Semi-numerical simulation of groundwater flow induced by periodic forcing with a case-study at an island aquifer

This paper presents an efficient method to analyze the aquifer response to periodic forcing. A complex transformation is used to change the time-dependent linear aquifer model into an equivalent time-independent problem of a complex function (referred to as the “complex amplitude” hereafter). The magnitude of the complex amplitude represents the amplitude of the sinusoidal fluctuation of the groundwater level, and the argument of the complex amplitude, the phase shift of the fluctuation. Different iterative methods can be used to obtain the numerical solution. A semi-analytical numerical solution of the groundwater level, which is numerical for the spatial variables and analytical for the time variable, can be obtained by implementing a simple inverse complex transform to the complex amplitude. The advantages of the time-independent method include ruling out of initial conditions, direct outputs of the amplitude and phase shift of different sinusoidal components of the water level fluctuations. On the contrary, the numerical solutions of the time-dependent model need further computational efforts for the analyses of the amplitudes and phase shifts of different sinusoidal components, and have to consider an initial condition whose impacts on the periodicity have to be eliminated by running sufficiently great number of tidal circles. A case study at an unconfined aquifer formed by fill materials near Lam Chau Island, Hong Kong SAR, PR China shows the applicability of the semi-numerical solution to analyze tide-induced watertable fluctuations. The aquifer parameters were estimated by minimizing a least-squares objective function to fit the complex amplitude of semidiurnal and diurnal components of the observed water level fluctuations. Compared with the parameter estimations of some of the previous analytical solutions, the numerical method gives not only better fitting to the water level observations, but also more aquifer parameters.