Predicting threshold exceedance by local block means in soil pollution surveys

Soil contamination by heavy metals and organic pollutants around industrial premises is a problem in many countries around the world. Delineating zones where pollutants exceed tolerable levels is a necessity for successfully mitigating related health risks. Predictions of pollutants are usually required for blocks because remediation or regulatory decisions are imposed for entire parcels. Parcel areas typically exceed the observation support, but are smaller than the survey domain. Mapping soil pollution therefore involves a local change of support. The goal of this work is to find a simple, robust, and precise method for predicting block means (linear predictions) and threshold exceedance by block means (nonlinear predictions) from data observed at points that show a spatial trend. By simulations, we compared the performance of universal block kriging (UK), Gaussian conditional simulations (CS), constrained (CK), and covariance-matching constrained kriging (CMCK), for linear and nonlinear local change of support prediction problems. We considered Gaussian and positively skewed spatial processes with a nonstationary mean function and various scenarios for the autocorrelated error. The linear predictions were assessed by bias and mean square prediction error and the nonlinear predictions by bias and Peirce skill scores. For Gaussian data and blocks with locally dense sampling, all four methods performed well, both for linear and nonlinear predictions. When sampling was sparse CK and CMCK gave less precise linear predictions, but outperformed UK for nonlinear predictions, irrespective of the data distribution. CK and CMCK were only outperformed by CS in the Gaussian case when threshold exceedance was predicted by the conditional quantiles. However, CS was strongly biased for the skewed data whereas CK and CMCK still provided unbiased and quite precise nonlinear predictions. CMCK did not show any advantages over CK. CK is as simple to compute as UK. We recommend therefore this method to predict block means and nonlinear transforms thereof because it offers a good compromise between robustness, simplicity, and precision