Slope length thresholds and factor interactions drive nonlinear transitions in bare slope soil erosion

Soil erosion is a major global environmental threat, and unraveling the complex, non-linear interactions among its drivers is crucial for effective mitigation. This study employed interpretable machine learning (IML) framework, combining Random Forest (RF) with SHapley Additive exPlanations (SHAP) analysis, on a meta-analysis of 385 indoor experiments to decipher these mechanisms. Results identified slope length (SL) as the dominant controller, explaining 28.45% and 45.16% of the variance in runoff and sediment yield, respectively. Critical, factor-specific thresholds that trigger abrupt shifts in erosion dynamics were uncovered: runoff increased sharply when rainfall intensity (RI) exceeded 75 mm/h, and SL of approximately 4.5 m acted as a critical geomorphic threshold between detachment-limited and transport-limited erosion states. More importantly, the influence of key factors like sand content and antecedent soil moisture was mediated almost entirely through synergistic interactions with other variables, as quantified by Interaction-to-Main Effect Ratio (IMER > 188%). This demonstrates that erosion is driven by SL-centered interaction networks and their nonlinear thresholds, advancing the theoretical framework of erosion process transition and providing a mechanistic basis for threshold-targeted conservation strategies.