Kriging provides a means of interpolating values for points not physically sampled using knowledge about the underlying spatial relationships in a data set to do so. Variograms provide this knowledge. Kriging is based on regionalized variable theory and is superior to other means of interpolation because it provides an optimal interpolation estimate for a given coordinate location. GS+ performs several types of kriging.
The Krig tab is part of the larger Interpolation Window:
Kriging Type
GS+ provides both ordinary and simple kriging. Ordinary kriging, the most commonly used type of kriging, assumes a constant but unknown mean that may fluctuate among local neighborhoods within a study area. In ordinary kriging the sum of kriging weights equals to one.
Ordinary kriging can be performed with external drift or with a polynomial trend. Kriging with a trend (also called universal kriging) employs a prior trend model, which is defined as a smoothly varying deterministic function. Five different polynomial trend terms can be included in the model: X linear, Y linear, X quadratic, Y quadratic, and XY quadratic; use the Define command to specify which terms to include:
Kriging with an external drift is an extension of kriging with trend. The trend model is limited to two terms m(u)=a0+a1f1(u) where m is the mean value for estimation neighborhood u and f1(u) is set to the secondary (external drift) variable. Use the Define command to assign a drift term to every interpolation grid point.
Simple kriging assumes the expectation of the random field to be known, and relies on a covariance function. Stationary simple kriging has a constant mean, which in GS+ is calculated as the mean of the input data Z. In non-stationary simple kriging, a locally varying mean is specified for every interpolation grid point using the Define command.
For continuous variables, indicator kriging estimates the probability that the interpolation point is greater than a particular cutoff value, specified by the user.
Variogram
Variogram models for isotropic and anisotropic variograms are defined and chosen using the Model command in the Autocorrelation Analysis window. Here in the Kriging window you can specify whether to use the isotropic or anisotropic model for each of the variograms used in the kriging system. You can also choose to use a relative variogram, in which the nugget and structural components are rescaled from 0 to 1.0.
Discretization grid
Choose either Point or Block kriging in this section. Your choice should be made on the basis of sampling design and variate characteristics. If samples were taken to represent an area around the actual sample point (e.g. if samples from an area around the sampling coordinate were composited before analysis), then block kriging may be more appropriate than punctual. If samples were taken to represent point values, then punctual kriging will be more appropriate.
For block kriging, you must define the discretization grid (also called the local grid), which is placed around the interpolation point when kriging. The interpolation estimate for that point is based on the mean value of estimates for each of the discretization grid points. You may specify the number of discretization grid points to use in the X and Y boxes; 2 points in the X direction and 2 points in the Y direction means that 4 discretization points will be used.
The size of the discretization grid depends on the interpolation grid. For a regular grid, the size is equivalent to the X and Y direction distance intervals, respectively (see Defining a Regular Interpolation Grid). For an irregular grid, the size is specified in the Define Interpolation Grid worksheet (see Block Size under Defining an irregular Interpolation Grid).