Analytical and Numerical Investigation of the Time-scale associated with Seawater Intrusion and Retreat in a Flux-controlled Coastal Aquifer System

Quantification of the time-scale associated with the movement of saltwater-freshwater interface is necessary for the development of efficient and effective controls of saltwater intrusion. This study presents a novel approach to understand the dynamics controlling the time-scale of saltwater intrusion and retreat. We derived an analytical solution for the time-scales of saltwater intrusion and retreat, for a flux-controlled coastal aquifer system, based on an implicit solution for the transient freshwater outflow into the sea. The simple analytical solution was able to produce the results comparable in trends of time-scale variation with the changing boundary to that obtained from the numerical simulations. We identify the flow continuity and the hydrostatic equilibrium across interface as the two processes primarily governing the time-scales. Our theoretical analyses demonstrate how different hydrogeological parameters and boundary conditions affect the above mentioned processes and subsequently control the time-scales. It was found that higher porosity, hydraulic conductivity or aquifer depth values results in longer time-scales. We quantify the temporal asymmetry in the saltwater intrusion and retreat, in the form of ratio of time-scale of interface-advance to interface-retreat, and found this ratio to be heavily dependent on changing boundary conditions and weakly influenced by aquifer parameters. The solution also has the potential to be used for the prediction purpose. The analytical nature of the solution enables us to conveniently incorporate seawater intrusion or retreat time-scale as an objective or constraint in a multi-objective optimization model for coastal aquifer management plans.