Use of a Fractional Brownian Motion Model to Mimic Spatial Horizontal Variation of Soil Physical and Hydraulic Properties Displaying a Power-law Variogram

Stochastic analysis of flow and mass transport in soil, usually assumes that soil hydraulic properties are stationary homogeneous stochastic processes with a finite variance. Some field data suggest that soil hydraulic distributions may have a fractal character with long-range correlations. In this study new field soil hydraulic data-sets, measured along transects of an Andosol and a Vertic-Fluvent soil, were analyzed for fractal behavior using a stochastic fractal function such as fractional Brownian motion (fBm) and power-law variogram fits to estimate the monofractal Hurst exponent H as a measure of self-similarity. Our analysis lend further support to the hypothesis that horizontal processes, that mimic fBm, will display a power-law variogram.