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Numerical methods in subsurface hydrology
Agricultural Meteorology, 11 (1973) 455-458 © Elsevier Scientific Publishing Company, Amsterdam-Printed in The Netherlands
B o o k Reviews
NumericalMethods in Subsurface Hydrology. Irwin Remson, George M. Hornberger and Fred J. Molz. Wiley, London, 1971, 389 pp., £8.00. In spite of the fact that finite-difference methods have been applied to problems in subsurface hydrology for more than a decade, a summary of available numerical techniques has not been readily available. Much of the initial research and development in this field was carried out by the oil industry, and, although some pertinent papers appeared in the applied mathematics and petroleum engineering journals, many of them were difficult reading for the hydrologist. Perhaps one could argue that numerical analysis has evolved so rapidly in recent years that a text on this subject would be obsolete before it came to press. This may be a valid criticism by those individuals who are familiar with the current literature;however, for hydrologists without a background in numerical analysis and who wish a pragmatic discussion of the subject as it pertains to their field of interest, Numerical Methods in Subsurface Hydrology is worthwhile reading. This book is principally concerned with introducing finite-difference techniques and demonstrating their application to the equations of flow through porous media. After introducing the concept of a potential the basic equations of subsurface flow are developed. A brief discussion of classical finite-difference theory follows in which the authors demonstrate how the partial differential equations may be approximated by a set of algebraic difference equations. It might have been worthwhile to consider more carefully in this discussion the use of variable-mesh nets, since they generally result in a much more efficient mathematical model. Although the discussion of methods for solving the difference equations is brief, it provides a lucid summary of techniques currently applied to subsurface-flow problems. One chapter is devoted to considering similarity solutions, and the final chapter consists of a rather brief discussion of the finite-element method and its application to ground-water-flow problems. The authors present their material at such a level that someone with a modest background in mathematics should be able to read the book easily and obtain adequate information to prepare a computer code to simulate subsurface flow. It is clearly not the authors' intent to demonstrate how the resultant mathematical models can be applied to field problems. Although a discussion of the difficulties to be anticipated in modelling field problems is beyond the scope of this book, and case histories are not considered, an outline of published numerical applications is provided as an appendix. For the benefit of the reader interested in more complex subsurface-flow problems, it might have been advantageous to demonstrate the broad scope of problems amenable
456
BOOK REVIEWS
to analysis by numerical techniques. For example, the transport of dissolved solids and heat in the subsurface (which is of increasing interest today and a challenging numerical problem) or the coupling of systems of equations such as occur in open-channel flow could have been discussed. I believe that this reference is a worthwhile addition to the hydrologist's library, although several additional topics could have been included in order to cover more completely the broad range of problems suggested by its title. GEORGE F. PINDER (Washington, D.C.)
The Ice Age in Britain. B. W. Sparks and R. G. West. Published by Methuen and Co. Ltd., London 1972, xvii + 302 pp., 171 illus., £5.50. Both of the authors of this book are well known for their specialist research papers on Pleistocene topics, but they indicate in the preface that they have written this work primarily for the non-specialist, as a broad study of the shortest period of geological time, the Pleistocene. They carry their story through the alternating cold and temperate phases of the Ice Age, to the point where in the Postglacial Neolithic Man was beginning the destruction of Britain's natural forests some 5,000 years ago. Ten chapters range over the General Geography of the Ice Age, the Causes of Ice Ages, Glacial Landforms, Periglacial features, the Stratigraphy of Ice Age Deposits, Ice Age Botany, Ice Age Zoology, Man in Ice Age Britain, Dating Ice Age Events, and the Physical Geography of the Last Interglacial in Britain. The book covers ground generally familiar to the university specialist, and provides a series of fascinating introductions to various topics for the interested layman and undergraduate. Indeed, there is much here which might be read with profit by research students specialising in some aspect of Pleistocene studies and this reviewer enjoyed dipping into the chapters on landforms, periglacial features and Pleistocene shorelines, for example, where a refreshingly clear presentation is made of the known facts. The authors do not hesitate to review some of the many remaining vexed problems concerning the Pleistocene - some of them concerned with events far beyond the confines of the British Isles - such as, the dating of Early and Middle Pleistocene successions. Pluvial and Interptuvial periods, the climatic implications of Interstadials and the difficulty of sub-dividing the glacial stages, the meaning and chronology of river terrace and marine beach sequences, and the reconstruction of former vegetation cover from collected pollen grains. There is a very clear account of the advantages, and pitfalls, of using botanical and zoological evidence for interpreting the alternating cold and temperate phases of the Pleistocene, with emphasis laid upon the need to consider carefully the principles upon which past plant and animal distributions can or cannot aid us in the interpretation of former environments. Some fundamental
B o o k Reviews
NumericalMethods in Subsurface Hydrology. Irwin Remson, George M. Hornberger and Fred J. Molz. Wiley, London, 1971, 389 pp., £8.00. In spite of the fact that finite-difference methods have been applied to problems in subsurface hydrology for more than a decade, a summary of available numerical techniques has not been readily available. Much of the initial research and development in this field was carried out by the oil industry, and, although some pertinent papers appeared in the applied mathematics and petroleum engineering journals, many of them were difficult reading for the hydrologist. Perhaps one could argue that numerical analysis has evolved so rapidly in recent years that a text on this subject would be obsolete before it came to press. This may be a valid criticism by those individuals who are familiar with the current literature;however, for hydrologists without a background in numerical analysis and who wish a pragmatic discussion of the subject as it pertains to their field of interest, Numerical Methods in Subsurface Hydrology is worthwhile reading. This book is principally concerned with introducing finite-difference techniques and demonstrating their application to the equations of flow through porous media. After introducing the concept of a potential the basic equations of subsurface flow are developed. A brief discussion of classical finite-difference theory follows in which the authors demonstrate how the partial differential equations may be approximated by a set of algebraic difference equations. It might have been worthwhile to consider more carefully in this discussion the use of variable-mesh nets, since they generally result in a much more efficient mathematical model. Although the discussion of methods for solving the difference equations is brief, it provides a lucid summary of techniques currently applied to subsurface-flow problems. One chapter is devoted to considering similarity solutions, and the final chapter consists of a rather brief discussion of the finite-element method and its application to ground-water-flow problems. The authors present their material at such a level that someone with a modest background in mathematics should be able to read the book easily and obtain adequate information to prepare a computer code to simulate subsurface flow. It is clearly not the authors' intent to demonstrate how the resultant mathematical models can be applied to field problems. Although a discussion of the difficulties to be anticipated in modelling field problems is beyond the scope of this book, and case histories are not considered, an outline of published numerical applications is provided as an appendix. For the benefit of the reader interested in more complex subsurface-flow problems, it might have been advantageous to demonstrate the broad scope of problems amenable
456
BOOK REVIEWS
to analysis by numerical techniques. For example, the transport of dissolved solids and heat in the subsurface (which is of increasing interest today and a challenging numerical problem) or the coupling of systems of equations such as occur in open-channel flow could have been discussed. I believe that this reference is a worthwhile addition to the hydrologist's library, although several additional topics could have been included in order to cover more completely the broad range of problems suggested by its title. GEORGE F. PINDER (Washington, D.C.)
The Ice Age in Britain. B. W. Sparks and R. G. West. Published by Methuen and Co. Ltd., London 1972, xvii + 302 pp., 171 illus., £5.50. Both of the authors of this book are well known for their specialist research papers on Pleistocene topics, but they indicate in the preface that they have written this work primarily for the non-specialist, as a broad study of the shortest period of geological time, the Pleistocene. They carry their story through the alternating cold and temperate phases of the Ice Age, to the point where in the Postglacial Neolithic Man was beginning the destruction of Britain's natural forests some 5,000 years ago. Ten chapters range over the General Geography of the Ice Age, the Causes of Ice Ages, Glacial Landforms, Periglacial features, the Stratigraphy of Ice Age Deposits, Ice Age Botany, Ice Age Zoology, Man in Ice Age Britain, Dating Ice Age Events, and the Physical Geography of the Last Interglacial in Britain. The book covers ground generally familiar to the university specialist, and provides a series of fascinating introductions to various topics for the interested layman and undergraduate. Indeed, there is much here which might be read with profit by research students specialising in some aspect of Pleistocene studies and this reviewer enjoyed dipping into the chapters on landforms, periglacial features and Pleistocene shorelines, for example, where a refreshingly clear presentation is made of the known facts. The authors do not hesitate to review some of the many remaining vexed problems concerning the Pleistocene - some of them concerned with events far beyond the confines of the British Isles - such as, the dating of Early and Middle Pleistocene successions. Pluvial and Interptuvial periods, the climatic implications of Interstadials and the difficulty of sub-dividing the glacial stages, the meaning and chronology of river terrace and marine beach sequences, and the reconstruction of former vegetation cover from collected pollen grains. There is a very clear account of the advantages, and pitfalls, of using botanical and zoological evidence for interpreting the alternating cold and temperate phases of the Pleistocene, with emphasis laid upon the need to consider carefully the principles upon which past plant and animal distributions can or cannot aid us in the interpretation of former environments. Some fundamental