Modeling Variably Saturated Flow in Stratified Soils with Explicit Tracking of Wetting Front and Water Table Locations

The locations of wetting front and water table are key variables in an integrated surface-groundwater modeling. In current land surface models, they are either diagnosed from pressure head profiles or predicted using certain parameterization schemes. Both approaches need to make assumptions on how pressure head changes vertically and numerical results may have large errors when these assumptions are violated. In this work, we propose a numerical framework which can explicitly track the locations of wetting front and water table. Existing numerical solvers modeling soil water movement usually use water content, pressure head, or both of them as prognostic variables while in this framework, two additional prognostic variables representing the locations of wetting front and water table are introduced. Besides, another two improvements are explored to make the framework stable and efficient. First, a new equivalent hydraulic conductivity formula accommodating nonlinear hydraulic curves is proposed. The formula is unconditionally stable and can yield oscillation-free solution of Richards’ equation in unsaturated homogeneous soils. Second, a mixed implicit-explicit temporal discretization is adopted. It uses an implicit scheme initially at every time step to improve the stability and accuracy while in case of failure of convergence it replaces the iterations with an explicit scheme to guarantee mass conservation. Based on these improvements the framework is potentially used to simulate variably saturated flow in stratified soils in land surface models. Six numerical tests covering various flow situations, boundary conditions, and soil geometries are carried out and illustrate the characteristics of the proposed framework.