Indicator Kriging

To utilize Indicator Kriging, select Indicator Kriging from the Parameters Window when the Interpolation methods step is selected. This interpolation method requires a grid, a search neighborhood, and that a spatial correlation model be defined for each IK cutoff first.

Then, press Show the results on the Steps Window to display the applicable result in the Graphics Window.

Indicator kriging (IK) is a geostatistical approach to geospatial modeling. SADA uses IK in the same fashion as ordinary kriging (OK). Like OK, the correlation between data points determines model values. However, IK makes no assumption of normality and is essentially a non-parametric counterpart to OK. (See Setting Normality/Lognormality Assumption.)

In addition to the indicator correlation structure (see Spatial Correlation and Indicator Kriging), SADA requires a definition of the neighborhood around the estimation point. The issue of neighborhood definition is important to inverse distance and ordinary kriging, as well. A discussion of neighborhood definitions is consolidated in Defining A Neighborhood.

Instead of assuming a normal distribution at each estimate location, IK builds the cumulative distribution function (CDF) at each point based on the behavior and correlation structure of indicator transformed data points in the neighborhood. To achieve this, IK needs a series of threshold values between the smallest and largest data values in the set. These threshold values, referred to here as IK cutoffs, are used to numerically build the CDF of the estimation point. For each IK cutoff, data in the neighborhood are transformed into 0s and 1s: 0s if the data are greater than the threshold and 1s if they are less. IK then estimates the probability that the estimation point is less than the threshold value, given this neighborhood of transformed data and a model of the IK cutoff correlation structure. Performing this operation for each cutoff across the range of data approximates the CDF at the estimation point. After the CDF is built, it must be post processed to produce probability maps and E-Type values for estimation maps and risk maps.

The details of the IK process are beyond the scope of this book. It is assumed the reader is familiar with indicator kriging before attempting this process. For more information on indicator kriging, see GSLIB Geostatistical Software Library and Users Guide by Deutsch and Journel (1992).