# Environmental Modeling: Using MATLAB®

Springer Science & Business Media, Aug 30, 2007 - Science - 392 pages
“Environmental Modeling using MATLAB R ” by Ekkehard Holzbecher is an excellent publication and a novel approach covering the intersection of two important, growing worlds – the world of environmental modeling and of mathematical software. Environmental modeling is a science that uses mathematics and comp- ers 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 devel- mentofdigitalcomputers,environmentalmodelshavebecomemoreandmore complex, requiring often numerical solutions for systems of partial di?erential equations. Mathematical software, such as MATLAB R , has been developed in the lasttwo decades. Thesepackageshavebeen particularlysuccessfulfor usersof 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 o?ers extremely valuable and cost-e?ective tools that improve the productivity 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 o?ers unique visualization tools that allow the user to immediately visualize and often animate simulation results. Scientists who become familiar with a tool like MATLAB R will never go back to previous ways of computer programming.

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### Contents

 Introduction 11 Environmental Modeling using MATLAB 3 12 Introduction to MATLAB 7 13 A Simple Environmental Model 20 14 MATLAB Graphics The Figure Editor 24 15MATLB Help System 25 References 27 Fundamentals of Modeling Principles and MATLABR 21 Model Types 29 22 Modeling Steps 30
 Advanced Modeling using MATLAB 205 Flow Modeling 206 111 The NavierStokes Equations for Free Fluids 208 112 The Euler Equations and the Bernoulli Theorem 213 113 Darcys Law for Flow in Porous Media 217 114 Flow in Unsaturated Porous Media 222 References 227 Groundwater Drawdown by Pumping 229

 23 Fundamental Laws 34 24 Continuity Equation for Mass 36 25 MATLAB Mﬁles 40 26 Ifs and Loops in MATLAB 42 27 Debugging of Mﬁles 44 Reference 46 Transport 31 The Conservation Principle 47 32 Ficks Law and Generalizations 49 33 The Transport Equation Mass Transport 55 34 Dimensionless Formulation 60 35 Boundary and Initial Conditions 61 References 63 Transport Solutions 65 42 A Simple Numerical Model 69 43 Comparison between Analytical and Numerical Solution 77 44 Numerical Solution using MATLAB pdepe 79 1D Inﬂow Front 83 References 85 Transport with Decay and Degradation 86 52 1D Steady State Solution 90 53 Dimensionless Formulation 92 54 Transient Solutions 98 References 100 Transport and Sorption 101 62 Retardation 107 63 Analytical Solution 109 64 Numerical Solutions 111 65 Slow Sorption 115 66 MATLAB Animations 119 References 121 Transport and Kinetics 123 72 Law of Mass Action for Kinetic Reactions 125 73 Monod MichaelisMenten and Blackwell Kinetics 126 74 Bacteria Populations 128 75 Steady States 130 References 134 Transport and Equilibrium Reactions 137 82 The Law of Mass Action for Equilibrium Reactions 141 83 Speciation Calculations 143 84 Sorption and the Law of Mass Action 147 85 Transport and Speciation 150 References 156 Ordinary Differential Equations Dynamical Systems 158 91 StreeterPhelps Model for River Puriﬁcation 160 92 Details of MichaelisMenten or Monod Kinetics 163 93 1D Steady State Analytical Solution 165 94 Redox Sequences 173 References 178 Parameter Estimation 181 102 Polynomial Curve Fitting 182 103 Exponential Curve Fitting 185 104 Parameter Estimation with Derivatives 189 105 Transport Parameter Fitting 196 106 General Procedure 199 References 204
 121 Conﬁned Aquifer 230 122 Unconﬁned Aquifer 232 123 Halfconﬁned Aquifer 235 124 Unsteady Drawdown and Well Function 237 125 Automatic Transmissivity Estimation 238 References 241 Aquifer Baseﬂow and 2D Meshing 243 132 1D Implementation 245 133 2D Implementation 246 134 Meshs and Grids 250 Reference 254 Potential and Flow Visualization 255 142 Potential and Real World Variables 258 Groundwater Baseﬂow and Well 260 144 MATLAB 2D Graphics 264 145 MATLAB 3D Graphics 268 References 270 Streamfunction and Complex Potential 271 152 The Principle of Superposition 275 153 Complex Analysis and Complex Potential 282 Vortices or Wells Systems 286 References 291 2D and 3D Transport Solutions Gaussian Puffs and Plumes 161 Introduction 293 162 2D Instantaneous Line Source 298 163 2D Constant Line Source 299 165 3D Constant Source 301 References 305 Image Processing and Georeferencing 307 172 Reading and Display 308 173 GeoReferencing 310 174 Digitizing 312 175 MATLABR Functions 314 References 316 Compartment Graphs and Linear Systems 317 182 Linear Systems 321 183 Eigenvalues and Phase Space 331 References 336 Nonlinear Systems 338 192 Competing Species 342 193 PredatorPrey Models 348 194 Chaos Lorenz Attractor 353 References 355 Graphical User Interfaces 357 202 The Transport GUI 366 References 369 MATLAB Data Import 370 Data Export 374 Data Presentation in a Histogram 375 Epilogue 379 References 380 MATLAB Command Index 381 Companion Software List 384 Index 385 Copyright

### Popular passages

Page 15 - ... the element in the ith row and jth column of the matrix Q3.
Page 15 - Matrix multiplication is only possible when the first matrix has the same number of columns as the second matrix has rows. If this requirement isn't met, the matrices are said to be "incompatible" and matrix multiplication cannot be performed.