Mapping the results of extensive surveys: The case of atmospheric biomonitoring and terrestrial mosses

In this paper we discuss some difficulties associated with the process of constructing maps of pollution from data obtained in surveys covering extensive areas. As we show here, these problems may be wide-ranging but are seldom recognized by investigators. The origin of the problems is the existence of multiple sources of pollution in the study area, each of different intensity and affecting areas of different extent. The particular spatial structure of the pollution sources interacts with the spatial layout of the samples, resulting in data sets with distributions that are very different from the usually assumed normal distribution, and characterized by heavy tails and gross outliers. These distributions arise because of incomplete sampling of small-scale pollution processes (i.e. those occurring on a spatial scale smaller than the spatial scale of the sampling grid). After discussion of the potential problems and appropriate techniques for analyzing this kind of data, we applied the proposed techniques to a real data set of heavy metal contents in terrestrial mosses. From the exercise we concluded that a) the first step in analysis of this kind of data must be to check for the presence of spatial structure on scales larger than the sampling grid, to avoid mapping noise, and b) the map generated must not contain information about pollution sources with a spatial scale smaller than the spatial scale of the sampling grid. We present and discuss the performance of robust statistical methods of testing for spatial structure (based on robust variograms and randomization testing) and of filtering the small-scale spatial processes (using median-polishing) prior to mapping.