A two-layer numerical model of soil moisture dynamics: Model development

Abstract

Simulating water moisture flow in variably saturated soils with a relatively shallow water table is challenging due to the high nonlinear behavior of Richards' equation (RE). A two-layer approximation of RE was derived in this paper, which describes vertically-averaged soil moisture content and flow dynamics in the root zone and the unsaturated soil below. To this end, the partial differential equation (PDE) describing RE was converted into two-coupled ordinary differential equations (ODEs) describing dynamic vertically-averaged soil moisture variations in the two soil zones subject to a deep or shallow water table in addition to variable soil moisture flux and pressure conditions at the surface. The coupled ODEs were solved numerically using the iterative Huen's method for a variety of flux and pressure-controlled top and bottom boundary conditions (BCs). The numerical model was evaluated for three typical soil textures with free-drainage and mixed flux-pressure head at the bottom boundary under various atmospheric conditions. The results of soil water contents and fluxes were validated using HYDRUS-1D as a benchmark. Simulated values showed that the new model is numerically stable and generally accurate in simulating vertically-averaged soil moisture in the two layers under various flux and prescribed pressure BCs. A hypothetical simulation scenario involving desaturation of initially saturated soil profile caused by exponentially declining water table demonstrated the robustness of the numerical model in tracking vertically-averaged moisture contents in the roots layer and the lower vadose soil as the water table continued to fall. The two-layer model can be used by researchers to simulate variably saturated soils in wetlands and by water resources planners for efficient coupling of land-surface systems to groundwater and management of conjunctive use of surface and groundwater.