River Seepage Conductance in Large-Scale Regional Studies

Flow exchange between surface and groundwater is of great importance be it for beneficial allocation and use of water resources or for the proper exercise of water rights. In large-scale regional studies, most numerical models use coarse grid sizes, which make it difficult to provide an accurate depiction of the phenomenon. In particular, a somewhat arbitrary leakance coefficient in a third type (i.e., Cauchy, General Head) boundary condition is used to calculate the seepage discharge as a function of the difference of head in the river and in the aquifer, whose value is often found by calibration. A different approach is presented to analytically estimate that leakance coefficient. It is shown that a simple equivalence can be deduced from the analytical solution for the empirical coefficient, so that it provides the accuracy of the analytical solution while the model maintains a very coarse grid, treating the water-table aquifer as a single calculation layer. Relating the empirical leakance coefficient to the exact conductance, derived from physical principles, provides a physical basis for the leakance coefficient. Factors such as normalized wetted perimeter, degree of penetration of the river, presence of a clogging layer, and anisotropy can be included with little computational demand. In addition the river coefficient in models such as MODFLOW, for example, can be easily modified when grid size is changed without need for recalibration.