Disturbance-driven Hillslope Diffusion Scales and Values Clarified by Extant Surface Roughness

Abstract:

In low-relief landscapes, the hillslope diffusion equation approximates the rate of topographic evolution due to disturbance driven sediment transport. Whereas this expression is appealing and performs well, the physical meaning of a hillslope diffusivity remains unclear. Here, a study of the disturbances that redistribute sediment on hillslopes clarifies a physical interpretation. We conceptualize the cumulative hillslope diffusivity, which is a rate constant for topographic degradation at large scales, as the aggregate of all surface disturbing processes. A numerical model that generates pit and mound topography from tree throw events illustrates this idea. Using the diffusion equation, we model the degradation of pits and mounds by all smaller scale disturbances. However, when examined at a larger scale, the effective hillslope diffusivity is composed of the small scale diffusivity plus the effect of tree throw. We also present a method to determine the background hillslope diffusivity using the extant hillslope roughness and rates of roughness production. Numerical simulations show that the variance of the surface roughness of a hillslope as introduced by pit and mound topography reaches a steady state when the rate of variance production (tree throw) is constant. The magnitude of the steady state variance is a function of variance production and decay (small scale diffusivity), so there is an opportunity to determine hillslope diffusivity values if the rates of variance production are known. This method yields estimates of the modern hillslope diffusivity which are useful in problems involving the human and climate change time scales.