Scale-dependent parameterization of groundwater-surface water interactions in a regional hydrogeological model

In regional hydrogeological models groundwater-surface water interaction is generally represented with a Cauchy boundary condition, in which a conductance parameter governs the exchange flux rate. In some models, the conductance is controlled by the streambed properties, since it has generally a lower hydraulic conductivity than the aquifer. However, depending on the specific system and the spatial discretization of the hydrogeological model, aquifer conductance can be a limiting factor for groundwater-surface water interactions. The present study introduces a new expression to represent the aquifer conductance as a function of aquifer properties, surface water network density and model discretization. This expression is based on the Dupuit-Forcheimer theory, the Ernst equation and vertical 2D numerical experiments at the field scale. The main assumptions used to derive our formulation are the presence of a no-flow boundary at the bottom of the hydrogeological model and the homogeneity of the aquifer. The expression is evaluated using simulations with 3D hydrogeological models at different spatial resolutions and compared against previously published parameterization approaches. The results show that the new expression outperforms the other approaches by capturing accurately both the grid-size and the surface water network density dependency of the conductance, which is caused by pressure head losses due to flow within the aquifer grid cell to the surface water, without any additional numerical calculation. Moreover, the proposed expression can be implemented directly in hydrogeological models thereby improving current approaches to represent groundwater-surface water interactions in regional hydrogeological models.