Optimal network design for spatial prediction of soil redistribution (137Cs) based on a minimax approach

Abstract

Measuring 137 Cs is considered an effective method to study soil redistribution rate and hence needs sampling at a number of sites. The spatial configuration of the network of sites to be sampled has a substantial effect on the soil redistribution assessment. Here, motivated by sampling 137 Cs, we adopted a model-based approach. For this, we chose the average kriging variance (AKV) as a design criterion. In fact, by minimizing the AKV of soil 137 Cs prediction in the paired sub-catchments of Iran's Golestan province, we determined the optimal sampling design in the case that no directly measured prior information of the primary variable of interest ( 137 Cs ) is available. However, the AKV depends on some unknown parameters and preliminary estimates of model parameters are not available. To overcome this problem, we apply the minimax approach which minimizes the maximum value of design criterion over the misspecification of parameters . The method is illustrated taking into account the ancillary information (slope%) from representative Sub-catchments ( Sample and Testifier, each around 190 ha in size ). A simulated annealing algorithm is used to search for an optimal design from among all possible designs. Since, the number of sampling points is often limited by time and budgetary constraints, we use a sequential-based method for selecting the sample size. It is shown that 60 sites are sufficient for the proposed Sample and Testifier sub-catchments.