{"product_id":"models-and-modeling-9781119130369","title":"Models and Modeling","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAn Introduction to Models and Modeling in the Earth and Environmental Sciences\u003c\/p\u003e offers students and professionals the opportunity to learn about groundwater modeling, starting \u003cp\u003efrom the basics. Using clear, physically-intuitive examples, the author systematically takes\u003c\/p\u003e \u003cp\u003eus on a tour that begins with the simplest representations of fluid flow and builds through\u003c\/p\u003e \u003cp\u003ethe most important equations of groundwater hydrology. Along the way, we learn how\u003c\/p\u003e \u003cp\u003eto develop a conceptual understanding of a system, how to choose boundary and initial\u003c\/p\u003e \u003cp\u003econditions, and how to exploit model symmetry. Other important topics covered include\u003c\/p\u003e \u003cp\u003enon-dimensionalization, sensitivity, and finite differences. Written in an eclectic and readable\u003c\/p\u003e \u003cp\u003estyle that will win over even math-phobic students, this text lays the foundation for a\u003c\/p\u003e \u003cp\u003esuccessful career in modeling and is accessible to anyone that has completed two semesters\u003c\/p\u003e \u003cp\u003eof Calculus.\u003c\/p\u003e \u003cp\u003eAlthough the popular im\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eAbout the companion website, xi\u003c\/p\u003e \u003cp\u003eIntroduction, 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Modeling basics, 4\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Learning to model, 4\u003c\/p\u003e \u003cp\u003e1.2 Three cardinal rules of modeling, 5\u003c\/p\u003e \u003cp\u003e1.3 How can I evaluate my model?, 7\u003c\/p\u003e \u003cp\u003e1.4 Conclusions, 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 A model of exponential decay, 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Exponential decay, 9\u003c\/p\u003e \u003cp\u003e2.2 The Bandurraga Basin, Idaho, 10\u003c\/p\u003e \u003cp\u003e2.3 Getting organized, 10\u003c\/p\u003e \u003cp\u003e2.4 Nondimensionalization, 17\u003c\/p\u003e \u003cp\u003e2.5 Solving for θ, 19\u003c\/p\u003e \u003cp\u003e2.6 Calibrating the model to the data, 21\u003c\/p\u003e \u003cp\u003e2.7 Extending the model, 23\u003c\/p\u003e \u003cp\u003e2.8 A numerical solution for exponential decay, 26\u003c\/p\u003e \u003cp\u003e2.9 Conclusions, 28\u003c\/p\u003e \u003cp\u003e2.10 Problems, 29\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 A model of water quality, 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Oases in the desert, 31\u003c\/p\u003e \u003cp\u003e3.2 Understanding the problem, 32\u003c\/p\u003e \u003cp\u003e3.3 Model development, 32\u003c\/p\u003e \u003cp\u003e3.4 Evaluating the model, 37\u003c\/p\u003e \u003cp\u003e3.5 Applying the model, 38\u003c\/p\u003e \u003cp\u003e3.6 Conclusions, 39\u003c\/p\u003e \u003cp\u003e3.7 Problems, 40\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 The Laplace equation, 42\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Laplace’s equation, 42\u003c\/p\u003e \u003cp\u003e4.2 The Elysian Fields, 43\u003c\/p\u003e \u003cp\u003e4.3 Model development, 44\u003c\/p\u003e \u003cp\u003e4.4 Quantifying the conceptual model, 47\u003c\/p\u003e \u003cp\u003e4.5 Nondimensionalization, 48\u003c\/p\u003e \u003cp\u003e4.6 Solving the governing equation, 49\u003c\/p\u003e \u003cp\u003e4.7 What does it mean?, 50\u003c\/p\u003e \u003cp\u003e4.8 Numerical approximation of the second derivative, 54\u003c\/p\u003e \u003cp\u003e4.9 Conclusions, 57\u003c\/p\u003e \u003cp\u003e4.10 Problems, 58\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 The Poisson equation, 62\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Poisson’s equation, 62\u003c\/p\u003e \u003cp\u003e5.2 Alcatraz island, 63\u003c\/p\u003e \u003cp\u003e5.3 Understanding the problem, 65\u003c\/p\u003e \u003cp\u003e5.4 Quantifying the conceptual model, 74\u003c\/p\u003e \u003cp\u003e5.5 Nondimensionalization, 76\u003c\/p\u003e \u003cp\u003e5.6 Seeking a solution, 79\u003c\/p\u003e \u003cp\u003e5.7 An alternative nondimensionalization, 82\u003c\/p\u003e \u003cp\u003e5.8 Conclusions, 84\u003c\/p\u003e \u003cp\u003e5.9 Problems, 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The transient diffusion equation, 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The diffusion equation, 87\u003c\/p\u003e \u003cp\u003e6.2 The Twelve Labors of Hercules, 88\u003c\/p\u003e \u003cp\u003e6.3 The Augean Stables, 90\u003c\/p\u003e \u003cp\u003e6.4 Carrying out the plan, 92\u003c\/p\u003e \u003cp\u003e6.5 An analytical solution, 100\u003c\/p\u003e \u003cp\u003e6.6 Evaluating the solution, 109\u003c\/p\u003e \u003cp\u003e6.7 Transient finite differences, 114\u003c\/p\u003e \u003cp\u003e6.8 Conclusions, 118\u003c\/p\u003e \u003cp\u003e6.9 Problems, 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 The Theis equation, 122\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Knight of the Sorrowful Figure, 122\u003c\/p\u003e \u003cp\u003e7.2 Statement of the problem, 124\u003c\/p\u003e \u003cp\u003e7.3 The governing equation, 125\u003c\/p\u003e \u003cp\u003e7.4 Boundary conditions, 127\u003c\/p\u003e \u003cp\u003e7.5 Nondimensionalization, 128\u003c\/p\u003e \u003cp\u003e7.6 Solving the governing equation, 132\u003c\/p\u003e \u003cp\u003e7.7 Theis and the “well function”, 134\u003c\/p\u003e \u003cp\u003e7.8 Back to the beginning, 135\u003c\/p\u003e \u003cp\u003e7.9 Violating the model assumptions, 138\u003c\/p\u003e \u003cp\u003e7.10 Conclusions, 139\u003c\/p\u003e \u003cp\u003e7.11 Problems, 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The transport equation, 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The advection–dispersion equation, 141\u003c\/p\u003e \u003cp\u003e8.2 The problem child, 143\u003c\/p\u003e \u003cp\u003e8.3 The Augean Stables, revisited, 144\u003c\/p\u003e \u003cp\u003e8.4 Defining the problem, 144\u003c\/p\u003e \u003cp\u003e8.5 The governing equation, 146\u003c\/p\u003e \u003cp\u003e8.6 Nondimensionalization, 148\u003c\/p\u003e \u003cp\u003e8.7 Analytical solutions, 152\u003c\/p\u003e \u003cp\u003e8.8 Cauchy conditions, 165\u003c\/p\u003e \u003cp\u003e8.9 Retardation and dispersion, 167\u003c\/p\u003e \u003cp\u003e8.10 Numerical solution of the ADE, 169\u003c\/p\u003e \u003cp\u003e8.11 Conclusions, 173\u003c\/p\u003e \u003cp\u003e8.12 Problems, 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Heterogeneity and anisotropy, 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Understanding the problem, 177\u003c\/p\u003e \u003cp\u003e9.2 Heterogeneity and the representative elemental volume, 179\u003c\/p\u003e \u003cp\u003e9.3 Heterogeneity and effective properties, 180\u003c\/p\u003e \u003cp\u003e9.4 Anisotropy in porous media, 187\u003c\/p\u003e \u003cp\u003e9.5 Layered media, 188\u003c\/p\u003e \u003cp\u003e9.6 Numerical simulation, 189\u003c\/p\u003e \u003cp\u003e9.7 Some additional considerations, 191\u003c\/p\u003e \u003cp\u003e9.8 Conclusions, 192\u003c\/p\u003e \u003cp\u003e9.9 Problems, 192\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Approximation, error, and sensitivity, 195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Things we almost know, 195\u003c\/p\u003e \u003cp\u003e10.2 Approximation using derivatives, 196\u003c\/p\u003e \u003cp\u003e10.3 Improving our estimates, 197\u003c\/p\u003e \u003cp\u003e10.4 Bounding errors, 199\u003c\/p\u003e \u003cp\u003e10.5 Model sensitivity, 201\u003c\/p\u003e \u003cp\u003e10.6 Conclusions, 206\u003c\/p\u003e \u003cp\u003e10.7 Problems, 207\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 A case study, 210\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Borax Lake Hot Springs, 210\u003c\/p\u003e \u003cp\u003e11.2 Study motivation and conceptual model, 212\u003c\/p\u003e \u003cp\u003e11.3 Defining the conceptual model, 213\u003c\/p\u003e \u003cp\u003e11.4 Model development, 215\u003c\/p\u003e \u003cp\u003e11.5 Evaluating the solution, 224\u003c\/p\u003e \u003cp\u003e11.6 Conclusions, 229\u003c\/p\u003e \u003cp\u003e11.7 Problems, 230\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Closing remarks, 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Some final thoughts, 233\u003c\/p\u003e \u003cp\u003eAppendix A A heuristic approach to nondimensionalization, 236\u003c\/p\u003e \u003cp\u003eAppendix B Evaluating implicit equations, 238\u003c\/p\u003e \u003cp\u003eB.1 Trial and error, 239\u003c\/p\u003e \u003cp\u003eB.2 The graphical method, 239\u003c\/p\u003e \u003cp\u003eB.3 Iteration, 240\u003c\/p\u003e \u003cp\u003eB.4 Newton’s method, 241\u003c\/p\u003e \u003cp\u003eAppendix C Matrix solution for implicit algorithms, 243\u003c\/p\u003e \u003cp\u003eC.1 Solution of 1D equations, 243\u003c\/p\u003e \u003cp\u003eC.2 Solution for higher dimensional problems, 244\u003c\/p\u003e \u003cp\u003eC.3 The tridiagonal matrix routine TDMA, 244\u003c\/p\u003e \u003cp\u003eIndex, 247\u003c\/p\u003e","brand":"John Wiley and Sons Ltd","offers":[{"title":"Default Title","offer_id":49528847794519,"sku":"9781119130369","price":64.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119130369.jpg?v=1731873259","url":"https:\/\/bookcurl.com\/products\/models-and-modeling-9781119130369","provider":"Book Curl","version":"1.0","type":"link"}