An approximate integral solution of vertical infiltration under changing boundary conditions

An approximate solution of the Richards equation was obtained with a spectral series solution for rain infiltration under changing boundary conditions. Prior to surface ponding a flux boundary condition was employed, which was followed by a concentration boundary condition. During this latter stage a flux matching boundary condition was used to describe the movement of the interface between the saturated and unsaturated zones. The solutions yield a general expression for ponding time, wetting front advance, and soil water profile. Infiltration rates beyond ponding include the effect of time dependent ponding height and saturation depth.

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