Spatiotemporal Patterns of Runoff–Erosion Relationships and Their Driving Mechanisms in Mountain–Plain Transitional Basins

Climate change and anthropogenic activities have substantially altered runoff generation and soil erosion processes. This study investigated the spatiotemporal patterns and influencing factors of the Potential Soil Erosion–Runoff Ratio (PERR), defined as the ratio of RUSLE-derived annual potential soil erosion amount to annual runoff volume, in the mountain–hill–plain transitional of Sanmenxia, China, from 1990 to 2015. Spatial statistical methods were integrated with comparative machine learning and SHAP-based interpretation. Among six candidate models, XGBoost achieved the best predictive performance, with R2 values of 0.914 and 0.839 for the temporal and spatial holdout sets, respectively. PERR exhibited marked interannual fluctuations without a statistically significant monotonic trend, while the sequential Mann–Kendall test identified candidate temporal shifts around 1994–1995 and 2014. Spatially, persistent hot spots were concentrated in the southern mountainous and hilly regions, whereas persistent cold spots occurred mainly in the northern plains, revealing a clear geomorphic gradient. Slope, cropland cover, and elevation had the highest mean absolute SHAP values within the fitted model. A pronounced nonlinear transition in the modelled PERR response occurred near a slope of 17°, representing a model-derived and scale-dependent transition range rather than a universal physical threshold. These findings demonstrate the utility of explainable machine learning for identifying spatial heterogeneity and nonlinear controls in the runoff–potential erosion relationship and provide quantitative support for spatially targeted soil and water conservation.