Book Review
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Pure and Applied Geophysics
Book Review Mathematical Modeling of Earth’s Dynamical Systems: A Primer by Rudy Slingerland and Lee Kump, Princeton University Press, 2011; ISBN: 978-0-691-14513-6 (Hardcover), ISBN: 978-0-691-14514-3 (paperback) ANDRZEJ ICHA1 The aim of mathematical modeling is to obtain in quantitative form information regarding the selected aspects of reality by use of the mathematical concepts and apparatus. The concise textbook: ‘‘Mathematical Modeling of Earth’s Dynamical Systems: A Primer’’ by R. Slingerland and L. Kump, provides the mathematical and computational background for earth scientists and students who are less familiar with the role of mathematical models in the geosciences, especially in the description of the Earth’s surface processes. The book starts with Chapter 1, where in the subsequent sections the authors present the basic philosophy of mathematical modeling. Overviewed are standard notions, definitions and steps in model building and solving. Two examples are described briefly: simulation of the Chicxulub Impact and the storm surge of hurricane Ivan in Escambia Bay. The last several subsections deal with well-posed differential dynamical models in the Hadamard sense. Chapter 2 deals with the numerical analysis background for a finite difference approach to solve partial differential equations. Some elements of matrix algebra are reviewed first. Convergence, stability, and consistency of finite difference schemes in the solution of a model, one-dimensional (1-D) diffusion equation are explained and discussed briefly. Chapter 3 is devoted to the box (or ‘‘toy’’) modeling. Toy models in geosciences are developed to
1 Pomeranian Academy in Słupsk, Institute of Mathematics, ul. Arciszewskiego 22d, 76-200 Słupsk, Poland. E-mail: [email protected]
make simpler the description of complex earth systems while preserving only essential attributes of key components and processes. The methodology of box modeling is presented through a few examples including: radiocarbon balance of the biosphere (as a one-box model); the carbon cycle (as a multibox model); 1-D energy balance climate model and Rothman Ocean (i.e., two reservoirs model of the Proterozoic Era ocean carbon cycle). Mathematical description of toy models leads to a system of ordinary differential equations with a prescribed set of initial conditions. As indicated in Chapter 2, the standard approach is to convert these equations to algebraic equations using finite differences and then use methods from linear algebra to solve the equations. Included are: the forward Euler method, predictor–corrector methods and the backward Euler method. Some remarks regarding the model enhancements are presented also. Chapter 4 discusses the 1-D diffusion equation, a paradigm for many of the physical problems in which a conservative property moves through space at a rate proportional to some gradient. Three examples are explored and analysed to illustrate the earth phenomena which can be concisely described by such an equation, namely: dissol
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