Geostatistics is a subset of statistics specialized in analysis and interpretation of geographically referenced data (Goovaerts, 1997; Webster and Oliver, 2001; Nielsen and Wendroth, 2003). In other words, geostatistics comprises statistical techniques that are adjusted to spatial data. Typical questions of interest to a geostatistician are:

how does a variable vary in space?

what controls its variation in space?

where to locate samples to describe its spatial variability?

how many samples are needed to represent its spatial variability?

what is a value of a variable at some new location?

what is the uncertainty of the estimate?

This began as an attempt to write the book that we wish we had read when we were trying to learn geostatistics, a task that turned out to be much more difficult than we originally envisaged. To the many people who provided encouragement, support, and advice throughout the writing of this book, we are very grateful.

We owe a lot to Andre Journel, without whom this book would never have been written. In addition to providing the support necessary for this project, he has been an insightful technical reviewer and an energetic cheerleader.

This introductory chapter presents a discrete approach specially designed for modeling the geometry and the properties of natural objects such as those encountered in biology and geology.

Geostatistics, developed originally in the mining industry from the 1950s onwards, is now being applied widely in environmental science for mapping, monitoring and management. It is based on the theory of random spatial processes. There are numerous examples in soil science, meteorology, agronomy, hydrology, ecology and some aspects of marine science. By taking into account and modelling spatial correlation, geostatistics provides unbiased predictions of environmental variables with minimum and known variance in ways that no other method does. The general technique of prediction is known as kriging. It requires a mathematical model to describe the spatial covariance, usually expressed as a variogram, which in its parameterized form has become the central tool of geostatistics. Successful kriging and estimation of the variogram depend on sampling adequately without bias and with suitable spatial configurations and supports. These differ somewhat from design-based estimation with its emphasis on random sampling. <...>