ABSTRACT
Environmental data are costly and difficult to collect, and quite often the sampled data are insufficient for further analysis. Kriging is a commonly accepted spatial interpolation method. The feasibility of kriging analysis depends on data quality and quantity. The quality of data refers to the adequacy of the data spread for the
assumed spatial prediction task. The quantity refers to the size of the sample and whether it is large enough. Today, we often face circumstances where a set of data is already collected, although from the viewpoint of kriging analysis the data are insufficient, and resampling is impossible because of cost and time limits. Therefore, a solution must be found. In this chapter, a mixed approach is achieved by combining gray differential equation models, particularly the GM(1,1) model, with an ordinary kriging approach. The combined approach is named GM(1,1)-kriging. The existing limited sample data available are expanded to produce a GM(1,1)-kriging map of a larger geographical area. The new approach addresses the issue of spatial data sampling design and provides improved spatial analysis results. This approach is illustrated using soil dioxin data collected from Midland County, Michigan.
