A mathematical approach to improving the representation of surface water–groundwater exchange in the hyporheic zone

Abstract

It is well known that land surface topography governs surface–groundwater interactions under some certain circumstances and can be separated in a Fourier-series spectrum that provides an exact analytical solution of both the surface and the underlying three-dimensional groundwater flows. We evaluate the performance of the current Fourier fitting process by testing on different scenarios of synthetic surfaces. We identify a technical gap and propose a new version of the approach which incorporates the spectral analysis method to help identify the statistically significant frequencies of the surface to guide the refinement and mesh. Our results show that the spectral analysis is the method that can help improve the accuracy of representing the surface, thus further improving the accuracy of predicting the bedform-driven hyporheic exchange flows.

Seasonal recharge mechanism of the upper shallow groundwater in a long-term wastewater leakage and irrigation region of an alluvial aquifer

“…Fundamental work on spectral analysis of groundwater systems was carried out by Gelhar and Wilson (1974). Recently, this method has often been used to study groundwater recharge, recharge timescales, and spatial scale variability (He and Guan, 2020;Houben et al, 2022). Spectral analysis of stable signals often uses the sine wave method to convert the signal into a regular trigonometric form (Beddows et al, 2016;Das et al, 2021).…”