Analytical solutions for freshwater lenses in stratified riparian aquifers

Abstract

Analytical solutions for defining stable freshwater lenses within saline riparian aquifers (“riparian lenses”) are largely limited to homogenous aquifers. However, real-world riparian aquifers typically consist of a surficial layer of low-permeability soils or deposits, the impact of which on the occurrence of riparian lenses has not been investigated. This study develops steady-state, sharp-interface analytical solutions for riparian lens shape and saltwater discharge in a two-layered riparian aquifer. The developed analytical solutions are verified by sand tank experiments and numerical simulations, showing good agreement. The sensitivity analysis based on the proposed analytical solutions suggests that aquifer stratification (i.e., considering a low-permeability layer overlying a high-permeability layer) leads to larger lenses in head-controlled systems (i.e., with the inland constant-head boundary) but smaller lenses in flux-controlled systems (i.e., with the inland constant-flux boundary), compared to the scenario of a homogenous aquifer. The surficial layer with hydraulic conductivity only an order of magnitude lower than the underlying high-permeability layer would have a pronounced effect on lens extent and volume. Importantly, the results suggest that the presence of the surficial low-permeability layer may lead to the outcropping of the groundwater table, favoring the occurrence of saline groundwater seepage near the edge of the river valley (i.e., a phenomenon reported by the field survey of the Murray River floodplains in South Australia). The analytical solution presented in this study can be used to provide a preliminary assessment of riparian lenses in saline stratified aquifers, expanding the applicability of analytical methods to more realistic riparian settings.