Topographic advection on fault-bend folds: Inheritance of valley positions and the formation of wind gaps

__Mathematical Modeling of Earth's Dynamical Systems__ gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. __Mathematical Modeling of Earth's Dynamical Systems__ helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. * Step-by-step lessons for representing complex Earth systems as dynamical models * Explains geologic processes in terms of fundamental laws of physics and chemistry * Numerical solutions to differential equations through the finite difference technique * A philosophical approach to quantitative problem-solving * Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more * Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class\_use/solutions.html Cover......Page 1 Title......Page 4 Copyright......Page 5 Contents......Page 6 Preface......Page 12 1 Modeling and Mathematical Concepts......Page 16 Pros and Cons of Dynamical Models......Page 17 Some Examples......Page 19 Example I: Simulation of Chicxulub Impact and Its Consequences......Page 20 Example II: Storm Surge of Hurricane Ivan in Escambia Bay......Page 22 Steps in Model Building......Page 23 Basic Definitions and Concepts......Page 26 Nondimensionalization......Page 28 A Brief Mathematical Review......Page 29 Summary......Page 37 First Some Matrix Algebra......Page 38 Solution of Linear Systems of Algebraic Equations......Page 40 General Finite Difference Approach......Page 41 Discretization......Page 42 Obtaining Difference Operators byTaylor Series......Page 43 Explicit Schemes......Page 44 Implicit Schemes......Page 45 How Good Is My Finite Difference Scheme?......Page 48 Stability Is Not Accuracy......Page 50 Summary......Page 52 Modeling Exercises......Page 53 3 Box Modeling: Unsteady, Uniform Conservation of Mass......Page 54 Example I: Radiocarbon Content of the Biosphere as a One-Box Model......Page 55 Example II: The Carbon Cycle as a Multibox Model......Page 63 Example III: One-Dimensional Energy Balance Climate Model......Page 68 The Forward Euler Method......Page 72 Predictor–Corrector Methods......Page 74 Stiff Systems......Page 75 Example IV: Rothman Ocean......Page 76 Backward Euler Method......Page 80 Model Enhancements......Page 84 Modeling Exercises......Page 86 4 One-Dimensional Diffusion Problems......Page 89 Example I: Dissolved Species in a Homogeneous Aquifer......Page 90 Example II: Evolution of a Sandy Coastline......Page 95 Example III: Diffusion of Momentum......Page 98 Summary......Page 101 Modeling Exercises......Page 102 5 Multidimensional Diffusion Problems......Page 104 Example I: Landscape Evolution as a 2-D Diffusion Problem......Page 105 Example II: Pollutant Transport in a Confined Aquifer......Page 111 Example III: Thermal Considerations in Radioactive Waste Disposal......Page 114 Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems......Page 116 An Explicit Scheme......Page 117 Implicit Schemes......Page 118 Case of Variable Coefficients......Page 122 Summary......Page 123 Modeling Exercises......Page 124 6 Advection-Dominated Problems......Page 126 Example I: A Dissolved Species in a River......Page 127 Example II: Lahars Flowing along Simple Channels......Page 131 Finite Difference Solution Schemes to the Linear Advection Equation......Page 137 Summary......Page 141 Modeling Exercises......Page 143 7 Advection and Diffusion (Transport) Problems......Page 145 Example I: A Generic 1-DCase......Page 146 Example II: Transport of Suspended Sediment in a Stream......Page 149 Example III: Sedimentary Diagenesis:Influence of Burrows......Page 153 Finite Difference Solutions to the Transport Equation......Page 158 QUICK Scheme......Page 159 QUICKEST Scheme......Page 161 Modeling Exercises......Page 162 8 Transport Problems with a Twist: The Transport of Momentum......Page 166 Example I: One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers’ Equation)......Page 167 An Analytic Solution to Burgers’ Equation......Page 172 Finite Difference Scheme for Burgers’Equation......Page 173 Solution Scheme Accuracy......Page 175 Diffusive Momentum Transport inTurbulent Flows......Page 178 Adding Sources and Sinks of Momentum:The General Law of Motion......Page 180 Summary......Page 181 Modeling Exercises......Page 182 Example I: Gradually Varied Flow in an Open Channel......Page 184 Explicit FTCS Scheme on a Staggered Mesh......Page 190 Four-Point Implicit Scheme......Page 192 The Dam-BreakProblem: An Example......Page 195 Summary......Page 198 Modeling Exercises......Page 200 10 Two-Dimensional Nonlinear Hyperbolic Systems......Page 202 Example I: The Circulation of Lakes, Estuaries, and the Coastal Ocean......Page 203 An Explicit Solution Scheme for 2-DVertically Integrated Geophysical Flows......Page 212 Lake Ontario Wind-DrivenCirculation: An Example......Page 217 Summary......Page 218 Modeling Exercises......Page 221 Closing Remarks......Page 224 References......Page 226 A......Page 232 B......Page 233 C......Page 234 D......Page 235 E......Page 236 F......Page 237 H......Page 238 K......Page 239 M......Page 240 N......Page 241 P......Page 242 S......Page 244 T......Page 245 Y......Page 246 Machine generated contents note: -- 1. Modeling and Mathematical Concepts -- Pros and Cons of Dynamical Models -- An Important Modeling Assumption -- Some Examples -- -- Example I Simulation of Chicxulub Impact and Its Consequences -- -- Example II Storm Surge of Hurricane Ivan in Escambia Bay -- Steps in Model Building -- Basic Definitions and Concepts -- Nondimensionalization -- A Brief Mathematical Review -- Summary -- -- 2. Basics of Numerical Solutions by Finite Difference -- First Some Matrix Algebra -- Solution of Linear Systems of Algebraic Equations -- General Finite Difference Approach -- Discretization -- Obtaining Difference Operators by Taylor Series -- Explicit Schemes -- Implicit Schemes -- How Good Is My Finite Difference Scheme? -- Stability Is Not Accuracy -- Summary -- Modeling Exercises -- -- 3. Box Modeling: Unsteady, Uniform Conservation of Mass -- Translations Example I Radiocarbon Content of the Biosphere as a One-Box Model -- -- Example II The Carbon Cycle as a Multibox Model -- -- Example III One-Dimensional Energy Balance Climate Model -- Finite Difference Solutions of Box Models -- The Forward Euler Method -- Predictor-Corrector Methods -- Stiff Systems -- -- Example IV Rothman Ocean -- Backward Euler Method -- Model Enhancements -- Summary -- Modeling Exercises -- -- 4. One-Dimensional Diffusion Problems -- Translations -- -- Example I Dissolved Species in a Homogeneous Aquifer -- -- Example II Evolution of a Sandy Coastline -- -- Example III Diffusion of Momentum -- Finite Difference Solutions to 1-D Diffusion Problems -- Summary -- Modeling Exercises -- -- 5. Multidimensional Diffusion Problems -- Translations -- -- Example I Landscape Evolution as a 2-D Diffusion Problem -- -- Example II Pollutant Transport in a Confined Aquifer -- -- Example III Thermal Considerations in Radioactive Waste Disposal Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems -- An Explicit Scheme -- Implicit Schemes -- Case of Variable Coefficients -- Summary -- Modeling Exercises -- -- 6. Advection-Dominated Problems -- Translations -- -- Example I A Dissolved Species in a River -- -- Example II Lahars Flowing along Simple Channels -- Finite Difference Solution Schemes to the Linear Advection Equation -- Summary -- Modeling Exercises -- -- 7. Advection and Diffusion (Transport) Problems -- Translations -- -- Example I A Generic 1-D Case -- -- Example II Transport of Suspended Sediment in a Stream -- -- Example III Sedimentary Diagenesis: Influence of Burrows -- Finite Difference Solutions to the Transport Equation -- QUICK Scheme -- QUICKEST Scheme -- Summary -- Modeling Exercises -- -- 8. Transport Problems with a Twist: The Transport of Momentum -- Translations -- -- Example I One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers' Equation) An Analytic Solution to Burgers' Equation -- Finite Difference Scheme for Burgers' Equation -- Solution Scheme Accuracy -- Diffusive Momentum Transport in Turbulent Flows -- Adding Sources and Sinks of Momentum: The General Law of Motion -- Summary -- Modeling Exercises -- -- 9. Systems of One-Dimensional Nonlinear Partial Differential Equations -- Translations -- -- Example I Gradually Varied Flow in an Open Channel -- Finite Difference Solution Schemes for Equation Sets -- Explicit FTCS Scheme on a Staggered Mesh -- Four-Point Implicit Scheme -- The Dam-Break Problem: An Example -- Summary -- Modeling Exercises -- -- 10. Two-Dimensional Nonlinear Hyperbolic Systems -- Translations -- -- Example I The Circulation of Lakes, Estuaries, and the Coastal Ocean -- An Explicit Solution Scheme for 2-D Vertically Integrated Geophysical Flows -- Lake Ontario Wind-Driven Circulation: An Example -- Summary -- Modeling Exercises.

Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables.

This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus.

Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems.

• Step-by-step lessons for representing complex Earth systems as dynamical models
• Explains geologic processes in terms of fundamental laws of physics and chemistry
• Numerical solutions to differential equations through the finite difference technique
• A philosophical approach to quantitative problem-solving
• Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more
• Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to reorganize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrainec coeffecients, and unfalsifiable models. Studentr using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. -- BACK COVER Gives earth scientists the useful skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, this book identifies the important geological variables of physical-chemical geoscience problems.