Analytical solutions for stream-aquifer flow exchange under varying head asymmetry and river penetration: Comparison to numerical solutions and use in regional groundwater models

An analytical approach is presented to characterize the local flow exchange conductance and boundary condition between a stream and a hydraulically connected aquifer. Due to the curvilinear nature of the flow pattern in the vicinity of the stream, with numerical procedures, very fine grids would have to be used in order to secure accurate results. This is a waste of numerical efforts when the solution can be obtained analytically. Here, we show that the local analytical procedure for the determination of the stream-aquifer flow exchange (SAFE) coefficient can be integrated within a regional numerical groundwater model through an original boundary condition. This is a very practical result. With this new approach, it is quite simple to calculate accurately the discharges on the two sides of the river when the heads are different. This is an important capability for example when wells are present near a river. The results show also that the extent of penetration of the stream is a factor in the estimation of the discharges. At the very least, the results can be used to choose a grid size that will yield correct estimates within an a priori selected acceptable level of accuracy.