Tide-induced head fluctuations in coastal aquifers of variable thickness

Abstract

In this work, a new analytical solution to describe tide-induced head fluctuations in aquifers of variable thickness is presented. The proposed model assumes a finite and confined aquifer with a thickness that increases or decreases quadratically with the distance to the coast. A closed-form analytical solution is obtained by solving a boundary-value problem with both a separation of variables method and a change of variables method. This solution is a generalization of the solution obtained by Cuello et al., Hydrogeological Journal, 2017, 25, 1509–1515. The analytical solution is expressed in terms of the wedging parameter, a parameter that depends on the length and thicknesses at the coast and at the inland edge of the aquifer. Positive values of the wedging parameter describe aquifers with increasing thickness towards land and negative values describe aquifers with a decreasing thickness in the inland direction. The comparison of the new solution and the solution for a finite aquifer with constant thickness indicates that the sign of the wedging parameter enhances or decreases the amplitude of the tide-induced signal. However, the differences in time-lag between both solutions are negligible near the coast. The slope factor, which quantifies the inconsistencies between aquifer diffusivities estimated from attenuation and time-lag data, is computed and analysed. Near the coast, slope factor values greater than one are obtained for negative wedging parameters while slope factor values less than one are obtained for positive wedging parameters. The analysis of the new solution also indicates that more reliable estimates of the hydraulic diffusivity can be obtained from time-lag data.