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Institute of Hydraulics, Hydrology and Water Resources Management Vienna University of Technology Karlsplatz 13/223 A-1040 Wien, Austria
bloeschl{at}hydro.tuwien.ac.at
Richard Webster and Margaret A. Oliver. John Wiley, New York, NY. 2001. Hardback, 271 pp. $105.00. ISBN 0-471-96553-7.
Geostatistics has become the method of choice for spatial estimation in many environmental disciplines. Software packages featuring easy-to-use geostatistical analysis and prediction tools abound. Along with their widespread use by scientists and practitioners alike, many books on the topic have been published in recent years. So why is there a need for yet another book on geostatistics? Geostatistics for Environmental Scientists is different from most of the other books available on the market. It is a practical guide on how to use geostatistical methods. To state it upfront, a very useful guide indeed, but it is not a textbook. This quite clearly defines the audience. A novice intending to learn and understand geostatistics from scratch will have difficulties with the mix in which some of the methods are presented and with some of the statistical and mathematical concepts required, such as biases and Fourier analysis. However, the book is ideal for practitioners with a general understanding of the underlying concepts who now want to know how best to apply them to their particular data set. It is also suitable for newcomers to the subject who are more interested in correctly applying the tools than in understanding their principles. The book provides a wealth of guidance on the most important aspects of any practical geostatistical analysis in the environmental sciences. It focuses on the two-dimensional case (i.e., geostatistical analysis and mapping in a landscape) in line with the main interest of most environmental scientists.
Geostatistics for Environmental Scientists is organized in the same way one would tackle a field investigation. The book starts with an introductory chapter on simple statistical quantities and screening methods. This chapter is practical and skips a rigorous introduction to probability concepts. Rather, it is a summary of those methods one would usually use in an initial examination of a data set. It then gives a brief overview of alternative spatial estimation methods to assist in the choice of method, but the recommendation is clear—"geostatistics has it all". The rationale for geostatistics, that is, the presence of spatial correlations, is discussed in the next chapter, including some of the underlying assumptions put into plain language. This chapter also dwells on the value of estimating the variable of interest for blocks rather than for individual points. A full chapter is devoted to the estimation of the sample variogram from data, and includes a treatment of anisotropy and drift, as well as a nice discussion of the reliability of the variogram. Alternative sampling schemes, such as nested sampling, are reviewed in the context of improving the reliability of the variogram. As in all the other chapters, practical advice abounds. Among other recommendations, in this chapter, the authors "... recommend that you have no fewer than 100 sampling points and ideally 150 to estimate the variogram reliably in two dimensions." In general, the number of points needed for reliably estimating the variogram depends, of course, on the accuracy required vs. resources available for the survey, sampling layout, measurement error, and the type of the underlying spatial variability, but in many cases these factors will indeed combine to what the authors recommend here. This example is illustrative of many of the recommendations in the book—they are concrete, meant for typical sampling and estimation scenarios, and they make perfect sense.
The next chapter deals with fitting the theoretical variogram to the sample variogram, often the crucial step in any geostatistical analysis. The view taken here is practical and refreshing in terms of the guidance given in choosing a variogram type based on a balance between mimicking the sample variogram and simplicity of the variogram model. Much emphasis is on the mathematical constraints to a valid variogram. The ensuing chapter is an aside on spectral analysis. Although the typical reader will probably not follow all the mathematics given here, there is enough intuitive explanation to make the relationship between power spectra and the variogram clear and to convey the merits of spectral analysis for periodic processes. The following chapter focuses on ordinary kriging. Block kriging is mixed into the description of kriging for points, which I found a little confusing. It may have been better to deal with block kriging in a separate subchapter, but otherwise this chapter is just as clearly written as the rest of the book. Illustrative examples of the kriging weights for different spatial setups are given, a nice way of intuitively demonstrating how the method works. Alternative kriging methods are briefly reviewed, including simple kriging, lognormal kriging, and universal kriging. Statistical anisotropy is also briefly covered. In the same chapter, cross validation is discussed. I believe there is room for more widespread use of cross validation in the environmental sciences for finding out just how good the interpolated estimates are, so a prominent discussion of cross validation in this book is to be welcomed. The next chapter is devoted to geostatistical methods that use one or more auxiliary variables to assist in interpolating the variable of interest, mainly focusing on co-kriging. Again, the various steps, including analysis of the cross-variogram, the kriging interpolation, and a discussion of the merits are provided. The last chapter is an extension chapter, as it does not dwell on finding a best interpolated surface but on the probabilities that the interpolated values are correct. The methods discussed here are disjunctive kriging and indicator kriging. This is a very apt way of rounding off a practical book on geostatistics. An appendix provides an "Aide-mémoire" summarizing of the most important steps in a spatial analysis, which I am sure many practitioners will thoroughly appreciate.
Throughout the book the main points are illustrated by case studies of soil surveys. With the authors having many years of experience as soil scientists this is an obvious choice; however, this by no means restricts the applicability of the book to the soil sciences. All the examples are sufficiently described to make them, and the book, useful for any environmental scientist, be she or he a soil scientist, hydrologist, ecologist, geographer, or environmental engineer.
Geostatistics for Environmental Scientists is a very readable book with a minimum of jargon and ample explanation of the mechanics and the context of geostatistics in plain language. It provides numerous practical recommendations on the choice and the application of methods. It is highly recommended.
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