Analytical estimation of sea-level rise impacts on the freshwater lenses of elliptical islands with sloping shorelines

The vulnerability of island freshwater lenses to rising sea levels has been assessed previously using sharp-interface analytical solutions that consider islands as circular or two-dimensional strips, or the lenses are treated as entirely underlain by seawater. However, many islands do not fit these basic conditions. The current study develops an analytical solution for the freshwater-saltwater interface in elliptical islands where the interface intercepts the aquifer base, and explores (for the first time for island lenses) the applicability of a dispersion correction to the analytical solution. An analysis of the lens response to sea-level rise (SLR) and the accompanying land-surface inundation (LSI) shows that for lenses entirely underlain by seawater, the primary impact of SLR is likely the associated LSI. Counterintuitively, lenses in contact with the aquifer basement may experience an increase in the freshwater volume with SLR, although this requires that LSI is limited (e.g., the shoreline is steep) and the water table is sufficiently deep (below the land surface) to allow it to rise commensurately with SLR. The analysis also shows that as the aspect ratio of the elliptical island increases (i.e., larger values approach strip islands and circular islands have a value of 1), the lens volume decreases (for a given island area). Thus, circular islands have the maximum freshwater storage per island area. Specifically, for typical island aquifer conditions, freshwater storage decreased over 50% as a/b increased from 1 to 10. The results obtained from this study and the new analytical solution are expected to assist in the rapid assessment of the freshwater resources of elliptical-like islands.