Motion of wetting fronts moving into partially pre-wet soil

We study the motion of wetting fronts for vertical infiltration problems as modeled by Richards’ equation. Parlange and others have shown that wetting fronts in infiltration flows can be described by traveling wave solutions. If the soil layer is not initially dry, but has an initial distribution of water content then the motion of the wetting front will change due to the interaction of the infiltrating flow with the pre-existing soil conditions. Using traveling wave profiles, we construct simple approximate solutions of initial-boundary value problems for Richards’ equation that accurately describe the position and moisture distribution of the wetting front. We show that the influences of surface boundary conditions and initial conditions produce shifts to the position of the wetting front. The shifts can be calculated by examining the cumulative infiltration, and are validated numerically for several problems for Richards’ equation and the linear advection–diffusion equati