Assessment of Three Infiltration Formulas based on Model Fitting on Richards Equation

The Richardʹs equation was used to numerically model 1D flow within unsaturated topsoil and solved using a two-step CrankNicolson scheme. Under constant water supply, the Darcy velocity obtained at the upper boundary, the ground surface, is regarded as the correct infiltration rate. Based on this, three infiltration-capacity formulas by Horton, Philip, and Green-Ampt were evaluated for three types of soil. Results demonstrated that all three formulas provide similar fits to the numerical results, but the Horton formula differs most as compared to the other two formulas in terms of infiltration rate. The cumulative infiltration curves were not distinguishable from each other. By perturbing the rainfall intensity, duration, and initial soil moisture content, regression results demonstrated that only the saturated hydraulic conductivity Ks can be used as a good estimator for parameter k (or fc) in all formulas. The other two parameters, however, will deviate from their original values. Only the latetime infiltration parameter (k or fc) can be predicted a priori using measured ks values.