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A stochastic‐geometric model of soil variation

Stochastic models of soil variation are used in geostatistical analysis, but in general they bear no relation to our mechanistic understanding of the processes in soil that cause its properties to vary spatially. It is proposed that we require a suitable stochastic model in which space is partitioned into discrete domains as a first step towards random spatial models that incorporate our understanding of processes in soil. Even though the soil is essentially continuous in its spatial variation, there are components of soil variation (e.g. differences between parent materials) which are discontinuous. This paper shows how variogram models can be derived directly from the Poisson Voronoi Tessellation (PVT), a stochastic‐geometric partition of d‐dimensional space. The PVT variogram models, for d= 2 and 3, were fitted to variograms estimated from data over disparate scales, including computerized tomographic images of soil aggregates (pixels of a few tens of micrometres long) and the land systems of Swaziland. In all cases, PVT variogram models fitted better than the conventional geostatistical ones. The good performance of PVT variogram models at these disparate scales encourages further work on tessellation models for soil variation. In principle such models could incorporate information on underlying factors of soil formation such as the spatial distribution of individual plants, the origin and growth of microbial colonies, spatial processes in soil chemistry (such as reaction–diffusion processes) and geometrical information on boundaries between geological strata or contrasting plant communities. PVT models may therefore be one component of a random model of soil variation which reflects our understanding of soil‐forming processes, and so have a stronger scientific basis than the models that are now in standard use.