Analytical methodology for determining the extent of pumped freshwater lenses in recharge-limited, circular islands

Island freshwater lenses are often subjected to pumping to support the freshwater needs of isolated communities. Investigations of the lens extent commonly involve the application of analytical solutions, although the effects of pumping from circular island aquifers have not been assessed in previous analytical methodologies. In this study, a new analytical solution is derived based on Green's functions that accommodate freshwater inputs (recharge) and outputs (multiple wells) when obtaining the head distribution and sharp-interface lens shape. The solution is verified using a finite-element model for an illustrative pumping scenario. The solution is also differentiated with respect to pumping rates, recharge, and island radius to obtain vulnerability indices to characterize the lens sensitivity to changes in stresses. Finally, the analytical methodology is modified to examine the effects of non-uniform recharge. Python code incorporating the new solution is included to enable users to investigate a range of recharge and pumping scenarios.