{"product_id":"models-and-modeling-isbn-9781119130369","title":"Models and Modeling","description":"\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 image of a geologist or environmental scientist may be the rugged\u003c\/p\u003e \u003cp\u003eadventurer, heading off into the wilderness with a compass and a hand level, the disciplines\u003c\/p\u003e \u003cp\u003eof geology, hydrogeology, and environmental sciences have become increasingly quantitative.\u003c\/p\u003e \u003cp\u003eToday’s earth science professionals routinely work with mathematical and computer models,\u003c\/p\u003e \u003cp\u003eand career success often demands a broad range of analytical and computational skills.\u003c\/p\u003e An Introduction to Models and Modeling in the Earth and Environmental Sciencesis written for \u003cp\u003estudents and professionals who want to learn the craft of modeling, and do more than just\u003c\/p\u003e \u003cp\u003erun “black box” computer simulations.\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 \u003cp\u003eDr. Jerry P. Fairley received his PhD in Earth Resources Engineering from the University\u003c\/p\u003e \u003cp\u003eof California, Berkeley. He was the Chief Hydrologist for Site Characterization on the US-\u003c\/p\u003e \u003cp\u003eDOE’s Yucca Mountain Project (1993–1995), and worked as a modeler for the Earth Sciences\u003c\/p\u003e \u003cp\u003eDivision of Lawrence Berkeley National Laboratory. He is currently a Professor of Geology\u003c\/p\u003e \u003cp\u003eat the University of Idaho, Department of Geological Sciences.\u003c\/p\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 image of a geologist or environmental scientist may be the rugged\u003c\/p\u003e \u003cp\u003eadventurer, heading off into the wilderness with a compass and a hand level, the disciplines\u003c\/p\u003e \u003cp\u003eof geology, hydrogeology, and environmental sciences have become increasingly quantitative.\u003c\/p\u003e \u003cp\u003eToday’s earth science professionals routinely work with mathematical and computer models,\u003c\/p\u003e \u003cp\u003eand career success often demands a broad range of analytical and computational skills.\u003c\/p\u003e An Introduction to Models and Modeling in the Earth and Environmental Sciencesis written for \u003cp\u003estudents and professionals who want to learn the craft of modeling, and do more than just\u003c\/p\u003e \u003cp\u003erun “black box” computer simulations.\u003c\/p\u003e","brand":"Wiley-Blackwell","offers":[{"title":"Default Title","offer_id":47989638791397,"sku":"NP9781119130369","price":72.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119130369.jpg?v=1761784913","url":"https:\/\/k12savings.com\/products\/models-and-modeling-isbn-9781119130369","provider":"K12savings","version":"1.0","type":"link"}