Soil erosion due to rainfall impact with inflow: an analytical solution with spatial and temporal effects

An approximate analytical solution is obtained for a physically based model of soil erosion on a gentle slope driven by rainfall impact in which there is inflow of clear or nearly clear water to the top of the soil bed. Comparison of the approximate analytical and numerical solutions shows very good agreement, except for the first few minutes of an erosion event. The approximate analytic solution is applied using data from an illustrative experiment to explore its physical features. The importance of adequately defining the soilʹs settling velocity characteristic through the use of a sufficient number of sediment size classes, especially for prediction at short times, is illustrated. The temporal variation in sediment concentration, except at short times, is shown to be more significant than the spatial variation down the eroding surface. Solution of the equations allows visualization of the rate of convective transport of sediment down the eroding surface, this rate decreasing as sediment size increased due to more frequent return of such particles to the soil surface in deposition.