Development of groundwater lens for transient recharge in strip islands

Abstract

Groundwater in surficial aquifers in small islands is stored in the form of freshwater lenses floating on the seawater due to density difference. Recharge from rainfall infiltration is one of the primary mechanisms that control the lens growth and decay. Unlike previous studies either assuming steady-state groundwater lenses or relying on numerical simulations, we derive an approximate analytical solution to describe the transient change of groundwater lenses for a time-dependent, fluctuating recharge rate. The approximate analytical solution is validated by numerical simulations of variable density flow and transport. Based on this analytical solution and dimensional analysis, we investigate the impact of periodic recharge, extended drought events and random time-series recharge on the time-dependent behavior of the lens thickness and volume. Results show that only slowly changing recharge patterns with long periods such as seasonal and yearly changes can cause significant fluctuations of groundwater lenses. In specific, 10%, 50% and 100% fluctuations correspond to dimensionless periods of 200, 500 and 1300, respectively, which are 69, 174 and 451 days for our specified hydrogeological parameters. Thus, assuming an average constant recharge rate may be valid for simulating the transient lens profile and volume for recharge patterns with short periods such as daily fluctuations. We further analyze the approximate analytical solution using the method of low-pass filter. The complex physical process of the lens development is fitted by a second-order system on the frequency domain. Such a filter passes sine-wave recharge components with frequencies smaller than the break frequency and attenuates those higher than the break frequency, yielding smooth profiles of the lens thickness and volume. By analyzing the recharge rate spectrum and comparing the component frequency with the break frequency, we demonstrate how the development of a groundwater lens is affected by the transient recharge in reported laboratory and field observations.