Estimating Unconfined Aquifer Diffusivity Using 1D Phase Spectral Analysis: A Case Study in the Middle Reach of the Hutuo River, North China Plain

Aquifer diffusivity is a basic physical parameter used in hydrogeological calculations and is important for the evaluation and rational utilization of water resources, pollution prevention, and wetland protection. In this study, with the assumptions of aquifer isotropy, i.e., no vertical flow and constant saturated aquifer thickness, by using the Fourier transform and convolution theorem, a 1D analytical solution of the phase spectrum for an unconfined aquifer system was derived, which subsequently led to a phase spectrum solution for aquifer diffusivity. To test the efficacy, the proposed method was applied to a study site in the middle reach of the Hutuo River in the North China Plain. The estimated aquifer diffusivity ranged from 1.9 × 103 to 4.9 × 104 m2/d, with a mean of 2.2 × 104 m2/d, which was consistent with the results obtained using power spectral analysis, pumping tests, and inverse numerical models. The phase spectral approach proposed in this paper can estimate the aquifer properties on a larger scale. If long time series of hydraulic heads are available, it can estimate hydrogeological parameters accurately and quickly. Considering the similarity of the linearized governing equations, it can also be applied to the river–aquifer system and the confined aquifer system.