Geostatistics for the Environmental Sciences

Kriging, Cokriging, Conditional Simulation, Inverse Distance Weighting (IDW), and other Interpolations

GS+ provides Kriging, Cokriging, Conditional Simulation, and Inverse Distance Weighting for interpolation across an area. Output is written to ASCII files that can be read for mapping by GS+, ArcView®, Surfer®, or other mapping or GIS programs.

Kriging provides an optimal interpolation of points across an area for which autocorrelation (semivariance) has been documented and measured with variograms or semivariograms. GS+ provides both block and punctual kriging, and allows the user to choose the most appropriate variogram / semivariogram model to use for the interpolation.

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

Conditional Simulation provides optimal interpolation whereby measured data values are honored at their locations. Other interpolation methods (including kriging) 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) is a classical interpolation technique 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).

An Interpolation Grid in GS+ allows the interpolation boundaries (whether kriging, conditional simulation, or IDW) to be defined and sets the intensity (grid spacing) at which the interpolation will occur.

Polygon Outlines in GS+ define irregular map boundaries and special areas to exclude from interpolation (whether kriging, conditional simulation, or IDW). An unlimited number of polygons can be defined by an unlimited number of vertices (x-y boundary points). The outline defined by the vertices can be visualized in Polygon Maps, which display the areas that will be included or excluded from interpolation. Exclusive and inclusive polygons are colored differently, and polygons can be nested within one another.

Cross Validation Analysis allows one to test different variogram / semivariogram models used for kriging and conditional simulation. Bootstrapping provides comparisons of the actual value of every point sampled vs. its estimated value when removed from the data set.