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This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.
This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.
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
An accessible introduction to the mathematical methods essential for understanding processes in the Earth and environmental sciences.
An introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering and many other fields. It looks under the hood of current simulation technology and provides guidelines on what to look out for when carrying out sophisticated simulation tasks.
Understanding earth systems and its dynamic behavior requires objective insights into the complex observational data sets and their interrelationships. Drawing meaningful inferences from such data is not always an easy task as the deterministic relationships between various geological variables often remain obscured. These interrelationships need to be determined empirically through the analysis of a large set of data and validated through numerical simulations. The ever widening horizon of techniques of numerical analysis and simulation now provides a good number of tools to aid the interpretation. However, due to the inherent complexity of earth science data, expert supervision is required at all stages of analysis from collection to dissemination. This ensures that the most appropriate methodology is adopted and the results remain consistent with the geological principles. Discussions on these practical issues often lie beyond the scope of textbooks and this is precisely where this book is placed. In this book eminent geoscientists present their experiences in analyzing and managing earth science data as well as in designing numerical models to simulate earth processes. Apart from giving a discourse of their own approach towards a particular research problem they also discuss at length the relative merits of alternative methodologies. These seven authoritative articles, richly illustrated, will be a valuable resource for research students and professionals interested in research and teaching in various branches of earth science like, tectonics, GPS geodesy, sedimentology, geographical information science, and evolutionary biology.
Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete
The groundwater science and engineering has been closely connected with various fields (1) Groundwater Hydrology, (2) Groundwater Hydraulics or Geohydraulics, (3) Fluid Dynamics in Porous Media, (4) Groundwater Quality Engineering, (5) Soil Physics, and (6) Hydrogeology or Geohydrology. The purpose of the book is to present an update textbook of groundwater hydraulics, which includes all of basic items in above-mentioned fields, to students (of graduate school), researchers and practitioners. The students and beginners who intend to specialize in groundwater hydraulics through one semester will master contents of the book.
High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.