Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions

Abstract

Solutions of the linearized one-dimensional Richards equation for discrete arbitrary initial and boundary conditions are presented. The result is the soil water content at any required time and depth in a semi-infinite unsaturated porous medium domain. The initial condition can be any discrete soil water content profile (e.g., experimentally measured) and the boundary condition can be any discrete water flux applied at the surface (e.g., experimentally derived). The procedure described in the paper is valid for any series of successive atmosphere-controlled and soil-controlled phases of infiltration or evaporation as required by the given boundary condition. The procedure provides the ponding time, the desiccation time and the surface water flux during the soil-controlled phases. The comparison among the proposed solutions and some exact analytical solutions is presented as well as the cumulative fluxes. As expected, the agreement between the proposed solutions and the exact analytical solutions depend on the time step chosen for the boundary condition and on the space step chosen for the initial condition.