A simplified equation of approximate interface profile in stratified coastal aquifers

Abstract

In this study, we provide a simplified equation with a new concise set of parameters defining the approximate interface profile in stratified coastal aquifers. We derive the solution directly by applying the Dupuit-Forchheimer approximation at the outset, and mathematically prove its sameness for the uniform flow in a vertical plane with the interface profile computed using the comprehensive discharge potential theory by Strack and Ausk (2015). We present a surprising result that interface elevation in the case with a seepage and outflow face at the coastal boundary turns out to be same as in which water table and interface coincides with the coastline. The interface profile is a function of the transmissivity-field centroid elevation and the total transmissivity of the freshwater-flow domain above the interface. We found that the boundary potential at the coast in the discharge-potential theory solution represents the first moment of the transmissivity. We also analyzed the differences in the interface profiles in aquifers with different hydraulic-conductivity contrasts for two sets of boundary conditions—constant head and constant flux. For a given-flux boundary, interface profiles in aquifer configurations with different conductivity contrasts converge in the upper part of the aquifer and diverge at the aquifer bottom, leading to different toe-positions. Conversely, for a given-head boundary, interface profiles in aquifer configurations with different conductivity contrasts significantly differ in the upper part of the aquifer, while converge at the aquifer bottom resulting in the same toe-position. We provide explicit solutions for the toe-position and freshwater discharge in unconfined aquifers, an extension to our previous work for confined aquifers. Insights from the newly identified parameters can also potentially help in reducing the uncertainty in the estimation of the real-world SWI extent and optimize the requirement of the extent of the hydraulic conductivity field characterization.