Variable scale effects on hillslope soil erosion during rainfall-runoff processes

The variation of soil erosion across scales remains a controversial issue. A theoretical framework, coupling the normalized Green-Ampt equation for infiltration, 1D kinematic wave model for overland flow, and WEPP erosion modeling approaches for soil erosion, was used to explain and quantify the direct effect of scale on the soil erosion process. The results show that the relation between interrill erosion and slope length accords with a power-law decreasing trend, while the relation of rill erosion versus slope length shows a power-law increasing trend. Moreover, the power-law scaling of interrill erosion becomes more prominent with an increase of rainfall duration and intensity but is nearly independent of the interrill erodibility factor. The rainfall duration, soil type, soil critical shear stress, sediment transport coefficient, and rill erodibility factor substantially influence the magnitude of scale effect on rill erosion, while rainfall intensity, slope gradient, and Manning's roughness have minor effects. It suggests that the scale effect on soil erosion is variable and dynamic for different erosion types, rainfall and soil characteristics, which can explain why the controversial scaling relationships of soil erosion exist in previous studies. The physically based soil erosion model WEPP is compared to the empirical models USLE and RUSLE at various scales. Only when rill erosion plays a dominant role in soil loss do all these models exhibit consistent scale effect on erosion. These results provide insights into the essence of scaling in the hillslope soil erosion process, which are expected to benefit the development of upscaling techniques for the large-scale hydrological, geomorphological, and ecological processes.