Spatial sampling plans to monitor the 3-D spatial distribution of extremes in soil pollution surveys

A spatial sampling strategy is proposed for monitoring the exceedances of soil pollutants over a given regulatory threshold in a discretized three-dimensional (3-D) portion of space. In each site of the study area, an indicator variable is defined assuming a value of 1 if the threshold is exceeded and 0 otherwise. The spatial distribution of such variables represents an expected probability map of exceeding the threshold, characterized by a certain degree of spatial dependence. The first and second order moments of the indicator variates can be estimated by making use of extreme value theory and models for threshold excesses. The MEV (minimum estimation variance) sampling strategy is then exploited to select sequentially a network of monitored locations which optimally predicts the proportion of sites in which the pollutant under study is exceeding a critical level. In order to illustrate the methods, a data set will be analyzed related to soil pollution concentrations of polycyclic aromatic hydrocarbons (PAHs) observed in an industrial site in Italy.