Approximate analytical solution of one-dimensional vertical unsaturated soil water movement equations under constant flux boundary conditions

Simple analytical solutions for one-dimensional unsaturated soil water infiltration are important for estimating soil hydraulic properties and optimizing irrigation practices. In this paper, we propose a method based on the functional extremal problem of the Richards equation to simulate the vertical infiltration of one-dimensional unsaturated soil water under constant flux. This method used the Brooks-Corey model to present the functional extremal problem and obtain the functional extremal solution of the Richards equation using the EulerLagrange and the integral median theorem. Hydrus-1D was used to obtain the numerical data of onedimensional vertical infiltration with a constant flux of 0.0001-0.001 (cm.min(-1)). By comparing the analytical results of the functional extremal solution with the numerical data, we derived the relationships between the infiltration characteristics (soil water content profile, cumulative infiltration, and infiltration time) and the major parameters (soil hydraulic parameters, constant flux qi, and vertical wetting front depth zf). The comparison results of the high fluxes conditions showed that the functional solution accurately described the onedimensional vertical infiltration in soils with the absolute air-entry suction hd >= 10 cm under a constant flux at the upper boundary.