Geostatistics for the Environmental Sciences

GS+ Features

GS+ – the premier geostatistical analysis program for desktop systems – was introduced in 1988 as the first integrated geostatistics program for the PC. It quickly became the geostatistics program of choice for users worldwide. Widely praised, GS+ was the first geostatistics package to offer all components – from variogram analysis through kriging and mapping – in an integrated package that provides the flexibility demanded by the specialist and the simplicity needed by the novice. GS+ runs on Windows XP, Vista, and Windows 7/8.

Variogram Analysis (Semivariance Analysis or Variography)

Comprehensive Semivariance Analysis provides both isotropic and anisotropic variograms. You have complete control over separation interval classes – choose constant interval classes or define different break points for every lag class. Anisotropic directions can be individually targeted, and variograms can be scaled to sample variance.


Variograms that appear in the Semivariance Analysis window – both isotropic and anisotropic – can be enlarged into their own windows, from which values and graphs can be printed, and from which each point along the curve can be decomposed into the pairs of points on which it is based.

Variogram Map

Variogram Surface Maps identify anisotropy quickly and accurately. Maps of semivariance in every compass direction (the center marks the origin of each variogram) allow the axis of maximum variation to be easily identified.

Model definition

Dynamic Variogram Modeling – GS+ can calculate model parameters for 5 types of models based on least squares (residuals) analysis, or individual model parameters can be specified directly by the user.

Variance clouds

Variance Cloud Analysis provides a graph of variance vs. separation distance for every pair of points that make up a specific lag class. This allows outlying pairs to be quickly identified and edited as needed.


h-Scattergram Analysis provides a graph of differences vs. separation distance for every pair of points that make up a specific lag class. This is another way to quickly identify outlying pairs and edit as needed.

Pair-wise variance

The Variance by Pair listing provides variance values and separation distances for each point in a specific variogram lag class.


GS+ provides four types of interpolation – Kriging, Cokriging, Conditional Simulation, and Inverse Distance Weighting. Output is written to ASCII files that can be read for mapping by GS+, ArcView®, or Surfer®.


Kriging provides optimal interpolation of points across a spatial domain for which autocorrelation has been documented and measured with variograms. GS+ provides both block and punctual kriging, and allows the user to choose the most appropriate variogram model to use for the interpolation.


Cokriging is a type of kriging that allows one to better estimate map values using a secondary variate sampled more intensely than the primary variate. If the primary variate is difficult or expensive to measure, then cokriging can greatly improve interpolation estimates without having to more intensely sample the primary variate.

Conditional simulation

Conditional Simulation provides optimal interpolation whereby measured data values are honored at their locations. Other interpolation methods will smooth out local details of spatial variation, which can be a problem when you are trying to map sharp spatial boundaries such as contamination hotspots or fault lines.

Inverse Distance Weighting (IDW)

Inverse Distance Weighting (IDW) provides classical interpolation based on nearest neighbor weighting. It is a simple interpolation method used in mapping programs that do not use geostatistics, and assumes spatial dependence among points close to one another (without measuring it).

Interpolation grid

The Interpolation Grid allows the user to define the boundaries of the interpolated area and the intensity (grid spacing) at which the interpolation will proceed.

Polygon outlines

Polygon Outlines define irregular map boundaries and special areas to exclude from kriging. An unlimited number of polygons can be defined by an unlimited number of vertices (x-y boundary points).

Polygon map

Polygon Maps display the areas that will be included or excluded from kriging. Exclusive and inclusive polygons are colored differently, and polygons can be nested within one another.

Cross Validation Analysis

Cross Validation Analysis allows one to test different variogram models; bootstrapping provides comparisons of the actual value of every point sampled vs. its estimated value when removed from the data set.