Modified Richards' Equation to Improve Estimates of Soil Moisture in Two-Layered Soils after Infiltration

Soil moisture distribution plays a significant role in soil erosion, evapotranspiration, and overland flow. Infiltration is a main component of the hydrological cycle, and simulations of soil moisture can improve infiltration process modeling. Different environmental factors affect soil moisture distribution in different soil layers. Soil moisture distribution is influenced mainly by soil properties (e.g., porosity) in the upper layer (10 cm), but by gravity-related factors (e.g., slope) in the deeper layer (50 cm). Richards' equation is a widely used infiltration equation in hydrological models, but its homogeneous assumptions simplify the pattern of soil moisture distribution, leading to overestimates. Here, we present a modified Richards' equation to predict soil moisture distribution in different layers along vertical infiltration. Two formulae considering different controlling factors were used to estimate soil moisture distribution at a given time and depth. Data for factors including slope, soil depth, porosity, and hydraulic conductivity were obtained from the literature and in situ measurements and used as prior information. Simulations were compared between the modified and the original Richards' equations and with measurements taken at different times and depths. Comparisons with soil moisture data measured in situ indicated that the modified Richards' equation still had limitations in terms of reproducing soil moisture in different slope positions and rainfall periods. However, compared with the original Richards' equation, the modified equation estimated soil moisture with spatial diversity in the infiltration process more accurately. The equation may benefit from further solutions that consider various controlling factors in layers. Our results show that the proposed modified Richards' equation provides a more effective approach to predict soil moisture in the vertical infiltration process.