Cokriging in GS⁺

Cokriging is an interpolation technique that allows one to better estimate map values if the distribution of a secondary variate sampled more intensely than the primary variate is known. 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.

Consider the following example. After an accidental uranium spill, soils were sampled across an 80 x 80 m area at a sample density indicated by the quartile plot below. Block kriging (following variography) resulted in the map of uranium concentrations on the right:

Soil carbon, easier to measure than uranium, was sampled at the same locations as uranium and additionally at another 60 locations as noted in the quartile map below left. Regression of carbon against uranium showed that the variates were highly correlated (right), suggesting that cokriging might improve the map of uranium.

Using carbon as a covariate to produce a cokriged map of uranium results in the below-right map, plotted next to the original map above. Note the substantial improvement in the definition of contour (isoline) differences, especially in the upper right quadrant of the map where the uranium was sampled most sparsely:

How do you perform cokriging? Prior to cokriging you must have

1. defined a covariate in the Field Assignment dialog, of the Data Worksheet;
2. performed semivariance analysis (including variogram modeling) for both the primary variate and the covariate; and
3. performed cross-semivariance analysis (including variogram modeling).

You will also have wanted to confirm that the covariate is in fact correlated with the primary variate by viewing the Regression Window in the Data Summary Window.  Note that there is no advantage to cokriging (over ordinary kriging) if the sample density of your primary variate is the same as for the secondary variate, or if the variates are uncorrelated.

Once the three variograms are modeled, you can choose the Cokrig tab in the Interpolation window: