A correction on coastal heads for groundwater flow models

Modeling groundwater flow in coastal aquifers is critical for managing freshwater resources and preventing saltwater intrusion. Prior research has shown that traditional constant-density groundwater models often misrepresent coastal boundaries, leading to inaccurate discharge estimates. This gap motivated the development of correction methods to improve model accuracy. Existing approaches either ignore density effects or use simplified approximations, which may introduce large errors. The need for a practical correction method became evident as numerical simulations revealed significant discrepancies in discharge calculations. The coastal boundary condition remains a key challenge in regional flow modeling. Previous studies have proposed various approximations, but none fully address the interface flow dynamics. This paper introduces a new correction based on analytical solutions for interface flow.

This study aims to provide a correction method for coastal heads in constant-density groundwater flow models. The correction is derived from analytical solutions for interface flow and is designed to improve discharge estimates at the sea boundary. The specific problem addressed is the inaccuracy of traditional models when applied to coastal aquifers. The motivation is to reduce large errors in discharge calculations that arise from ignoring density variations. The correction is intended for both confined and unconfined aquifers. The study evaluates two previous correction methods and quantifies their errors. The goal is to facilitate rapid and accurate estimation of freshwater flux from hydraulic head measurements. The proposed method allows for better representation of the coastal boundary condition in regional models.

The study derives a correction formula for coastal heads based on analytical solutions for interface flow. The correction is applied to both confined and unconfined aquifers. For confined aquifers, the corrected head is ((α + 1)/α)hs  - B/2α, where hs is the mean sea level, B is aquifer thickness, and α is the density factor. For unconfined aquifers, the corrected head is hs1+α/α. The accuracy of the correction is verified by comparing constant-density Darcy's law solutions with variable-density numerical simulations. Two previous correction methods are evaluated for error magnitude. A sensitivity analysis is conducted to assess the impact of aquifer parameters on discharge errors. The location of observation wells relative to the toe is analyzed as a factor affecting estimation accuracy.

The correction method significantly improves discharge estimates at the coastal boundary. For confined aquifers, applying ((α + 1)/α)hs  - B/2α reduces errors compared to uncorrected models. For unconfined aquifers, using hs1+α/α provides accurate results. The corrected Darcy's law solution aligns with variable-density numerical simulations. Previous correction methods introduce errors exceeding 100% in typical coastal aquifer scenarios. The location of observation wells strongly influences estimation accuracy. Aquifer length relative to the toe determines the proportion of constant-density flow. The corrected method enables rapid and accurate freshwater flux estimation from hydraulic head measurements.

The study demonstrates that the proposed coastal head correction improves discharge estimates in groundwater flow models. The correction is derived from interface flow solutions and validated against numerical simulations. The correction works for both confined and unconfined aquifers. The authors suggest that the corrected Darcy's law solution is consistent with variable-density flow simulations. The study shows that uncorrected methods can lead to large errors in discharge calculations. The location of observation wells is a key factor in estimation accuracy. The correction allows for better representation of the coastal boundary in regional models. The authors propose that this method facilitates accurate freshwater flux estimation from hydraulic head measurements.