Modeling the spatial distribution of soil properties by generalized least squares regression: Toward a general theory of spatial variates

Assessment of the spatial distribution of soil properties has achieved considerable interest among soil scientists, both for testing hypotheses about soil formation processes and for predicting the properties of soils at nonsampled locations (mapping). In this paper, we provide a discussion of the various approaches to the modeling of spatial variates, and we propose a modeling framework that is able to incorporate the most important effects usually found in spatial variates, including fixed and random spatial effects, spatial trends, and heteroscedasticity. We provide a case study of the analysis of eight soil properties in a mountain catchment in the Spanish Pyrenees. As explanatory covariates, we use several topography parameters, which can be related to the pedogenetic processes active in the area. Several of them proved useful for explaining the variability of soil properties, explaining up to 77% of their variance. We focus on the importance of model selection in order to determine which effects are relevant for modeling each soil parameter. We find that the full model is not necessarily optimal for all the variables tested and that the model should be adapted to the complexity of each individual case. This paper is a contribution to the discussion on the modeling of spatial variates and to the eventual development of a general theory of spatial variates.