Modification of the RUSLE slope length factor based on a multiple flow algorithm considering vertical leakage at karst landscapes

Heterogeneous karst surfaces exerted scaling effects whereby specific runoff decrease with increasing area. The existing RUSLE-L equations are limited by the default implicit assumption that the surface-runoff intensity is constant at any slope length. The objective of this study was to modify the L-equation by establishing the functional relationship between surface-runoff intensity and karst slope length, and to evaluate its predictive capability at different resolution DEMs. Transfer grid layers were generated based on the area rate of surface karstification and considered the runoff transmission percentage at the exposed karst fractures or conduits to be zero. Using the multiple flow direction algorithm united with the transfer grid (MFDTG), the flow accumulation of each grid cell was simulated to estimate the average surface-runoff intensity over different slope lengths. The effectiveness of MFDTG algorithm was validated by runoff plot data in Southwestern China. The simulated results in a typical peak-cluster depression basin with an area rate of surface karstification of 6.5% showed that the relationship between surface-runoff intensity and slope length was a negative power function. Estimated by the proposed modified L-equation ((al_x^(b+1)/22.13)^m), the L-factor averages of the study basin ranged from 0.35 to 0.41 at 1, 5, 25 and 90 m resolutions respectively. This study indicated that the modified L-equation enables an improved prediction of the much smaller L-factor and the use of any resolution DEMs on karst landscapes. Particular attention should be given to the variation of surface-runoff intensity with slope length when predicting L-factor on hillslopes with runoff scale effect.