New insights into the differences between the dual node approach and the common node approach for coupling surface–subsurface flow

Abstract. The common node approach and the dual node approach are two widely applied approaches to coupling surface–subsurface flow. In this study both approaches are analyzed for cell-centered as well as vertex-centered finite difference schemes. It is shown that the dual node approach should be conceptualized and implemented as a one-sided first-order finite difference to approximate the vertical subsurface hydraulic gradient at the land surface. This results in a consistent dual node approach in which the coupling length is related to grid topology. In this coupling approach the coupling length is not to be interpreted as a nonphysical model parameter. Although this particular coupling approach is technically not new, the differences between this consistent dual node approach and the common node approach have not been studied in detail. In fact, this coupling scheme is often believed to be similar to the common node approach. In this study it is illustrated that in comparison to the common node approach, the head continuity at the surface–subsurface interface is formulated more correctly in the consistent dual node approach. Numerical experiments indicate that the consistent dual node approach is less sensitive to the vertical discretization when simulating excess infiltration. It is also found that the consistent dual node approach can be advantageous in terms of numerical efficiency.