Spectral Analysis of River Resistance and Aquifer Diffusivity in a River‐Confined Aquifer System

Abstract

Hydraulic connections between a river and an adjacent aquifer are controlled by the river resistance and aquifer diffusivity. In this paper, we derive a spectral solution linking the power spectrum of river stage fluctuations to that of the hydraulic head of a confined aquifer by means of a physical scaling factor. The physical scaling factor represents an algebraic expression of the river resistance and aquifer diffusivity and is included in an exact spectral solution derived herein. Statistical measures of the aquifer diffusivity and river resistance are provided by fitting the solution versus observed groundwater hydraulic head obtained at several distances and/or frequencies. At a study site in the middle reach of the Yangtze River and downstream of the Three Gorges Dam in China, we find systematic damping of the hydraulic head variations with distance from the river, which follows a fractal pattern driven by the river stage. In general, the estimated parameters are consistent with results reported in the literature, which supports the validity of the proposed spectral approach, although the paper discusses advantages and limitations due to application conditions.

Groundwater‐stream connectivity from minutes to months across United States basins as revealed by spectral analysis

“…Values of Singh, 2004;Wang & Wörman, 2019). Specifically, TF approaches 1 for short separation distances between the well and stream, long signal periods, and large aquifer diffusivities.…”

“…It is important to note that TF in open aquifers is influenced by a number of interacting factors, including disturbances from nearby stream stage fluctuations, changes in local recharge, and groundwater extraction, to name a few. In the simple case of a one‐dimensional, linear aquifer without vertical recharge, TF ranges from 0 to 1, and the amplitude of the water table fluctuation relative to the stream stage fluctuation depends on distance to the stream‐aquifer interface, hydraulic diffusivity, and frequency (Shih, 1999; Singh, 2004; Wang & Wörman, 2019). Specifically, TF approaches 1 for short separation distances between the well and stream, long signal periods, and large aquifer diffusivities.…”

“…Schuite et al (2019) used frequency‐domain analysis of hydrological signals, such as stream discharge and precipitation, to constrain catchment properties. Other studies have developed approaches in the frequency domain for estimating river resistance and hydraulic diffusivity in confined aquifers (Shih, 1999; Wang & Wörman, 2019). In headwaters of the Mississippi River, Wu et al (2020) used frequency‐domain analysis to show that hyporheic exchange moderates stream temperature fluctuations, particularly at higher frequencies, but river regulation reduces the moderating effect.…”

Analytical Solutions for Steady-State Multiwell Aquifer Tests in Rectangular Aquifers by Using Double Fourier Transform: A Case Study in the Ordos Plateau, China

“…Therefore, no data of storativity, specific yield, or aquifer diffusivity can be obtained. These parameters are vital for the management of groundwater resources, the evaluation of surface water-groundwater interactions, and the protection of the ecological environment [22][23][24][25]. Solutions regarding transient behaviors should be considered in the future.…”

On River‐Aquifer Exchange Flow With Irregular and Semipervious Bank

“…At present, numerical models can be used to build various kinds of irregular bank geometries for a river‐aquifer interaction scheme, but often with laboring and tedious preparations for setting up the model properly. Analytical solutions have the advantages of low computational cost, fast performance, enhanced understanding of physical processes, and rapid inversion of hydraulic properties, and can also be used as a benchmark for validating numerical models (Liang et al., 2020; Moench & Barlow, 2000; Wang & Wörman, 2019; Xian et al., 2020). To establish an analytical model for describing the transient flow in a river‐aquifer system with a sloping bank due to river stage fluctuation, the one‐dimensional (1‐D) Boussinesq equation (BEQ) was often adopted as the governing equation (e.g., Jiang & Tang, 2015; Li et al., 2000; Liang et al., 2020; Sun et al., 2011; Tang et al., 2016).…”