Harmonic analysis method for hydraulic diffusivity in confined aquifers considering river resistance: An alternative to spectral analysis

Abstract

Recent methodological advancements in hydrogeological characterization have established spectral analysis as a new approach for quantifying riverbank aquifer hydraulic diffusivity. Under idealized conditions characterized by the absence of sedimentary layers at the river-aquifer interface, the power spectral differential between river and groundwater levels manifests a linear relationship with zero intercept, where the characteristic slope exhibits a direct proportionality to hydraulic diffusivity. However, the incorporation of outlet capping layer effects introduces frequency-dependent intercept terms, complicating parameter estimation due to the limitations of frequency-domain resolution and spatial data availability. This investigation introduced a Harmonic Analysis Least Squares (HALS) methodology designed to overcome these constraints. We developed a series solution to quantify the dynamic relationship between confined aquifer groundwater levels and river stages, incorporating river resistance effects on groundwater system dynamics. The proposed methodology was evaluated using field data collected from a four-well monitoring network within the Yangtze River-Honghu Lake basin. Parameter estimates derived through the HALS framework were subsequently implemented in a numerical model, enabling comparison between simulated results, field observations, and conventional spectral analysis outcomes. The HALS methodology demonstrated reliable predictive accuracy, particularly evident at Monitoring Well D, where parameter estimation yielded a river resistance of 38,136 m and hydraulic diffusivity of 8.89 × 10⁵ m²/day. Forward modeling simulations suggested optimal parameter values of 5.00 × 10⁶ m²/day for hydraulic diffusivity and 39,185 m for river resistance. Comparative analysis revealed that the HALS approach outperformed traditional Least Squares Estimation spectral methods through enhanced temporal information preservation, enabling more robust parameter estimation via optimized data utilization. This methodology addresses limitations in conventional slope-intercept approaches, particularly in single-well monitoring scenarios, while maintaining mathematical consistency with established spectral methods when outlet capping effects become negligible. This methodology can be extended to characterize permeability at lake-groundwater interfaces and inversely estimate aquifer parameters under tidal forcing condition in estuarine environments.