Spatial prediction of soil properties with copulas

The uncertainty of a prediction of a spatial property may only be fully described if the property is assumed to be a realization of a multivariate random variable. Model-based geostatistical methods are generally based on the assumption that the random variable is multivariate Gaussian. However this model is implausible for many soil properties. For example, observations of cadmium concentrations from the French National Soil Monitoring Network include outliers which arise because of isolated pollution and other local anomalies. We introduce a more general multivariate function for the spatial analysis of soil properties based on copulas. The dependence structure and marginal distributions of this function are specified separately. A copula-based model with a Gaussian dependence structure and generalized extreme value marginal distributions is fitted to the observations of cadmium across France. The expected concentration of cadmium is permitted to vary with parent material. This model is used to predict the distribution of cadmium concentrations at unsampled sites conditional on the observed data. Upon cross-validation the copula-based model performs better than existing model-based approaches. However further generalizations, such as the use of non-Gaussian copulas, are required to ensure a complete description of the complexity of the variation of cadmium in French soils.