Coupled finite-volume model for 2D surface and 3D subsurface flows

Surface-subsurface interactions are an intrinsic component of the hydrologic response within a watershed; therefore, hydrologic modeling tools should consider these interactions to provide reliable predictions, especially during rainfall-runoff processes. This paper presents a fully implicit coupled model designed for hydrologic evaluation in wetlands, agricultural fields, etc. The model uses the depth-averaged two-dimensional (2D) diffusion wave equation for shallow surface water flow, and the three-dimensional (3D) mixed-form Richards equation for variably saturated subsurface flow. The interactions between surface and subsurface flows are considered via infiltration in dynamic equilibrium. A general framework for coupling the surface and subsurface flow equations is adopted, based on the continuity conditions of pressure head and exchange flux rather than the traditional conductance concept. The diffusion wave surface water equation is used as an upper boundary condition for the initial-boundary value problem of variably saturated subsurface flow. The coupled system of equations governing surface and subsurface flows is discretized using the finite-volume method in space and an implicit scheme in time. Component modules and the coupled flow model have been tested by comparing numerical results with published experimental data and analytical solutions. The verified integrated flow model has been applied to simulate the rainfall-runoff processes in a published field-scale experiment and the Deep Hollow Lake watershed, Mississippi. The results have demonstrated that the established numerical model is capable of simulating 3D subsurface flow and 2D surface shallow water flow as well as predicting the interactions between them.