Abstract
Watertable fluctuations and seawater intrusion are characteristic features of coastal unconfined aquifers. The dynamic effective porosity due to watertable fluctuations is analyzed and then a modified (empirical) expression is proposed for the dynamic effective porosity based on a dimensionless parameter related to the watertable fluctuation frequency. After validation with both experimental data and numerical simulations, the new expression is implemented in existing Boussinesq equations and a numerical model, allowing for examination of the effects of the dynamic effective porosity on watertable fluctuations and seawater intrusion in coastal unconfined aquifers, respectively. Results show that the Boussinesq equation accounting for the vertical flow in the saturated zone and dynamic effective porosity can accurately predict experimental dispersion relations (that all existing theories fail to predict), highlighting the importance of the dynamic effective porosity in modeling watertable fluctuations in coastal unconfined aquifers. This in turn confirms the utility of the real-valued expression of the dynamic effective porosity. An outcome is that the phase lag between the total moisture (above the watertable) and watertable height measured in laboratory experiments using vertical soil columns (1D systems) can be ignored when predicting watertable fluctuations in coastal unconfined aquifers (2D systems). A dynamic effective porosity that is, by comparison, smaller than the soil porosity leads to a reduction in vertical water exchange between the saturated and vadose zones and hence watertable waves can propagate further landward. The dynamic effective porosity further plays a critical role in simulations of seawater intrusion, since it predicts a more landward seawater-freshwater interface and a higher position of the upper saline plume.
Highlights
As a transition zone between the ocean and land, coastal unconfined aquifers respond to interactions between terrestrial fresh groundwater and seawater
Since saltwater intrusion is affected by watertable fluctuations, we further examine to what extent the dynamic effective porosity will affect saltwater intrusion in coastal unconfined aquifers based on numerical simulations
The success of equation (11) highlights the significant role played by the dynamic effective porosity on watertable fluctuations, and so confirms that equation (7a) fitted by nonlinear least squares can be used to describe the relation between the dynamic effective porosity and fluctuation frequency. This in turn suggests that the phase lag between the total moisture and watertable height measured in laboratory experiments using vertical soil columns can be ignored when predicting watertable fluctuations
Summary
As a transition zone between the ocean and land, coastal unconfined aquifers respond to interactions between terrestrial fresh groundwater and seawater. To underline the effects of vertical flow on watertable fluctuations, Nielsen et al (1997) and Liu and Wen (1997) proposed an intermediate-depth Boussinesq equation based on different approximation methods. All these investigations ignore unsaturated flow that arises when the watertable rises and falls, which affects predictions of watertable fluctuations (e.g., Gillham, 1984; Kong et al, 2016; Luo et al, 2018). Following the method of Parlange and Brutsaert (1987), Jeng et al (2005b) further improved the Boussinesq model by proposing a higher-order capillarity correction These modifications were all based on the 1D Boussinesq equation (horizontal flow only) without explicit consideration of the vertical flow ( the effect of the unsaturated zone is considered indirectly). Since saltwater intrusion is affected by watertable fluctuations, we further examine to what extent the dynamic effective porosity will affect saltwater intrusion in coastal unconfined aquifers based on numerical simulations
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