Predicting topsoil heavy metal content of parcels of land: An empirical validation of customary and constrained lognormal block kriging and conditional simulations

Abstract

Soil contamination by heavy metals is an important problem in many countries. As a first step in mitigating the related health risks, one has to delineate zones where metal concentrations exceed tolerable levels. Predictions of metal concentrations 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 involves therefore a local change of support. Using data from an extensive survey of heavy metals in the soils around a metal smelter, we validate in this study geostatistical block predictions with measured heavy metal concentrations that were representative for the mean metal content on 53 parcels with areas of 500–5500m2. Block predictions were computed by conditional simulations (CS) and several variants of lognormal universal (LUK), constrained (LCK) and covariance-matching constrained (LCMCK) block kriging from observations with quasi-point support (2–100m2). Lognormal block kriging predictions were either computed based on the assumption that both observations and block means are lognormally distributed or by averaging lognormal point kriging predictions. Target quantities were the block means of metal content in 0–20cm depth and exceedance of regulatory thresholds by these means. CS gave the most precise predictions, both of block means and of threshold exceedance. However, the advantage was not pronounced: LUK, although slightly negatively biased, predicted block means nearly as well and was not much worse than LCK, LCMCK or CS when predicting threshold exceedance. LCK was partly positively biased (in particular when averaging lognormal constrained point kriging predictions) and was clearly less precise than LUK and CS when predicting block means. All four methods predicted threshold exceedance with good success as judged by the areas under Receiver Operating Characteristic curves (0.78–0.92). The good performance of LUK was rather surprising because nonlinear transforms of customary block kriging predictions are commonly known to be biased because kriging predictions are smoother than the target quantities. The relative success of LUK must be attributed to dense soil sampling around the validation parcels that dominantly lay in the severely contaminated part of the survey domain where a lot of soil samples had been taken. When sampling is dense the smoothing bias of block kriging does not matter much. In this situation, we can expect only limited gains in the precision of predictions by more sophisticated methods such as CS and LCK.