A new method is proposed for the classification of data in a spatial context, based on the minimization of a variance-like criterion taking into account the spatial correlation structure of the data. Kriging equations satisfying classification bias conditions are then derived for interpolating the rainfall data while taking into account the classification.

Compositional data are very common in the earth sciences. Nevertheless, little attention has been paid to the spatial interpolation of these data sets. Most interpolators do not necessarily satisfy the constant sum and nonnegativity constraints of compositional data, nor take spatial structure into account. Therefore, compositional kriging is introduced as a straightforward extension of ordinary kriging that complies with these constraints. In two case studies, the performance of compositional kriging is compared with that of the additive logratio-transform. In the first case study, compositional kriging yielded significantly more accurate predictions than the additive logratio-transform, while in the second case study the performances were comparable.