Ground Water in Barrier Islands-Theoretical Analysis and Evaluation of the Unequal-Sea Level Problem.
Keywords:Ghyben-Herzberg lens, island hydrology, hydrogeology, finite difference models, beach tides
The Ghyben-Herzberg lens in a strip island is symmetric with respect to the centerline of the island, if recharge and hydraulic conductivity are uniform across the island and effective sea level (i.e. the level of ground-water outflow) is the same on both sides of the island. The unequal- or two-sea level problem results when effective sea level is higher on one side, as would be the case in some barrier islands because of wave runup and the effect of a sloping beach on water-table tides. An approximate analytical solution is available for the cross-island variation of water-table elevation and depth to interface in an unequal-sea level island, but derivation of the water-table position in this solution makes the usual Ghyben-Herzberg assumption that salt-water head is zero. This assumption is not valid here because salt-water head must vary across the island in association with a salt-water flow that would be driven by the unequal sea levels. A finite-difference solution for the configuration of the two-sea level lens is developed here. The model takes into account the across-island variation in salt-water head. The model handles the resulting nonlinear differential equation with an iterative scheme in which the Thomas Algorithm is used to solve the finite-difference equations during each iteration. Results of a parametric study of the asymmetry of the lens vs magnitude of sea-level difference indicate: (1) use of the approximate analytical solution that ignores the nonzero saltwater head can produce significant errors, especially with respect to the volume of the lens, and (2) the effect of the difference in effective sea levels is apt to be overshadowed by the effects of non-uniform recharge and/or hydraulic conductivity. The latter effects become relatively more important in islands that are larger, more highly recharged, and/or have a lower overall hydraulic conductivity.