Mapping risk of soil nutrient deficiency or excess by disjunctive and indicator kriging

For many practical problems in land management, information about soil properties, relative to threshold values that may be of practical importance (regulatory limits, management guidelines etc.), is needed at unsampled sites. Nonlinear geostatistical methods allow us to estimate the probability that the true value of a soil property at an unsampled location exceeds a specified threshold, conditional on our observations at sampled sites. Two principal techniques for this purpose are indicator kriging (IK) and Gaussian Disjunctive Kriging (DK). There are some theoretical reasons to prefer the latter, although it is based on more restrictive assumptions about the variability of the soil properties that are to be mapped. The objective of this study was to compare DK and IK empirically. This was done using a large data set on available phosphorus in the topsoil of a field in Nebraska. A prediction subset of the data (247 points) was extracted and DK and IK were used to estimate, from these data, for each of the remaining (1622) validation data points, the conditional probabilities that available phosphorus was less than or equal to three threshold values. The two techniques were then compared by computing the proportion of the validation sites incorrectly classified, with respect to each threshold, by reference to the conditional probabilities. In fact IK and DK gave very similar results by this criterion. It was concluded that neither of the techniques could be generally recommended in preference to the other. There are practical considerations that could determine the best method to use in any given circumstance and these are summarized in a decision tree.