A stochastic-geometric model of the variability of soil formed in Pleistocene patterned ground

- A stochastic geometric model is proposed for the ECa of soil in relict patterned ground.
- The model is non-Gaussian: soil knowledge is used systematically in estimation.
- The model better reproduces the continuity of small ECa values than does a Gaussian.

In this paper we develop a model for the spatial variability of apparent electrical conductivity, ECa, of soil formed in relict patterned ground. The model is based on the continuous local trend (CLT) random processes introduced by Lark (2012b) (Geoderma, 189-190, 661-670). These models are non-Gaussian and so their parameters cannot be estimated just by fitting a variogram model. We show how a plausible CLT model, and parameters for this model, can be found by the structured use of soil knowledge about the pedogenic processes in the particular environment and the physical properties of the soil material, along with some limited descriptive statistics on the target variable. This approach is attractive to soil scientists in that it makes the geostatistical analysis of soil properties an explicitly pedological procedure, and not simply a numerical exercise. We use this approach to develop a CLT model for ECa at our target site. We then develop a test statistic which measures the extent to which soils on this site with small values of ECa, which are coarser and so more permeable, tend to be spatially connected in the landscape. When we apply this statistic to our data we get results which indicate that the CLT model is more appropriate for the variable than is a Gaussian model, even after the transformation of the data. The CLT model could be used to generate training images of soil processes to be used for computing conditional distributions of variables at unsampled sites by multiple point geostatistical algorithms.