Approximate analytical solutions for assessing the effects of unsaturated flow on seawater extent in thin unconfined coastal aquifers

This study develops approximate analytical solutions for seawater extent in unconfined coastal aquifers considering unsaturated flow, and assuming steady-state, sharp-interface conditions, for both constant flux (flux-controlled aquifers) and constant head (head-controlled aquifers) inland boundary conditions. These analytical solutions were verified with numerical simulations of variable-saturation and variable-density flow. The results show that neglecting unsaturated flow underestimates the steady-state seawater extent, particularly for flux-controlled aquifers. This occurs because the vadose zone transmits part of the freshwater flux towards the sea, leading to a lower watertable and, consequently, a more landward seawater extent. Larger capillary fringes accompanying finer-grained sediments (and smaller pore sizes) cause more landward locations of the interface toe for both flux-controlled and head-controlled aquifers. The ratio of the capillary fringe thickness to the saturated zone thickness controls the relative difference in the interface toe location between cases with and without unsaturated flow. When this ratio is 17.3%, the relative difference in the interface toe location is 30% for the flux-controlled aquifer (base scenario adopted in the current study). The presented analytical solutions provide improved predictions of the steady-state seawater extent in thin unconfined aquifers, particularly for those with relatively large capillary fringe thicknesses.