A novel two-dimensional numerical model developed for slope soil erosion

Slope erosion is the main source of soil erosion. Simulated slope erosion sediment yield and its development process have great significance for quantitative erosion evaluation at the spatiotemporal scale. In this study, a loess slope erosion experiment was implemented indoors to establish a sediment carrying capacity formula suitable for loess slope erosion. A two-dimensional slope erosion numerical model was developed based on the developed sediment carrying capacity formula, and the model was verified by a simulated indoor slope rainfall erosion experiment. The results showed that the corrected slope sediment transport capacity formula is suitable for loess slopes, which have a higher prediction precision. The developed erosion numerical model simulation was verified by simulated rainfall slope erosion experiments. Regarding the evaluation metrics for slope simulation accuracy, the Nash-Sutcliffe efficiency (NSE) values were 0.83 for the runoff rate and 0.66 for the sediment concentration, R² values were 0.89 for the runoff rate and 0.73 for the sediment concentration, and the relative bias (RB) values were -5.02% for the runoff rate and -1.02% for the sediment concentration. The spatial contribution rate of slope erosion was analysed based on the simulation results, and the most severely eroded areas were the middle and lower parts of the slope. The erosion contribution rate reached 69.59% on the 1-4 m area of the slope. The research results can further improve loessal slope erosion process simulation and prediction.