can be most easily traced in the surface-temperature field. For numerical calculations of currents in Lakes Ladoga and Onego, over the thermal bar and full stratification period, a 3D nonlinear diagnostic model was used (Akopyan et al., 1984; Filatov, 1991; Beletsky et al., 1994); it had previously been used for ocean dynamics studies (Sarkisyan, 1977; Demin and Sarkisyan, 1977). The 3D diagnostic and prognostic circulation models for the description of meso- and macro-scale processes of Lakes Ladoga and Onego have a resolution in the horizontal plane of approximately 2-4 km; they were created by (Beletsky et al., 1994). Lake-wide circulation patterns typical for spring and summer conditions in two of the largest European lakes have been shown to depend heavily on the two important hydrodynamical processes: the thermal bar and wind-induced upwellings. Calculations showed that in spring when the thermal bar exists the circulation pattern is fairly regular. Lake-wide cyclonic circulation induced generally by the density gradients (geostrophic currents) occupies a narrow zone between the shore and the front of the thermal bar. Wind observations from meteorological stations around the lake reveal that at the early stages of the thermal bar a local atmospheric cyclone appears due to the sharp temperature gradients between the lake and the land surface. This cyclonic vorticity of the wind serves as an additional source of cyclonic circulation in the lake. In a closed waterbody with complex bottom relief, however, wind fluctuations cause topographic vortices, eddies, or circulations, or topographic Rossby waves (Csanady, 1977). Topographic waves have been considered for waterbodies with ideal shape. Allender and Saylor (1979) have described the generation of topographic waves in a lake of simple elliptic shape with a parabolic bottom. Calculations of topographic waves for several phases show that topographic motions normally have 'double-gyre' circulation. In Lake Ladoga, as an effect of the wind, there appeared signs of the development of motions with a tendency towards anticlockwise rotation. The main gyres fall apart and relatively small eddies with a horizontal size of the order of several kilometres are formed (Kondratyev et al., 1989; Kondratyev and Filatov, 1999). The difference in the bottom and shore slope between the western and the eastern parts of

28


[Ch.l

the lake caused a disagreement in the frequency of topographic waves and baroclinic Kelvin waves. Hence, topographic waves by the eastern shore left Kelvin waves 'behind'. In this case spectra of the currents show two energy maxima corresponding to the mentioned waves in the low-frequency scale. The data reveal large-scale current and temperature variability in both lakes with several energy peaks (Fig. 1.11), reflecting the lakes' response to the atmospheric forcing and their strong variability with a hydrological 'weather' scale. Bear in mind Mortimer's (1979) remarks about the 'underwater' weather, which follows atmospheric weather changes. The wind-induced coastal upwellings are among the main components of the abovementioned hydrological weather in Lakes Ladoga and Onego. In response to the wind, coastal upwellings continually change their strength and locations, which can be most easily traced in the surface-temperature field. In the case of especially strong winds, the area occupied by the cold upwelled water, can reach up to 30% of Lake Onego's surface (Filatov, 1991). In the evolution cycle of coastal upwelling, three main phases can be discerned: generation, steady-state and relaxation (Beletsky et al., 1994). Usually after a few hours of moderate wind forcing a double-gyre circulation becomes dominant in a large lake. The prominent features of double-gyre circulation are narrow coastal currents in the direction of the wind and a broad countercurrent in the deeper part of the lake (Bennet, 1974). With wind-induced upwelling, in the case of string winds the thermocline can reach the lake surface. This fact is vital for the lake ecosystem because of the enhancement of water exchange between the epilimnion and the hypolimnion and, as a consequence, the ventilation of the hypolimnion and the increased supply of nutrients to the epilimnion. After the cessation of the wind, upwelling relaxation begins. Following Csanady (1977), two types of relaxation event were identified (Beletsky et al., 1994). Type-l relaxation is characterized by simultaneous anticlockwise propagation of cold and warm temperature fronts and by the relevant coastal jet reversals around the lake. In contrast to Type-l , only one front moves in the case of the Type-2 relaxation. Mortimer (1963) was the first to discover such warm front propagation along the southern coast of Lake Michigan; later, another case of Type-2 relaxation was described for Lake Ontario (Simons and Schertzer, 1987). Near the eastern shore of Lake Onego the coastal jet structure is clearly seen; intense currents are also observed along the thermal front zone. The observations showed that the upwelling front moved along the eastern coast to the north, in the direction which coincided with the direction of Kelvin wave propagation. Diagnostic and prognostic model calculations have demonstrated that Type-2 relaxation leads to the enhancing of cyclonic circulation in Lake Onego (Fig. 1.12). The evolution of wind-induced upwellings has been described in Lake Onego with a focus on thermal front dynamics and circulation pattern changes (Beletsky et al., 1994). The effect of rivers on the formation of large-scale circulation in the summer period is negligible. Coastal streams observed in lakes are divided into jets and plumes. The former are jets which do not possess neutral buoyancy in relation to the

Sec. 1.3]


29

Fig. 1.12. Results of prognostic calculations of (a) water temperature and (b) currents in Lake Onego (Beletsky et al., 1994).

lake water, but do have momentum; the latter are jets with positive buoyancy but zero momentum (Csanady, 1977). Jets and plumes can also be recorded by space imagery data. Jets in lakes may fall under the effect of being trapped by the shore. These circulations spread several kilometres into the lake with an anticlockwise direction of motion under the slight action of eddy diffusion, which is demonstrated by the appearance of the 'plume' in the space image. During the most intensive upwellings the dilution of sewage in this area is accompanied by the movement of sewage from the hypolimnion to the surface (Kondratyev and Filatov, 1999). Coastal upwelling in lakes was studied experimentally on Lake Onego by Bojarinov et al. (1994), on Lakes Ladoga and Onego by Filatov (1991), and on the Great American Lakes by Csanady (1977), Simons (1975, 1976), and Simons and Schertzer (1987). The basis for the study of upwelling in the lakes was mainly the data of long-term observations at moored buoy stations. Several types of upwelling were singled out: Ekman near-shore upwelling, flotation , and offshore upwelling in the centre of anticlockwise circulations with a dome kind of water-temperature structure. Remote sensing techniques with IR sensors have been used to study features of upwelling in Lakes Ladoga and Onego (Filatov et al., 1990). The average period of upwelling relaxation is less than the synoptic period . Therefore, simultaneous manifestations of upwelling by the western and eastern shores are quite rare. For Lake Ladoga, however, such cases have been recorded in the data of long-term remote sensing IR observations from the airborne laboratory of the Hydrometeorological Service for 1968-1992. The space remote sensing combined with ship-based observations and the results of modelling at upwellings in different lake zones allowed adjustment of the integral water circulation schemes obtained earlier to various hydrometeorological conditions. In hydrological spring and autumn periods


[Ch. I

during the presence of the thermal bar, Ekman near-shore upwellings do not appear in the lake (Fig. 1.13). Water circulations, however, are quite changeable, even when winds remain steady. Continuing water circulation is important for the formation of circulation under specific conditions, though sufficiently prolonged winds (up to 0.5 of the synoptic period) in certain directions quickly change water circulation. For the formation of Ekman near-shore upwellings these are northern and southern point winds. The period of upwelling relaxation is about two times shorter than the period of upwelling formation. Our estimates suggest that the speed of water rising and sinking was 10-2 and 5 x 10-2 cm/s respectively. Indirectly, the persistence of cyclonic circulation at the early stages of the thermal bar may be confirmed by analysis of the surface-temperature pattern. For this purpose we used remote sensing observations of Lakes Ladoga and Onego derived from an airborne laboratory, AN-28, and satellites equipped with infrared radiometers. As the observation indicate (Filatov et al., 1990; Filatov, 1991), wind-induced upwellings are practically absent until the stratified zone occupies less than approximately 40% of the surface area. Presumably cyclonic circulation can be persistent at that time in both lakes, even in the presence of strong winds (Fig. 1.13). Progressive warming of the lake during the summer leads to the advance of the thermal bar front into the deep part of Lake Ladoga and to the increased spatial extent of the stratified zone. Thermal gradients between the land and water become weaker and the local atmospheric cyclone vanishes; this makes lake-wide cyclonic (a

(b

.,

~

\~ v\~I

t

r

Fig. 1.13. Diagnostic scheme of integral circulations in Lake Ladoga (a) and Lake Onego (b) , locations of Ekman's near-shore upwelling zones (I-IV) for early spring with thermal bar (a), summer with thermal bar (b and c), period of full stratifications (d and e) and autumn (f) under the special directions of wind (2).

Sec. 1.3]

The cycle of substances in Lake Ladoga

31

circulation more and more responsive to wind fluctuations. In this period windinduced upwellings arise in the various parts of the lake. Wind-induced upwellings are also frequent during the full stratification period. Though cyclonic circulation remains typical, especially for the deep central and northern basins, local anticyclonic circulation connected with upwellings in the southern shallow part of the lake are frequently generated. Data of long-term observations (1965-1992) in Lake Onego were used to describe more than 50 cases in different zones of the lake. They sometimes are recorded simultaneously. The observations and modelling results show that no Ekman's upwelling occurs in the lake in the spring and autumn thermal bar period, and there is usually no total anticlockwise water circulation in the period of complete thermal stratification. At a climatic scale of the average of currents in the largest lakes of Europe the cyclonic circulation of waters dominates. In the winter phase when these lakes covered completely or partially by ice the circulation of waters is a very weak (less than 2cm s"), But on the Great American Lakes (Beletsky et al., 1999; Beletsky and Schwab, 2008a, b) the intensity of circulation of cyclonic character is higher in the winter phase than in the summer stratification period due to the joint effect of wind and bottom relief, and also density. This is a basic difference in the singularities of the hydrodynamics between the Great European and the Great American Lakes. 1.4 THE CYCLE OF SUBSTANCES IN LAKE LADOGA AND THE DYNAMICS OF ITS WATER ECOSYSTEM 1.4.1 Lake ecosystem phosphorus supply During the last 40 years Lake Ladoga has undergone the process of anthropogenic eutrophication. The rapid increase of phosphorus content in the lake water played the initial role in the evolution of its ecosystem. Natural surface waters of the temperate zone in the northern hemisphere are poor in phosphorus as a result of specific hydrochemical processes in conditions of higher humidity. From the three main components which are necessary for the construction of living substance by autotrophic organisms (the primary production) - phosphorus, nitrogen and carbon - the lake ecosystem is strictly limited only by phosphorus. Its transmission into the lake is exceptionally correlated with the discharge of tributaries (surface, underground runoff) and precipitation. A deficit of nitrogen and carbon in water is compensated by supply of these elements from the atmosphere as a result of gas exchange (carbon) and algal fixation. The ecological status of Lake Ladoga remained oligotrophic in the middle of the twentieth century and the low phosphorus water content was the limiting factor for the development of vital processes. Phosphorus income in the lake

Until the beginning of the 1960s river runoff phosphorus income in Lake Ladoga was 1790 t Pyear"! and, in total, including precipitation and industrial wastewaters,

32


[Ch. I

Fig. 1.14. Total phosphorus loading into Lake Ladoga for 1961-2006.

2430tPyeac l . The dynamics of phosphorus loading into the lake during the research period is shown in Fig. 1.14 (Lake Ladoga ... , 1992, Table 17, pp.78-79; Lake Ladoga .. . , 2002; Petro va et al., 2005; Rumyantsev and Drabkova, 2006; Raspletina, 1992). The main source of phosphorus supply was the Volkhov River, which drained waters, enriched by phosphorus easily dissolved from the sedimentary rocks of the lImen Lake catchment. The rapid changes in the lake phosphorus supply in the mid-1960s appeared to be related to the Volkhov River water composition. Sewage superphosphates waters from the Volkhov aluminium plant enriched with phosphorus compounds were discharged into the Volkhov River. The mean annual concentration of total phosphorus in the Volkhov River waters increased from 48l!gPI- 1 in 1959-1960 to 230 l!gPI- 1 in 1976-1979. Simultaneously, as a result of human activity in the catchment, total phosphorus concentration doubled in two other large tributaries of Lake Ladoga, the Svir River and the Burnaya River (Vuoksa). In numerous other small rivers of the Lake Ladoga catchment observed total phosphorus concentrations were 1.5-4 times higher. In general, the annual supply of phosphorus in the lake was 7100tP year"! during 1975-1983, and in 1982 it reached 8110t. Phosphorus loading decreased after 1983 and made up 6100tPyear- 1 for the period 1984-1990. The year 1991 appeared to be abnormal for that period as phosphorus income reached the value of 8200t P year:" . A much more noticeable decline of phosphorus loading to 3580tPyear- 1 on average was registered in 1996-2005 (Lake Ladoga ... , 2002; Petrova et al., 2005; Rumyantsev and Drabkova, 2006; Raspletina, 2006, personal communication) .

Sec. 1.4]

33


Table. 1.2. Phosphorus concentrations in the waters of Lake Ladoga (averaged for the period of open waters) (J.lg Ptota11-1) (Raspletina, 1992; Raspletina and Susareva, 2002, p.77; Raspletina, 2006, personal communication). Limnic

zone I Coastal zone II Declinal zone III Profunda1 zone IV Ultraprofunda1 zone A111ake

1976- 1981- 1984- 1987- 1990- 1994- 1999 2000 2000- 2004 2005 2006 2003 1980 1983 1986 1989 1993 1998 46 27 28 24

37 27 22 22

32 24 21 22

31 23 20 20

43 21 19 19

23 17 16 17

26 27 22 16

24 21 21 21

20 18 16 16

20 16 12 12

18 17 13 12

17 15 13 12

26

23

22

21

20

17

22

21

17

13

13

13

Phosphorus concentrations over the waterbody increased rapidly as a result of mixing the contaminated waters of the Volkhov River into the dense circulation system with currents oriented from the south to the north along the eastern coast. The distribution of phosphorus concentrations conserved the general tendency of maximum values in Volkhov Bay and minimum values in the northern deep regions. Table 1.2 shows the distribution of total phosphorus concentrations within different lake regions (see Fig. 1.6) during the observed period of time, the gradual decline of its variability over the waterbody and some general decline of phosphorus content in the water column as a result of sedimentation (Lake Ladoga . . . , 1992; Lake Ladoga ... , 2002; Petrova et al., 2005; Rumyantsev and Drabkova, 2006; Raspletina, 2006, personal communication). The increase of phosphorus concentration in Lake Ladoga, the element that always limited the lake productivity level, accelerated the beginning of the next phase of anthropogenic eutrophication - primary production growth.

1.4.2 Phytoplankton in the Lake Ladoga ecosystem In large lakes, where pelagic prevails over littoral, such as in Lake Ladoga, the algal plankton community - phytoplankton - is the basic allochthonous organic matter producer. The succession of mass phytoplankton species composition in Lake Ladoga took place in two stages. Until the end of the 1960s the lake phytoplankton was typical for large, deep, cold-water, oligotrophic waterbodies. Diatomic algae prevailed there all through the year, forming quantity and biomass maxima during the spring. Four typical species were observed, all four of which were diatomic. In quantity dominants rarely exceeded 1 million cells per litre. Total species composition was diverse - 380 species and types. Besides diatomic algae, green and blue-green algae were observed, especially in summer. The increase in phosphorus concentration led to a rapid intensification of algal development and expansion of its mass representatives. The total species composition had changed a little, but the quantity of dominants reached millions and tens of millions cells per litre. By 1976


[Ch.l

22 dominant types were registered; 7 diatomic, 11 blue-green, 3 green and 1 yellowgreen algae were among them. In an annual cycle of phytoplankton development up to the 1960s in the coastal and declinal zones (zone I and zone II) three maxima were observed - the maximal in spring and the other two, lesser in magnitude, in summer and autumn. In the deep part of the lake, as a result of slow spring warming, only the summer-autumn maximum formed. The dates of seasonal succession of the most developed forms during the period of lake eutrophication remained the same. It derives from the fact that in large, deep lakes the dates are determined in general by the warming and cooling regimes of water masses in various parts of the waterbody. Spring plankton in the coastal and declinal zones, the development of which is observed when water temperature is below +8°C, remained almost entirely diatomic. In summer diatomic plankton were to a considerable extent replaced by representatives of the other groups, mainly by blue-green algae. In summer and autumn algal development in the coastal and declinal zones reached a magnitude comparable with the spring level. In deep zones only the summer maximum remained, but algal quantity at this period reached the values typical for shallower areas. Detailed analysis of the changes that took place in widely spread groups of algae during 1970-1990 makes it possible to draw a conclusion about the sequence and the regularity of phytoplankton succession. In the first considerable outbreak of algal development in 1970, when the quantity exceeded normal inter-annual variations, the dominant role was played by the most widespread species of the oligotrophic period: Aulacosira islandica in spring, Fragilaria crotonensis, Tribonema affine, Aphazimenon flosaquae and Woronichinia naegeliana in summer. Beginning in 1972 the dominant succession became obvious, marked by the mass development of Microcystis representatives in summer, and then, in late spring of 1975, Diatoma elongatum var. elongatum. New widely spread species belonged to algae that are common in eutrophic lakes. Among species that determined later the type of phytoplankton succession in the process of anthropogenic eutrophication of the lake, the typical inhabitants of an oligotrophic waterbody were: diatomic, Aulacosira islandica, Asterionella formosa, and Fragilaria crotonensis; yellow-green, Tribonema affine; and blue-green, Afazimenonflosaquae and Woronichinia naegeliana. To algae, the mass development of which usually occurs in eutrophic lakes, belonged: diatomic, Diatoma elongatum var. elongatum; and a number of blue-green algae from the genera Oscillatoria and Microcystis. The most typical representatives of bluegreens were Oscillatoria tenuis and Microcystis aeruginosa. Until 1980 the role of species typical for eutrophic waterbodies grew among both mass and episodically appearing algae. Phytoplankton reached the maximum diversity in 1981-1985. Low water temperatures limited the enrichment of spring dominant phytoplankton groups by new species. In the thermally active area of the coastal and declinal zones the most cold water species in Lake Ladoga, Aulacosira islandica, remained dominant. Its quantity varied from year to year but the tendency of growth was preserved. In early spring when the temperature is below +6°C Aulacosira was the only dominant and phytoplankton was almost monocultural. The traditional species plankton of the oligotrophic period in late spring and early

Sec. 1.4]


35

summer, Asterionellaformosa, was displaced from summer to the late spring phase. Diatoma elongatum var. elongatum, the representative of eutrophic lakes, replenished the dominant group in the late spring stage. These diatom algae developed most intensively in 1980-1985. In the deep profundal and ultraprofundal zones of Lake Ladoga, spring phytoplankton growth starts only at the end of June; in July, Aulacosira vegetation lasts less than a month and complexes Asterionella or Asterionella-Diatoma appear during epilimnion formation, i.e. at the beginning of the hydrological summer. The dominance of Diatoma over Asterionella was also observed there until 1985. In summer blue-green algae typical of the eutrophication process (Oscillatoria in July and Microcystis in August) by 1985 almost completely replenished the former summer diatom complexes (Asterionella and Fragilaria). But, depending on weather conditions, their growth level fluctuated considerably. Starting from 1986-1987 a new stage of phytoplankton succession has begun. The species typical for eutrophic lakes were replenished by the former dominants of the oligotrophic period more distinguishably. The amount of Asterionella increased once more in spring. Afanizomenon flosaquae, the typical representative of Lake Ladoga plankton, became dominant in summer. The secondary succession of mass form became especially obvious in 1989, when Woronichinia naegeliana appeared and Tribonema affine growth rate increased rapidly. By 1994 Fragilaria crotonensis became dominant. The composition of Lake Ladoga phytoplankton dominant groups was restored and became the same as it was during the oligotrophic ecosystem stage in 1956-1963. Interpretation of the succession of widely spread phytoplankton species in the lake eutrophication process may be found in particularities of algae ecology. The special role of each plankton species is determined to a great extent by its productivity: an ability to reproduce in favourable conditions. At the same time, the need of different species for phosphorus, as the energy supply for their productivity and the development of the rate at which they consume phosphorus are constrained by the range of its concentrations. The determination of functional characteristics for particular species in Lake Ladoga was conducted experimentally by the autography method using carbon 14C and phosphorus p 33 isotopes (Gutelmacher and Petrova, 1982). Experimentally obtained values of carbon assimilation coefficients (CAC) and of phosphorus (F AC) per cell biomass unit characterize correspondingly individual productive abilities and the need for phosphorus of algal species. To a large degree these characteristics depend on species cell dimensions: the metabolism of small organisms is more active. Nevertheless they reflect evolutional features of species ecology. The least need in phosphorus supply (PAC) and the poorest productivity (CAC) are common for oligotrophic stage species, in conditions of restricted supply of biogenic elements supply. High values for these indicators are typical for mass algae of eutrophic waterbodies (Table 1.3). It is obvious that it is not that essential for species to belong to the same type: the need for phosphorus of the diatom Diatoma elongatum and yellow-green Tribonema affine is nearly equal. At the same time the consumption of these two species is higher than that of blue-green Afanizomenon and Woronichinia of the oligotrophic period, and is much less than that of blue-green algae typical of the eutrophic stage. The

36


[Ch.1

Table 1.3. Main ecological parameters of dominant species of plankton in Lake Ladoga. Species

Volume CAC of cell, 3 J.lm

FAC

CACI FAC

Water temperature in period of species growth, TOC

Aulacosira islandica Asterionella formosa Diatoma elongatum Fragilaria crotonensis Tribonema affine Oscillatoria tenuis Aphanizomenon flosaquae Microcystis aeruginosa Woronichinia naegeliana

4000

1.6

0.03

53

0.1-8

1010

2.7

0.05

54

5-20

80

640

17.3

1.09

16

6-20

70

1360

2.6

0.04

65

8-20

60

529 85 137

18.9 48.2 5.1

1.06 2.40 0.28

18 20 18

8-20 10-20 10-20

40 100 20

113

28.3

2.07

14

15-20

90

118

4.8

0.32

15

10-20

20

Reduction of production under wind > 10 mis, in % 60

ratio of CAC/FAC is an important characteristic and reflects the cell production per unit of phosphorus consumption. Observation data attest that species of the oligotrophic type, being content with lower phosphorus concentrations, use it twice as effectively as eutrophic type species. At the first stage of anthropogenic eutrophication the rapid increase of phosphorus supply is favourable for every waterbody species. Thus highly productive forms develop faster, driving less productive species aside. For algae consuming phosphorus in considerable quantities (Microcys tis, Oscillatoria) very high phosphorus concentrations are necessary for their mass development. During the maximum spreading period of their quantity the rate of phosphorus turnover reduces to several hours. That explains their appearance as the dominant group no earlier than the phosphorus concentration reaching 20-25 ug Ptotall-l. As the intensification of biological processes proceeds during eutrophication, the inner phosphorus cycle becomes more active at the expense not only of phytoplankton but also of bacterial consumption. Phosphates, composing nearly half of total phosphorus content in lake water, could be regarded as phosphorus available for algae consumption. Knowing the habitats and the dates of the expansion of particular seasonal algae complexes over the lake, mean and upper limit rates of their phosphorus consumption, the rate of phosphorus turnover in various parts of the lake can be estimated. Calculations, based on 1982 observation materials, have shown that the turnover time of biologically active phosphorus in the lake is about 2.5 days. In retrospective calculation for the oligotrophic period let us

Sec. 1.4]


37

conclude that, despite the low phosphorus concentration in the water, its turnover was by one order of magnitude slower - 25 days. Hence, along with the development of the eutrophication process the phosphorus deficit appears for phosphorusdependent algae once again, but this time because of its intensive consumption by hydrobionts. Thus, after a period of eutrophic stage species prevalence, the inhabitants of oligotrophic lakes gain the advantage once more, since they consume phosphorus more conservatively and they are better adjusted to lower phosphorus concentrations. Alignment of vegetation period with low water temperatures and resistance to unfavourable weather conditions, especially to intensive wind mixing, are additional conditions of species competitiveness in large cold lakes such as Lake Ladoga. Spring diatoms Aulacosira and summer-autumn blue-greens Aphanizomenon and Woronichinia have these advantages in Lake Ladoga. In the earliest models of the Lake Ladoga ecosystem (Menshutkin and Vorobyeva, 1987; Leonov et al., 1991; Leonov et al., 1995; Astrakhantsev et al., 1992) phytoplankton was represented as a homogeneous biomass. Naturally this description is rather generalized and does not consider considerable differences of productive features and ecological peculiarities of mass species. These features determine the direction of succession among species and the final productivity of the algal community. The first step towards more detailed description of phytoplankton in Lake Ladoga ecosystem models was the division of phytoplankton into three ecological groups. Mass spring, cold water algae, mainly Aulacosira Islandica, formed the first group. Summer and summer-autumn diatoms and blue-greens, typical for the oligotrophic stage were included in the second group. The third group consisted of blue-greens, the new dominants whose ecological demands were formed in shallow eutrophic well heated lakes, rich in biogenic elements. Low rates of phosphorus (FAC) and carbon assimilation (CAC) and a considerable increase of production per unit of consumed phosphorus (CAC/ FAC) are typical for the first group. The second group species are better adjusted to high temperatures, but have a relation between phosphorus and carbon assimilation rates that is similar to that of the first group; they are both inhabitants of oligotrophic waterbodies. The species in the third group, typical for eutrophic lakes, became dominant in summer and autumn at the first stage of Lake Ladoga eutrophication. They need a high phosphorus concentration for mass development and their productivity is high. They produce less organic matter per unit of phosphorus consumed than oligotrophic stage species. Such a division of phytoplankton into three groups enables us to reproduce in the model the dynamics of the general production process during anthropogenic eutrophication of the lake. At the next stage of model development, in order to obtain a more realistic version of mass algae species succession, the main mechanism of phytoplankton community transformation, a more detailed description of algae was achieved by including, as an unknown variable, each seasonally dominant species.


[Ch.l

The total balance of organic matter from phytoplankton production (autochthonous) in Lake Ladoga at the beginning of eutrophication process was about half of its income from the catchment (allochthonous). Inter-annual variations due to different weather conditions were essential (on average, threefold). Under the influence of increased phosphorus supply, phytoplankton production by 1978 had risen by more than one order of magnitude. The value of phytoplankton primary production and mass species composition changed in two stages. During periods of eutrophic stage species prevalence, phytoplankton production for the vegetation period was on average 49 gCm- 2 (production load) and 353-2357 thousand tons C from the lake surface (1977-1985). The amount of autochthonous organic matter produced by phytoplankton became equal to the allochthonous organic matter that came from the catchment. When the prevailing role of traditional dominants in the phytoplankton community was restored (1986-1990) the production load also increased in some degree because of the more important role of the deep zones, on average, up to 76gCm-2 • The production for the vegetation period from the lake, 681-1636 thousand tons C, slightly decreased. The amount of autochthonous organic matter was approximately 1.5 times greater than the annual income of allochthonous organic matter. The increased rate of organic substance accumulation in the lake ecosystem was an important signal of the changes in the trophic status of the waterbody. According to measurements taken in 1996-1998 mainly during the summer period, the daily primary production of phytoplankton was approximately 200-400 g C m ? day"! (Lake Ladoga, 2000; Timakova and Tekanova, 2004, Tekanova and Timakova, 2007), that is close to the values observed in 1977, 1981, 1982 and 1988. In these years the total production for the vegetation period was within the limits 45-65 g C m-2 , and the amount of organic substances produced by phytoplankton was in the range from 800 to 1125 thousand tons of carbon from the lake surface.

Cryptophyte algae From the middle of 1980s the share of cryptophyte algae in Lake Ladoga phytoplankton has grown. These organisms attracted researchers' attention during studies of anthropogenic eutrophication mainly after more sophisticated optical research methods came into existence. In this connection the single-cell flagella species group was isolated, mostly from the pyrophyte algae, into the independent division of cryptophytes. Cryptophytes appear periodically in considerable amounts in all freshwater bodies of all trophic states (Stewart and Wetzel, 1986). Usually their mass development takes place between maxima of seasonal dominants, coinciding with peaks of bacterial destruction, which is probably linked with their mixotrophic nutrition type (utilization of the phosphorus supply along with phosphates, compounds of low molecular fractions of organic matter). Unfortunately, the absence of data on the functional characteristics of the species (individual values of phosphorus assimilation rates from different sources, their carbon assimilation rate and also the carbon forms available for this group) does not allow us yet to define

Sec. 1.4]


39

their input in primary production, and, possibly, destruction, of organic matter in model simulations. 1.4.3 Bacterioplankton, water fungi and destruction processes Bacterioplankton is the main biological community that carries out organic matter mineralization process (destruction) and recurrence of biogenic elements in the lake's turnover. Lake Ladoga in the 1960swas an oligotrophic waterbody with a low level of bacterioplankton development homogeneously distributed over the waterbody. Higher bacterial quantities were registered only in the northwestern part of the lake near to the Priozersk paper pulp mill. The level of bacterioplankton development by the 1980s had tripled in the southern coastal part of the lake and doubled in its deep regions. In 1977-1987 mean annual bacterial total amounts increased from 400 to 800 thousand cells ml"! in the epilimnion and from 200 to 400 thousand cells ml"! in the hypolimnion. Bacterial amounts reach two maxima in a yearly cycle: a spring maximum, a little higher, in May, and a summer maximum in August. The spring maximum is mainly related to the inflow of floodwaters enriched with organic matter from the catchment and summer one to the period of maximum phytoplankton development. The greatest bacterial development in the hypolimnion is registered from July to October without distinct maxima. Inter-annual fluctuations of bacterial amount occur in the epilimnion and they gradually grew in the period 1970-1990. Mean bacterial production, derived from experimentally determined carbon heterotrophic assimilation, during 1981-1987 for the whole Lake Ladoga in spring was 143.9-292.6 thousand tons C; in summer it was 48.1-765.8 thousand tons C; and in autumn 41.1-1704.8 thousand tons C. The deep regions have the major role in producing bacterial organic matter in the lake. Bacterial production of the deep areas, especially in summer, exceeded phytoplankton primary production. In balanced lake ecosystems, bacterial production usually is 3-5 times lower than phytoplankton primary production. It seems that, during the period of anthropogenic eutrophication in Lake Ladoga, the abovementioned ratio is one of the essential indicators of destabilization of the lake ecosystem Aleksandrova, 1973. Organic matter destruction by bacterioplankton in Lake Ladoga in 1981-1987 was 24-94% of its total biochemical transformation (70% in general). Microorganisms mineralized 1.5-3.7 times more organic matter than was produced by phytoplankton. The total bacterial destruction during the period of open water in the lake volume made up 855.5-3375.2 thousand tons C, including 315.8-945.7 thousand tons C in spring, 151.3-2376.5 thousand tons C in summer, and 131.61535.2 thousand tons C in autumn. The autumn of 1985 was especially rich in phytoplankton (5502 thousand tons C). Unfortunately destruction for the whole vegetation period was not estimated because of the lack of spring observations, but in the summer and autumn period its value was 7074 thousand tons C. The value of bacterial destruction during the vegetation period in the lake water volume after 1981 exceeded the total amount of annual phytoplankton primary production and allochthonous organic matter from the catchment. Thus the

40


[Ch.l

heterotrophic component of the lake energy budget exceeded autotrophic component, and that was an essential point in ecosystem reconstruction. According to 1990s data (Lake Ladoga ... , 2002), the amount of bacterial destruction was 45-92% of the total biochemical transformation of organic matter (on average 68%); in other words it did not decrease, compared with the previous decade, though the phosphorus load into the lake declined. Fungi

Beginning from 1978 a new group of organic matter destructors, water fungi, was registered in Lake Ladoga (Qureshi and Dudka, 1974; Pourroit and Meybeck, 1995). Initially mass development of micoflora was observed in the southern area of the lake after the spring maximum of diatomic algae. Later, in summer 1986, fungi appeared continually in all lake zones and their maximum quantity equalled 32 500 diaspore per litre in the profundal zone. Experimental studies of comparative bacterial and fungi input in heterotrophic carbon assimilation revealed that in March, in the northern deep part of the lake, fungi assimilated 0.02-0.29 ug C 1-1 day"! and bacteria - 0.06-0.27 ug C 1-1 day", In August these values were 0.04-0.21 ug C 1-1 day"! and 0.01-0.81 ug C 1-1 day"! respectively. Carbon assimilation by fungi prevailed in the bottom water layers and coastal shallow areas; assimilation by bacteria prevailed in tghe summer epilimnion. The intensive water fungi development in Lake Ladoga and other large lakes was registered only during only the period of anthropogenic eutrophication. Fungi are capable of deep transformation of the most conservative components of dissolved organic matter. Regeneration and phosphorus consumption by bacteria

The process of organic matter destruction is accompanied by phosphorus regeneration. Using personal experimental data T. N. Maslevtseva (Lake Ladoga ... , 1992) estimated phosphorus regeneration in the process of destruction by heterotrophic organisms in Lake Ladoga at 1725 thousand tons a year. The rate of phosphorus consumption by bacteria in Lake Ladoga, according to experimental records in 1987-1989, varied over a wide range. It changed from 0.4 JlgPl- 1 min"! in June (water temperature 24.4°C) to 0.001 JlgPl- 1 min"! in September (water temperature 10.2°C). The rate of phosphorus consumption by bacteria is probably related to their amount, to the water temperature and to the supply of biologically available mineral phosphorus. The spatial distribution of phosphorus consumption rates by bacteria was usually in proportion to the change of these parameters. The rate of phosphorus consumption by bacteria in the dark was one order of magnitude less than during daylight. Such rates in May in the coastal and declinal zones were 0.003-0.050 ug P 1-1 min-I, and 0.010-0.040 ug P 1-1 min"! in profundal zones. The value varied in June in two shallow zones from 0.001 to 0.100JlgPl- 1 min"! and in profundal zone it was 0.0004-0.013 JlgPl- 1 min-I. The rate constants changed within the range 0.006-0.140min- 1 • The maximum intensive phosphorus

Sec. 1.4]


41

turnover was registered more often in July: the turnover period was 2-9 min. In most cases it was the same in May and in July: 20-100min. 1.4.4

Zooplankton

Zooplankton diversity in Lake Ladoga usually consists of lake species common in northernwestern Russia and widespread in the temperate zone of the northern hemisphere. By now, more than 370 zooplankton species are registered in Lake Ladoga. The main groups are rotifers (Rotatoria), protista (Protozoa), cladocerans (Cladocera), and copepods (Copepoda). The general plankton composition, as a mass species group, has not changed since the first half of the twentieth century. But essential changes have taken place in the quantitative composition of particular species and systematic groups, typical in the process of anthropogenic eutrophication. By 1976 the role of rotifers, both in quantity and in biomass, increased by 2.5 times; for cladocerans that was by 2 times. The ratio of copepods in plankton decreased from 24% to 20% in quantity and from 45% to 40% in biomass. Zooplankton distribution over the lake is defined by a number of factors and the most important among them is the depth and water mass dynamics determined by peculiarities of the thermal regime. Zooplankton quantity in early summer is related to the development of rotifers, in August to cladocerans, and in September to copepods. The maximum values of zooplankters quantity and biomass in the coastal zone exceeded 600 thousand specimens m" and 13 gm-2 , and in the profundal zone 400 thousand specimens m -3 and 17 g m -2. The role of zooplankton in the functioning of an ecosystem depends on the differences in zooplankter nutrition. According to nutrition type, zooplankton organisms are divided into two groups: those that consume phytoplankton filtrators and detritus particles with bacteria living on them, and those that are predators. Some species at different age stages switch to another type of nutrition: young individuals are filtrators and adults are predators. Filtrators have a greater degree of influence on biological and biochemical ecological cycles, compared with predators, due to huge amounts of filtrated water in the process of nutrition. The features, characterizing the role of zooplankton in ecosystem processes, are the rate of nutrition (food allowance) and the volume of filtrated water, which is related to the quantity of nutrition consumed and to its concentration. The limiting factor is nutrient electivity which is more frequently related to the dimensions of zooplankters and their nutrient objects. Particles of the scale fraction of 20-40 urn are those most available to zooplankters (Gutelmacher, 1988). Comparing filtrators' nutritional composition with the primary production of the lakes allows us to estimate the ratio of primary production in the food chain of a waterbody. The value of the primary production consumed by zooplankton is in reverse proportion to the primary production of the waterbody. It is nearly 40% in oligotrophic lakes and decreases to 4-8% in eutrophic lakes or in those undergoing the eutrophication stage. According to publications, zooplankton in Lake Ladoga during 1977-1988 in various limnic zones consumed from 3.9% to 22% of the primary production (Gutelmacher, 1988).

42


[Ch.l

Knowing the productivity of Lake Ladoga zooplankton makes it possible to estimate calculations based on 1977-1981 data (Smirnova, 1988). The mean value of filtrators' production during the vegetation period in the coastal zone was 75-80gCm-2 , and in the profundal zone was 120-192gCm-2 • At the same time primary production of predators decreased noticeably: in the coastal zone from 47 gCm- 2 to 19g Cm-2 , and in the profundal zone from 48 g Cm-2 to 12 g Cm v'. The reduction of the predators' contribution to plankton reconstruction is typical during the process of anthropogenic eutrophication. The phosphorus excretion rate by crustacean plankton in spring was 108 J,.lgPm-2 day" (coastal zone) and 204 J,.lgPm-2 day"! (profundal zone). The role of summer zooplankton in the phosphorus cycle was considerably larger: from 2022J,.lgPm- 2 (ultraprofundal zone) to 5000 J,.lgPm-2 day"! (declinal zone). Crustacean phosphorus excretion in autumn was nearly the same as in spring, but in deep zones (8301538J,.lgPm-2day-l) was much higher than in shallow ones (107-217J,.lgPm- 2 day"), Calculations accomplished in July 1987 were based on the same method (Smirnova, 1988) and the value for a day's phosphorus excretion by zooplankton (filtrators and predators) was obtained varying from 0.3 to 315 J,.lgPm-2 day" The author estimated the phosphorus quantity being returned to the lake cycle from zooplankton during the vegetation period as 2.9 thousand tons.

1.4.5 The role of the zoobenthos in the ecosystem The zoobenthos is the animals living on the bottom of the waterbody: protista (protozoa), worms, sponges, molluscs, crustaceans and the larvae of insects. The zoobenthos is divided currently into the meiobenthos and the macrobenthos. The lake meiobenthos is composed of small organisms with a body size 0.3-4.0mm and weights up to 1-2 mg. Among them exist permanently meiobenthic (nematodes, ostracods, garpacticids, bottom Cyclopes, tartigrades and so on) and also the bottom stages of zooplankters, for example, planktonic Cyclopes. Nematodes and inferior crustaceans play an important role in the Lake Ladoga meiobenthos, larvae of Hironomids and Oligochaetes are the most important among the electively meiobenthic. The size of the lake macrobenthos varies from a few millimetres to centimetres. The major systematic groups are Oligochaetes, Hironomids, Hammarids and Molluscs. Oligochaetes prevail in Lake Ladoga at depths of more than a hundred metres. At lower depths various fauna of Oligochaetes, Hammarids, Hironomids and Molluscs could be found with Hammarids prevailing by biomass. Benthic animals live on the surface or in the upper layer of the lake sediments. Prey and predators can be found among them. Prey zoobenthos feeds mainly on detritus or fine silt particles of bottom sediments. The shallow areas of the waterbody are rich in benthic fauna that could be explained by the variety of bottom types, better heating of the water column, the abundance of phytoplankton that die off yielding then a detritus rich in organic substance. The poverty of benthic communities in the central deep areas of large lakes is characterized by monotonous bottoms and two other important factors. Detritus, which is formed in the

Sec. 1.4]


43

epilimnion as a result of phytoplankton die-off, to a large extent is mineralized by bacterioplankton and zooplankton during the lake summer stratification. It reaches the hypolimnion and the bottom impoverished in organic matter, which is vital for benthic animals. Besides, the larvae of insects (Hironomids) cannot survive in the deep and have moved off the shore regions of the lake bottom, as favourable conditions are required for the imago. That is why Oligochaetes predominate at depths of more than 100m. The most intensive development of meiobenthos organisms in Lake Ladoga is registered in the coastal zone, especially within the littoral zone: up to 600 thousand specimens m ? and a biomass of7.5 gm-2 • There is less intensive development in the profundal zone: up to 200 thousand specimens m ? and a biomass of 6.5 gm- 2 (Kurashov, 2002). Maximum values of quantity and macrobenthos biomass are in the declinal zone: about 700 thousand specimens m ? and biomass of 23 gm- 2 , while in the profundal and ultraprofundal zones they did not exceed 850 specimens m ? and a biomass of 2.2gm-2 • The functional characteristics of meiobenthos and macrobenthos in Lake Ladoga were compared by Kurashov (1994, 2002) in order to estimate the role of each community in the lake ecosystem. The calculations show that, in energy equivalent for the whole lake, benthos produces during June-September 33.49 kJ m-2 , including for macrobenthos 22.31 kJm- 2 and meiobenthos 11.18kJm-2 (1 gC corresponds to 39.49 kJ/m2) . The benthic community consumes 223.93 kJ m ? (macrobenthos 124.18kJm-2 , meiobenthos 99.7kJm-2) . During respiration 88.99kJm-2 is dissipated (45.83 kJm- 2 by macrobenthos and 43.16 kJm- 2 by meiobenthos). The highest mean value of the ratio between the meiobenthos and macrobenthos productions is registered in the coastal zone: 109.8%; the lowest is registered in the ultraprofundal: 13.2%. The relation of the respiration consumptions of the two benthic communities, describing their participation in the transformation of organic matter and energy in these zones is, respectively, 177% and 32% (1 gC is equivalent to 39.22kJ). On average for the whole lake meiobenthos production is 50%, and its respiration value is 94%, of macrobenthos production. Again, averaged over the lake, benthos production was 1.6% of the primary production and 2.4% of bacterial destruction. It follows that the meiobenthos consumes 4.7% of phytoplankton production and 6.9% of bacterioplankton production and the macrobenthos 5.9% and 8.6% respectively. In the lake phosphorus turnover zoobenthos plays a visible role (Kurashov, 1994). Since released mineral phosphorus is one of the final products of the water animal's metabolism, the release rate can be estimated using the energy exchange rate (Gutelmacher, 1988). Thus, the value of phosphorus excretion for benthic organisms is estimated indirectly by estimating energy expenditures on respiration. Mean values of phosphorus excretion by zoobenthos of Lake Ladoga during one season (May-October, 180 days) were equal to 366 tons for the coastal zone, 299.2 tons for the declinal zone, 52.8 tons for for the profundal zone, 11 tons for the ultraprofundal zone and 719 tons for the whole waterbody (Kurashov, 1994). Special attention should be paid to data obtained by E. A. Kurashov about essential changes in species composition and the values of meiobenthic community biomass in the profundal and ultraprofundal zones, started in 1998 and clearly seen

44


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in 1999-2000 (Lake Ladoga ... , 2002). The author noted the appearance in Lake Ladoga bottom deep water areas of mass diapaused copepodites concentrations of planktonic Cyclops, typical for large lakes only, when they undergo long-term and heavy anthropogenic impact, as in Lake Constance (Bodensee). Such radical meiobenthos structure change in deepwater areas is a new manifestation of the anthropogenic eutrophication, in this instance in one of the most conservative biotopes of the lake ecosystem. 1.4.6

Dissolved organic matter

A pool of dissolved organic matter is a buffer system, which is able to accumulate different compounds and return them under various conditions in the lake turnover. Hence, dissolved organic matter is an important element, sustaining the lake ecosystem stability. In lakes with low productivity the income of allochthonous organic matter often prevails, especially when inflowing waters have a high humic content. Although it was accepted for a long time that only 1-10% of allochthonous organic matter can be used and decomposed by bacteria, there are numerous evidences of its participation and even dominance in biological carbon cycles in humic lakes. Bacterial utilization of allochthonous organic carbon, according to the opinion of a number of authors, should be considered separately as a mobilization of energy from an external source, by analogy with photosynthesis (Jones, 1992; Jansson et al., 2003). Bacterial energy mobilization dominates not only in coloured lakes but also in lakes with high water transparency (Karlsson et al., 2002). The content of organic matter in lake water is usually estimated by the concentration of the 'total organic carbon' (TOC). For a long time it was constant in Lake Ladoga, about 7536 thousand tons of C in the lake volume from 1956-1963 until 1981. The average concentration fluctuated over seasons in 1976-1979 within 8.1-13.7mgCl- 1 in shallow areas and within 8.2-10.4mgCl- 1 in deep areas; but the mean magnitude for the lake remained constant (8.3 mg C 1-1). The first rapid decline in these values was recorded in summer 1981, when TOC concentration in two deep zones was equal to 4.4mgCl- l . This determined the general reduction of organic carbon in the lake to 5811 thousand tons. That was the year, when organic matter destruction dominated in the Lake Ladoga ecosystem; it was associated not only with bacterial activity but also with the showing up of mass water fungi, especially in the winter period. In 1983-1984 the kinetic curves of biochemical oxygen consumption changed radically; that also testified that the species composition of organisms - destructors of organic matter - had changed. According to the experimental data ofT. M. Tregubova and T. P. Kulish the transformation degree of lake organic matter increased (Lake Ladoga . . . , 1992). In succeeding years both seasonal variations of TOC in all lake areas and changes of the total carbon store became constant. In 1983-1985 total storage of TOC in the lake grew considerably, that could be explained by maximum summer phytoplankton activity in deep water areas and was equal to 8263-8626 thousand tons. The next, more extended, period

Sec. 1.4]


45

of low organic carbon content in lake waters was formed by 1988 and continued until 2000. This period was characterized by minimum low limits of TOC seasonal variations in all areas (4.9-18.8mgCI- 1 in shallow parts and 3.4-11.8mgCI- 1 in deep areas), and the storage in the lake volume was equal 5266-7536 thousand tons. In 2001-2003 the maximum upper limits of TOC concentrations in the lake (8.530.4mgCI- 1 in shallow areas and 7.3-30.0mgCI- 1 in deep areas) promoted the maximum storage of organic matter generation in the lake ecosystem, equal to 9080 thousand tons in 2003. In the years 2004-2007 the TOC amount decreased in the lake from 7627 thousand tons C to 5993 thousand tons in 2006 and to 6447 thousand tons C in 2007. Such high inter-annual variations of organic matter accumulation rates, non-inherent in large lakes, indicated severe ecosystem destabilization. Conservative fraction of dissolved organic matter - water humic substance

Lake Ladoga studies have shown that more than 80% of total organic carbon is bound to a conservative fraction of DOC - water humic substance (Korkishko et al., 2002). It was shown that nowadays water humic substance is more actively entrained into the organic carbon cycle compared to the period before the anthropogenic eutrophication. Water humic substance is a unified, highly molecular complex, including besides carbon, a large amount of the biogenic elements contained in lake waters. According to experimental studies the humic substance coming to Lake Ladoga with inflow waters is in a maximum recovered form and the level of its oxidation does not exceed 3-10%. But in deep parts of the lake the oxidation level of humic substance can reach 70-75% and that points to its oxidation in lakes. The transformation process is accompanied by changes in the element composition of humic substance, particularly as the result of a decrease in the phosphorus content per carbon unit (in atomic equivalent, by 2-5 times). Experimental data make it possible to conclude that, although high molecular humic complex, inflowing with tributaries is subjected to a biochemical oxidation less than 10%, this process is accompanied by the disruption of chemical links and further generation of humic substance with lower molecular mass and low-level molecular compounds. A part of the biogenic elements is converted into the low-level molecular fraction of humic substance. Later this fraction can be subjected to biocatalytic oxidation by lake organisms, possessing peroxidized and catalysed activity, and that facilitates the return of biogenic matter, including phosphorus, to the lake turnover. As was mentioned earlier, intensive phytoplankton development in the process of anthropogenic eutrophication led to an increase in the consumption rate by this community by only an order of magnitude as compared with the lake oligotrophic stage. More phosphorus is needed by destructors, especially bacterioplankton. The internal phosphorus deficit in biologically available form stimulates the emergence of organisms' communities capable of the biocatalytic decomposition of the molecular fractions of low-level humic complexes, at the same time drawing into lake turnover a part of the conservative organic matter. Lifetime phytoplankton excretions also possess biocatalytic activity, and the higher the primary production level, the greater their role in the lake processes. As a result, the pool of biologically available

46


[Ch.l

phosphorus grows, sustaining further development of autochthonous organic matter production and allochthonous matter destruction. The studies conducted in 1995-1999 have shown that the relative content of humic substance high-level molecular fraction in Lake Ladoga was sufficiently stable, at 85-95% of TOC level. By 2003 the amplitude of spatial-temporal variations increased by 36-97%. Up to 64% of dissolved organic matter as low-level molecular fraction was transferred into the lake turnover during different seasons in the coastal zone; in profundal zone, up to 51%; in the ultraprofundalzone, up to 27%. This proves the existence of at least two- to three-fold acceleration of carbon and, hence, of phosphorus cycles in the lake processes, and explains the absence of the expected phytoplankton productivity reduction under conditions of permissible phosphorus loading (petrova et al., 2005). According to standard station measurements of a longitudinal section of Lake Ladoga in 2003-2007, the of low-level molecular fraction of organic matter in the lake volume was: in spring (May-beginning of June), about 2 thousand tons C; and in summer (July-August), 3.2-4.5 thousand tons C. Probably because of its entrainment; the total amount of dissolved organic matter in the lake at that time varied from 5993 to 9080 thousand tons C. Changes in the ratio between carbon and phosphorus in the high-level molecular fraction of humic substance during its transformation in the lake enable us to estimate the quantity of phosphorus transferred to the low molecular fraction, i.e., to biologically available forms. It should be, during the period 2003-2007, in spring for the whole lake, 2-6 thousand tons of phosphorus; in summer, 6-9 thousand tons; in autumn, 2.5-8 thousand tons; while the general storage of total phosphorus in Lake Ladoga was estimated at 12 thousand tons in 2003 and at 10 thousand tons in 2007.

1.4.7 The role of seston and bottom sediments in the lake phosphorus cycle Generation of seston

Generation of seston (suspended matter) in water column of Lake Ladoga, sedimentation and transformation rates were studied in 1987-1988 in two small bays. The materials collected during these experiments showed the dynamics of seston and its components, particularly phosphorus, during sedimentation to the bottom layers. The concentration of total phosphorus in suspended solids increased from 6 to 32JlgPI- I , and, in the hypolimnion, from 6 to 59 JlgPI- I . Very high concentrations were recorded at the beginning of October - up to 119 JlgPI- I . The accumulation rate of phosphorus in seston was, in the epilimnion, 6.2-12 JlgPm- 2 day", and in the hypolimnion, 13-17JlgPm-2 day", The average seston sedimentation rate was 1-6.6mg (m- 2 day") in the epilimnion and 3.7-20 mg m ? day"! in the hypolimnion. In the epilimnion seston has a high content of labile organic matter; in the hypolimnion it is already transformed considerably, containing mainly mineralized phosphorus compounds.

Sec. 1.4]

The cycle of substances in Lake Onego and its water ecosystem 47

Transport of substances through the water - bottom interface

The diffusive flux exists practically all the time, but it becomes the main transport mechanism only in anaerobic conditions during the stagnation period (Ignatyeva, 1997). In aerobic conditions convective transfer plays the main role in the transport of phosphorus from the bottom sediments to the water. In modern conditions Lake Ladoga sediments are formed mainly by suspended solids of autochthonous origin. The role of allochthonous substances is essential only in the coastal zone. The modern sedimentation rate for the larger part of the lake is small: from 0.06 mm year" in the southern sandy shallow part to 0.5-0.6 mm year" in the area of maximum depth in the profundal and ultraprofundal zones. Income ofphosphorus

The income of phosphorus to the bottom sediments takes place basically as a component of organic compounds. The weight ratio C :P in the organic matter of the upper layer of bottom sediments is 40 : 90. The average phosphorus accumulation rate in bottom sediments in different lake zones is: in the coastal areas, 0.46 mg P day"; in the declinal zone, 0.59; in the profundal zone, 0.39; in the ultraprofundal zone, 0.70mgPday-l. The annual income of phosphorus to the bottom sediments in the different zones is 620, 1140, 830 and 760 tons year-I, respectively, in total 3350 tons over the whole lake. The declinal zone is the place of initial accumulation and mineralization of organic substances in the hypolimnion. The average proportion of buried phosphorus for the whole lake from its influx to the bottom is 74% or 2475 tons annually. The declinal zone and the shallower parts of the profundal zone are the main regions where mineral layers in bottom sediments are formed. They are not only accumulating phosphorus but also become the barrier in the path of vertical diffusion of phosphorus. The phosphorus sedimentation is 56% of the external phosphorus load, and dumping is 41%. Calculation of the phosphorus flux from bottom sediments showed that its mean value for the lake is 0.13mgPm-2 day-lor 0.05gPm-2year- l, 875 tons of phosphorus is released annually from the bottom sediments of Lake Ladoga (coastal zone, 155, declinal, 285, profundal, 215, ultraprofundal, 220 tons year-I). The calculated value of phosphorus released from bottom sediments is 26% of its sedimentation and 15% of the external phosphorus load. Part of the released phosphorus is transported to the trophogenic layer and can be used for phytoplankton primary production; the remaining phosphorus, staying in the hypolimnion, can be utilized by microorganisms (Ignatyeva, 1997).

1.5 THE CYCLE OF SUBSTANCES IN LAKE ONEGO AND ITS WATER ECOSYSTEM The distribution and the rate of anthropogenic eutrophication differ in Lakes Ladoga and Onego. In Lake Onego, with its more complicated morphometry and

48


[Ch.l

water current structure, the distribution of the phosphorus which is brought into the lake by tributaries and which comes directly from industrial and community wastewaters is not involved in the lake-wide cycle as in Lake Ladoga. Water enrichment with phosphorus up to the levels triggering the enhancement of eutrophication takes place, as a rule, in the bays, which is where the tributaries and waste waters are received. 1.5.1

The phosphorus supply to the Lake Onego ecosystem

River inflow is the main source of phosphorus income both for Lake Onego and Lake Ladoga. The prevailing role belongs to three main tributaries - the Shuya River, the Vodla River and the Suna River, that bring altogether about 90% of the biogenic influx from the catchment area; the input of other rivers, inflowing from the southeast to the lake is less essential (Lozovik et ai., 2006; Lozovik and Raspletina, 1999; Pirozhkova 1990). The phosphorus loading that came via the main tributaries varied insignificantly from 1980 till the middle of 1990 and depended mainly on the dryness of the year (Fig. 1.15). A considerable decline in phosphorus content in the main tributaries was observed during the second half of the 1990s, due to the economic crisis in the country, when the usage of mineral fertilizers in agriculture and, as a result, biogenic matter washout reduced significantly. After the year 2000 the total phosphorus transport via the tributaries equalled 441 tons. Industrial and communal waters of enterprises located in the coastal area in this case are of less importance. Their share of Ptotal is 174 tons annually.

p

tons

1100

1000 900

800 700

600 500

400

960

965970

9751980 -1985 '1990 '1995 2000 2005 2010

Fig. 1.15. Total phosphorus loading (tons per year) to Lake Onego for 1963-2006.

Sec. 1.5]

The cycle of substances in Lake Onego and its water ecosystem 49

Phosphorus contained in industrial sewage waters distinctively influences water composition in the lake's large bays. It is determined by phosphorus load value and the intensity of water exchange in the bays and the lake pelagial part of the lake. Povenetsky Bay receives a small amount of phosphorus from Medvezhyegorsk city wastewaters compared with the other bays. Phosphorus concentration in the bay waters has not varied much in recent decades and equals on average 10.1 JlgPI- I. Wastewater phosphorus there is partially buried in silts, and its content in the coastal zone slightly increases (Belkina, 2003; Belkina et al., 2006). The process of anthropogenic eutrophication is apparently not revealed here. The wastewaters of Petrozavodsk city, communal ones mainly, treated biologically, enrich the bay waters and the contiguous lake areas with phosphorus. A sharp increase in phosphorus loading in Petrozavodsk Bay began in the 1980s as a result of the intensification of agriculture and forestry and of population growth in the lake catchment. By the middle of the 1990s the total anthropogenic phosphorus, Ptotah impact was on average 2.7 gm-2 and the natural phosphorus (via tributaries) was 1.2 g m ? annually. The total phosphorus income to Petrozavodsk Bay from the catchment itself was at that time 333 tons year": The situation has changed drastically since the late 1990s: P total income via tributaries was 111 tons year-I, and from sewage waters was 103.6 tons year"! and 214.6 tons year"! annually in total (Sabylina, 2007). Nowadays the total phosphorus income from the lake catchment and with Petrozavodsk city wastewaters is estimated to equal 223.8 tons year" for Petrozavodsk Bay, which permits us to consider Petrozavodsk Bay to be the main phosphorus supplier to the central lake areas. Mean annual Ptotal concentration in Petrozavodsk Bay waters equalled 25 JlgPI- I in the 1980s; it declined to 17 JlgPI- I in 1990s and was recorded to be 20 JlgPI- I in 2000-2007. Intensive water exchange between Petrozavodsk Bay and the central lake areas is determined both by the basin structure, with its gradual decline towards the deep regions, and also by the tributaries efficient water volume, 3.09 krrr' year" (Filatov et al., 2006). The water exchange period equals 14-20 days during the summer period, rehabilitating the bay water quality, and, in particular, reducing the phosphorus concentration in the water. Wastewaters flowing into Kondopoga Bay in the water, specified as organomineral, contain a large amount of suspended matter. According to the degree of phosphorus supply coming in with the sewage waters, the bay water composition differs crucially from that of other lake regions. The incoming over several decades the amount of phosphorus coming into the bay varied in accordance with the production volumes of, and environmental measures taken by, the local paper-mill. Phosphorus carry-over grew considerably at the beginning of the 1980s, and rather rapidly after the launch of the first turn of biological refining station at the Kondopoga paper-mill plant, and at that point the phosphorus load due to tributary inflow was exceeded. The total amount of phosphorus, Ptotah in the river inflow through the Kondopoga channel was relatively permanent and equalled 28 tons year": Phosphorus concentration reached values of 15-40 JlgPI- I in Kondopoga Bay. In the late 1990s the phosphorus flux from the municipal treatment plant was 2.5 times the income from tributaries. P total carry-over into the bay via river inflow


[Ch.l

and from wastewaters reached 120 tons in 2004 (Sabylina, 2007). Phosphorus loading (0.5 g m ? year-I) on Kondopoga Bay exceeded the level permitted for an oligotrophic waterbody (Vollenweider, 1975). Kondopoga Bay has a long coastline (its length is 30 km) and its water exchange period equals 1.93 years. Water exchange with the lake water masses is hindered and much more sewage water is located there than in Petrozavodsk Bay. Total phosphorus income via river inflow and precipitation in Lake Onego in the first half of the 1990s is estimated at 1005tons year-I, but by 2001-2002 it decreased to 676 tons year-I. Phosphorus outflow via the Svir River at that time was 298 and 230 tons year" respectively. Nearly 70% of the annual phosphorus income (70% in the 1960s and 66% in 2001-2002) remains in the lake. Phosphorus in Lake Onego bottom sediments

Phosphorus enters Lake Onego bottom sediments mainly with the suspended particles fraction ( < 0.01 mm). The accumulating ability of Lake Onega bottom sediments towards phosphorus and the phosphorus accumulation rate in bottom sediments vary on a large scale depending on sediment type, on the morphological peculiarities of the lake basin, on the hydrodynamic conditions and on the degree of anthropogenic impact. Studies conducted by Semenovich (1973), Vasileva et. al., 1999) and Belkina (2003) on Lake Onego exposed regularities in the spatial distribution of phosphorus in bottom sediments and its tendency to be transformed under anthropogenic impact. During four decades of intensive catchment exploration, and of industrial and municipal development in the lake coastal regions, phosphorus concentrations increased in sediments over almost all of the lake bottom. Nowadays the total phosphorus amount in the surface layer solid phase (O-5cm) in bottom sediments is above the natural concentration level (from 0.05% up to 0.7%) and it increases with water bodydepth and the degree of sediment dispersiveness. The highest concentrations are measured in industrial sediments in Kondopoga and Petrozavodsk Bays. Regardless of granulometric bottom sediment feature, phosphorus exists mainly in a form of non-organic compounds, except for the Kondopoga Bay bottom sediments which contain suspended solids from papermill plant sewage waters. Before the dispersive wastewater facility and the biological refining station were put into operation, the major part of the solid discharge sedimented in the upper part of the bay. Nowadays intensive phosphorus accumulation is registered in the regions more than 10km distant, from the plant. During the last 20 years the phosphorus amount (in the 0-5 em layer) in the bay bottom sediments increased by 1.5-2 times. Reducing conditions (Eh up to 60 mV) point to the development of anaerobic processes in the sediment strata and the formation of secondary waterbody pollution conditions by phosphorus. Particle size distribution (high ferric phosphate ratio) and high phosphorus concentrations in porous waters (up to 1000JlgPI- I) in the upper bottom sediment layers prove that there is also an intensive development of eutrophication processes in this bay (Belkina, 2003). A noticeable phosphorus content increase in silts is observed in Bolshoe Onego bay, which appears to be a kind of settling area and sedimentation zone for

Sec. 1.5]

The cycle of substances in Lake Onego and its water ecosystem

51

suspended matter coming from Kondopoga Bay. River and terrigenous discharge is negligible here. During last 15 years Ptotal concentration doubled in general. The labile phosphorus ratio is 60-70% from Ptotal. Total phosphorus concentration in the bottom sediments of the central lake region on average tripled during the last two decades and that of labile phosphorus increased by more than an order of magnitude. The bottom sediments in Petrozavodsk Bay are formed as a result of the lake, the river and municipal sewage waters mixing. The River Shuya waters, which contain in suspended matter plenty of persistent organic matter of humic origin, essentially influence the formation of bottom sediments in the northwestern part of the bay. Suspended matter of anthropogenic origin accumulates along the western coast of the lake. The phosphorus level in bottom sediments, compared with 1980s data increased by 1.5 times. Maximal concentrations are registered near municipal wastewater outlets. A part of Povenets Bay called Large Bay has the lowest anthropogenic and river impact, unlike Petrozavodsk and Kondopoga Bays. Data obtained in the 1970s shows that the phosphorus content in silts increased to some extent there. The peculiarity of bottom sediments in Lake Onego is their high accumulative capacity towards phosphorus. In the central waterbody regions on average nearly 80% of the phosphorus income is buried in the bottom sediments. Similar values for the bottom accumulation capacity (about 70%) are obtained for Lake Ladoga and the Great American Lakes Erie and Ontario, which reflects characteristic features of large, deep, cold-water bodies (Chapra and Sonzogni, 1979; Raspletina, 1992; Bostrom et al., 1982; Manning, 1987; Sandman et al., 1999, Ignatyeva, 2002). Reconstructive conditions, developed in the sediments of polluted bays, provide immobilization and the return of phosphorus back into the water column (Belkina, 2003). Internal phosphorus loading estimation by the balance method has shown that phosphorus removal from bottom sediments in polluted bays is 3-60 times higher than from bottom sediments in the lake central regions - l Dmg PmFday"! and 0.03 mg Prn f day", Industrial silts in Kondopoga and Petrozavodsk Bays are characterized by poor retaining capacity. The phosphorus-retaining coefficient of polluted silts is estimated to be in the range of 20-60%.

1.5.2

Biological communities in the Lake Onego eutrophication state

Phytoplankton The first display of changes in the phytoplankton community along with phosphorus impact increasing is the growth of quantity characteristics and, then, the change in species type. Lake Onego phytoplankton is represented by a diverse flora (780 taxonomic units), common for large, deep, cold oligotrophic lakes of the temperate zone. As in the pelagic so in the littoral zone plankton diatoms (50%), green (26%), yellow-green (10%) and blue-green (8%) algae are presented diversely. The dominant


[Ch.l

complex is represented by species common for Lake Onego: the diatoms Aulacoseira islandica, Aulacoseira subarctica, Aulacoseira alpigena, Asterionella formosa, Tabellariafenestrata; the blue-green algae Coelosphaerium kuetzingianum f. kuetzingianum, Oscillatoria limosa, Oscillatoria planctonica; and the yellow-green algae Dinobryon divergens (Vislyanskaya, 1998, 1999; Chekrizeva, 2008). For Lake Onego phytoplankton, as for other deep temperate zone waterbodies, a seasonal dynamic of one or two peaks of the main characteristics is typical, with the maximum occurring during the vegetation period of diatomaceous algae. In the process of lake eutrophication and pollution as a result of wastewater discharges, phytoplankton, in general, did not undergo considerable structural changes. So, as a result of dominance all through the year of diatoms (60%), it still preserves its floristic diversity and the systematic inter-relations between algae departments typical for oligotrophic waterbodies. In spring plankton the dominant role belongs to recent-years dominants from the diatomaceous algae group. Along with summer heating of the water column, a more diverse complex is developed with summer diatom forms prevailing with a considerable amount of yellow-green, green and blue-green algae. The representation of species that are common, not only for higher trophic level waterbodies, but also as indicators of organic pollution, noticeably increase. For deep lake areas (central region, Povenets and large Onego bays) comparison of modern data (2004-2006) with those published earlier (Vislyanskaya, 1999; Petrova, 1969, 1971, 1973, 1990), testifies that there is insignificant change in phytoplankton development level. A distinct increase in the quantity characteristics of phytoplankton communities occurred in the northwestern areas - Kondopoga and Petrozavodsk Bays. Phytoplankton amount in Petrozavodsk Bay grew during the increase of phosphorus loading on the aquatic ecosystem, especially during the development of spring algae complexes, up to 1.7-3.0 million cells 1-1 and its biomass value reached 5-9gm- 3 • Much deeper changes in the phytoplankton community were observed in Kondopoga Bay and were related to the changes in the quality of wastewater composition. Until the 1960s the phytoplankton community structure was similar to that of the open regions of the lake. Local surges in green chlorococcales blue-green development were registered that designated the existence of organic pollution. The situation began to change rapidly in the 1970s after the launch of the paper-mill sewage waters purifying station and the consequential enlargement of phosphorus income into the bay. In the early 1980s it became obvious that the dominant group, consuming relatively small amounts of phosphorus, was enlarged by eutrophic waterbody species, highly productive, but demanding for their development high phosphorus concentrations in the water. By 1989 algae quantity increased by 5 times (1226 thousands cells 1-1), and its biomass doubled comparing with 1982. Since the end of the 1990s, along with enhancement of the number of species typical of shallow eutrophic lakes, the former dominants of the oligotrophic period started to develop intensively again. These species have the advantage over eutrophic ones that they are satisfied with lower phosphorus concentrations in the water mass.

Sec. 1.5]

The cycle of substances in Lake Onego and its water ecosystem

53

The composition of bay phytoplankton dominants at this new level was identical to that observed during oligotrophic period in the late 1960s and 1970s. At the same time the phytoplankton development level remained high enough (1200 thousand cells 1-1). Similar features of phytoplankton development level in Petrozavodsk and Kondopoga Bays can be marked out: considerable phytoplankton quantity and biomass growth in spring, as a result of intensive Aulacoseira islandica subsp. helvetica, the oligotrophic period dominant, significant blue-green and green chlorococcales algae, along with diatoms development when the summer phytocoenosis structure is relatively stable; and summer and autumn phytoplankton prevailing in the annual cycle (Vislyanskaya, 1999). Primary phytoplankton production

Determination of primary production in Lake Onego was the focus of a number of studies (Romanenko, 1966; Sorokin and Fyodorov, 1969; Petrova, 1973; Rossolimo, 1977; Trifonova et al., 1982; Umnova, 1982; Vislyanskaya, 1999). Since 1989 monitoring has been based on these studies and it covers nearly all the waterbody. By primary production magnitude Lake Onego can be classified as a typical oligotrophic waterbody, excepting Kondopoga and Petrozavodsk Bays, where the ecological state is characterized by mesotrophic features. During 17 years period from 1989 to 2006, primary production values over the major part of the lake (central and southern areas, Petrozavodsk Bay, Small Onego, Povenets and Zaonezsky Bays, and Unitskaya Bay) did not change essentially, and were less than 100mgCm-2 day": In the frontal zone where the eutrophicated bays meet the open pelagic areas, and where during the periods of dynamic activity of water masses contamination penetrates (Bolshoe Onego and the northwestern part of the open area), phytoplankton production values are slightly increased up to 150mgCm-2 day" (Table. 1.4). Table 1.4. Phytoplankton production in different Lake Onego regions in summer period, mg Crrr' 0, where H o is a given value. Let us write down model equations (Marchuk and Sarkisyan, 1980; Marchuk et al., 1987)

au au au au 1 ap a (au) -+u-+v-+w--lv=---+k zat ax ay Bz Pw ax Bz Bz

a ( k -au) +a ( kau) +ax x ax ay Y ay

(2.1)

et et et et at + u ax + v ay + w az =

ap az = -pg,

(2.3)

au all aw_ ax + ay + Bz - o,

(2.4)

a (aT) az liz az

a (aT) lIx ax

+ ax

p = p(T,P).

v

a (

+ ay

lIy

aT) ay ,

(2.5) (2.6)

Here = (u(x, y, z, t), v(x, y, z, t), w(x, y, z, t)), is the water velocity vector; I is the Coriolis parameter; P(x,y,z, t) is the pressure; T(x,y,z, t) is the water temperature; p is freshwater density; Pw is the average freshwater density; g is gravity acceleration; kx(x, y, z, t), ky(x,y, z, t), kz(x,y, z, t) is the coefficient of turbulent viscosity; and vx(x,y, z, t), vy(x,y, z, t), vz(x,y, z, t) is the coefficient of turbulent diffusion. The system of equations (2.1)-(2.5) provided that density p is given by (2.6), includes five unknown functions: projections of velocity vector, u, v, w, hydrodynamic pressure P and temperature T. When applying boundary conditions it should be kept in mind that for many large lakes the river inflow and outflow have to be taken into account because of their role in lake water balance, thermal regime and water quality generation. It is also important to include precipitation and evaporation, which is simpler to do by varying river inflow and outflow. A free waterbody surface is given by a function ~(x,y, t), i.e. the equation z = ~(x,y, t). Since the main objective of hydrothermodynamic modelling is to reproduce a large-scale climatic circulation, for large deep lakes it is possible to consider that ~(x,y, t) is small compared to waterbody depth and that surface boundary conditions can be applied on undisturbed water surface at z = 0 (Kamenkovich, 1973; Pedlosky, 1986). This is true both for kinematic and dynamic boundary conditions. On the surface of lakes such as Lakes Ladoga and Onego the horizontal atmospheric

72

Hydrothermodynamics of large stratified lakes

[Ch.2

pressure gradient is neglected and it is assumed that P(x,y, z, t) in equations (2.1)-(2.3) is a deviation of the hydrostatic pressure from atmospheric pressure. Let us write down the boundary conditions at a surface z = 0:

k z

au _

Tx

k,

Bz - Pw '

av =

(2.7)

Ty •

Bz

Pw

Here T x , Tv are wind stresses. For w on the surface at z = 0 the boundary condition is applied

w=

8~

Bt '

Q

Q

= 0,1.

(2.8)

When Q = 0, this is the 'rigid lid' boundary condition (Kamenkovich, 1973; Pedlosky, 1986); when Q = 1, this is a linear approximation of the condition

w = 8~ + U 8~ + v 8~ 8t Bx 8y at the free surface. On a waterbody bottom at z = -H(x,y) for u, v, w the slip boundary conditions are prescribed (2.9)

u = v = w = 0, or TH x

8u 8N

Pw

w= where T!f,

H

8v 8N 8H 8x

T --L Pw

(2.10)

8H 8y

(2.11)

-U--V-,

Tf bottom friction stresses, and 8cp _

8cp

8cp

+ k y ay

aN = k x ax cos(n, x)

cos(n, y)

8cp

+ k, az cos(n, z)

is a derivative along the co-normal. On the vertical lateral boundary of the waterbody the following boundary conditions are used: on the solid part of the boundaries (2.12)

u = v = 0, at the inflow and outflow rivers sites

u= ur ,

v=

Vr

(2.13)

where u-, Vr are given functions of space coordinates and time. For temperature boundary conditions the following are used: at z = 0

8TI

Vz -

Bz

So

1 =-v-Q, cpPw

(2.14)

A climatic circulation model for large stratified lakes

Sec. 2.3

73

where Q is the heat flux through the surface of waterbody, or (2.15)

Tis = T s,

where T, is a surface temperature; at bottom and solid lateral boundaries the thermal isolation conditions are prescribed

aT =

aN

0

'

et et aN =. V x ax cos(n, x)

et

+ "» ay

et cos(n,y) + V z az cos(n, z).

(2.16)

At the sites of inflowing rivers the following condition is used

;~- vnCT- Tr) =

0,

(2.17)

where v" is the projection of velocity vector on the outer normal to the 'live' river transect, and T, is the given water temperature in the river. At the sites of outflow rivers the condition (2.16) is applied. Besides boundary conditions the initial conditions at t = 0 should be given u(x,y,z, 0) = uo(x,y,z),

v(x,y,z,O) = vo(x,y,z),

T(x,y,z,O) = To(x,y,z)

(2.18)

There now exist enough examples of this type of mathematical model application to solve prognostic problems of ocean dynamics. One of the first was a model by Bryan (1969, 1975). Nowadays the three-dimensional ocean model developed at Princeton (USA) in 1977 (Blumberg and Mellor, 1987) is one the most widespread numerical circulation models. This model has been updated from time to time. One of the latest revisions was done in 1996 (Mellor, 1996). It is also used to model large stratified lakes.

2.3 A CLIMATIC CIRCULATION MODEL FOR LARGE STRATIFIED LAKES 2.3.1

General comments

A large number of studies are devoted to mathematical modelling of the dynamics and thermal regime of the greatest lakes of the world. Mathematical modelling results of the Great American Lakes are presented in Bennet (1974, 1978), Simons (1973, 1974, 1975, 1976), Lick (1976); of Lake Sevan in Satkisyan (1977); of Lake Issyk-Kul in Arkhipov (1986); of Lake Ladoga in Okhlopkova (1966), Akopyan et al. (1984), Astrakhantsev and Rukhovets (1988), Astrakhantsev et al. (1987, 1998) and others. The review of works devoted to lake modelling can be found in monograph of Filatov (1983, 1991). At the present time, for the hydrodynamic modelling of large stratified lakes three-dimensional oceanic models are used that have proved to be reliable. One of them is the already-mentioned model of Blumberg and Mellor (1987) and its modifications. So this model, based on the primitive equations (2.1)-(2.6), is used for the hydrothermodynamic regime study of the Great American Lakes (Beletsky et al., 1999; Beletsky and Schwab, 2008a, b; Chen et al., 2002; Beletsky et al., 2006).

74


[Ch.2

For reproducing large stratified lakes climatic circulation the authors use a slightly modified mathematical model of the ocean climatic circulation (Marchuk and Sarkisyan 1980; Marchuk et al., 1987). The latest model is a simplification of the model described in section 2.2.2. The climatic circulation model used by the authors (Astrakhantsev and Rukhovets, 1993; Astrakhantsev et al., 1998, 2003) has a number of differences compared with the ocean climatic circulation model (Marchuk and Satkisyan, 1980; Marchuk et al., 1987). This model takes into consideration factors that are not so essential for the ocean, such as river tributaries inflow and outflow, precipitation and evaporation. As the equation of state a nonlinear equation is used, i.e, water density anomaly in fresh water plays a substantial role in the formation of waterbody circulation (the fields of velocity flows and fields of temperature) when its temperature equals 4°C. Furthermore, in the equation for density evolution (Marchuk and Sarkisyan, 1980; Marchuk et al., 1987) the terms describing the horizontal turbulent diffusion of density are absent. The analysis of temporal-spatial scales shows that in equations of heat distribution for large lakes, terms describing horizontal turbulent diffusion are as significant as terms describing vertical heat turbulent diffusion. Let us estimate, as is usually done (Sarkisyan, 1977; Filatov, 1983; and others), the comparative value of terms

aza (Vz aT) az

and

a ( aT) ax Vx ax '

in the equation of heat distribution, using characteristic values of variables in these terms for Lake Ladoga. To perform such estimates let introduce the following notation for the characteristic scales of the corresponding variables and functions: L - characteristic linear scale in horizontal direction, H - characteristic linear scale in vertical direction, v~ - characteristic scale for the coefficient of horizontal heat turbulent diffusion, v~ - characteristic scale for the coefficient of vertical heat turbulent diffusion,

TO - characteristic scale for water temperature. Introducing nondimensional values

x=x/L, y=x/L, z=z/H,

Vx =

V

vx/v~, z = vz/v~,

follows:

T=

T/To; let us transform the terms we are interested in as V~

L2TO

a(_ aT) ax .

ax

V

x

Thus the comparative estimates of the considered terms is reduced to a comparison of values v~/H2 and v~/L2: characteristic scales of variables and functions for Lake Ladoga we have taken from the publications of Filatov (1983) V~

v~

L

H

5 ·10-3ms-1

102ms- 1

105m

102m


Sec. 2.3

75

Calculations give o

2= 5.10-7 H2

'

For Lake Onego similar estimates are of the same order of magnitude, despite the fact that Lake Onego is smaller than Lake Ladoga. Hence, for these lakes it is not reasonable to neglect terms describing horizontal diffusion of heat, since they do not differ considerably from the retained terms. For this reason, in the model of lake climatic circulation, equation (2.5) is used without modifications. In the model of large-scale climatic circulation of the ocean (Marchuk and Sarkisyan, 1980; Marchuk et al., 1987), in equations of motion nonlinear terms and terms describing horizontal turbulent impulse exchange are neglected. Such simplification of the motion equations for large stratified lakes can be justified, as was mentioned above, after comparative analysis of different motion equation terms for the dimensional-temporal scales of the waterbodies examined. Taking into account the evolution of large-scale dynamics elements over time, it is impossible to make this analysis universal. So, for example, in Lake Ladoga in summer during the period of developed stratification the difference between bottom and surface temperatures exceeds 15°C, and in autumn vertical homothermy is observed. The specific surface flow velocity in ice-free Lake Ladoga is about 10- 1 m, and under ice the velocity is less by an order of magnitude. The same considerations are true for the differences in other hydrothermodynamic characteristics for various parts of the lake. According to Filatov (1983), the coefficient of vertical turbulent viscosity in the upper layer is about 5 . 10-3 m2 s", as near the bottom its magnitude is around 5 . 10-5 m2 s:'. To justify excluding nonlinear terms and terms describing horizontal turbulent viscosity let us determine an order of Rossby and Ekman numbers (Sarkisyan, 1977)

where uo is the characteristic horizontal velocity, 1is the Coriolis parameter, Land H are characteristic values of horizontal and vertical linear scales, and k~, k~ are characteristic values of coefficients of horizontal and vertical turbulent viscosity, accordingly. For Lake Ladoga and Lake Onego, with the water surface free of ice, beyond coastal and the near-bottom boundary layers it is possible to consider as characteristic scales the following:

uo =

10-1ms-1 ,

Then we will get that

L= 105m,

1= 10-4 S-

1

,

H= 10m,

76


[Ch.2

This simple analysis shows, that neglected nonlinear terms in the motion equation and terms describing horizontal turbulent viscosity are small, compared with other terms of these equations. Besides, it follows from this statement that in the near-surface layer the known geostrophic relations (the balance between pressure gradient and Coriolis force (see, for example, Sarkisyan, 1977)) are not suitable even for rough estimations. As already mentioned, the magnitude 105 s, used as the characteristic timescale, equals the synoptic scale. Taking this value into account in the relative analysis of terms in the motion equation, we will find that the order of coefficients with derivatives in time is 10- 1, and that is why there is no reason to neglect them. For the near-bottom layer, during the period of developed stratification, dimension analysis shows that the Rossby number and the horizontal Ekman number are of the same order, around 10-3 • Thus the relative roles of nonlinear terms and terms describing horizontal turbulent viscosity change, but, as mentioned above, they are still small compared with the retained terms of the equations. A special treatment is needed for the coastal and near-bottom boundary layers. But the possibility of their reproduction in the frame of the general threedimensional computational model of the waterbody depends on the resolution of the grid used. According to estimates and velocity field observation data, the nearcoastal boundary layer in Lake Ladoga does not exceed several kilometres (not more than 10 km), and the near-bottom layer does not exceed several metres (Filatov, 1983, 1991). The rectangular grid used in the discrete model permits a grid size of about 2.5 km in the horizontal dimension. It is obvious that this does not allow correct reproduction of the coastal boundary layer. Insofar as grid steps along the vertical axis in the deep part have an order of tens of metres, then in fact the same situation takes place in the near-bottom boundary layer. It is worth mentioning that at the present time the authors use for computations a grid with 0.6-km resolution in the horizontal direction and larger number of steps in the vertical direction than in Astrakhantsev et al. (1998, 2003). This approach has improved modelling results. These aspects will be discussed more precisely when the modelling results are described. The remarks and plausible reasoning mentioned above make it possible to conclude that model selection for the reproduction of the climatic circulation of a large stratified lake is sufficientlyjustified. Further, when discussing the computation experiments we will once more return to the problem of model adequacy. 2.3.2 Mathematical formulation The equations of motion and continuity, where the deviation of pressure from atmospheric is replaced by the relation from the hydrostatic equation (2.3) in the following way:


Sec. 2.3

77

look like (2.19) (2.20) (2.21)

It should be emphasized that compared with equations (2.1) and (2.2) momentum terms and terms describing horizontal turbulent exchange have been neglected here. The Coriolis parameter I, is considered constant for the sake of simplicity. As equation of state one of the empirical relations such as

p = p(T), is accepted, where the dependency between density and pressure is not taken into consideration. For Lake Ladoga with depths not exceeding 230 m it is justified. For Lake Baikal in the model developed by Tsvetova (2003) the dependency between density and pressure is taken into account. As for the considered model, the following equation of state is used (Simons, 1973)

p(T) = Pw[1 - 6.8 . 10-6(T - 4)2],

[T] = DC.

(2.22)

The heat transfer equation in the climatic circulation model for lakes coincides with equation (2.5):

et a ( x aT) a ( y aT) a ( aT) at + u et ax + v et ay + W et az = ax V ax + ay v ay + az Vz az

(2.23)

Coefficients vx , vy, Vz in (2.23) and k z in (2.19)-(2.20) are considered to be the functions of variables x, y, z and t. For projection of the velocity vector the boundary conditions are the following:

k,

au I Bz

So

T

x

k,

Pw

wl so =

Q

av I Bz

So

T

y

(2.24)

Pw

a~

at'

(2.25)

where T x , T» are the horizontal components of the wind stress; on the bottom when z = -H(x,y)

k, P

I

= k;

U

+ V2,

C::I=k;

en- - Ven wi So = - U -, ax ay

2+V

(2.26) (2.27)

78


where

V=

r,

[Ch.2

r,

(U, V) is the vector of average depth velocities U=

~

u(x,y,z, t)dz,

V=

~

v(x,y,z, t)dz,

at the vertical lateral surface (2.28) where v" is the projection of the velocity vector onto the external normal to the lateral surface and VQ

0 in solid boundary points (no-flux boundary condition), = { prescribed values in inflow and outflow river sites.

The boundary conditions for T (x, y, z, t) here are determined in the same way as for equation (2.5); these are conditions (2.14), (2.16) and (2.17). For further convenience we will repeat them: on the waterbody surface at z = 0

aT I

aN

= _1_

cpPw

So

Q

(2.29)

'

on all solid boundary and in sites of outflowing rivers

aTI aN

(2.30)

=0, SOUl

at locations of outflowing rivers

[~~- vnCT- Tn)] Iso =

(2.31)

O.

2.3.3 Realization of the model In this section we will discuss some aspects of the mathematical model important for the development of the discrete model (Astrakhantsev and Rukhovets, 1993). First of all it should be mentioned that equations

v

wl so=

div = 0,

a~ Q

at'

wl S2 =

-u

en en ax - v By '

are equivalent to equations divv= 0,

en- - Ven wi S2 = - U -, ax ay

(2.32)

In fact, averaging (integrating) the continuity equation along the z axis in a range from -H(x,y) to 0, we will get the equality

r .- r r -H

a dlvvdz=-a X

-H

a udz+-

aY

-H

vdz+wl so -

(aH )I "»:X + ven aY- +w S2,


Sec. 2.3

79

from which this equality follows. It is worth noting here, that instead of using the boundary condition (2.25), equation (2.32) eliminates the need to comply with two boundary conditions for w (at the surface (2.25) and at the bottom (2.27)). Such a necessity arises from determining w from the continuity equation, as is common in geophysical hydrodynamic models. Using equations (2.32) along with equations (2.19), (2.20) and boundary conditions (2.24), (2.26) and (2.28) makes it possible at every time-step, assuming that function T(x,y, z, t) is known, to formulate the closed mathematical problem for defining U, V and e. Actually, let us average equations (2.19), (2.20) and boundary conditions (2.28) by z within limits from -H(x,y) to 0, applying boundary conditions (2.24) and (2.26). Then for determining U, V and ~ we will get the following system of equations 8_

at

fV

+ g W = _ h jUV+~_-L( f8PdZdz',

ax

H

Hpw

Hpw

J-H z ax

(2.33) Q

8(, + 8(HU)

at

+ 8(HV) =

ax

ay

0

and boundary condition 1 V1aso = Va == H

r-H

(2.34)

vnl S1 dz.

Boundary conditions (2.26) at the waterbody bottom, used for receiving the system (2.33), (2.34), represent the well known simplest parameterization of waterbottom friction (Stommel, 1963). Such parameterization in the linearized representation was used in Marchuk and Sarkisyan (1980). Boundary conditions (2.26), naturally, are quite a rough parameterization. In computer experiments to reproduce the climatic circulation of Lake Ladoga (Astrakhantsev and Rukhovets, 1988) parameterization by local velocities was used, for example, at the bottom, the following boundary conditions were imposed

Kz

;U!

=

J/ +

Kz

t!

=

+ v2 .

(2.35)

We will point out, that equations (2.19), (2.20) seemingly do not require the definition of boundary conditions (2.28) at the vertical lateral boundary because (2.19) and (2.20) do not contain derivatives of functions u and v with respect to variables x and y. Nevertheless, the condition (2.28) is necessary if we want heat and mass conservation laws to be met. The selection of the boundary condition (2.31) at inflowing rivers is related to the fact that in the discrete model is easier to impose boundary conditions of the second and third type (natural boundary conditions) and also because, when condition (2.31) is used, it is possible to reproduce accurately in the discrete model the law of heat variation. If we keep in mind the real values of vx , vy, vz , then it easy

80


[Ch.2

to understand that boundary condition (2.31) can be interpreted as an approximation by a penalty method of the conventional boundary condition imposed at inflowing rivers

Tlsin 2.3.4

=

r;

Generalized formulations of the mathematical model

To build a discrete (numerical) model approximating the original mathematical model the authors turned to the generalized formulation of the initial model in the form of integral equations equivalent to the original equations. This approach is rather traditional. It dates back to works by Courant et al. (1940) and Ladizhenskaya (1970). For the equations of geophysical hydrodynamics this approach was used in the works ofPenenko (1981), Astrakhantsev and Rukhovets (1986) and others. This approach is also used when discrete models are built using the finite element method. Heat distribution equation

Multiplying equation (2.23) by an arbitrary differentiable function (x,y, z, t) and integrating the obtained equality over the domain n, after the integration by parts of higher derivatives and taking into account boundary conditions (2.29)-(2.31), the following integral identity is obtained

et

J8icI>dO fl

= -

J( fl

Vx

et a

et a

et a dO + --i- J Q dS ax ay Bz cpPw n

So

+ Lin vo(T- Tr)cI>dS,

(2.36)

dO = dxdydz.

Law of heat variation in a waterbody

Assuming that in this identity == 1 and integrating by parts the convective terms, we will get the equality a J Tdn=J TdivVdn-J v"TdS+J Vo(T-Tr)dS+--i-J QdS. at n n an Sin cpPw So By virtue of boundary conditions after the multiplication by c;Pw this equality will take the form:

J

: c;Pw Tdn = t n

J Q dS - c;Pw J voTdS - c;Pw J voT dS - QC;Pw J ~~t TdS. So

r

SOUl

Sin

So

(2.37) It is generally agreed to call this equality the law of heat variation.


Sec. 2.3

81

Momentum equations Momentum equations (2.19), (2.20) correspond with the following integral identities:

J lv

J at o

au dO -

J

J Pw dS Bz Bz - gJo aa~x dO + k2 J uJU2 + V2

dO = -

0

0

k, au

a dO +

T

x

So

S2

Jax cI> dO, J k, avBz awBz dO + J Pw W dS

x cos(n, z) dS -

J avat w + J luw dO

o

dO = -

0

af

fl

T

0

(2.38)

y

So

-gJo =~WdO+k2J Y x cos(n, z) dS -

J fl

S2

VJU2+ V2w

af ay "I]!dO,

(2.39)

where , Ware arbitrary differentiable functions. The derivation of these identities is similar to that of the heat distribution equation. Law of mechanical energy variation Let the deviation of a pressure from atmospheric be represented in the form:

gpw(~ - z) + g

p =

f

p'dz' == -gpw z

+ P',

p' = p - Pw·

It should be noted also that in equalities (2.38) and (2.39) functions can be rewritten as follows

af = ~ ax ax

(.!-fp' dZ)' Pw

af = ~ ay ay

z

cr- dZ). Pw

Substituting into the identities (2.38) and (2.39) as and

u =

u =

Pw U ,

af/ax and aflay

z

w

Pw v

After the identical rearrangements, integrating by parts, and taking into consideration continuity equation and boundary conditions for w, the following relation is derived

ata Pw

J u2 + v2 0 --

2

J -oj

+

(TxU

So

So

dO = -Pw

J fl

+ TyV) dS - k2pw

p,a~ dS -

at

J

SinUSout

k,

[(00)2 az + (av)2] az

dO -

J' fl

J (uU + vV)JU2 + V2 dS S2

P'vndS.

gp wdO

82


[Ch.2

r

Let us replace pI in this equality with the formula

r' in the integral, containing

ata

[J

a~/at.

= gpwf.

+g

(2.40)

p' dz'

We come to

2

u + v2 n Pw - 2 - dO+a

J gPw"2~2] dS So

J (TxU + TyV) dS - k2pwJ (uU + vV) JU2 + V2 dS - J r'v; dS. +

So

SO

(2.41)

Sin US out

This mathematical relationship describes variations of the mechanical energy of horizontal movements. Further, we will call this relation a law of mechanical energy variation (conservation). This law is one of the characteristics of our model of climatic circulation in a stratified lake. Let compare this law with the other one for the model formulated in section 2.2.2. We will write it down without going into the details of its derivation,

+ v2 ~2] ata [Jn Pw -u 2 - dO + a J So gpw "2 dS 2

= -

In

-J

n

+

pw{ k x

[

(=:Y (=:Y] +

+ ky

[

(=;Y (=;Y] +

gplwdn+J (UTx+VTy)dS+J

J.

~U~~

So

Pw ( : u; + : ; vr ) dS -

+ k, [

(~:Y + (=:Y] }dO

Pw u;;v; vndS Sin U S out

J.

~U~t

r's; dS - a

J Po u ~

2 ;

v2

~; dS. (2.42)

Skipping the details due to differences in boundary conditions at the bottom of the waterbody in compared models, we compare only the terms describing dissipation: at characteristic scales of horizontal velocity uo = 10- 1 m s", linear horizontal dimension of the waterbody L = 105 m, and average depth of the waterbody 50m, we will find that the dissipative terms absent from (2.41) are by at least two order of magnitude smaller than the present dissipative term. Laws of heat and mechanical energy variation (2.37) and (2.41) for the model of climatic circulation practically coincide with the analogous relations for the 'full' model described in section 2.2.2, despite the fact that the equations of climatic


83

circulation were obtained by simplification of the 'full' model equations. The similarity of these laws is one of the confirmations of the physical adequacy of the model of climatic circulation in a waterbody to represent reality. 2.3.5 About the discrete model For the computer realization of a climatic circulation model of a large stratified lake a discrete model was developed by the authors and an algorithm for computation was suggested (Astrakhantsev and Rukhovets, 1986, 1993; Astrakhantsev et al., 1998, 2003). The first finite-difference models of large-scale ocean dynamics originate in the publications of Sarkisyan (1977), Bryan (1969) and Marchuk and Sarkisyan (1980). As has already been mentioned, by the present time a lot of computational algorithms have been developed for the realization of three-dimensional mathematical ocean circulation models. Here only the work previous to the authors' discrete model will be mentioned. This is the study ofPenenko (1981), where discrete models for the approximation of hydrothermodynamic models of the atmosphere are constructed by the method of sum approximation. The same method was used for the construction of the Lake Baikal discrete model (Tsvetova, 1977). The first discrete model for the reproduction of the climatic circulation of large stratified lakes was constructed by the authors using the method of sum approximation of the integral identities (2.36), (2.38), (2.39), representing generalized formulations of mathematical model equations (Astrakhantsev and Rukhovets, 1986). On the basis of this model the annual climatic circulation of Lake Ladoga was reproduced (Astrakhantsev et al., 1987; Astrakhantsev and Rukhovets, 1988). Later Astrakhantsevand Rukhovets (1993) developed a discrete model; its computer realization was completed only in 1999 (Astrakhantsev et al., 1998). This model is used at present in the authors' studies of Lake Ladoga and Lake Onego dynamic modelling (Astrakhantsev et al., 2003; Rukhovets et al., 2006c). The creation of discrete models usually starts with decomposition of the mathematical model into separate blocks such as, for example, equations of motion, heat transfer equations and others. The capacity of sufficiently powerful computers allows us to solve the problems only on grids for which, strictly speaking, it is not always possible to confirm that discrete models at full scale adequately reproduce the 'behaviour' of mathematical models. That is why it is especially important to require from discrete models the correct reproduction of the main qualitative and quantitative properties of the models. As has been mentioned by many authors during the development of discrete models, it is desirable to obtain the following objectives: - implementation of the main relationships between the blocks of the discrete model and the blocks of the mathematical model; - implementation for the discrete model of the laws of conservation (variation) discrete analogues of mathematical model conservation laws which should be implemented precisely, for example, with round-off error precision, not with approximation error precision.

84


[Ch.2

These statements are especially important in the development of long-term computational models. The sum approximation method used by the authors first allowed us to develop schemes for three-dimensional approximation on a minimal seven-point pattern; secondly the approach selected by the authors allowed us to reproduce in discrete form the main properties of the initial mathematical model, such as heat transfer, mass conservation, mechanical energy changes of horizontal motion and others. For the Navier-Stokes equations difference schemes with the feature of convective terms neutrality were constructed by Ladizhenskaya (1970). The authors used this approach for the construction of the heat transfer equations scheme. Further details concerning the discrete model developed by the authors and the methods of its construction can be found in (Astrakhantsev et al., 2003).

3 Climatic circulation and the thermal regime of the lakes

3.1 THE CLIMATIC CIRCULATION IN LAKES LADOGA AND ONEGO FROM OBSERVATIONAL DATA AND ESTIMATES The definition of 'climatic circulation' for large stratified lakes has already been given in the previous chapters. Let us briefly discuss the climatic circulations of Lake Ladoga and Lake Onego characteristics on the basis of observations and empirical calculations (Hydrological Regime . . . , 1966; Tikhomirov, 1968, 1982; Demin and Ibraev, 1989; Filatov, 1983, 1991; Lake Onego, 1999). The lake water mass dynamics depends on various factors. Firstly, there is the influence of atmosphere - roughness, friction resistance on the water surface, heat exchange through the water surface (cooling or heating), moisture exchange (precipitation and evaporation). The nature of the dynamic and thermal processes is also defined by the morphometry of a lake and the river runoff (tributaries inflow and outflow). Atmosphere-water interactions, heat flux, tributary inflow and outflow generate density stratification and, as a result of water temperature distributions, create water currents. Lakes Ladoga and Onego are both dimictic. In autumn and spring vertical homogeneity is observed in the lakes. In spring, after ice melting, the upper layer heating starts. As the maximal density of fresh water is observed, when the water temperature is nearly 4°C, convective mixing arises as a result of heating. Gradually it reaches the bottom, as in winter, both in Lake Ladoga and Lake Onego, water temperature is lower than the temperature of the maximum density (in winters with fractured ice cover, the water temperature near the bottom in Ladoga goes down to 2°C (Tikhomirov, 1963)). Water column mixing takes place for the second time during autumn cooling. Lake Ladoga

When the water temperature in spring exceeds 4°C, vertical stratification starts to develop in the lake. At that time heating increases hydrostatic stability. Wind-mixing

86

Climatic circulation in Lakes Ladoga and Onego

[Ch.3

results in the formation of an upper mixed layer (epilimnion) and a thermocline (metalimnion) below it. It is worth noting that twice a year, as already noted, the mixed layer reaches the bottom. In the ocean, unlike in lakes, the salinity stratification prevents the penetration of the mixed layer to great depths. Vertical stratification reaches its maximum development by the end of summer. A massive dome of cold water with a temperature of about 4 DC is formed in the bottom layers (hypolimnion). Autumn cooling destroys stratification. Inverse stable stratification is built up in winter. The temperature gradients during this period are small, the amplitude of temperature fluctuations is within the interval 0-4 The thermal bar is an important phenomenon in the lake and is related with horizontal stratification (Tikhomirov, 1963). In spring, after ice melting, the heat flux to the waterbody can be considered with reasonable accuracy to be homogeneous over the whole surface. That is why shallow coastal waters are heated more strongly than the deep part of the lake. Due to temperature stratification in the 4 C isotherm area, are intensive downwelling flux of 'dense' water is formed (Tikhomirov, 1963, Zilitinkevich and Terzhvik, 1989; Zilitinkevich et al., 1992). The frontal zone generated by this flux is called a thermal bar, as already mentioned in Chapter 1. In the heating process the 4 DC isotherm moves farther from the coast to the deep part of the lake until the water temperature exceeds 4 C. According to observations (Tikhomirov, 1963, 1982) the speed of thermal bar movement in Lake Ladoga is on average 0.15kmday-l, sometimes reaching 0.6kmday-l. The thermal bar substantially influences the flow field. Its front divides the lake into two parts almost without horizontal exchange between them. The thermal bar exists in Lake Ladoga for 2.0-2.5 months (from the end of April till the middle of July). It is worth mentioning that the thermal bar plays an important role in the transfer of substances coming into the lake via tributaries and surface runoff. Thus all incoming substances are concentrated in the coastal zone while the thermal bar is in existence. A brief description of water-temperature variability in Lake Ladoga given here and in Chapter 1 shows that it is significant in both the vertical and horizontal directions. That is why the application of one- and even two-dimensional models to reproduce the temporal dynamics temperature field is rather problematic. The problem of water-temperature field reconstruction and its evolution, as mentioned by a number of researchers, is in fact the only large-scale dynamics issue that can be reliably verified since water temperature is measured almost regularly. It is also true when considering large lakes. Lake Ladoga according to Tikhomirov (1982) 'is a classical water object, where fully and clearly thermal structures are revealed'. A vast experimental database has made it possible to compare modelling results and observations, both qualitatively and quantitatively. It is worth mentioning that reproduction of annual thermal dynamics for Lake Ladoga using a numerical model was performed for the first time by Astrakhantsev et al. (1987) and Astrakhantsevand Rukhovets (1988). Large-scale circulations in Lake Ladoga have not been studied as well as the thermal regime, in spite of long-term research. The results of experimental studies, summarized in the book Hydrological Regime and Water Balance of Lake Ladoga (Malinina, 1966) give an impression of the large-scale circulation in spring, summer DC.

D

D

Sec. 3.2]

On the problem of simulating climatic circulation

87

and autumn (partly) periods. Late autumn and especially winter circulation in Lake Ladoga, as in many other large lakes, is not well known. An intensive cyclonic circulation during the open water period is observed in Lake Ladoga, as in other large stratified lakes in the northern hemisphere (Okhlopkova, 1966; Filatov, 1983, 1991). A deep understanding of the large-scale circulation in Lake Ladoga was achieved using mathematical modelling. Computations of currents were reported in the following publications: Okhlopkova (1966) and Filatov (1983, 1991). In the pioneer work of Okhlopkova (1966) density currents were calculated by a dynamic method using the data of thermal observations during spring, summer and autumn. The results of current simulations presented by Filatov (1981, 1991). In these publications, full three-dimensional models of geophysical hydrodynamics in diagnostic version were used to compute flow fields in Lake Ladoga. Lake Onego

As has been mentioned, Lake Onego is smaller than Lake Ladoga and located to the northwest of Lake Ladoga. Nevertheless the general characteristics of temperature field evolution are similar to those of Lake Ladoga. Later in this chapter were present annual climatic circulation calculation results for Lakes Ladoga and Onego obtained with the computer models formulated in mathematical terms in section 2.3. This chapter content is based on the authors' works (Astrakhantsev et al., 1998, 2003; Lake Onego, 1999; Rukhovets et al., 2006d).

3.2 ON THE PROBLEM OF SIMULATING CLIMATIC CIRCULATION To reproduce the climatic circulation the numerical periodic solution of the mathematical model (2.19)-(2.31) with a period equal to one year should be found. It is natural to assume that all external forcing periodic functions of time with a period equal to one year, i.e. cp(x,y, z, t + 1 year) = cp(x,y, z, t). In order to build the periodic solution, as is usually done, the initial conditions for v and T should be given: vlt=o = Vo = (uo(x,y,z), vo(x,y,z), wo(x,y,z)), 11t=o = To(x,y,z),

(3.1)

and then the initial boundary value problem (2.19)-(2.31), (3.1) has to be solved until we get a periodical solution. To get the periodical solution of the problem (2.19)-(2.31) let us introduce denotations: Vp = (up, vp, wp), Tp . In this case it is essential to estimate the physical time needed by the system to obtain a periodical regime. It is natural, that T ---+ Tp , ---+ p at t ---+ 00, that is why a 'transition time' here means a time interval after which the differences between T and Tp , vand vp are already small.

v v

88


[Ch.3

It is understandable that to estimate this time interval is not simple. Let us confine ourselves to an elementary estimate of the time interval to get the periodical solution of the mean water temperature value of the waterbody:

Tn(t) =

me~(o)

In

T(x,y, z, t) dO

(3.2)

According to the heat transfer mechanisms in the waterbody (2.37) for difference 8 == T - Tp we will get an equation

~J 8ds=-J dt 0

vQ8ds.

SOUl

When the right-hand side of this equation is replaced by qr80, where qr == VQ mes(Sout) - a discharge of outlet river and

8n(t) =

me~(o) In 8 dO.

As a result the following ordinary differential equation is obtained: d qr -80=---80·

dt

mes(!1)'

its solution has the following form:

80(t) = 80(0) e-q,t/mes(O). These simple discussions show, that the time interval for getting the periodical regime for the value To, with reasonable accuracy is defined by the lake waterexchange period. If we will take into consideration that Lake Ladoga's volume equals approximately 908 krrr', and the annual discharge of the Neva River is 74 krrr', then the water-exchange period for Lake Ladoga is about 12 years. The waterexchange period in Lake Onego is the same - approximately 12 years. Thus, the physical time for the computation period should be not less than 12 years. Two obvious remarks should be made here. First, it follows from the above elementary reasoning that the right choice of initial conditions accelerates transition to the periodical regime; second, the magnitude of mes(!1)/qr may, in fact, differ considerably from the period of water exchange in the lake. This problem will be discussed below more precisely in connection with the problem of admixture diffusion. If a waterbody is closed, the periodical regime for To is always true, as (T - Tp)o = const. For a closed waterbody, Tp(x,y, z, t) in the problem (2.19)-(2.31) is defined with accuracy up to constant. To get an estimate of the nonlinear initial boundary problem solution (2.19)(2.31), (3.1), convergence to the periodical problem (2.19)-(2.31) solution is demanding. For the complete ocean dynamic linear model solution, stabilization rates are obtained, which are equivalent, due to linearity, to the transition rate to the periodical regime (Marchuk and Sarkisyan, 1980). For the nonlinear model (2.19)(2.31) we will confine ourselves to simple considerations to help us in estimating the time needed to adjust the temperature field to a given periodical in time velocity field

On the problem of simulating climatic circulation

Sec. 3.2]

89

at periodical boundary conditions for the heat diffusion equation. As an example we will discuss the problem for 8 = T - Tp • a8

7ft =

&8 a8 k x ax2 - u ax' 8lx=o

u > 0,

= 0,

0 ~ x ~ Lx,kx = const,

= a81 x x=L x

8

(3.3)

0,

81t=0 = To(x),

(3.4)

where To(x) is a given function. The transition time for the solution of the problem (3.3)-(3.4) to a period is a time of the problem solution convergence to zero. The problem (3.3)-(3.4) can be described as heat diffusion in a channel, where the initial temperature distribution is given, and liquid (water) moves along the channel axis with a speed u = const. Here we assume that density variations do not affect the dynamics of the fluid. Let solve the problem (3.3)-(3.4) explicitly. By introducing a substitution 8(x, t) = e(u/2kx)xTJ(x, t), we will get for TJ(x, t) the problem 8T] a2 TJ 8t = k x 8x 2 TJlx=o = 0;

(k x

-

u2 4kx'TJ

(3.5)

=~ + ~ 'TJ) 1_ = 0 x-Lx

TJI t=O = e-(u/2kx)XTo(x).

(3.6)

Using the Fourier method we can find that

where

Vn

are the roots of the equation 2k x tgv=--v. uLx

Since, usually ul.; » 2k x , then it is simple to find first several roots: VI ~ 7f, vz ~ 27f. Coefficients TJn are Fourier coefficients of the function e-(u/2kx)xTo(x). It is obvious, that

II e-(u/2kx)x8(x , t) II L2(O,Lx)

=

x)t x)x 11'.11(x / ' t) II L2(O,Lx) < - e-(,} /4k II e-(u/2k T,o(x)II L2(O,Lx)

From this we can get an estimate Lx 11 81Ii2(o,Lx ) = 0 8 2(x , t) dx :::;

J

118 e(u/2kx )xIIL 2(o ,L x ) 118 e-(u/2kx )xIIL x (o,L x )

< e-(,}/4kx)tll e-(u/2kx)xT, (x) II x max Ie(u/2kx)xI 11811 0 L2(O,Lx) O:5x:5L L2(O,Lx) x x)t+(u/2kx)Lx ~ e-(,} /4k 11 81I L2(o,Lx ) II To(x) II L2(o,Lx ) ·

90


[Ch.3

1181IL2(O,Lx)' we will get < e(u/2kx)Lx-(zil/4kx )t llT, (x) I . 0 L2(O,Lx )

By dividing both parts of this inequality with

(3.7) 11 8 11L2(O,Lx ) The estimate (3.7) at t < 2Lx /u at first glance, permits 1181IL2(O,Lx) not to diminish, but this is not correct because of the following energy estimate 2 ~ dt 118L2(O,L < 0 x) -

•

It can be easily obtained, multiplying (3.3) in scalar form by 28 and integrating by parts:

:t

I e IlL =

-

J:2 2k (=~) x

2 dx

-

ue (L x , t) < o. 2

It is worth noting that estimate (3.7) at t < 2L x /u makes it possible for 1181IL2(O,Lx) to diminish slowly. And it should be stressed also, that at t < 2Lx /u for 1181IL2(O,Lx) is guaranteed the diminishing along the exponent (3.7). The results of this example can be interpreted in the following way. The value Lx/u for a channel is equal to mes(!1)/q, where mes(!1) is the water volume in the channel, and q is the discharge though the cross-section of the channel, so that the value mes(!1)/q is the time for water exchange in the channel. Thus, there are some reasons to assume that with reasonable accuracy the transition time of the temperature field to velocity field in Lake Ladoga differs not more than several times from the water-exchange period in water body. The transition-time problem of velocity field to the given periodic temperature field will be dealt with again. The stream function equation in the model with upper surface boundary condition (2.25) at Q = 0, i.e. 'rigid lid' condition, will be used. Introducing stream function W with the formulae 18w

U = H By '

18w

V= - H

ax '

(3.8)

out of (2.33), (2.34) the following boundary value problem for determination of of w will be derived:

(3.9)

o < s < L, where L is the length of 8So.

(3.10)

Setting of external forcing

Sec. 3.3]

The equation (3.9) will be simplified by replacing IVwl/H = VU2 Vs = (Us, Vs) and

IVsl, where

Us=

~S)J U(x,y,t)dxdy, 0 So

Vs=

mes

(1

8

+ 8y

- [8 = -k2l Vsl -

(1

8 Con is the zooplankton growth rate. The term ZR is the excretion rate of nitrogen and phosphorus mineral forms by zooplankton in the process of metabolism. This magnitude was calculated in the model of Menshutkin and Vorobyeva (1987), according to Gutelmacher (1982), in proportion to wastes from metabolism. Detritus supplies are refilled from phyto- and zooplankton dying, and from nondigested nutrition, that is reflected in the expression for the term Des: (6.8) where U is the coefficient for nutrition digestion by zooplankton, En is the rate of detritus grazing by zooplankton. The transformation of detritus into dissolved mineral form as the result of bacterioplankton life activity is considered in equations (6.3)-(6.6) with terms Rn and RN representing the transformation rate of phosphorus and nitrogen from detritus to dissolved form. In equation (6.7) term hAProd describes the oxygen flux in water as a result of photosynthesis, and other terms describe oxygen consumption in zooplankton respiration and detritus destruction. It is assumed in the model that the composition of elements of the phyto- and zooplankton biomass is unchangeable and such that C:N:P=40:10:1. It is supposed that 1mg of raw biomass contains 2.5 ug of phosphorus, 25 ug of nitrogen and 100 ug of carbon; then determination conversion coefficients for phosphorus and nitrogen quantity in the phyto- and zooplankton biomass can be added kp = 2.5 ug Prng"! of raw biomass, k N = 25 ug N mg" of raw biomass.

The following measurement units for substances were set in the model: [A]=mgl- 1,

[Z]=mgl- 1,

[DP] = JlgPI- 1,

[P]= JlgPI- 1,

[DN] = JlgNI- 1,

[N]= JlgNI- 1

[OX] = mg l"

While constructing the model it was assumed that in each elementary grid cell in the ecosystem model the balance of phosphorus and nitrogen is valid if transport processes are neglected. These natural requirements are formulated as the equalities (see (5.4)):

+ Z) + DP + P = const, Ntotal == kN(A + Z) + DN + N = const. Ptotal == kp(A

(6.9)

The form of terms in (6.1)-(6.6), describing the transformation of substances, requires the validity of the following equality Ep

+ En

- con = 0,

(6.10)

Sec. 6.3]

Ecosystem model for Lake Onego, based on the turnover of biogens

191

that arises as a necessity of the correctness of equation (5.5) with the respect to the considered model. Fulfilment of (6.10) on the basis of present knowledge about the modelled processes cannot be guaranteed. That is why, to satisfy (6.10), the description of the processes was simplified in the model. The meaning of equality (6.10) is that zooplankton nutrient consumption consists of phytoplankton and detritus. Due to this fact the description seems to be appropriate. It is impossible to satisfy the equation; all its terms are derived independently. That is why, in the model of Menshutkin and Vorobyova (1987), all terms were constructed in such a way that equality (6.10) was valid. The construction of the model (6.1)-(6.6) was carried over from that of Menshutkin and Vorobyeva (1987) and was formulated as a system of partial differential equations. Boundary conditions

Boundary conditions for the system of equations (6.1)-(6.7) are applied in compliance with boundary conditions for system (5.1). At the waterbody surface So as z = 0 fluxes of substances A, Z, DP, DN, P and N are prescribed; these are conditions (5.6). At the waterbody bottom, as z = H(x,y) and there is a solid vertical boundary for all substances except OX, boundary conditions (5.9) are applied. At tributary sites, Sin and at outlet sites, Sour, boundary conditions (5.8) and (5.9) are used respectively. Boundary conditions for the equation (6.7) are applied in the following way. At the waterbody surface z = 0 the condition Vz

aox = &

*

rno(OX - OX)

(6.11)

describes oxygen exchange at the water-atmosphere interface, where rno is the aeration coefficient, OX* is the saturation oxygen concentration in water, [OX] is the dimension of OX in mg OXI- I . The value OX* in grid cells is calculated using the well-known empirical relation (Vavilin, 1983): OX* = 14.61996 - 0.4042T - 0.0842T 2

-

0.009T 3 ,

where T is the water temperature in Celsius degrees. According to Vavilin (1983, p. 133) the re-aeration coefficient rno varies within the range 0.2-1.25 day ", At the waterbody bottom z = -H(x,y), the boundary condition for 16 is given as follows:

aox aN

=kb OX .

(6.12)

This boundary condition is determined by processes of oxygen consumption and release in bottom sediments. The value of coefficient k b is defined in the model on the basis of measurements data provided to the authors by Ignatyeva (1997). At tributary sites the boundary condition for OX can be given in the form (5.8), and (OX)r

==

OX*(Tr),

where T, is the given water temperature at the tributary site.

192

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

For model realization in the case of Vx = v y = 0 at tributary sites for DP, DN, P, N and OX, the boundary condition (5.10) is used, and at outlets no boundary conditions are applied for any substances. For phyto- and zooplankton at tributary sites, two versions of boundary conditions were used, either (5.10), or (5.11). Variation laws

For Ptotal and Ntotal, due to the fact that when (6.10) is true (6.9) is also correct and variation laws (5.12) are valid, we will present only the variation law for dissolved oxygen, since boundary conditions for OX differ from boundary conditions for other substances. For example, the law of variation in the concentration of OX has the following form:

:t JOXdn=J mo(OX*-OX)dS-J kb OX d S -J v,,(OX)r dS - J v"OXdS n

~

~

Sin

+

In

SOUl

[hAProd - hzzr - hDPRp - hDNRN] dO.

(6.13)

Discrete analogues of the variation laws for Ptotal, Ntotal and OX were used in computational experiments to control the simulation results. 6.3.3

The discrete model

The discrete analogue of the formulated mathematical ecosystem model, except for the biotic block, was built in section 5.3. The construction of the biotic block is a particularization of equations (5.16). Biotic block of the model

II:j;

Variations of every substance concentration in the cell during the time-step h, from the moment t to t+h t are written as (see (6.1)-(6.7)): .6.A

== h t( -mpA + Prod -

Ep),

.6.Z == ht(-mzZ + U· Con - ZR), .6.DP

== ht(kpDes -

== h t( -kp(Prod -

.6.N == ht(-kN(Prod -

(6.15) (6.16)

Rp),

.6.DN == ht(kNDes - RN), .6.P

(6.14)

+ Rp), ZN) + R N),

ZR)

.6.0X == ht(hAProd - HzZR - hDPRp - hDNRN).

(6.17) (6.18) (6.19) (6.20)

Sec. 6.3]


193

The dependencies of coefficients mp , m, and coefficients, in terms Prod, Con and Des, used in (6.14)-(6.20) on temperature and solar radiation in many cases are formulated as piecewise linear functons (Menshutkin and Vorobyeva, 1987), which in practice approximated curves with saturation. Curves with saturation gained acceptance in the description of the abovementioned relations - Michaelis-Menten equations (Bierman and Dolan, 1981). Further, all piecewise-linear functions are given using the standard template YI, f(X,XI,X2,YI,Y2)

=

YI { Y2,

when x < Y2 - YI

+ X2 -Xl when

Xl,

(X -

Xl),

Xl

~

X

~

X2,

(6.21)

> X2·

X

The definition of primary production, Prod, begins with calculation of the growth coefficient P/B using the following formula (6.22) where dependence of P/B on the following factors is reflected: water temperature T, solar radiation (illuminance level), mineral phosphorus and mineral nitrogen concentrations, and also phytoplankton concentration. The equality (6.22) is based on Liebig's Law of the minimum law (Bierman and Dolan, 1981), according to which controlling is the most limiting factor. Sometimes to determine primary production the minimum operator is replaced with a multiplication operator (Jorgensen, 1976; Di Toro, 1976; Leonov et al., 1991). Each of the coefficients in the right-hand side of (6.22) is defined using functions in the form of (6.21): P/B T = f(T, T min, Tmax, p/B¥n, p/B¥n, P/B Tax), P/Bs = f(S, 0, Smax, 0, P/B ax),

s

P/Bp = f(P, 0, P max, 0, P/Brpax), P/BN = f(N, 0, N max, 0, P/B Nax ), P/BA =f(A,O,Amax, P/B ax, p/Btfn).

(6.23)

s

Specific values of parameters in formula (6.23) are derived on the basis of observations (Petrova, 1982; Modern State . . . , 1987) and multiple investigations (Vinberg, 1960; Gutelmacher, 1988). As is stressed by Menshutkin (1993) the introduction of production rate dependency on temperature requires caution, because the phytoplankton community reacts to water-temperature variations, not by production decline but by changes in species composition: warm-loving species are replaced with cold-loving and vice versa. This note is important for understanding the factors affecting the phytoplankton succession. Later on we will return to this remark. The dependence of production rate on solar radiation takes into account the elevation of the Sun at all times at the latitude of Lake Onego.

194


[Ch.6

Naturally, the production rate is controlled by biogen concentrations and also by phytoplankton concentration. In (6.23) the following values of parameters are used:

P/B ~x = 2 day ",

s

Smax = 220,

P/B ax = 10 day" ,

P max = 23 ug PI-I,

P/Bpax = 2 day ",

N max = 120 JlgNl- 1,

P/B Nax = 2 day ",

Amax = 0.5 ug 1-1,

p/Btfn = 1.2day-l.

Then the growth of biomass during time-step h, is defined as

htProd = min(ht/B x (A

+ Amin) x PL, P x PL/kp,N x PL/kN ) .

(6.24)

Here the value Amin = 0.05 Jlg- 1 is introduced in order to avoid zero values of A; otherwise the process of primary production growth will never start. It is supposed that phytoplankton generation takes place only in the near-surface layer with a depth of PL', where enough light penetrates. The coefficient PL in (6.24) determines the part of the elementary cell where photosynthesis occurs, i.e. the part of the cell volume above the depth PL': 1,

(PL)ijk =

if IZk - hk-l(Z)/21

< PL'

0, if IZk - hk(Z)/21 < PL' -PL' + IZk + hk(Z)/21 (hk - 1(Z) + hk (z))/2 .

(6.25)

The thickness of the photosynthesis layer PL' is controlled by water transparency, which, in turn, besides the background value, also depends on shadowing effect of phytoplankton and detritus:

PL' = f(A

+ DP/kp, Sesmin, Sesmax, Lmax, Lmin),

(6.26)

where Sesmin = 1 Jlgl- 1, Sesmax = 8 Jlgl- 1, Lmax = 8m, Lmin = 2m. Mortality coefficients mp and m, are defined in the following manner: mp =

f(A, A min , Amax, mpin, mrpax),

Amin = 2 ug 1-1, Amax = 8 ug 1-1, mpin = 0.1 day",

mrpax = 0.98 day "

(6.27)

and (6.28)

Sec. 6.3]


195

where

m~ = f(T, T~n' T~ax, mfmin' mfmax), T~n = 2.2°C,

T~ax = 3.9°C,

mfmin = 0.05 day",

mfmax = 0.1 day-I.

(6.29)

Phyto- and zooplankton mortality was assumed to dependent on their own concentration. With increase of concentration the mortality grew up to a certain limit value. For zooplankton in coefficient m, its mortality in summer and autumn months was taken into account due to intensive preying on planktonic crustaceans. The zooplankton biomass growth is defined in the model as follows: (6.30) U . Con = U x TK x (Z + Zmin) xf(PD, Fmin, Fmax, 0, Con max ) where U = 0.75 is the coefficient of nutrient assimilation by zooplankton; TK is a non-dimensional coefficient; TK = f(T:mn' T~ax, TKmin, TKmax),

T:mn =

2°C,

T~ax = 22°C,

TKmin = 0.43,

TKmax = 2.3;

(6.31)

Zmin = 0.05Jlg1-1 has the same meaning as Amin; PD = A

+ h, Prod + Det,

(6.32)

Det = min(DP/kp , DN/kN ) , F min = 0.2 ug 1-1,

F max = 0.8 ug 1-1,

Con max = 0.7 day":

(6.33)

The dependence of phytoplankton growth on nutrient concentration PD was defined as threshold value (0.2mgl- 1) and saturated (0.8mgl- 1) concentration. Below the threshold value the feeding stopped, and above the saturated value filtration for feeding became constant. Variation of zooplankton feeding needs with temperature change is included using the correction factor TK. According to (6.32) detritus is a part of nutrients; Det is the died-off biomass of phyto- and zooplankton. It is worth mentioning that in the model DP and DN are variables determining the amount of organic phosphorus and organic nitrogen in detritus. In this model, as in many others, the invariability of elementary phyto- and zooplankton biomass composition is assumed. The application of this assumption concerning detritus is justified by the aim to reduce the number of parameters for ecosystem description. The determination of detritus concentration using formula (6.33) and of light absorption using formula (6.26) is sufficiently conventional.

196


[Ch.6

The variation of concentrations DP and DN in the model is defined in accordance with (6.16) and (6.17); phosphorus and nitrogen concentrations in died-off phyto- and zooplankton, and in undigested nutrition, are defined by terms h, k p Des and h, k N Des respectively. Regeneration of mineral phosphorus and nitrogen as a result of bacterioplankton life activity was supposed to depend only on temperature and the existing stock of died-off organic matter: R p = DP xf(T, RN = DN xf(T,

rz: T~ax,Rprn-,Rpax),

rs: T:mx, RWn, R Nax),

where

0.05 day",

R pax = 0.21 day",

RWn = 0.03 day",

R Nax = 0.05 day":

Rpin =

The supply of mineral phosphorus and nitrogen are regulated in the model by their consumption by phytoplankton in (6.18) and (6.19), regeneration processes, and also at the expense of the term Z R, which represents excretion of mineral phosphorus (kpZ R) and mineral nitrogen (k N ZR) as a result of zooplankton life activity (Gutelmacher, 1982). The construction of the term ZR is given in the form (6.34)

where ZRo = 0.25 day ", TKis defined according to (6.31). To finalize the description of the biotic block of the discrete model, let us consider the construction of terms E p and En. The natural assumption, that gazing rate of phytoplankton and detritus is proportional to their concentrations, i.e. E p = E AZ x (A

+ htProd),

En = E nz x Del.

As was mentioned above, obtaining the balance of phosphorus and nitrogen in every elementary cell is necessary to satisfy the equality (6.10). To provide the fulfilment of the condition (6.10), the reasonable assumption is made that E AZ = E nz = E and E = Con/(A

+ h t Prod + Det).

(6.35)

Total variation of substances content in cells IIJj;

Equalities (6.14)-(6.20) enable us to write down equation (5.17) for all substances, included in the model. These equations are approximations of a system of differential equations (6.1)-(6.7) and corresponding boundary conditions.

Sec. 6.3]


197

Discrete analogues of the variation laws

For total phosphorus and total nitrogen the discrete analogues of conservation laws (5.12), written for Ptotal and Ntotal are valid. These discrete analogues are derived in an obvious manner from (5.18). For dissolved oxygen the discrete analogue (6.13) is satisfied. 6.3.4 Reproduction of Lake Onego annual ecosystem functioning The lake ecosystem functioning simulations were performed for two versions of biogenic loading. The first version corresponded to an annual loading equal to 1003t P total year"! and 117739 t N total year ": The loading expresses the mean annual loading for the periods 1986-1987 and 1992-1997 (Filatov, 1999, pp. 62-64). According to observation data, tributaries bring in 705 t Ptotal year " , atmospheric precipitation gives 95 tPtotalyear-l and waste waters 203 tPtotalyear-l. For nitrogen it is the following: from tributaries 13167tNtotalyear-l, from atmospheric precipitation 3800tNtotalyear-l and from waste waters 772tNtotalyear-l (Filatov, 1999). The annual distribution of biogenic loading into the lake and its distribution among tributaries is based on biogen outflow data (Shuya River, 201 tPtotalyear-l and 2259 t N total year': Vodla River, 194 t P total year " and 3353 t P total year " t N total year; Suna River, 28 tPtotalyear and 1714t Ntotalyear-l), and data on annual water flow distribution in the lake tributaries. Analysis of the annual distribution data for biogenic loading shows that it strongly correlates with the annual distribution of water inflow, is why additional income ofbiogens into the lake with waste waters and precipitation were distributed in the model according to the revealed relation. The second version corresponded to an annual loading for the period 20012002 and equalled 786 tPtotalyear-l and 15051 tNtotalyear-l (the data was obtained at Northern Water Problems Institute, Karelian Research Centre of the RAS by Basov and Lozovik). A decline in biogen loading is related mainly with decline of phosphorus income from tributaries: in 2001-2002 tributaries carried out 517 t P total year"! and 10 562 t Ntotalyear-l of biogens, though before that period it was 706 tPtotalyear-l and 13167tNtotalyear-1. Biogen carry-over with waste waters also declined, from 203 t P total year"! and 772 t N total year"! to 174 t P total year"! and 689 t N total year-I. Annual distribution data for biogens Ptotal and Ntotal are shown in Table 6.1 (Rukhovets and Filatov, 2003). The reproduction of the annual lake ecosystem functioning for each biogenic loading version consisted of receiving a discrete model periodical solution, approximating the system of equations in partial derivatives described above, and reproducing the processes studied. All external impacts, biogenic income, water inflow and discharge, were set as periodical functions with a period equal to one year. In order to construct the periodical solution, calculations were performed on a period of not less than 15 years. This exceeds the Lake Onego retention period. The retention period determines the lake ecosystem response to external impact. Data on water temperature and current velocity regimes obtained while constructing the full-year

198

[Ch.6


Table 6.1. Annual distribution of total phosphorus and total nitrogen (in tons) in the water inflow of the Vodla, Shuya, Suna (Kondopoga canal) and Vitegra rivers in 2001-2002 (data from NWPI). 2001 spring IV

V

2002

summer VI

VII

VIII

IX

X

E

winter

autumn XI

XII

I

II

III

River Vodla p

9

18.5 13

N

280

558

320

19.8 15.7

20

276

250 299

230

15

10.3 3.8

3.7 3.7

3.2

135.7

250

107

75

75

74

2794

River Shuya p

12.4 29.2

14

7

5.6

8.2 7.8

7.8

5.0

4.7 4.7

4.7

111.1

N

230

270

130

82

125 100

100

91

91

98

106

1871

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climatic circulation in Lake Onego, which was discussed in Chapter 3, were applied in the computation process. Analysis of modelling results

Modelling results are shown in Figs 6.1-6.14. Raw phytoplankton biomass mean annual dynamics in the Lake Onego epilimnion are presented in Fig. 6.1 for both loading versions. Mean phytoplankton biomass values in spring for the 1989-1993 period according to published figures (Filatov, 1999, Table 5.2, p. 150) for Bolshoye Onego, Petrozavodsk and Kondopoga bays considerably differ and equal 1.3mg 1-1, 7.1 mg l"! and 14.2mgl- 1 respectively. In our computation results for the first loading version, the maximum value of mean concentrations in spring equals 2.1 mg 1-1.


Sec. 6.3]

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Fig. 6.1. Phytoplankton biomass concentration in the epilimnion of Lake Onego (mg l"). Climatic circulation underloading: 1003 t Pyear" , 17739 t Nyear"! (solid line); 786 t Pyear", 15051 t Nyear" (dotted line).

In summer time during 1989-1993 according to the same data, corresponding data in these bays equal 0.9mg 1-1, 1.22mg I-I and 2.3 mg I-I respectively. In numerical experiments, calculations of the summer phytoplankton biomass mean concentration value in the lake epilimnion give l.4mgl- 1 (Fig. 6.1). There are two maxima in mean phytoplankton biomass annual dynamics (Fig. 6.1), One at the end of June and the second at the beginning of October. Observation data gives the same picture (Filatov, 1999, Table 5.1, p.149), the phytoplankton biomass value in October of 1991 and 1993 in Bolshoye Onego Bay is noticeably higher than in September. Thus, the results of phytoplankton calculations for the first loading version qualitatively and numerically coincides with observation data. Presented in Fig. 6.2, mean raw zooplankton biomass annual dynamics values reach a maximum magnitude later than phytoplankton biomass, as was expected. According to computation results the minimum magnitude of mineral phosphorus concentrations minimum magnitude in epilimnion coincides with phytoplankton biomass spring maximum (Fig. 6.3). Modelled values of mineral phosphorus concentrations fluctuations in this picture are within the range of similar observed characteristic alterations in the region of Central Onego (Filatoved., 1999; pp.149-154). The results of simulations of phyto- and zooplankton raw biomass dynamics, organic phosphorus and organic nitrogen concentrations (in detritus), dissolved-inwater mineral phosphorus and dissolved-in-water mineral nitrogen over the waterbody of the Petrozavodsk Bay are shown in Figs 6.7-6.14. The behaviour of reviewed

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Fig. 6.2. Zooplankton biomass concentration in the epilimnion of Lake Onego (mg l"). Climatic circulation underloading: 1003 t Pyear" , 17739 t Nyear"! (solid line); 786 tP year:", 1505 t Nyear" (dotted line).

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Fig.6.3. Mineral phosphorus concentration in the epilimnion of Lake Onego (J1g I-I). Climatic circulation under loading: 1003tPyeac', 17739tNyear- 1 (solid line); 786tPyear- l , 15051 t Nyear" (dotted line).


Sec. 6.3]

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Fig. 6.4. Detrital phosphorus concentration in epilimnion of Lake Onego (ug l"). Climatic circulation underloading: 1003 t Pyear", 17739 t Nyear" (solid line); 786 t Pyear" , 15051 t Nyear "! (dotted line).

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215.

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