Optimized multi-phase sampling for soil remediation surveys

We develop an algorithm for optimizing the design of multi-phase soil remediation surveys. The locations of observations in later phases are selected to minimize the expected loss incurred from misclassification of the local contamination status of the soil. Unlike in existing multi-phase design methods, the location of multiple observations can be optimized simultaneously and the reduction in the expected loss can be forecast. Hence rational decisions can be made regarding the resources which should be allocated to further sampling. The geostatistical analysis uses a copula-based spatial model which can represent general types of variation including distributions which include extreme values. The algorithm is used to design a hypothetical second phase of a survey of soil lead contamination in Glebe, Sydney. Observations for this phase are generally dispersed on the boundaries between areas which, according to the first phase, either require or do not require remediation. The algorithm is initially used to make remediation decisions at the point scale, but we demonstrate how it can be used to inform over blocks.