Applying the RUSLE and the USLE-M on hillslopes where runoff production during an erosion event is spatially variable

The assumption that runoff is produced uniformly over the eroding area underlies the traditional use of Universal Soil Loss Equation (USLE) and the revised version of it, the RUSLE. However, although the application of the USLE/RUSLE to segments on one dimensional hillslopes and cells on two-dimensional hillslopes is based on the assumption that each segment or cell is spatially uniform, factors such as soil infiltration, and hence runoff production, may vary spatially between segments or cells. Results from equations that focus on taking account of spatially variable runoff when applying the USLE/RUSLE and the USLE-M, the modification of the USLE/RUSLE that replaces the EI30 index by the product of EI30 and the runoff ratio, in hillslopes during erosion events where runoff is not produced uniformly were compared on a hypothetical a 300 m long one-dimensional hillslope with a spatially uniform gradient. Results were produced for situations where all the hillslope was tilled bare fallow and where half of the hillslope was cropped with corn and half was tilled bare fallow. Given that the erosive stress within a segment or cell depends on the volume of surface water flowing through the segment or cell, soil loss can be expected to increase not only with distance from the point where runoff begins but also directly with runoff when it varies about the average for the slope containing the segment or cell. The latter effect was achieved when soil loss was predicted using the USLE-M but not when the USLE/RUSLE slope length factor for a segment using an effective upslope length that varies with the ratio of the upslope runoff coefficient and the runoff coefficient for the slope to the bottom of the segment or cell was used. The USLE-M also predicted deposition to occur in a segment containing corn when an area with tilled bare fallow soil existed immediately upslope of it because the USLE-M models erosion on runoff and soil loss plots as a transport limited system. In a comparison of the USLE-M and RUSLE2, the form of the RUSLE that uses a daily time step in modeling rainfall erosion on one-dimensional hillslopes in the USA, on a 300 m long 9% hillslope where management changed from bare fallow to corn midway down the slope, the USLE-M predicted greater deposition in the bottom segment than predicted by RUSLE2. In addition, the USLE-M approach predicted that the deposition that occurred when the slope gradient changed from 9% to 4.5% midway down the slope was much greater than the amount predicted using RUSLE2.