Sensitivity of travelling wave solution to Richards equation to soil material property functions

Richards equation describes water transport in soils, but requires as input, soil material property functions specifically relative hydraulic conductivity and relative diffusivity typically obtained from the soil–water retention curve (SWRC) function (involving capillary suction head). These properties are often expressed via particular functional forms, with different soil types from sandstones to loams represented within those functional forms by a free fitting parameter. Travelling wave solutions (profile of height ξ^ against moisture content Θ) of Richards equation using van Genuchten’s form of the soil material property functions diverge to arbitrarily large height close to full saturation. The value of relative diffusivity itself diverges at full saturation owing to a weak singularity in the SWRC. If, however, soil material property data are sparse near full saturation, evidence for the nature of that divergence may be limited. Here we rescale the relative diffusivity to approach unity at full saturation, removing a singularity from the original van Genuchten SWRC function by constructing a convex hull around it. A piecewise SWRC function results with capillary suction head approaching zero smoothly at full saturation. We use this SWRC with the Brooks–Corey relative hydraulic conductivity to develop a new relative diffusivity function and proceed to solve Richards equation. We obtain logarithmic relationships between height ξ^ and moisture content Θ close to saturation. Predicted ξ^ values are smaller than profile heights obtained when solving using the original van Genuchten’s soil material property functions. Those heights instead exhibit power law behaviour.