Green‐Ampt infiltration model for sloping surfaces

Abstract

This work quantifies and explains the direct physical effects of slope angle on infiltration and runoff generation by extending the Green‐Ampt equation onto sloping surfaces. A new extended solution using identical precipitation hydrographs was compared to the original formulation and then used to calculate the infiltration and runoff generation for different slope angles but for identical horizontal projection lengths. Homogeneous and isotropic soil is assumed, and two different boundary conditions for vertical rainfall are studied: ponded infiltration and infiltration under steady rainfall. Infiltration under unsteady rainfall was found to be similar to cases with steady rainfall. Both theoretical and numerical results show that infiltration increases with increasing slope angle. For cases with ponded infiltration the slope effect was generally not significant for mild to moderate slopes, but the slope effect became more important for low‐intensity and short‐duration rainfall events, especially as it delayed the time for ponding. It was also found that the cumulative vertical infiltration depth ( I hp ) at ponding (or the initial loss) increases with increasing slope angle. The model was compared to Richards' equation on horizontal and sloping surfaces and found to perform well. The model's applicability for nonuniform slopes was discussed, and it was found that the model is generally applicable for isotropic and mildly anisotropic soils except for some small‐scale topographic elements. Finally, the occurrence of nonvertical rainfall could increase runoff with increasing slope angle when rainfall deflects a large angle to upslope.