One-Dimensional Numerical Cascade Model of Runoff and Soil Loss on Convergent and Divergent Plane Soil Surfaces: Laboratory Assessment and Numerical Simulations

A one-dimensional numerical overland flow model based on the cascade plane theory was developed to estimate rainfall-induced runoff and soil erosion on converging and diverging plane surfaces. The model includes three components: (i) soil infiltration using Horton’s infiltration equation, (ii) overland flow using the kinematic wave approximation of the one-dimensional Saint-Venant shallow water equations for a cascade of planes, and (iii) soil erosion based on the sediment transport continuity equation. The model’s performance was evaluated by comparing numerical results with laboratory data from experiments using a rainfall simulator and a soil flume. Four independent experiments were conducted on converging and diverging surfaces under varying slope and rainfall conditions. Overall, the numerically simulated hydrographs and sediment graphs closely matched the laboratory results, showing the efficiency of the model for the tested controlled laboratory conditions. The model was then used to numerically explore the impact of different plane soil surface geometries on runoff and soil loss. Seven geometries were studied: one rectangular, three diverging, and three converging. A constant soil surface area, the rainfall intensity, and the slope gradient were maintained in all simulations. Results showed that increasing convergence angles led to a higher peak and total soil loss, while decreasing divergence angles reduced them.