Gstat is a program for the modelling, prediction and simulation of geostatistical data in one, two or three dimensions. Geostatistical data are data (measurements) collected at known locations in space, from a function (process) that has a value at every location in a certain (1, 2 or 3-D) domain. These data (or some transform of them) are modelled as the sum of a constant or varying trend and a spatially correlated residual. Given a model for the trend, and under some stationarity assumptions, geostatistical modelling involves the estimation of the spatial correlation. Geostatistical prediction (`kriging') is finding the best linear unbiased prediction (the expected value) with its prediction error for a variable at a location, given observations and a model for their spatial variation. Simulation of a spatial variable is the creation of randomly drawn realizations of a field given a model for the data, possibly conditioned on observations.
In gstat, geostatistical modelling comprises calculation of sample variograms and cross variograms (or covariograms) and fitting models to them. Sample (co-) variograms are calculated from ordinary, weighted or generalised least squares residuals. Nested models are fitted to sample (co-) variograms using weighted least squares, and during a fit each single parameter can be fixed. Restricted maximum likelyhood estimation of partial sills is also implemented. In the interactive variogram modelling user interface of gstat, variograms are plotted using the plotting program gnuplot.
Gstat provides prediction and estimation using a model that is the sum of a trend modelled as a linear function of polynomials of the coordinates or of user-defined base functions, and an independent or dependent, geostatistically modelled residual. This allows simple, ordinary and universal kriging, simple, ordinary and universal cokriging, standardised cokriging, kriging with external drift, block kriging and ``kriging the trend'', as well as uncorrelated, ordinary or weighted least squares regression prediction. Simulation in gstat comprises uni- or multivariable conditional or unconditional multi-Gaussian sequential simulation of point values or block averages, or (multi-) indicator sequential simulation.
Besides many of the common options found in other geostatistical software packages, gstat offers the unique combination of
Chapter 2 explains the concepts behind gstat and its basic methods and prediction or simulation modes. Chapter 3 treats the simple, multiple, multivariable and stratified modes, and change of support (block kriging). Chapter 4 is a complete reference of the command file syntax. Chapter 5 explains how the program can be further controlled, for instance by using start-up files, command line options or environment variables. Finally, Chapter 6 lists a number of example command files that demonstrate most of the capabilities of gstat (these files are part of the program distribution). The appendices contain more technical details: equations for modelling and prediction (A) and error messages and help information (C). Suggestions for improvement of gstat or this manual are welcome--send them to
A mailing lists for announces (version releases etc.) regarding gstat, exists:
or visit the gstat home page, http://www.geog.uu.nl/gstat/.