Incorporating transport processes into a coupled model ofsurface and subsurface interactions

In hydrology, ecology, and environmental management and protection there is increasing attention paid to how water and solutes are exchanged between the atmosphere, the land surface (including open water bodies), and the subsurface (soils and aquifers). In addition, the transfer and transport of contaminants and other solutes is intricately linked to water dynamics. Appropriate mathematical equations governing surface and subsurface processes of water flow and solute transport exist but can be very difficult to solve, owing to nonlinearities, sharp propagation fronts, heterogeneities, and other factors. Further complexity is added when interactions, or coupling, across the land surface interface are taken into account. In this work we consider the implications of these complexities on appropriate numerical schemes for solving flow and transport in a coupled surface--subsurface model. Such a model needs to balance accuracy and efficiency on many fronts: linearization schemes (in particular for the strongly nonlinear Richards equation); adaptive and nested time stepping (that considers also the different characteristic scales of surface and subsurface dynamics); resolution of advection-dominated transport phenomena; calculation of the velocities and discharges that are passed from the flow module to the transport solver; and representation of the land surface boundary condition and of the exchange terms for solutes and water across this interface. A prototype model will be presented that is based on the three-dimensional Richards equation for flow in variably saturated porous media, a path-based (rill flow) diffusion wave approximation to the Saint-Venant equations for surface dynamics on hillslopes and in stream channels, and the classical advection-dispersion-reaction equation with first-order mass transfer. Numerical solution schemes include mixed finite elements for discretization of the flow equations and coupled finite element-finite volumes for the transport equation.