A stochastic geometric model for continuous local trends in soil variation

This paper develops and demonstrates a model of stochastic spatial variation. It is proposed that this model may represent soil variability according to a particular mode under which the soil varies continuously, showing short-range lateral trends induced by local effects of the factors of soil formation which vary across the region of interest in an unpredictable way. The trends in soil variation are therefore only apparent locally, and the soil variation at regional scale appears random. Such variation might be expected in a landscape where the soil varies along topographic catenas which repeat across the region in response to a drainage pattern which is not entirely regular in spacing or orientation, and is therefore unpredictable. The Continuous Local Trend (CLT) mode of soil variation may also be expected where gradients of soil properties are induced around individual plants, or plant roots.In the stochastic model the local trend is assumed to be described by a function of distance to the nearest event in a realisation of a random spatial point process. A model is developed here in which the point process shows complete spatial randomness, so it is called the Poisson Continuous Local Trend (PCLT) model. The covariance function for the PCLT with a general distance function is developed and some hypothetical examples are shown, including one in which the variogram of a soil property is inferred by using a published topofunction. The PCLT model is then fitted to the empirical variogram of some data on soil water content in a gently undulating clay landscape, and the multiple point statistics of the PCLT model for these data are compared with those of a corresponding multivariate normal model.

► A model is proposed for short-range, globally unpredictable, lateral trends in soil.
► The model is based on a stochastic geometric distance function.
► The model is fitted to data on soil water content in an undulating landscape.
► The model has multiple point statistics very different from a multigaussian process.