Stochastic sediment transport in soil erosion

Abstract

A stochastic model governing the downslope transport of a sediment particle during an erosion event is described. Particles alternate between resting on the soil bed and being transported by the overland flow. Probability densities and moments are constructed for the distribution of a particle's position at a given time, and also for time of passage to a given location. We show that a suitable averaging of the stochastic particle motions in our model gives rise to the deterministic erosion differential of Hairsine and Rose (Hairsine, P., Rose, C., 1991. Soil Sci. Soc. Am. J. 55 (2), 320–324). The model generalized H. Einstein's stochastic model (Der Geschiebebetrieb als Wahrscheinlichkeitsproblem, Verlag Rascher, Zurich, 1937) for bedload transport in streams.