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

It is well known that land surface topography governs surface–groundwater interactions under some 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 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. HIGHLIGHTS Identify a research gap in the traditional Fourier fitting approach in the hyporheic exchange model.; Propose a new mathematical approach that incorporates spectral analysis to improve the accuracy of the Fourier fitting process.; Verify the validity of spectral analysis in the Fourier fitting process with synthetic scenarios.