Algebraic model for one-dimensional horizontal water flow with arbitrary initial soil water content

A simple analytical solution of the equation for the one-dimensional horizontal permeability of soil water is important for estimating the hydraulic properties of soil. Our main objective was to develop analytical solutions to the nonlinear Richards equation, with constant-saturation upper boundary and an arbitrary initial soil water content (SWC) for horizontal absorption. We estimated the infiltration rate based on the hypothesis proposed by Parlange and carried out a series of transformations based on the Brooks–Corey model to obtain a theoretical function of the one-dimensional movement of water in unsaturated soil under an arbitrary initial SWC. The algebraic analytical solutions were simple, and the selection of the initial SWC was arbitrary. We assumed three scenarios of linear distributions of initial SWC, and Hydrus-1D software was used to simulate horizontal infiltration. Based on the comparison of algebraic and numerical results, the corrected algebraic model was proposed and verified by the arbitrary initial water content conditions when the maximum SWC was less than the half of saturated water content. The proposed method provides a description of horizontal infiltration for the heterogeneous initial SWCs.