Order theoretical tools for the evaluation of complex regional pollution patterns

The mathematical and statistical evaluation of environmental data gains an increasing importance in environmental chemistry as the data sets become more complex. It is inarguable that different mathematical and statistical methods should be applied in order to compare results and to enhance the possible interpretation of the data. Very often several aspects have to be considered simultaneously, for example, several chemicals entailing a data matrix with objects (rows) and variables (columns). In this paper a data set is given concerning the pollution of 58 regions in the state of Baden-Wurttemberg, Germany, which are polluted with metals lead, cadmium, zinc, and with sulfur. For pragmatic reasons the evaluation is performed with the dichotomized data matrix. First this dichotomized 58 x 13 data matrix is evaluated by the Hasse diagram technique, a multicriteria evaluation method which has its scientific origin in Discrete Mathematics. Then the Partially Ordered Scalogram Analysis with Coordinates (POSAC) method is applied. It reduces the data matrix in plotting it in a two-dimensional space. A small given percentage of information is lost in this method. Important priority objects, like maximal and minimal objects (high and low polluted regions), can easily be detected by Hasse diagram technique and POSAC. Two variables attained exceptional importance by the data analysis shown here: TLS, Sulfur found in Tree Layer, is difficult to interpret and needs further investigations, whereas LRPB, Lead in Lumbricus Rubellus, seems to be a satisfying result because the earthworm is commonly discussed in the ecotoxicological literature as a specific and highly sensitive bioindicator.