STOCHASTIC AND STATISTICAL METHODS IN HYDROLOGY

AND ENVIRONMENTAL ENGINEERING

VOLUME 2

STOCHASTIC AND STATISTICAL MODELLING WITH GROUNDWATER

AND SURFACE WATER APPLICATIONS

Water Science and Technology Library VOLUME 10/2

Series Editor: V. P. Singh, Louisiana State University,

Baton Rouge, U.S.A.

Editorial Advisory Board:

S. Chandra, Roorkee, U.R., India J. C. van Dam, Pijnacker, The Netherlands

M. Fiorentino, Potenza, Italy W. H. Hager, Zürich, Switzerland N. Harmancioglu, Izmir, Turkey

V. V. N. Murty, Bangkok, Thailand J. Nemec, Genthod/Geneva, Switzerland A. R. Rao, West Lafayette, Ind., U.S.A.

Shan Xu Wang, Wuhan, Hubei, P.R. China

STOCHASTIC AND STATISTICAL METHODS IN HYDROLOGY

AND ENVIRONMENTAL ENGINEERING

Volume 2

STOCHASTIC AND STATISTICAL MODELLING

WITH GROUNDWATER AND SURFACE WATER

APPLICATIONS edited by

KEITH W. HIPEL Departments of Systems Design Engineering and

Statistics and Actuarial Science, University of Waterloo,

Waterloo, Ontario, Canada

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

Library of Congress Cataloging-in-Publication Data

S t o c h a s t i c an d s t a t i s t i c a l method s 1 n hydrolog y an d environmenta l eng1neerIng.

p. cm . — (Wate r sc ienc e an d technolog y l i b r a r y ; v . 10 ) Papers presente d a t a n I n t e r n a t i o n a l conferenc e hel d a t th e

U n i v e r s i t y o f Water loo , Canada, June 21-23 , 1993 . Inc lude s Index .

Contents : v . 1 . Extreme va lues : f l ood s an d drought s / e d i t e d b y K e i t h W. H1pel — v . 2 . S t o c h a s t i c an d s t a t i s t i c a l mode l l in g wit h groundwater an d su r fac e wate r a p p l i c a t i o n s / ed i te d b y K e i t h W . H i p el — v . 3 . Time s e r i e s a n a l y s i s I n hydrolog y an d environmenta l eng ineer in g / e d i t e d b y K e i t h W. Hipe l . . . te t a l . l — v . 4. E f f e c t i v e environmenta l management fo r s u s t a i n a b l e development / e d i t e d b y Ke i t h W. Hipe l an d L i p i n g Fang .

1. H y d r o l o g y — S r a t i s t i c a l methods—Congresses. 2 . S t o c h a s t i c p rocesses—Congresses . I . S e r i e s . GB656.2.S7S815 199 4 551 .48* 0 1'5195~dc20 94-2770 8

Printed on acid-free paper

Al l Rights Reserved © 1994 Springer Science+Business Media Dordrecht

Originally published by Kluwer Academic Publishers in 1994 No part of the material protected by this copyright notice may be reproduced or

utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and

retrieval system, without written permission from the copyright owner.

ISBN 978-94-010-4467-7

ISBN 978-94-010-4467-7 ISBN 978-94-011-1072-3 (eBook)DOI 10.1007/978-011-1072-3

In Memory of Professor T.E. Unny(1929 - 1991)

The Editor of this volume, Professor Keith W. Hipel (left), is showing ProfessorUnny posters for the International Conference on Stochastic and Statistical Methodsin Hydrology and Environmental Engineering held in his honour June 21 to 23, 1993.The photograph was taken at the University of Waterloo on December 20, 1991, eightdays before Professor Unny's untimely death.

TABLE OF CONTENTS

PREFACE .

AN INTERNATIONAL CELEBRATION

ACKNOWLEDGEMENTS .....

Xl

xv

xix

PART I:

PART II:

GENERAL ISSUES

Unny Symposium: Why are we Here?S.J. BURGES

Stochastic Differential Equations in Environmental Modellingand Their Numerical SolutionP. E. KLOEDEN

The Meaning of Stochasticity, Randomness and Uncertaintyin Environmental ModelingM. A. TUMEO

GROUNDWATER

3

21

33

Indentification of Stochastic Dispersion ModelsA. W. HEEMINK and H. F. P. VAN DEN BOOGAARD 41

Solving and Calibrating Groundwater Flow Systemswith the Penalty MethodL. R. BENTLEY 55

Calibration of Groundwater Models by Optimization of Parametersin Homogeneous Geological ZonesD. THIERY 69

Stochastic Characterization of Aquifer Heterogeneity from Drill Log DataA. 1. ALI and U. LALL 83

Groundwater Contaminant Transport: Estimating The Pollution at a WellM. DE GEE, J. GRASMAN, O. A. VAN HERWAARDEN,C. J. VAN DER HOEK and J. J. A. VAN KOOTEN 99

Transport by Two-Dimensional Random Velocity Fields:Effective Dispersion Coefficients of a Finite PlumeG. DAGAN 113

Spatial Correlation Analysis of Two-Dimensional Solute Transportin the Unsaturated ZoneH. YASUDA, R. BERNDTSSON, A. BAHRI, H. PERSSON,A. GULLBERG and K. JINNO 127

viii

PART III:

PART IV:

TABLE OF CONTENTS

Geostatistical Consideration on the Water Retention Volume and PoreVolume in Unsaturated Granular Material Composed of Various ParticlesT. NAKAO and M. FUJITA 139

Derivation of a Distribution for the Piezometric Head in Groundwater FlowUsing EntropyD. E. BARBE, J. F. CRUISE and V. P. SINGH 151

£1 and £2 Estimators in Groundwater Problems: Parameter Estimatesand CovariancesY. XIANG, N. R. THOMSON and J. F. SYKES 163

A Version of Dynamic-Stochastic Modelling of Hydrological ProcessesY. M. GUSEV 175

SURFACE WATER

Computational Methods in Stochastic River Waters Quality ModelingP. A. ZIELINSKI and K. PONNAMBALAM 187

A Random Flight Model in General CoordinatesP. A. BLOKLAND and A. W. HEEMINK 197

Application of a Distributed Parameter Filter to Predict Simulated TidalInduced Shallow Water FlowR. C. CURl, T. E. UNNY, K. W. HIPEL and K. PONNAMBALAM 211

Stochastic Behaviour of Storage in Conceptual ReservoirsKARMESHU and V. B. LAL 225

Stochastic Response of Storage Function Model for Flood RunoffM. FUJITA, N. SHINOHARA, T. NAKAO and M. KUDO 241

Stochastic Model of Finite Storage Processes: Input with Finite SupportD. FOX, Y. ZARMI and A. ZEMEL 255

STOCHASTIC OPTIMIZATION

A Regularized Algorithm for Solving Two-Stage StochasticLinear Programming Problems: A Water Resources ExampleD. S. YAKOWITZ 271

Stochastic Characterization of Optimal Response of a Hydroelectric SystemVia Dynamic ProgrammingL. F. R. REIS and F. H. CHAUDHRY 285

TABLE OF CONTENTS ix

PART V:

PART VI:

MOMENT ANALYSIS

Estimating Mean and Covariance of the Solution of a Linear Systemwith Random CoefficientsK. PONNAMBALAM, D. THANGARAJ and C. THAMAYANTHI 301

Second Moment Analysis of Dynamic Systemswith Probabilistic Components in the Frequency DomainG. L. GREIG 309

OTHER TOPICS

Uncertainty Analysis in Global Carbon Dioxide ModelingW. F. CURl, K. PONNAMBALAM and E. A. MCBEAN 325

A Real-Time Estimation of the Accuracy of Short-Term Rainfall PredictionUsing RadarT. TAKASAO, M. SHIIBA and E. NAKAKITA 339

Fourier Approximations for Estimation and Smoothing of IrregularlyObserved Spatial ProcessesJ. M. ANGULO, A. S. AZARI, R. H. SHUMWAY and Z. T. YUCEL 353

Author Index . 367

Subject Index. 369

PREFACE

Objectives

The current global environmental crisis has reinforced the need for developing flexiblemathematical models to obtain a better understanding of environmental problems sothat effective remedial action can be taken. Because natural phenomena occurring inhydrology and environmental engineering usually behave in random and probabilisticfashions, stochastic and statistical models have major roles to play in the protectionand restoration of our natural environment. Consequently, the main objective of thisedited volume is to present some of the most up-to-date and promising approachesto stochastic and statistical modelling, especially with respect to groundwater andsurface water applications.

Contents

As shown in the Table of Contents, the book is subdivided into the following mainparts:

PART IPART IIPART IIIPART IVPART VPART VI

GENERAL ISSUESGROUNDWATERSURFACE WATERSTOCHASTIC OPTIMIZATIONMOMENT ANALYSISOTHER TOPICS

Part I raises some thought-provoking issues about probabilistic modelling of hydro­logical and environmental systems. The first two papers in Part I are, in fact, keynotepapers delivered at an international environmetrics conference held at the Universityof Waterloo in June, 1993, in honour of Professor T.E. Unny. In his keynote pa­per, Dr. S. J. Burges of the University of Washington places into perspective thehistorical and future roles of stochastic modelling in hydrology and environmentalengineering. Additionally, Dr. Burges stresses the need for developing a sound scien­tific basis for the field of hydrology. Professor P.E. Kloeden of Deakin University inAustralia provides an introduction to stochastic differential equations with examplesin the environmental sciences. Stochastic differential equations provide a means forproperly capturing the physical aspects of environmental systems and do indeed holda promising future. In the final paper in Part I, Dr. M.A. Tumeo reviews the em­ployment and meaning of the concepts of uncertainty, stochasticity and randomnessin environmental modelling.

Xl

xii PREFACE

Due to the widespread pollution of underground aquifers throughout the world,groundwater modelling has become a research area of great demand. One of theenvironmental catastrophes that brought groundwater pollution to the forefront ofinternational news is the infamous Love Canal debacle in New York state, whereold toxic chemical dumps seriously polluted the groundwater that seeped into nearbydwellings. The papers in Part II contain a host of new research ideas and applicationsin groundwater modelling written by international experts from many different coun­tries. The powerful mathematical tools that are utilized in these landmark papersinclude stochastic differential equations, finite differences and finite elements.

The papers in Part III investigate the probabilistic modelling of water on the surfaceof the earth. As in the previous section, there is a distinct international flavour tothis set of first class papers.

In Part IV, there are two papers dealing with stochastic optimization of water re­sources systems using stochastic linear programming and dynamic programming. Theresearch manuscripts published in Part V pertain to moment analysis problems. Fi­nally, a variety of interesting topics, including carbon dioxide modelling and rainfallprediction, are described in the papers falling within Part VI.

Audience

This book should be of direct interest to anyone who is concerned with the latestdevelopments in stochastic and statistical methods in the environmental sciences.Accordingly, the types of Professionals who may wish to use this book include:

Water Resources EngineersEnvironmental Scientists

HydrologistsCivil EngineersEarth Scientists

GeographersPlanners

StatisticiansSystems Engineers

Management Scientists

Within each professional group, the book should provide useful information for:

ResearchersTeachersStudents

Practitioners and Consultants

PREFACE xiii

When utilized for teaching purposes, the book could serve as a complementary textat the upper undergraduate and graduate levels. For instance, in a course involvedwith applying stochastic differential equations to environmental problems, this vol­ume could be used along with the 1992 book by P.E. Kloeden and E. Platen, which isentitled The Numerical Solution of Stochastic Differential Equations, and is publishedby Springer-Verlag, Berlin. Researchers should obtain guidance and background ma­terial for carrying out worthwhile research projects in the probabilistic modelling ofgroundwater and surface water systems. Consultants who wish to keep their compa­nies at the leading edge of activities in environmetrics and thereby serve their clientsin the best possible ways, will find this book to be an indispensable resource.

AN INTERNATIONAL CELEBRATION

Dedication

The papers contained in this book were originally presented at the internationalconference on Stochastic and Statistical Methods in Hydrology and Envi­ronmental Engineering that took place at the University of Waterloo, Waterloo,Ontario, Canada, from June 21 to 23, 1993. This international gathering was held inhonour and memory of the late Professor T.E. Unny in order to celebrate his life­long accomplishments in many of the important environmental topics falling withinthe overall conference theme. When he passed away in late December, 1991, ProfessorT.E. Unny was Professor of Systems Design Engineering at the University of Water­loo and Editor-in-Chief of the international journal entitled Stochastic Hydrology andHydraulics.

About 250 scientists from around the world attended the Waterloo conference inJune, 1993. At the conference, each participant was given a Pre-Conference Pro­ceedings, published by the University of Waterloo and edited by K.W. Ripe!. This584 page volume contains the detailed conference program as well as the refereedextended abstracts for the 234 papers presented at the conference. Subsequent to theconference, full length papers submitted for publication by presenters were mailedto international experts who kindly carried out thorough reviews. Accepted paperswere returned to authors for revisions and the final manuscripts were then publishedby Kluwer according to topics in the following four volumes:

TIME SERIES ANALYSIS IN HYDItOLOGY ANDENVIRONMENTAL ENGINEERING

edited byKeith W. Hipe!, A. Ian McLeod, U. S. Panu and Vijay P. Singh

EFFECTIVE ENVIRONMENTAL MANAGMENT FORSUSTAINABLE DEVELOPMENT

edited byKeith W. Hipe! and Liping Fang

EXTREME VALUES: FLOODS AND DROUGHTSedited by

Keith W. Ripel

as well as the current book on:

STOCHASTIC AND STATISTICAL MODELLING WITHGROUNDWATER AND SURFACE WATER APPLICATIONS

edited byKeith W. Hipe!

xv

xvi AN INTERNATIONAL CELEBRATION

The Editors of the volumes as well as Professor Unny's many friends and colleaguesfrom around the globe who wrote excellent research papers for publication in thesefour volumes, would like to dedicate their work as a lasting memorial to ProfessorT. E. Unny. In addition to his intellectual accomplishments, Professor Unny will befondly remembered for his warmth, humour and thoughtful consideration of others.

Conference Organization and Sponsorships

The many colleagues and sponsors who took part in the planning and execution of theinternational conference on Stochastic and Statistical Methods in Hydrologyand Environmental Engineering are given below.

Organizing Committee

K. W. Hipel (Chairman) A. I. McLeodU. S. Panu V. P. Singh

International Programme Committee

S. AI-Nassri (Malaysia)H. Bergmann (Austria)J. Bernier (France)B. Bobee (Canada)B. Bodo (Canada)D. S. Bowles (U.S.A.)W. P. Budgell (Norway)S. J. Burges (U.S.A.)F. Camacho (Canada)S. Chandra (India)C-L. Chiu (U.S.A.)J. Ding (China)L. Duckstein (U.S.A.)A. H. EI-Shaarawi (Canada)M. Fiorentino (Italy)E. Foufoula (U.S.A.)I. C. Goulter (Australia)Y. Y. Haimes (U.S.A.)N. Harmancioglu (Turkey)S. Ikebuchi (Japan)Karmeshu (India)M.1. Kavvas (U.S.A.)J. Kelman (Brazil)J. Kindler (Poland)G. Kite (Canada)T. Kojiri (Japan)R. Krzysztofowicz (U.S.A.)

Z. Kundzewicz (Poland)Gwo-Fong Lin (Taiwan)C. Lemarechal (France)L. Logan (Canada)D. P. Loucks (U.S.A.)I. B. MacNeill (Canada)A. Musy (Switzerland)P. Nachtnebel (Austria)D. J. Noakes (Canada)N. Okada (Japan)R. M. Phatarford (Australia)V. Privalsky (U.S.S.R.)D. Rosbjerg (Denmark)J. D. Salas (U.S.A)G. A. Schultz (Germany)S. Serrano (U.S.A.)U. Shamir (Israel)S. P. Simonovic (Canada)S. Sorooshian (U .S.A.)A. Szollosi-Nagy (France)C. Thirriot (France)W. E. Watt (Canada)S. J. Yakowitz (U.S.A.)V. Yevjevich (U.S.A.)Y. C. Zhang (China)P. Zielinski (Canada)

AN INTERNATIONAL CELEBRATION

University of Waterloo Committee

xvii

A. BogobowiczS. BrownD. BurnsC. DufournaudJ". FangG. Farquhar

T. HollandsJ. D. KalbfleischE. LeDrewE. A. McBeanK. PonnambalamE. Sudicky

Financial Support

Conestoga/Rovers and AssociatesCumming Cockburn LimitedDepartment of Systems Design Engineering, University of WaterlooFaculty of Engineering, University of WaterlooNatural Sciences and Engineering Research Council (NSERC) of Canada

Sponsors

American Geophysical UnionAmerican Water Resources AssociationAssociation of State Floodplain ManagersCanadian Society for Civil EngineeringCanadian Society for Hydrological SciencesIEEE Systems, Man and Cybernetics SocietyInstituto Panamericano de Geografia e HistoriaInternational Association for Hydraulic ResearchInternational Association of Hydrological SciencesInternational Commission of Theoretical and Applied LimnologyInternational Commission on Irrigation and DrainageInternational Institute for Applied Systems AnalysisInternational Statistical InstituteInternational Water Resources AssociationLakehead UniversityLouisiana State UniversityNorth American Lake Management SocietyThe International Environmetrics SocietyThe Pattern Recognition SocietyThe University of Western OntarioUniversity of Waterloo

xviii AN INTERNATIONAL CELEBRATION

University of Waterloo

President James Downey, Opening and Banquet AddressesD. Bartholomew, Graphic ServicesDanny Lee, Catering and Bar Services ManagerD. E. Reynolds, Manager, Village 2 Conference CentreT. Schmidt, Engineering PhotographerAudio Visual CentreFood ServicesGraduate Students in Systems Design Engineering

Technical Assistance

Mrs. Sharon BolenderMr. Steve FletcherMr. Kei FukuyamaMs. Hong GaoMs. Wendy StonemanMr. Roy Unny

ACKNOWLEDGEMENTS

The Editor would like to sincerely thank the authors for writing such excellent papersfor publication in this as well as the other three volumes. The thoughtful reviews ofthe many anonymous referees are also gratefully acknowledged. Moreover, the Editorappreciates the fine contributions by everyone who attended the Waterloo conferencein June, 1993, and actively took part in the many interesting discussions at the paperpresentations.

Additionally, the Editor would like to say merci beaucoup to the committee membersand sponsors of the Waterloo conference listed in the previous section. Dr. E. Sudicky,University of Waterloo, kindly assisted in organizing groundwater sessions at theWaterloo conference. Doctors K. Ponnambalam, A. Bogobowicz and V. Quintana,all from the University of Waterloo, as well as Dr. P. A. Zielinski of Ontario Hydro,helped to plan special sessions and review papers. Finally, he sincerely appreciates allthe thoughtful personnel at Kluwer who assisted in the publication of the volumes. Inparticular, the Editor is grateful to Dr. Petra D. Van Steenbergen, Acquisition Editor,and Professor V.P. Singh who is the Editor of the Water Science and TechnologyLibrary book series in which this volume is published.

Keith W. HipelProfessor and ChairDepartment of Systems Design Engineering

Cross Appointed Professor toDepartment of Statistics and Actuarial ScienceUniversity of Waterloo

April, 1994

XIX