Abstract. Understanding the head distribution in aquifers is crucial for the evaluation of groundwater resources. This article develops an analytical model for describing flow induced by pumping in an L‐shaped fluvial aquifer bounded by impermeable bedrocks and two nearly fully penetrating streams. A similar scenario for numerical studies was reported in Kihm et al. (2007). The water level of the streams is assumed to be linearly varying with distance. The aquifer is divided into two sub-regions and the continuity conditions of hydraulic head and flux are imposed at the interface of the sub-regions. The steady-state solution describing the head distribution for the model without pumping is first developed by the method of separation of variables. The transient solution for the head distribution induced by pumping is then derived based on the steady-state solution as initial condition and the methods of finite Fourier transform and Laplace transform. Moreover, the solution for stream depletion rate (SDR) from each of the two streams is also developed based on the head solution and Darcy's law. Both head and SDR solutions in real time domain are obtained by a numerical inversion scheme called the Stehfest algorithm. The software MODFLOW-2005 is chosen to check the accuracy of the head solution for the L-shaped aquifer. The steady-state and transient head distributions within the L-shaped aquifer predicted by the present solution are compared with the numerical simulations and measurement data presented in Kihm et al. (2007). The SDR solution is employed to demonstrate its use as a design tool in determining well location for required amounts of SDR from nearby streams under a specific aquifer pumping rate.
Characterization of a fluvial aquifer at a range of depths and scales: the Triassic St Bees Sandstone Formation, Cumbria, UK