On the Rill Net in a Slope System

Abstract

A stochastic differential equation is introduced for the theoretical analysis of rill development on a bare slope. The equation is based on two basic hypotheses ; the joining probability is proportional to the number of rills and the branching probability is proportional to relative width (width/depth). It is argued in the model experiment that these hypotheses are appropriate and that the most probable number of rills is given by the steady-state solution for the equation derived from the hypotheses. It is also shown that the model is fundamentaly valid for a real bare slope in the field and that the most probable number of rills on the slope can be estimated by using the equation.