Two-way Regionalized Classification Of

Suggested Running Head: Application of two-way RC in the assessment of hydrodynamic dispersion 2 ABSTRACT Zones of mixing between shallow groundwaters of different composition were unravelled by " two-way regionalized classification " , a technique based on Correspondence Analysis, Cluster Analysis and Discriminant Analysis, 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 data set: 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 m 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. 3 NOTATION Below is the alphabetical list of mathematical symbols used throughout this paper. Latin Symbols d-geometric mean diameter of a granular material (e.g. soil sample) D (D L , D T)-Coefficient of hydrodynamic dispersion (longitudinal and transverse) E i-classification score of group i f i (x)-score of vector x in the frequency curve (f) of group i F-factor grad(h)-hydraulic gradient h-number of rows along the height of a grid k-number of groups present in a multivariate site-related data set K-hydraulic conductivity l-number of columns along the width of a grid m t-total porosity m e-effective porosity n-number of samples (or sites) in the working database p-number of variables describing the samples (or sites) in the working database prob i-prior probability of group's i membership Prob i-posterior probability of group's i membership S-matrix of within-group variances and covariances t-time v-velocity of a solute dissolved in water along the mean …