Soil erosion due to rainfall impact with no inflow: a numerical solution with spatial and temporal effects of sediment settling velocity characteristics

Dynamic changes take place in the nature of sediment eroded from bare soil at low slopes by rainfall impact when there is no inflow of water at the top of the eroding slope. This relates initially to fine soil sediment not settling back onto the soil after the rainfall impact. Coupled partial differential equations describing such dynamic changes have been solved numerically for a bed of soil, bounded at its upper end, and subject to a constant rainfall rate. This solution allows prediction of the change with time and downslope distance in the concentration and settling velocity (or size) characteristics of eroding sediment, allowing critical evaluation of the assumption of space-independent sediment characteristics made in prior approximate analytical solutions of the equations involved. Following the determination of as yet unpredictable soil-related parameters in the equations, the solution was tested by comparison with experimented data on two soils of contrasting structural stability, namely a vertosol [The Australian Soil Classification (1996)] and a aridisol. Investigations included the determination of a minimum number of sediment size classes required to adequately describe the settling velocity characteristics, based on the shape of the underlying basic settling velocity characteristic, which is used to predict the dynamics of sediment deposition. The effect on the solution of observed structural breakdown in soil aggregation due to rainfall impact was investigated, leading to more accurate predictions of the settling velocity characteristics of eroded sediment. Other sources of discrepancy between theory and observation remain to be determined.