A simplified approach for the evaluation of groundwater flow in stream-aquifer interaction

Stream-aquifer interaction process plays an important role in modulating flood wave propagation in a channel. The most elementary understanding of stream-aquifer interaction can be interpreted by the flux direction between a surface water body and the underlying aquifer. At the time of floods, stream stage rises, and the water gets infiltrated into the aquifer, and this process gets reversed at the time when the stream stage gets declined. Therefore, an integrated mechanism between the surface and subsurface flows is particularly important for models, where the response of the system is based on simultaneous interactions between these two major flow domains. In this study, numerical simulation of a flood wave has been demonstrated considering stream-aquifer interaction. The calibration has been executed on a hypothetical flood event accessed by routing a known stage hydrograph for a channel reach having a rectangular cross section which fully penetrates the adjoining aquifer given by Zitta and Wiggert (Water Resour Res 7:1341-1345, 1971). A simplified mathematical approach, based on Darcy's law, has been presented here for the solution of groundwater flow equations. The results obtained from the adopted procedure are also compared with the solution proposed by Zitta and Wiggert in 1971. The NSE and RMSE (m(3)/s) estimate assessed for the simulated hydrographs using the proposed methodology with respect to the procedure adopted by Zitta and Wiggert (Water Resour Res 7:1341-1345, 1971) is 0.9983 and 0.8544, respectively. Therefore, the use of Simpson's (3/8)-rule is not suggestible due to its complicated calculation and its sensitivity, and it is better to use the proposed simplified approach for the evaluation of lateral flow.

Automated summary

The interaction between stream and aquifer plays a crucial role in flood wave propagation in a channel, with water flux direction being the most basic understanding of this process. During floods, water infiltrates into the aquifer as stream stage rises, and this process reverses as the stage declines, highlighting the importance of an integrated mechanism between surface and subsurface flows in determining the system's response. Numerical simulation of flood waves considering stream-aquifer interaction has been demonstrated in this study, with a simplified mathematical approach based on Darcy's law used for evaluating groundwater flow equations and compared with previous methods for calibration. The results indicate a high level of accuracy and suggest using the proposed simplified approach for evaluating lateral flow, rather than the more complex and sensitive Simpson's (3/8)-rule.