A correction on coastal heads for groundwater flow models

We introduce a simple correction to coastal heads for constant-density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant-density flow) if the coastal heads are corrected to ((α+1)/α)h_s-B/2α, in which h_s is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value hs1+α/α. The accuracy of using these corrections is demonstrated by consistency between constant-density Darcy's solution and variable-density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant-density flow relative to variable-density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant-density groundwater flow models.