Arsenic in Michigan soil: Spatial stratification for environmental regulatory purposes

State environmental regulatory agencies in the U.S. often establish a default background standard for naturally occurring elements in the soil, water, and air. The background standard is determined and then used as a benchmark across the entire jurisdiction. A variety of statistical techniques are used to determine this standard, but often ignore any inherent spatial dependencies within the jurisdiction. If the analysis indicates a specific site exceeds the default standard, additional background sampling and analysis must usually be performed. Frequently, this additional sampling is found to be unnecessary simply because the natural background levels were elevated for this particular site. Conversely, potential contamination may be overlooked in areas where the natural background levels are much lower. Thus, a single default background standard seems inadequate within this context. This paper proposes the use of dissimilarity coefficients based on kriging estimates as a means to regionalize background standards. Along with cluster analysis techniques, these dissimilarity coefficients provide a means to stratify the population into geographic sub-areas. A regulatory agency may now define multiple default background standards based on geographic location. To illustrate, this paper examines a case study concerning residential soil arsenic for 83 Michigan counties.