Analytical single-potential, sharp-interface solutions for regional seawater intrusion in sloping unconfined coastal aquifers, with pumping and recharge

Contamination of groundwater by intruding seawater is a major problem in many parts of the world. This work derives novel analytical solutions for addressing this problem by extending the Girinskii–Strack concept of discharge potential to represent regional, steady-state, sharp-interface seawater intrusion in a sloping unconfined coastal aquifer. The aquifer has hydraulic conductivity K, is recharged uniformly at the rate r, receives an inflow at its land boundary and has a collector trough (or well gallery idealised as line sink) located at the distance lw from the coastline that penetrates the aquifer and draws groundwater at the rate qw. The theory rests on the approximation of a linearised gravity-part of the hydraulic potential. Analytical solutions for the discharge potential are derived, through which the hydraulic head, the flow depth and the sharp interface, and particularly the location of the interface toe, lT, are also determined. These solutions simplify to known results for the horizontal aquifer case. The utility (and robustness to uncertainty regarding the base slope) of the results in applications is demonstrated in the regional example of the Akrotiri Coastal Aquifer, Cyprus. Recasting the problem in non-dimensional form provides a relationship for the dependence of the relative interface toe location lT/lw on the appropriately normalised difference between the groundwater flow just up-gradient of the collector trough, qo, and the pumping rate, qw, given values of the base slope, r/K and Hsea/lw, where Hsea is the sea-surface elevation above the aquifer base at the coastline. That relationship frames a common groundwater management problem in coastal aquifers subject to a certain exploitation scheme, with lT as decision variable. In an exploratory demonstration study, non-dimensional sets of performance curves are calculated for the regional Akrotiri aquifer. In general, the derived analytical solutions can be used for first-order assessments of seawater intrusion vulnerability and management possibilities across a wide range of current regional coastal aquifer conditions and/or projected water demand, groundwater management and climatic change scenarios.