Statistical description of slope-dependent soil transport and the diffusion-like coefficient

[1] For hillslopes undergoing "diffusive" soil transport, it is often assumed that the soil flux is proportional to the local land-surface gradient, where the coefficient of proportionality is like a diffusion coefficient. Inasmuch as transport involves quasirandom soil particle motions related to biomechanical mixing and similar dilational processes, a slope-dependent relation arises from a balance between particle fluxes that tend to loft a soil and gravitational settling of particles into available pore space. A specialized form of the Fokker-Planck equation adapted to such particle motions clarifies how the particle flux involves advective and diffusive parts. This in turn contributes to a kinematic description of the diffusion-like coefficient. Ingredients of this coefficient include an active soil thickness, a characteristic particle size, the porosity in excess of a consolidated porosity, and the rate of particle activation as a function of depth. These last two ingredients, vertical porosity structure and activation rate, in effect characterize the magnitude and frequency of settling particle motions related to biological activity and thereby set the rate constant of the transport process. The significance of land-surface slope is that it is a measure of the downslope component of slope-normal lofting that is balanced by settling. Because the diffusion-like coefficient contains the soil thickness, the analysis suggests that the soil flux is proportional to the "depth-slope" product. The analysis is consistent with published profiles of soil creep displacement and with published estimates of soil flux obtained by downslope integration of soil production rates for hillslopes in California and Australia.