Abstract
Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate.
Highlights
Groundwater level has been widely investigated by experimental or field data collection, numerical methods, and analytical approaches
Paniconi and Wood [1] developed a three-dimensional finite element numerical model based on the Richards equation to deal with catchment scale simulations
Brutsaert [2] derived an analytical solution to the linearized Boussinesq equation and studied the response of the groundwater flow per unit width of the slope with consideration of zero water depth at the downstream boundary condition, corresponding to the free drainage of the unconfined aquifer
Summary
Groundwater level has been widely investigated by experimental or field data collection, numerical methods, and analytical approaches. Dralle et al [6] derived a new analytical solution to the linearized hillslope Boussinesq equation with spatially variable recharge by the method of eigenfunction expansion, and discussed the hydrologic response of topography to base flow discharge properties. In their study, they claimed that their solutions exactly reproduce previous results, e.g., Verhoest and Troch [7] and Troch et al [5], for the case of spatially uniform recharge, and perfectly match the numerical solutions by a finite difference scheme for the case of spatially variable recharge.
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