Analytical Solutions for Fresh Groundwater Lenses in Small Strip Islands With Spatially Variable Recharge

Abstract

AbstractGroundwater lens may provide the primary freshwater supply for the inhabitants of small islands. The lens profile and volume are sensitive to spatially variable recharge caused by topography, soil type, land cover, evapotranspiration and human activities. We derive analytical solutions based on the sharp‐interface approximation to describe transient and steady‐state lens profiles for spatially variable recharge rates in small strip islands. The derived solutions are validated by a steady‐state solution for simple spatial recharge patterns and numerical simulations. Numerical investigations show that the spatial recharge pattern has a significant impact on the lens profile. For a given constant total recharge, smaller recharge areas or a more concentrated recharge rate can result in a larger lens volume. The volume increase can be over 20% compared with the lens volume of a uniform recharge. For the steady‐state lens profile corresponding to a point recharge, the squared lens thickness peaks at the recharge location and linearly decreases to the boundary, resulting in a triangle shape for the profile of squared lens thickness. Moreover, compared with recharges in other locations, recharge in a small area at the domain center has the greatest impact. Uncertainty analysis can be conveniently implemented based on the derived analytical solution to investigate the lens behavior under spatially variable recharge with uncertainties. Results show that the lens volume tends to have a larger variance for a recharge rate with a higher variance and longer correlation length.