Modeling rainfall infiltration on hillslopes using Flux-concentration relation and time compression approximation

Rainfall infiltration on hillslopes is an important issue in hydrology, which is related to many environmental problems, such as flood, soil erosion, and nutrient and contaminant transport. This study aimed to improve the quantification of infiltration on hillslopes under both steady and unsteady rainfalls. Starting from Darcy's law, an analytical integral infiltrability equation was derived for hillslope infiltration by use of the flux-concentration relation. Based on this equation, a simple scaling relation linking the infiltration times on hillslopes and horizontal planes was obtained which is applicable for both small and large times and can be used to simplify the solution procedure of hillslope infiltration. The infiltrability equation also improved the estimation of ponding time for infiltration under rainfall conditions. For infiltration after ponding, the time compression approximation (TCA) was applied together with the infiltrability equation. To improve the computational efficiency, the analytical integral infiltrability equation was approximated with a two-term power-like function by nonlinear regression. Procedures of applying this approach to both steady and unsteady rainfall conditions were proposed. To evaluate the performance of the new approach, it was compared with the Green-Ampt model for sloping surfaces by Chen and Young (2006) and Richards' equation. The proposed model outperformed the sloping Green-Ampt, and both ponding time and infiltration predictions agreed well with the solutions of Richards' equation for various soil textures, slope angles, initial water contents, and rainfall intensities for both steady and unsteady rainfalls.