Conditional Gaussian co-simulation of regionalized components of soil variation

Stochastic simulations are increasingly used to represent and characterize the spatial structure and uncertainty of soil properties. Due to the potential presence of scale dependencies, simulations of the total variables can represent a mixture of spatial components operating at different scales, which may be better interpreted separately. While coregionalization analysis and factorial kriging provide means to characterize and estimate scale-specific components of variation, no methods are available that allow a proper representation of their spatial structure and an assessment of their spatial uncertainty. In this paper, the formulation of cokriging of regionalized components and regionalized factors is first reviewed, after which a method for the conditional Gaussian co-simulation of regionalized components and regionalized factors is presented. We highlight the need for performing conditional simulations for all structures jointly to reduce the correlation between components for different structures and avoid any bias on the sum of simulated components. Simulations obtained with this method adequately represent both the specific features of, and the uncertainty associated with, each scale of variation, as modeled in a coregionalization analysis. The method is applied to an agronomic dataset to characterize the spatial uncertainty of regionalized components of plant available phosphorous and potassium in the soil and illustrate advantages of this new simulation approach.