Mathematical Geology, Vol. 21, No. 4, 1989

Book Review Computer Simulation in Physical Geography by M. J. Kirkby, P. S. Naden, T. P. Burt, and D. P. Butcher John Wiley and Sons, New York, 1987, 227 p., $49.95 (US) To see new books appearing that can help explain the applications of computers in geosciences is a real delight. This one can serve as an introduction to previous work, but suffers shortcomings of which the reader should be wary. The book is divided into two parts. Part I (Chapters 1-5) gives an overview of model types in physical geography (or in any other science). These model types include "simple" models termed by the authors "Black Box," process models (in the sense of Kmmbein, 1963), and physically based models based on mass balance or energy balance or combined with a statistical component to make "stochastic models." Part II (Chapters 6-8) discusses some ideas of modeling, including formulating and building the model, testing the model, and more esoteric aspects of model selection and design. Chapter 1 has a nice discussion of mass balance problems and explains that stochastic models are a more inclusive group than mass and energy balance models. The idea of randomness in model results is introduced with simple examples. Chapter 2 tries to introduce regressions as part of the discussion of black box models. The discussion here is weak, such as when the authors claim that " a high correlation shows that the relationship between X and Y is strong and sensitive; the regression may therefore be used for prediction." Chapter 3, more current than others in this part, discusses stream erosion processes (without mentioning widely available programs such as HEC-6; U.S. COE, 1977). In chapter 4, a nice review of energy balance in evapotranspiration emphasizes the author's idea that "the one area where an energy budget is important is in microclimatology." " . . . this balance is perhaps most important.., for estimating evapotranspiration... " . Then, to read four pages later "There are better and more sophisticated methods for estimating evapotranspiration... , " referring back to Chapter 3 on ("simplier' ') process models is disquieting. Chapter 5 completes Part I with a discussion of stochastic models. We are told (p. 96) that the central limit theorem "states that the sum of over 30 random variables is always normally distributed, whatever the original distribution of 487 0882-8121/89/o5oo-o4875o6.oo/1 © 1989 International Association for Mathematical Geology

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the values used." ARIMA is defined (p. 97) as "arithmetic moving average." This is in a statistical section discussing time series models without reference to the work of Box and Jenkins (1982). Other awkward or erroneous information is sufficiently common that the instructor will have to be on his/her toes to guard against its unwitting acceptance by students who might use the book. Part II of the text is considerably cleaner in form and execution. The authors integrate the text by drawing on examples from the first part. Chapter 6 describes succinctly many forms of solution of equations, why different methods are needed, and some strengths and weaknesses. It ends with sage advice " T h e impression you may get from the sequence of checking and rechecking is that a program is never finished and perfect. That is t r u e . . . " but you must decide "when the program is good enough." Chapter 7 discusses calibration and verification. The authors use terms differently than in the U.S. where verification refers to comparison of code to desired equations and validation refers to comparisons to reality. The authors use verification with this latter sense. The discussion of calibration covers estimating process values from field data and optimizing values through sensitivity analysis where data are insufficient. This latter problem is described nicely. Section 7.3 is the weakest; the ideas are interesting but unclear because the equations are not presented well: for example, E = sl ( Q o b s i - - aobsi) 2NOW sl is not defined, but if we assume, as the authors seem to mean, that it is a sum, then we get E = 0. The discussion of Data Requirements for Modelling in Section 7.4 is also interesting, especially ideas on sensitivity studies. This section also suffers annoying problems. Are the Fi's (p. 171) the same as those given on p. 166? What is the source of c (c = 0.2) (p. 172)? Chapter 8 illustrates how the methods of Chapters 1-5 can each yield a version of the same system. Some considerations in choice of modelling style--time scale and forces--are appropriate and are exemplified nicely. The impact of the decision of exactly what to model in the system is also explained. The authors here express a healthy appreciation of uncertainty. The book is 227 pages long with just a few tables but with many illustrations of good quality. All of the computer programs listed in the book are available separately from the publisher on floppy disk. The price of the disk seems excessive because complete listings are available in the book. Prices of copying and distribution of disks can't be that great. The listings are "compressed," that is, semicolons separate items that normally are listed on separate lines. This saves paper in the text but does make them more challenging to read. Even with this compression, the codes take quite a lot of space. Unfortunately, with the obscurity of the code (variable names such as CC, CQ, etc.), it can hardly serve as a good teaching tool for beginners. All the programs are in BASIC, chosen for its transportability by the authors; but, the programs might have been as flexible, more up-to-date, and faster if done in " C . "

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Numerous typographical errors of the kind not caught by a spelling program (flood ~ food, is ~ if, etc.) are present. These suggest lack of editorial review at the publisher. As a pedagogic tool, the text suffers several weaknesses and appears not to have been reviewed carefully from a teaching viewpoint. For example, the reader is informed (p 69) that " I n setting up a mass balance or energy balance model, a flow or systems diagram should be drawn." No reference is made to others who have shown examples of these in physical geography, nor are general discussions of such diagrams referenced. Moreover, no examples of real diagrams are shown, but only a variety of hypothetical flow diagrams (boxes and arrows) are presented. Another limitation for use in teaching is that the book contains no formal exercises that could guide application or training in specifics. This would be necessary at the undergraduate level where the book clearly is pitched. The biggest concerns are paucity of references and their lack of recency. A text like this one should make the field more accessible to the student by providing copious references. A total of 108 references are given at the ends of chapters. That location is an inconvenience for later referencing or crosschecks and browsing. The authors show a tendency to reference themselves (p = 0.2). Perhaps this is because the manuscript was originally written for a workshop short course led by the authors in 1985. The book would have benefited by editing the short course notes in this respect. References are scanty, especially for the superficial level of coverage given topics in the text. Are the references up-to-date? They are spotty and show the individual author's inpact upon the chapters. Part II is much better in this respect with a marked tendency to reference works from this decade. Perhaps Part I, with its emphasis on different types of models in physical geography, should have an historical flavor. Yet, when one chapter has no references from this decade and two chapters have only one each, the recency of the coverage should be questioned. Two appendices are given; the first is a glossary. The second summarizes generic routines called in all programs. Examples are input or output routines. The authors have done a commendable job of making the code as machine independent as possible. The index, 7 pages long, contains some real oddities. Examples include *EXEC and terms where the only reference is to the glossary (Appendix A). The authors have produced a work that could be useful to those teaching at the undergraduate level. In an introduction to computer applications in geosciences, this could be a useful supplement. Usually, the beginning geoscience student will already have some introduction to computer use, so this book might be relegated to courses in computer simulation or as a supplement to a course in physical geography/geomorphology. One other use could be as a text in a course devoted to computer simulation in physical geography; but, it is a rare department that has such a course. The kind of course would probably be too

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advanced to benefit from this text. For example, because each of the programs is no more than 100 lines in BASIC, little opportunity exists to explore scientific subtleties. Richard G. Craig

Department of Geology Kent State University Kent, Ohio 44242, USA REFERENCES Box, G. E. P. and Jenkins, G. M. 1982, Time Series Analysis: Forecasting and Control, 2nd ed., Holden-Day, San Francisco, California. Krnmbein, W. C., 1963, A Geological Process-Response Model for Analysis of Beach Phenomena, Bull. Beach Erosion Board, v. 17, pp. 1-15. U.S. Army Corps of Engineers, 1977, HEC-6, Scour and Deposition in Rivers and Reservoirs, User's Manual, Hydrologic Engineering Center, Davis, California.

Mathematical Geology, Vol. 21, No. 4, 1989

Book Review Statistical Analysis of Spherical Data by N. I. Fisher, T. L. Lewis, and B. J. J. Embleton Cambridge University Press, Cambridge and New York, 1987, 329 p., $65.00 (US) This very practical book explains how to analyze data sets which are the directions in three dimensions of oriented lines (e.g., facing directions of planes, direction of remanent magnetization) and of unoriented lines (e.g., the normal to a plane, the axis of maximum susceptibility). Such data sets naturally are thought of pictorially as sets of points on the unit sphere, hence the title. Everyone with this sort of data should have access to this book. Fisher is curently writing another book on the two-dimensional case. This book presents clearly the best and most modern statistical methods. It assumes that the research worker has a computer and encourages the user to produce graphical as well as numerical output. No programs are given, though some appear in cited references. However, each problem is considered via an illustrative real data set, and the reader is shown first how to display the data-the exploratory phase, T~oughly. Then he/she is given a sequence of computing instructions via formulae and told how to interpret the resulting numbers. This is followed by references and footnotes, to help the reader who wishes to go into the analysis further. Chapters 1 to 4 should be read by everyone. They constitute an up-to-date mini-course in statistics; all the mathematical and statisitical words and concepts needed later are explained. Some of the material given on probability plots, simulation methods, the permutation, jackknife and bootstrap methods, is still not known, and/or routinely used, in earth sciences. It is, alas, true that many courses and books on statistics still present the subject in a rigid way with great emphasis on methods to verify the obvious, which the reader must simply believe are valid. Further, mathematically derived methods rest upon assumptions, and so may be misleading, if these assumptions are false. Thus one needs to check assumptions as far as one can. Because there is a limit to this, the methods used should not be overly sensitive to undetectable deviations from assumptions, i.e., be "robust." The fact is that, by computer simulation, the 491 0882-8121/89/0500 049 l $06.00/1 © 1989 International Association for Mathematical Geology

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user can usually convince himself/herself and not take stuff on trust. However, no point exists in re-inventing the wheel--the methods given in this book have been checked in this way. The excitement of science lies in the ideas. The major part of the labor comes with the careful collection of data. Statistical analysis of data should generate ideas and provide valid estimates of unknown parameters and form support for, or rejection of, theories about the phenomena being investigated. Once the data are at hand, an obvious temptation exists to skimp on the further labor of analysis. Hopefully this book will help to carry workers with orientation data safely through this last step in their research. Chapters 5, 6, and 7 cover the more standard methods needed with one or more samples of unit vectors (directed lines) or axes (undirected lines). Chapter 8 deals with correlation, regression, and temporal/spatial analysis, which have been less studied but are the focus of much recent work. A slip occurs in the description of the Jupp-Mardia correlation tests--deviations from means should be used. (A list of the few typographical errors and slips may be obtained from the authors.) The cited work of Mackenzie (1957) and Moran (1976) on the estimation of rotations recently has been carried much further by Chang (1986), Thompson and Prentice (1987), and others. There has been more work on the topic of § 8.4.3, the estimation of apparent polar wander paths, e.g., Jupp and Kent (1987). With the natural exception of work done after this book was written, it is an exhaustive account and the authors are to be congratulated. Geoffrey S. Watson Fine Hall, Washington Road Princeton University Princeton, New Jersey 08544, USA. REFERENCES

Chang, T., 1986 Spherical Regression: Ann. Stat. v. 14, p. 907-24. Jupp, P. E., and Kent, J. T., 1987 Fitting Smooth Paths to Spherical Data: Appl. Stat. v. 36, p. 34-46. Thompson, R., and Prentice, M. J., 1987AlternativeMethod of Calculating Finite Plate Rotations: Phys. Earth PlanetInteriors v. 48, p. 79-83.