Correction factor to account for dispersion in sharp-interface models of terrestrial freshwater lenses and active seawater intrusion

In this paper, a recent analytical solution that describes the steady-state extent of freshwater lenses adjacent to gaining rivers in saline aquifers is improved by applying an empirical correction for dispersive effects. Coastal aquifers experiencing active seawater intrusion (i.e., seawater is flowing inland) are presented as an analogous situation to the terrestrial freshwater lens problem, although the inland boundary in the coastal aquifer situation must represent both a source of freshwater and an outlet of saline groundwater. This condition corresponds to the freshwater river in the terrestrial case. The empirical correction developed in this research applies to situations of flowing saltwater and static freshwater lenses, although freshwater recirculation within the lens is a prominent consequence of dispersive effects, just as seawater recirculates within the stable wedges of coastal aquifers. The correction is a modification of a previous dispersive correction for Ghyben-Herzberg approximations of seawater intrusion (i.e., stable seawater wedges). Comparison between the sharp interface from the modified analytical solution and the 50% saltwater concentration from numerical modelling, using a range of parameter combinations, demonstrates the applicability of both the original analytical solution and its corrected form. The dispersive correction allows for a prediction of the depth to the middle of the mixing zone within about 0.3 m of numerically derived values, at least on average for the cases considered here. It is demonstrated that the uncorrected form of the analytical solution should be used to calculate saltwater flow rates, which closely match those obtained through numerical simulation. Thus, a combination of the unmodified and corrected analytical solutions should be utilized to explore both the saltwater fluxes and lens extent, depending on the dispersiveness of the problem. The new method developed in this paper is simple to apply and offers a wider range of application relative to the previous sharp-interface freshwater lens solution.