Integrated surface–groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model

Interactions between surface and groundwater are a key component of the hydrologic budget on the watershed scale. Models that honor these interactions are commonly based on the conductance concept that presumes a distinct interface at the land surface, separating the surface from the subsurface domain. These types of models link the subsurface and surface domains via an exchange flux that depends upon the magnitude and direction of the hydraulic gradient across the interface and a proportionality constant (a measure of the hydraulic connectivity). Because experimental evidence of such a distinct interface is often lacking in field systems, there is a need for a more general coupled modeling approach. A more general coupled model is presented that incorporates a new two-dimensional overland flow simulator into the parallel three-dimensional variably saturated subsurface flow code ParFlow [Ashby SF, Falgout RD. A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations. Nucl Sci Eng 1996;124(1):145–59; Jones JE, Woodward CS. Newton–Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems. Adv Water Resour 2001;24:763–774]. This new overland flow simulator takes the form of an upper boundary condition and is, thus, fully integrated without relying on the conductance concept. Another important advantage of this approach is the efficient parallelism incorporated into ParFlow, which is exploited by the overland flow simulator. Several verification and simulation examples are presented that focus on the two main processes of runoff production: excess infiltration and saturation. The model is shown to reproduce an analytical solution for overland flow, replicates a laboratory experiment for surface–subsurface flow and compares favorably to other commonly used hydrologic models. The influence of heterogeneity of the shallow subsurface on overland flow is also examined. The results show the propagation of uncertainty due to subsurface heterogeneity to the overland flow predictions and demonstrate the usefulness of our approach. Both the overland flow component and the coupled model are evaluated in a parallel scaling study and show to be efficient.