Image-well solution for island aquifers with pumping, recharge, and complex coastlines

This study presents an innovative mathematical framework that integrates a new analytical solution with the image-well method to model island aquifers under the combined influences of pumping, recharge, and complex coastline geometries. Past analytical solutions often rely on simplified boundary conditions and assume axially or radially symmetric coastline geometries, limiting their ability to address multiple stressors and complex island geometries. In contrast, the proposed framework leverages the computational speed and simplicity of analytical modeling while incorporating an image-well approach to accommodate boundaries with arbitrary shapes. To validate the method accuracy and robustness, convergence analyses and comparisons with an established analytical solution are conducted. Additionally, new indices are introduced to evaluate the sensitivity of the freshwater–saltwater interface depth to various forcings and to assess uncertainties in vulnerability indices. An illustrative case study, based loosely on Kinmen Island, Taiwan, is used to demonstrate the applicability of the approach to optimize the pumping rates for multiple wells while ensuring that the interface depth remains within safe limits. Overall, the presented methodology provides a flexible and efficient tool for groundwater resource management in coastal regions, enabling assessment of saltwater intrusion risk and informing sustainable water-use strategies for coastal regions under dynamic environmental conditions.