Analytical solution to linearized groundwater responses in sloping unconfined leaky aquifers under transient surface recharge

The increasing frequency of extreme climate events due to global warming has intensified water scarcity during prolonged droughts, highlighting the urgent need for effective water resource management. In Taiwan, where land availability is limited and population density is high, reservoirs serve as the primary storage mechanism; however, groundwater still accounts for approximately one-third of the total water supply. This study investigates groundwater level responses in a sloping, unconfined, leaky aquifer subjected to transient surface recharge and temporally varying boundary conditions, represented using Heaviside step functions. The governing Boussinesq equation is linearized through a time-dependent averaging strategy to enable analytical tractability, and then solved using the generalized integral transform technique (GITT). A convergence and validity analysis of the linearization is provided to justify this approximation. Model validation is conducted by comparing the analytical results under uniform recharge and horizontal slope conditions with prior benchmark studies. The proposed method demonstrates improved computational efficiency compared with Laplace-transform-based approaches. The findings indicate that steeper aquifer slopes shift peak water levels downslope, hydraulic conductivity controls the drawdown rate, and even small leakage rates exert a significant influence on groundwater dynamics.