Modeling observed saturation overshoot with continuum additions to standard unsaturated theory

In uniform soils that are susceptible to unstable preferential flow, the water saturation exhibits a nonmonotonic profile upon continuous infiltration. This overshoot cannot be described by the conventional Richards equation. Here, solutions to the infiltrations using a popular nonequilibrium extension to the Richards equation are obtained using the traveling wave nature of the saturation profile. Quantitative comparisons are made to recent measurements of saturation overshoot. The nonequilibrium solutions can be made to fit the flux range of the overshoot, but the fit to the tip saturations is fair to poor at best. Also, small changes in porous media size and roughness require large changes in the magnitude of the nonequilibrium term to match the flux range. The results suggest that the nonequilibrium capillary pressure does not include the correct physics that controls the overshoot.