Coupling Approaches for Surface Water and Groundwater Interactions in Watershed Modeling

In the core of an integrated watershed model is the coupling among surface water and subsurface water flows. Mathematical, there are two approaches of surface/subsurface coupling based on the physical nature of the interface: continuous or discontinuous assumption. Physically, only the continuous case exists in nature. However, when a far less permeable layer exists at the interface, the layer may be removed for computational efficiency. Under such circumstances, the discontinuous simplification may be justified. Numerically, there are three strategies of coupling between surface water and groundwater water: time-lagged, iterative, and simultaneous solutions. Current literature is dominated by the discontinuity assumption with the simultaneous solution strategy. Since modelers often resort to the simplest, fastest schemes in practical applications, it is desirable to quantify potential errors and the performance specific to each coupling scheme. This paper evaluates these coupling schemes in watershed modeling with WASH123D. Numerical experiments are used to compare the performance of each coupling approach and strategy for different types of surface water and groundwater interactions. These experiments are done in terms of errors in state variables (e.g., water depth and pressure head) and fluxes (e.g. infiltration/seepage rate). It is found that different coupling approaches and strategies are justifiable for only the specific flow problem of physical setting of interfaces and the specific scale of time and space. Therefore, for practicality and for accurate and efficient simulations, a watershed simulator should include various options of mathematical approaches and numerical strategies. However, the time-lagged strategy should be avoided since it generally produces too much error in solutions in fluxes, thus causing problem of mass conservation across the interface.