Iterative solution of a stochastic differential equation: an efficient method for simulating soil variability

Abstract

A simple and efficient method was developed to simulate one-, two- and three-dimensional random fields with one particular kind of variogram for each dimension. The proposed method used an iterative numerical scheme to solve a stochastic differential equation. Since the procedure required minimal computer memory and computation time, it was especially attractive for simulating a large number of points in studying spatial distributions of soil properties. Furthermore, the procedure produced accurate realizations of random fields, in terms of simulation mean and covariance. The mean values and the covariances or variogram structures calculated from the simulated data by the proposed procedure matched closely to the theoretical values and functions. The procedure was app!ied to simulate spatial variability of soil water content, soil chemicals, and soil reflectance in the real field. Based on available measured data of these soil properties, conditional simulations using the proposed technique were compared with kriged results. Both methods produced very similar spatial distributions of the soil properties.