Models and Modeling: An Introduction for Earth and Environmental Scientists

INDICE: 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

• ISBN: 978-1-119-13036-9
• Editorial: Wiley–Blackwell
• Encuadernacion: Rústica
• Páginas: 264
• Fecha Publicación: 04/11/2016
• Nº Volúmenes: 1
• Idioma: Inglés