A three-parameter runoff probability model for long-slope croplands in the black soil region of Northeast China - Yiting Huang; Yuhao Gao; Junxi Chen; Ziheng Feng; Yi Zhang; Yangbo He; Zhengchao Tian; Lirong Lin; Jiazhou Chen (Journal of Hydrology: Regional Studies)
Study region: The Mangang black soil region of Northeast China, characterized by long or ultra-long slopes (100–4000 m), is experiencing severe water erosion. Study focus: Soil erosion has worsened, particularly on long slopes, due to precipitation variability and tillage disturbance. Existing models struggle to predict runoff because they fail to capture nonlinear shifts among multiple runoff-generation mechanisms. To address this, a probabilistic runoff model with three parameters (β, μ, τ) was developed, coupling infiltration, re-infiltration, and exfiltration with Hortonian, Betsonian, and Duncanian regimes. By extending the Sheridan framework with an exponential exfiltration function, the model estimates runoff coefficients based on slope length and soil saturation. It was validated using rainfall plots, field observations (1–600 m), and literature data, and benchmarked against the Sheridan model and HYDRUS-2D. New hydrological insights: The model reveals a “hook-shaped” nonlinear relationship between slope length and runoff coefficient (R2 =0.92–0.99, KGE=0.87–0.98), with a turning point (Tp, 100–200 m) marking the shift from decreasing to increasing runoff. A new threshold, τ (incomplete saturation slope length), reflects saturation-driven exfiltration feedback, dividing slopes into: (1) Wetting zone (0-Tp): dominated by Hortonian runoff; (2) Transition zone (Tp-τ) with rapid exfiltration and gully initiation; (3) Saturated zone (>τ): dominated by Duncanian runoff. Compared with HYDRUS-2D, the model improves runoff distance estimation by 25 % and reduces runoff errors by 37–62 %, supporting adaptive land management.