[1] The classic Ghyben-Herzberg estimate of the depth of the freshwater-saltwater interface together with the Dupuit approximation is a useful tool for developing analytical solutions to many seawater intrusion problems. On the basis of these assumptions, Strack (1976) developed a single-potential theory to calculate critical pumping rates in a coastal pumping scenario. The sharp interface assumption and, in particular, this analytical solution are widely used to study seawater intrusion and the sustainable management of groundwater resources in coastal aquifers. The sharp interface assumption neglects mixing and implicitly assumes that salt water remains static. Consequently, this approximation overestimates the penetration of the saltwater front and underestimates the critical pumping rates that ensure a freshwater supply. We investigate the error introduced by adopting the sharp interface approximation, and we include the effects of dispersion on the formulation of Strack (1976). To this end, we perform numerical three-dimensional variable density flow simulations. We find that Strack's equations can be extended to the case of mixing zone if the density factor is multiplied by an empirically derived dispersion factor [1 − (a T /b′) 1/6 ], where a T is transverse dispersivity and b′ is aquifer thickness. We find that this factor can be used not only to estimate the critical pumping rate but also to correct the Ghyben-Herzberg estimate of the interface depth. Its simplicity facilitates the generalization of sharp interface analytical solutions and good predictions of seawater penetration for a broad range of conditions. Citation: Pool, M., and J. Carrera (2011), A correction factor to account for mixing in Ghyben-Herzberg and critical pumping rate approximations of seawater intrusion in coastal aquifers, Water Resour. Res., 47, W05506,

We study the combined effect of heterogeneity in the hydraulic conductivity field and tidal oscillations on the three-dimensional dynamics of seawater intrusion in coastal aquifers. We focus on the quantification of its impact on solute mixing and spreading of the freshwater-seawater interface. Threedimensional Monte Carlo realizations of log-normally distributed permeability fields were performed, and for each realization, numerical variable density flow and solute transport simulations were conducted. Mixing is characterized by the spatial moments of concentration. The enhanced solute mixing is quantified by an effective dispersion coefficient. The simulations show that heterogeneity produces an inland movement of the toe location along with a significant widening of the transition zone, which is linearly proportional to the product of the arithmetic mean of the correlation lengths in the three spatial dimensions (k a ) and the permeability field variance (r 2 lnk ). We find that once tidal oscillations are included, as the degree of heterogeneity increases, the combined effect of heterogeneity and tidal oscillations on mixing and spreading of the interface reduces. This is explained by the fact that an increase in the log-permeability variance induces an increase in both the effective permeability and the spatial connectivity, which implies a more uniform hydraulic response to tidal forcing and, as a result, the degree of mixing decreases. This study also identifies that the mixing behavior induced by tidal oscillations in heterogeneous coastal aquifers is controlled by the effective tidal mixing number (n e tm ) which depends on the amplitude, the period, the storativity, and the effective horizontal permeability.

While the hydraulics of tidally dominated groundwater systems have been studied extensively, tidally induced solute spreading in the fresh-saltwater transition zone of coastal aquifers remains largely unexplored. Here we systematically quantify tidal impacts on solute mixing and spreading in seawater intrusion problems for an idealized homogeneous system. Mixing is characterized by the spatial moments of the solute concentration distribution and quantified by an effective dispersion coefficient. Parametric analysis reveals that the key dimensionless parameter controlling the tidal mixing behavior is the tidal mixing number (n tm ) which depends on the tidal amplitude, the period and the hydraulic diffusivity. We find that for n tm 600, tides lead to a significant impact on the shape and location of the interface. The maximum effect on transverse and longitudinal dispersion occurs for large values of storativity, a hydrogeologic parameter that has been previously understated in terms of its significance. Large storativity implies a nonuniform hydraulic response to the tidal forcing, such that the resulting nonuniform time-dependent velocity field enhances mixing. As a result, the interface spreads mainly at the bottom of the aquifer, where the saline end of the mixing zone migrates seaward, whereas the spatial extent of low salt concentrations migrates landward. These insights critically underpin quantitative guidance on the inclusion and exclusion of tidal effects in the analysis of seawater intrusion.