The Matérn function as a general model for soil variograms

The variogram is important in pedometrics for describing and quantifying soil spatial variability. Therefore, it is essential to have a model that can describe various spatial processes and to use appropriate techniques for estimating its parameters. The Matérn model is a generalization of several theoretical variogram models that incorporates a smoothness parameter. We show the flexibility of the Matérn model using simulation and apply the Matérn model to some soil data in Australia. Parameters of the Matérn model were determined by restricted maximum likelihood (REML), and weighted nonlinear least-squares (WNLS) on the empirical variogram. The Matérn model is shown to be flexible and can be used to describe many isotropic spatial soil processes. The REML method fits the local spatial process correctly, however the drawback is the lengthy computation. Meanwhile WNLS fits only the shape of the calculated empirical variogram, and parameters estimated from WNLS can be misleading. From this study, the smoothness parameter of soil data from point measurement appears to be in the range of 0.25–0.50 and can be considered to be a rough spatial process.