Two-Way Regionalized Classification of Multivariate Datasets and its Application to the Assessment of Hydrodynamic Dispersion

Abstract

Zones of mixing between shallow groundwaters of different composition were unravelled by “two-way regionalized classification,” a technique based on correspondence analysis (CA), cluster analysis (ClA) and discriminant analysis (DA), aided by gridding, map-overlay and contouring tools. The shallow groundwaters are from a granitoid plutonite in the Fundão region (central Portugal). Correspondence analysis detected three natural clusters in the working dataset: 1, weathering; 2, domestic effluents; 3, fertilizers. Cluster analysis set an alternative distribution of the samples by the three clusters. Group memberships obtained by correspondence analysis and by cluster analysis were optimized by discriminant analysis, gridded over the entire Fundão region, and converted into “two-way regionalized classification” memberships as follows: codes 1, 2 or 3 were used when classification by correspondence analysis and cluster analysis produced the same results; code 0 when the grid node was first assigned to cluster 1 and then to cluster 2 or vice versa (mixing between weathering and effluents); code 4 in the other cases (mixing between agriculture and the other influences). Code-3 areas were systematically surrounded by code-4 areas, an observation attributed to hydrodynamic dispersion. Accordingly, the extent of code-4 areas in two orthogonal directions was assumed proportional to the longitudinal and transverse dispersivities of local soils. The results (0.7–16.8 and 0.4–4.3 m, respectively) are acceptable at the macroscopic scale. The ratios between longitudinal and transverse dispersivities (1.2–11.1) are also in agreement with results obtained by other studies.