Uncertainty and sensitivity analysis of spatial predictions of heavy metals in wheat

Heavy metals seriously threaten the health of human beings when they enter the food chain. Therefore, policymakers require precise predictions of heavy metal concentrations in agricultural crops. In this paper we quantify the uncertainty of regression predictions of Cd and Pb in wheat (Triticum aestivum L.) and the contributions to the uncertainties in these predictions associated with inputs to the regression model. For each node of the 500- x 500-m grid covering the arable soils in The Netherlands, a latin hypercube sample size of 1000 is constructed from the uncertainty distributions of the explanatory variables (pH, soil organic matter [SOM], and heavy metal concentration in soil), the regression coefficients, and the random term of the regression model. This sample is used as input for the regression model to obtain 1000 values from the uncertainty distributions of the log(Cd) and log(Pb) concentration in wheat. There were no nodes where the recent EU quality standards for Cd and Pb (0.2 mg kg(-1) fresh wt.) in wheat were almost certain to be exceeded. For most nodes with clay soils, the quality standard for Cd in wheat almost certainly will not be exceeded; for Pb this is much less certain. The uncertainty in the Cd concentration in soil contributes most to the uncertainty in the predicted Cd concentrations in wheat (36% on the average), followed by the random term of the regression model (23%). For Pb the contribution of the random term is by far the largest (52%).