Frequency distribution and scaling of soil texture and hydraulic properties in a stratified deep vadose zone near Maricopa, Arizona.

We analyze the distributional and scaling properties of soil texture data measured to a depth of 15 meters over an area of 3600 m^2 in a vadose zone near Maricopa, Arizona, and of hydraulic properties estimated on the basis of these data with the Rosetta neural network pedotransfer model. We find that vertical and horizontal spatial increments of all variables exhibit Gaussian or symmetric heavy-tailed distributions, nonlinear power-law scaling in a midrange of separation distances (lags), breakdown in power law scaling at small and large lags, extended power-law scaling at all lags, and various degrees of vertical to horizontal anisotropy. Both sets of variables are amenable to interpretation by viewing them as stationary and anisotropic samples from spatially correlated sub-Gaussian random fields subordinated to truncated fractional Brownian motion (tfBm) or truncated fractional Gaussian noise (tfGn).