An improved method of calculating infiltration into unsaturated soil by discretizing moisture domain

Abstract:

We propose an improved approach of calculating infiltration into unsaturated soils. The approach is built on a general concept of discretizing the moisture domain instead of the traditional spatial discretization (Talbot and Ogden, 2008. A method for computing infiltration and redistribution in a discretized moisture content domain. Water Resour. Res. 44, W08453, doi:10.1029/2008WR006815). The entire moisture domain is divided into numerous moisture bins of small increment. The hydraulic conductivity and diffusivity are strongly non-linear functions of water content, which makes the solution of Richards equation challenging. After discretizing into soil moisture bins, we can treat the conductivity and diffusivity in individual bins as moisture dependent constant evaluated at given moisture content corresponding to each bin. For each bin, we can solve the flow equations analytically since the hydraulic conductivity and diffusivity can be treated as a moisture dependent constant. We then develop analytical solutions for each bin to determine the convective and diffusive water amounts at each time step. Then the moisture amount ahead of the convective front for each bin will be redistributed to the next bin. By performing the calculations for all moisture bins, we can then compute the moisture profile, the infiltration rate and the cumulative infiltration at each time step. The proposed approach shows satisfactory agreement compared against the numerical solutions of Richards equation for several soil types. In addition to the agreement in infiltration rate and cumulative infiltration, particular improvement is observed in the evolution of moisture profiles.