Error index for additional sampling to map soil contaminant grades

Abstract

Soil contaminant grades classified by thresholds of concentrations are important for land use and management. Mapping of the soil contaminant grades only focuses on the precise prediction of the relationship between the contaminant concentration of each spatial units and a predefined threshold. Thus, unlike sampling for other purposes, additional sampling should add more sites in areas with a high possibility of misclassification and fewer or no sites in areas with a low possibility of misclassification. To guide additional sampling for mapping of the soil contaminant grades, an error index based on Indicator Kriging (IK) is proposed in this paper. By linear transformation of the predicted value of IK and summing the standard variance of the prediction error, the error index contains both the closeness of predicted value to the threshold and the uncertainty of the prediction, and can reflect the possibility of misclassification of the soil contaminant grades. Also, due to the adoption of IK, it can avoid the smoothing effect, remove or lower the unstationary variation of original data by indicator transform, and do not required normal distribution to model the error variance. Based on the error index, an optimization method for additional sampling to map soil contaminant grades is then put forward by defining an objective function and employing the Spatial Simulated Annealing optimization method. The chromium concentration data of the study area in central China were used as a case study. According to a comparison of the proposed additional sampling optimization method with spatially even sampling method and spatially random sampling method, the case study demonstrated that the proposed optimization method based on the error index is superior to the other methods in improving the prediction precision of soil contaminant grades and that its performance is stable. The results suggest that the error index proposed in this paper can be used to generate a design for additional sampling to improve the mapping precision of soil contaminant grades.