Mapping Heavy Metals in Soil by (Non-)Linear Kriging: an Empirical Validation

Abstract

Linear kriging is a well established method for predicting soil variables such as pollutants at unsampled locations. Various empirical validation studies showed that their precision is equivalent or slightly superior to other linear smoothing techniques. Quite often, however, correctly assessing prediction uncertainty, i.e. the conditional distribution of the target quantity given the available information, is similarly important. Evaluating the risks of soil pollution and choosing optimal decisions in remediation and land management are examples where correct inference of the conditional distribution is essential. The nonlinear kriging methods provide estimates of this distribution and are therefore used increasingly in environmental sciences. Despite their use for partly more than 20 years, empirical evidence about their performance is still scanty. The paper reports the results of an empirical comparison of linear, lognormal, indicator, and disjunctive kriging for predicting heavy metal concentrations in the soils of a region in the Swiss Jura mountains. The main conclusions from the study are: (i) Linear and all the non-linear kriging methods were equally precise, even for data where the Gaussian model was clearly inappropriate, (ii) All the nonlinear methods modelled the conditional distributions equally well, and no method was consistently superior to the others. Linear kriging, supplemented with the assumption of normally distributed prediction errors, failed for non-Gaussian data, (iii) Sampling variation was the key factor which controlled success or failure, and it affected all the methods similarly.