Adaptability analysis and model development of various LS-factor formulas in RUSLE model: A case study of Fengyu River Watershed, China

The slope length and slope steepness factor (LS-factor) formula in the Revised Universal Soil Loss Equation (RUSLE) has a considerable level of uncertainty due to the existence of multiple methods. In this study, four commonly used formulas for the slope length factor and two formulas for the slope gradient factor were chosen and combined based on their applicability to the specific research context. Based on the ModelBuilder in ArcGIS Pro 3.0, a RUSLE calculation model (RUSLE-Cal model) was constructed in the study, which can automatically calculate the soil erosion modulus using four commonly used RUSLE formulas and one combination formula. Taking the Fengyu River watershed in China as a case study, this research analyzes the uncertainty of different LS-factor formulas and validates the accuracy of RUSLE simulation results using measured sediment data. The optimal combination of LS-factor formulas is selected, and an in-depth analysis is conducted on the origins and suitability of each formula. The accuracy validation results indicate that, for the Fengyu River watershed, the optimal combination of L-factor and S-factor formulas were determined based on the slope gradient. Specifically, L1 formula was used when slope ≤ 10°, and L3 formula was used when slope greater than 10°. Similarly, S1 formula was used when slope ≤ 18°, and S2 formula was used when slope greater than 18°. The RUSLE model achieved the best simulation results with a relative error of 5.55%. The results of the uncertainty analysis indicate that the four formulas have a significant impact on the simulated soil erosion, with a RE ranging from −99.18% to 31.49%. Therefore, based on literature review and formula analysis, a suitability selection table for L-factor and S-factor formulas is provided, which can provide formula basis for the improvement of soil erosion in watershed models.