Distribution of depth of overland flow on desert hillslopes and its implications for modeling soil erosion

Abstract Data collected during field experiments on hillslopes in southern Arizona reveal that the depth of overland flow in interrill areas can be approximated by a negative exponential distribution. Soil erosion over the greater part of most hillslopes is equal to detachment capacity. Flow detachment in interrill areas is generally modeled using a Du Boys-type equation in which shear stress is calculated using the mean depth of flow. It is shown that using the mean depth rather than the distribution of depth can result in the severe underestimation of flow detachment. Insofar as the exponential density is characterized by a single parameter that is the reciprocal of the mean, a knowledge of the mean depth is all that is needed to specify the distribution. Thus utilization of the depth distribution rather than the mean depth does not require any additional information, yet it yields much more accurate estimates of flow detachment and, hence soil erosion in interrill areas.