Calibrating the wetting front pressure head of the Green and Ampt infiltration model

Abstract

The Green–Ampt (GA) model is a classical analytical solution of the Richards equation used to predict soil water infiltration. Based on a modified form of Darcy's law, it assumes piston‐like flow with a constant pressure head at the soil surface and in the saturated zone, separated from the unsaturated region by a sharp wetting front. Model performance depends strongly on the wetting front pressure head ( h _f ), a difficult‐to‐measure and highly sensitive parameter. We developed a polynomial equation to estimate the optimal h _f for the GA model by comparing GA predictions with HYDRUS simulations of cumulative infiltration. A total of 5151 soil particle size distributions across the soil textural triangle were evaluated under six initial water conditions, ranging from wet to dry. The corresponding Van Genuchten–Mualem (VGM) parameters were obtained using Rosetta, and infiltration rates were simulated for 12 h by numerically solving the Richards equation in HYDRUS. The h _f parameter was calibrated by minimizing the root mean squared logarithmic error (RMSLE) between GA and HYDRUS simulations and evaluated its performance using the Nash–Sutcliffe efficiency (NSE) metric. Based on these calibrated values, a polynomial function was derived through stepwise regression using VGM parameters and initial matric potential ( h ₀ ) as predictors. The polynomial was validated with 92 soils from two independent databases (UNSODA and HYBRAS). Performance metrics, including RMSLE and NSE, showed that the proposed polynomial reliably estimates h _f across different soil textures and initial conditions, outperforming some existing formulations and improving the applicability of the GA model, particularly for monolayer soils.