A coupled model for surface and subsurface flow and transport

A coupled surface and subsurface flow and transport model is developed and applied to simulations of flow and transport in a wetland. The coupled model links two-dimensional shallow water flow and transport to three-dimensional, variably-saturated ground water flow and transport. Unsteady, two-dimensional surface flow is approximated using the shallow water equations, and surface transport using the advection-dispersion equation. Both surface equations are solved by means of a finite volume based numerical model. The Godunov-type model calculates fluxes by means of Roe's approximate Riemann solver. Second order accuracy in time is achieved by means of an explicit predictor-corrector time scheme, and in space by means of the monotone upstream scheme for conservation laws. The subsurface module solves the mixed form of Richards' equation for variably-saturated flow in three dimensions, and the advection-dispersion equation for transport. The subsurface solutions are found numerically using a Galerkin-type finite element method. It provides the flexibility of solving the matrix equations using Gaussian elimination for banded matrices, the conjugate gradient method for symmetric matrices or the ORTHOMIN method for asymmetric matrices, and also incorporates an adjustable time step into the scheme. The two domains are physically and seamlessly linked. The node coordinates on the top surface of the ground water grid are identical to those of the surface grid. The surface nodes are uniquely identified by each component of the coupled model, and the water depths and solute concentrations calculated by the surface model are applied as specified boundary conditions in the subsurface model. These values are updated at each time step. Conversely, the vertical component of the Darcian fluxes calculated by the subsurface are used as infiltration rates for the source term in the shallow water equation, and the concentration values found by the ground water transport equation are used as source or sink terms in the surface transport code. Transferred mass is checked at each time step to insure that conservation of mass is maintained.