An Introduction to Models and Modeling in the Earth and Environmental Sciences offers students and professionals the opportunity to learn about groundwater modeling, starting from the basics. Using clear, physically-intuitive examples, the author systematically takes us on a tour that begins with the simplest representations of fluid flow and builds through the most important equations of groundwater hydrology. Along the way, we learn how to develop a conceptual understanding of a system, how to choose boundary and initial conditions, and how to exploit model symmetry. Other important topics…mehr
An Introduction to Models and Modeling in the Earth and Environmental Sciences offers students and professionals the opportunity to learn about groundwater modeling, starting from the basics. Using clear, physically-intuitive examples, the author systematically takes us on a tour that begins with the simplest representations of fluid flow and builds through the most important equations of groundwater hydrology. Along the way, we learn how to develop a conceptual understanding of a system, how to choose boundary and initial conditions, and how to exploit model symmetry. Other important topics covered include non-dimensionalization, sensitivity, and finite differences. Written in an eclectic and readable style that will win over even math-phobic students, this text lays the foundation for a successful career in modeling and is accessible to anyone that has completed two semesters of Calculus. Although the popular image of a geologist or environmental scientist may be the rugged adventurer, heading off into the wilderness with a compass and a hand level, the disciplines of geology, hydrogeology, and environmental sciences have become increasingly quantitative. Today's earth science professionals routinely work with mathematical and computer models, and career success often demands a broad range of analytical and computational skills. An Introduction to Models and Modeling in the Earth and Environmental Sciencesis written for students and professionals who want to learn the craft of modeling, and do more than just run "black box" computer simulations.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Dr. Jerry P. Fairley received his PhD in Earth Resources Engineering from the University of California, Berkeley. He was the Chief Hydrologist for Site Characterization on the US- DOE's Yucca Mountain Project (1993-1995), and worked as a modeler for the Earth Sciences Division of Lawrence Berkeley National Laboratory. He is currently a Professor of Geology at the University of Idaho, Department of Geological Sciences.
Inhaltsangabe
About the companion website xi Introduction 1 1 Modeling basics 4 1.1 Learning to model 4 1.2 Three cardinal rules of modeling 5 1.3 How can I evaluate my model? 7 1.4 Conclusions 8 2 A model of exponential decay 9 2.1 Exponential decay 9 2.2 The Bandurraga Basin Idaho 10 2.3 Getting organized 10 2.4 Nondimensionalization 17 2.5 Solving for ¿ 19 2.6 Calibrating the model to the data 21 2.7 Extending the model 23 2.8 A numerical solution for exponential decay 26 2.9 Conclusions 28 2.10 Problems 29 3 A model of water quality 31 3.1 Oases in the desert 31 3.2 Understanding the problem 32 3.3 Model development 32 3.4 Evaluating the model 37 3.5 Applying the model 38 3.6 Conclusions 39 3.7 Problems 40 4 The Laplace equation 42 4.1 Laplace's equation 42 4.2 The Elysian Fields 43 4.3 Model development 44 4.4 Quantifying the conceptual model 47 4.5 Nondimensionalization 48 4.6 Solving the governing equation 49 4.7 What does it mean? 50 4.8 Numerical approximation of the second derivative 54 4.9 Conclusions 57 4.10 Problems 58 5 The Poisson equation 62 5.1 Poisson's equation 62 5.2 Alcatraz island 63 5.3 Understanding the problem 65 5.4 Quantifying the conceptual model 74 5.5 Nondimensionalization 76 5.6 Seeking a solution 79 5.7 An alternative nondimensionalization 82 5.8 Conclusions 84 5.9 Problems 85 6 The transient diffusion equation 87 6.1 The diffusion equation 87 6.2 The Twelve Labors of Hercules 88 6.3 The Augean Stables 90 6.4 Carrying out the plan 92 6.5 An analytical solution 100 6.6 Evaluating the solution 109 6.7 Transient finite differences 114 6.8 Conclusions 118 6.9 Problems 119 7 The Theis equation 122 7.1 The Knight of the Sorrowful Figure 122 7.2 Statement of the problem 124 7.3 The governing equation 125 7.4 Boundary conditions 127 7.5 Nondimensionalization 128 7.6 Solving the governing equation 132 7.7 Theis and the "well function" 134 7.8 Back to the beginning 135 7.9 Violating the model assumptions 138 7.10 Conclusions 139 7.11 Problems 140 8 The transport equation 141 8.1 The advection-dispersion equation 141 8.2 The problem child 143 8.3 The Augean Stables revisited 144 8.4 Defining the problem 144 8.5 The governing equation 146 8.6 Nondimensionalization 148 8.7 Analytical solutions 152 8.8 Cauchy conditions 165 8.9 Retardation and dispersion 167 8.10 Numerical solution of the ADE 169 8.11 Conclusions 173 8.12 Problems 174 9 Heterogeneity and anisotropy 177 9.1 Understanding the problem 177 9.2 Heterogeneity and the representative elemental volume 179 9.3 Heterogeneity and effective properties 180 9.4 Anisotropy in porous media 187 9.5 Layered media 188 9.6 Numerical simulation 189 9.7 Some additional considerations 191 9.8 Conclusions 192 9.9 Problems 192 10 Approximation error and sensitivity 195 10.1 Things we almost know 195 10.2 Approximation using derivatives 196 10.3 Improving our estimates 197 10.4 Bounding errors 199 10.5 Model sensitivity 201 10.6 Conclusions 206 10.7 Problems 207 11 A case study 210 11.1 The Borax Lake Hot Springs 210 11.2 Study motivation and conceptual model 212 11.3 Defining the conceptual model 213 11.4 Model development 215 11.5 Evaluating the solution 224 11.6 Conclusions 229 11.7 Problems 230 12 Closing remarks 233 12.1 Some final thoughts 233 Appendix A A heuristic approach to nondimensionalization 236 Appendix B Evaluating implicit equations 238 B.1 Trial and error 239 B.2 The graphical method 239 B.3 Iteration 240 B.4 Newton's method 241 Appendix C Matrix solution for implicit algorithms 243 C.1 Solution of 1D equations 243 C.2 Solution for higher dimensional problems 244 C.3 The tridiagonal matrix routine TDMA 244 Index 247
About the companion website xi Introduction 1 1 Modeling basics 4 1.1 Learning to model 4 1.2 Three cardinal rules of modeling 5 1.3 How can I evaluate my model? 7 1.4 Conclusions 8 2 A model of exponential decay 9 2.1 Exponential decay 9 2.2 The Bandurraga Basin Idaho 10 2.3 Getting organized 10 2.4 Nondimensionalization 17 2.5 Solving for ¿ 19 2.6 Calibrating the model to the data 21 2.7 Extending the model 23 2.8 A numerical solution for exponential decay 26 2.9 Conclusions 28 2.10 Problems 29 3 A model of water quality 31 3.1 Oases in the desert 31 3.2 Understanding the problem 32 3.3 Model development 32 3.4 Evaluating the model 37 3.5 Applying the model 38 3.6 Conclusions 39 3.7 Problems 40 4 The Laplace equation 42 4.1 Laplace's equation 42 4.2 The Elysian Fields 43 4.3 Model development 44 4.4 Quantifying the conceptual model 47 4.5 Nondimensionalization 48 4.6 Solving the governing equation 49 4.7 What does it mean? 50 4.8 Numerical approximation of the second derivative 54 4.9 Conclusions 57 4.10 Problems 58 5 The Poisson equation 62 5.1 Poisson's equation 62 5.2 Alcatraz island 63 5.3 Understanding the problem 65 5.4 Quantifying the conceptual model 74 5.5 Nondimensionalization 76 5.6 Seeking a solution 79 5.7 An alternative nondimensionalization 82 5.8 Conclusions 84 5.9 Problems 85 6 The transient diffusion equation 87 6.1 The diffusion equation 87 6.2 The Twelve Labors of Hercules 88 6.3 The Augean Stables 90 6.4 Carrying out the plan 92 6.5 An analytical solution 100 6.6 Evaluating the solution 109 6.7 Transient finite differences 114 6.8 Conclusions 118 6.9 Problems 119 7 The Theis equation 122 7.1 The Knight of the Sorrowful Figure 122 7.2 Statement of the problem 124 7.3 The governing equation 125 7.4 Boundary conditions 127 7.5 Nondimensionalization 128 7.6 Solving the governing equation 132 7.7 Theis and the "well function" 134 7.8 Back to the beginning 135 7.9 Violating the model assumptions 138 7.10 Conclusions 139 7.11 Problems 140 8 The transport equation 141 8.1 The advection-dispersion equation 141 8.2 The problem child 143 8.3 The Augean Stables revisited 144 8.4 Defining the problem 144 8.5 The governing equation 146 8.6 Nondimensionalization 148 8.7 Analytical solutions 152 8.8 Cauchy conditions 165 8.9 Retardation and dispersion 167 8.10 Numerical solution of the ADE 169 8.11 Conclusions 173 8.12 Problems 174 9 Heterogeneity and anisotropy 177 9.1 Understanding the problem 177 9.2 Heterogeneity and the representative elemental volume 179 9.3 Heterogeneity and effective properties 180 9.4 Anisotropy in porous media 187 9.5 Layered media 188 9.6 Numerical simulation 189 9.7 Some additional considerations 191 9.8 Conclusions 192 9.9 Problems 192 10 Approximation error and sensitivity 195 10.1 Things we almost know 195 10.2 Approximation using derivatives 196 10.3 Improving our estimates 197 10.4 Bounding errors 199 10.5 Model sensitivity 201 10.6 Conclusions 206 10.7 Problems 207 11 A case study 210 11.1 The Borax Lake Hot Springs 210 11.2 Study motivation and conceptual model 212 11.3 Defining the conceptual model 213 11.4 Model development 215 11.5 Evaluating the solution 224 11.6 Conclusions 229 11.7 Problems 230 12 Closing remarks 233 12.1 Some final thoughts 233 Appendix A A heuristic approach to nondimensionalization 236 Appendix B Evaluating implicit equations 238 B.1 Trial and error 239 B.2 The graphical method 239 B.3 Iteration 240 B.4 Newton's method 241 Appendix C Matrix solution for implicit algorithms 243 C.1 Solution of 1D equations 243 C.2 Solution for higher dimensional problems 244 C.3 The tridiagonal matrix routine TDMA 244 Index 247
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