A formulation for vertically integrated groundwater flow in a stratified coastal aquifer

We present the comprehensive discharge potential for steady three-dimensional flow in horizontally stratified coastal aquifers with a horizontal base and a vertical coastline. The gradient of this comprehensive potential gives the vertically integrated discharge throughout the aquifer, i.e., the specific discharge vector as a function of three-dimensional space integrated over the saturated portion of the aquifer. The boundary values of the comprehensive potential along the coast can be computed precisely, given the geometry of the aquifer: the hydraulic conductivities of the strata, the elevations of the horizontal planes that separate the strata, and the elevation of the impermeable base of the aquifer relative to sea level. Boundary conditions of the comprehensive potential may either be given in terms of its gradient, or computed from given heads along the boundaries. The governing equation of the comprehensive potential is the Poisson equation in areas of infiltration and the Laplace equation elsewhere. The computation of interface elevations, piezometric heads, and the vertical distribution of flow requires that an assumption be made regarding the relation between the comprehensive potential and piezometric heads. We adopt the Dupuit-Forchheimer approximation for this purpose and make use of the Ghyben-Herzberg equation. We present several applications of the approach and find that the stratification may have a significant effect on the boundary value of the comprehensive potential, and thus on the flow rates in the aquifer.