An unsteady analytical solution for a layered Tóthian basin subjected to time-dependent water table boundary

An analytical solution is developed for predicting hydraulic head variation in a layered Tóthian basin driven by an unsteady water table boundary at the surface. The separation of variable method in conjecture with quasi-orthogonal Fourier series is used to arrive at the analytical solution. The correctness of the proposed solution is confirmed by comparing the hydraulic head and recharge/discharge variation with an existing analytical model for simplified flow geometry. The proposed model evaluates the recharge/discharge rate, pathline, distribution of stagnation points, and residence time distribution. Further, a sensitivity study is performed to measure the importance of different flow and aquifer parameters. The study highlights that the pathline followed by the water particle in a Tothian basin with an unsteady water table boundary doesn't follow a typical smooth path; instead, it takes a curly path. Further, the residence time distribution is found to follow a heavy-tailed distribution.