Artificial aquifer recharge and pumping: transient analytical solutions for hydraulic head and impact on streamflow rate based on the spatial superposition method

The behaviour of transient groundwater mounds in response to infiltration from surface basins has been studied for decades, but some common settings still lack analytical solutions. It has been shown that applying mathematical integration to the line-sink solution developed by Hantush in the 1960s for pumping an unconfined aquifer, considering recharge over the surface of a defined area, is identical to his solution for groundwater mounding below a rectangular basin. This implies that the superposition principle can, generally, be used to directly include pumping wells, as well as aquifer boundaries, to derive a unique solution. Moreover, other line-sink solutions can be used with a spatial superposition method for addressing a variety of hydrogeological settings, provided the behaviour of the relevant partial differential equations is linear. Based on this principle and on existing line-sink solutions, several analytical solutions are proposed that are able to consider a rectangular recharging area and a pumping well in an unconfined aquifer: (1) near a stream, (2) between a stream and a no-flow boundary, with and without the influence of natural recharge, (3) near a stream that partially penetrates an aquifer and (4) for a multi-layer aquifer. For cases including streams, transient solutions of the impact on streamflow rate are also presented. The proposed analytical solutions will be of practical use for managed aquifer recharge, in particular the design of structures for artificially recharging an aquifer, possibly pumped by one or several wells.