Environmental modeling : Using MATLAB

Environmental Modeling

.

Ekkehard Holzbecher

Environmental Modeling

Using MATLAB®

Priv.-Doz. Dr.-Ing. Dipl.-Math. Ekkehard Holzbecher

Georg-August Universit€at G€ottingen

Goldschmidtstr. 3

37077 G€ottingen

[email protected]

Additional material to this book can be downloaded from http://extra.springer.com.

ISBN 978-3-642-22041-8 e-ISBN 978-3-642-22042-5

DOI 10.1007/978-3-642-22042-5

Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2011941398

# Springer-Verlag Berlin Heidelberg 2012

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Dedicated to

my children Gesa and Gero

.

Foreword

The book has two aims:

(a) To introduce basic concepts of environmental modeling and

(b) To exercise the application of current mathematical software packages

To the target group belong all natural scientists who are dealing with the

environment: engineers from process and chemical engineering, physicists,

chemists, biologists, biochemists, hydrogeologists, geochemists, ecologists ...!

As the book is concerned with modeling, it inevitably demands some mathemat￾ical insight. The book is designed to

1. Be a door opener to the field for novices without any background knowledge of

environmental modeling and of MATLAB®, and

2. To surprise those, who have some expertise, with advanced methods which they

have not been aware of

For this book MATLAB® was chosen as the computer tool for modeling,

because

1. It is powerful, and

2. It is available at most academic institutions, at all universities and at the research

departments of companies

Other mathematical products could have been selected from the market, which

would perform similarly well for most application problems presented in the

various chapters. But MATLAB® is rather unique in it’s strong capabilities in

numerical linear algebra.

There are 20 chapters in the book. The first chapters are concerned with

environmental processes and their simulation: (1) transport, consisting of advec￾tion, diffusion and dispersion, (2) sorption, (3) decay or degradation, (4) reaction,

either kinetic or thermodynamic. Following aim (b) there are sub-chapters inserted

for the introduction of MATLAB® modeling techniques. The first part of the book

ends with chapters on ordinary differential equations and parameter estimation

(inverse modeling).

vii

The second part of the book starts with chapters on flow modeling. Flow, if

present, is an important, but mostly also complex part within an environmental

compartment. Core MATLAB® allows simple flow set-ups only. Therefore the

focus is on potential flow, which has applications in hydro (water) and aero (air)-

dynamics as well as in porous media (seepage and groundwater). Concepts of

MATLAB® are deepened within these chapters. At the very end special topics

appear: image processing and geo-referencing, graphs, linear systems, the phase

space and graphical user interfaces.

Berlin

viii Foreword

Foreword to the Second Edition

The consistently commendatory and positive reactions that I obtained unanimously

for the first edition of ‘Environmental Modeling’ encouraged me to work on a

second improved and extended version of the book and the accompanying software,

which is available herewith. The reader may allow me to cite some surely

exaggerating voices from the Internet:

Excellent work. It will be more helpful for the younger researchers also for the sr. scientists

for understanding basics and applications of MATLAB in environmental engg. It is THE

BEST book.

I love this book, because you wrote it in a programming manner and I love programming, so

I learnt advection and diffusion excellent. Because after I read the equation I modeled it in

Matlab and saw the results. And it remains in my mind. I want to thank you because of

writing this book. It helps a lot to the students and researchers to learn environmental

modeling deeply.

Special thanks to my students at the Georg-August Universit€at, G€ottingen, and at

Freie Universit€at, Berlin, who gave me clues on how the mathematical viewpoint,

taken in this book, is conceived by an audience that is usually not especially trained

in topics as mathematical physics. Some of the improvements directly result from

the work with the students.

A new chapter was added, in which an introduction into numerical methods is

given – an important topic that was missing in the first edition, as I was told by some

readers.

Special focus has been laid to extend the capability to use ‘Environmental

Modeling’ as a reference book. The list of keywords in the MATLAB® command

index, although not covering the complete list of commands, has been extended

significantly. Personally I think that this is the major improvement in relation to the

first edition. I hope that in that way the book will help readers and modelers to

understand the commands quickly and to apply them correctly.

Final thanks to all people at the mentioned universities, the publishers at

Springer Verlag, Heidelberg, and the people of the bookprogram of MathWorks.

G€ottingen

ix

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Preface

“Environmental Modeling using MATLAB®” by Ekkehard Holzbecher is an

excellent publication and a novel approach covering the intersection of two impor￾tant, growing worlds – the world of environmental modeling and of mathematical

software.

Environmental modeling is a science that uses mathematics and computers to

simulate physical and chemical phenomena in the environment (e.g., environmental

pollution). This science was initially based on pen-and-paper calculations using

simple equations. In the last 50 years, with the development of digital computers,

environmental models have become more and more complex, requiring often

numerical solutions for systems of partial differential equations.

Mathematical software, such as MATLAB®, has been developed in the last two

decades. These packages have been particularly successful for users of personal

computers. Mathematical software provides a set of tools for solving equations both

analytically and numerically. This is a major improvement in comparison to the

programming tools (e.g., FORTRAN) previously used by scientists. Mathematical

software offers extremely valuable and cost-effective tools that improve the pro￾ductivity of the programmer by at least an order of magnitude. The use of these

tools also minimizes the risk of programming errors. In addition, mathematical

software offers unique visualization tools that allow the user to immediately

visualize and often animate simulation results.

Scientists who become familiar with a tool like MATLAB® will never go back

to previous ways of computer programming.

The book “Environmental Modeling using MATLAB®” provides a clear, com￾prehensive, and very instructive introduction to the science of environmental

modeling, and more importantly, includes the MATLAB® codes for the actual

solutions to the environmental equations. MATLAB® codes are listed in the book

and also included as more complete versions in an attached CD1

.

1 The first edition of the book included a CD. Readers of the second edition obtain the

accompanying software via Internet.

xi

I highly recommend this book to both beginners and expert environmental

professionals. The book will be particularly useful to those scientists who have

postponed learning and using mathematical software. This book will open a new

world to them!

Paolo Zannetti

President, The EnviroComp Institute

Editor of Book Series on Environmental Modeling

xii Preface

Acknowledgements

A book on such a wide topic as this one includes experiences and knowledge shared

with lots of other people. I ask for understanding that I mention no names here. To

be fair, giving one name would make it necessary to add numerous others. As one

and only exception I want to mention my wife Susanne for reading the first edition

of the book, correcting stylistic errors, providing improved formulations and for

mental support.

Thanks to Humboldt University Berlin (HUB), the Leibniz Institute of Freshwa￾ter Ecology and Inland Fisheries (IGB), to the Weierstrass Institute for Applied

Analysis and Stochastics (WIAS), to the Geosciences of Freie Universit€at Berlin

(FUB) and of Georg-August Universit€at G€ottingen. Special thanks to the students

who attended the modeling courses in Berlin and G€ottingen, for their questions and

for their ideas. Without them I would not have become so familiar with the

software. Parts of the book are based on seminar scripts.

Especially I want to thank The MathWorks, Inc (http://www.mathworks.com/)

for providing the most recent versions of the MATLAB® software as well as other

support by including the book in the MathWorks Book Program.

xiii

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