An assessment of seawater intrusion overshoot using physical and numerical modeling

Authors

  • Leanne K. Morgan,

    Corresponding author
    1. National Centre for Groundwater Research and Training, Flinders University, Adelaide, South Australia, Australia
    2. School of the Environment, Flinders University, Adelaide, South Australia, Australia
    • Corresponding author: L. K. Morgan, National Centre for Groundwater Research and Training, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia. (leanne.morgan@flinders.edu.au)

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  • Leonard Stoeckl,

    1. Federal Institute for Geosciences and Natural Resources (BGR), Hannover, Germany
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  • Adrian D. Werner,

    1. National Centre for Groundwater Research and Training, Flinders University, Adelaide, South Australia, Australia
    2. School of the Environment, Flinders University, Adelaide, South Australia, Australia
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  • Vincent E. A. Post

    1. National Centre for Groundwater Research and Training, Flinders University, Adelaide, South Australia, Australia
    2. School of the Environment, Flinders University, Adelaide, South Australia, Australia
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Abstract

[1] In recent years, a number of numerical modeling studies of transient sea-level rise (SLR) and seawater intrusion (SWI) in flux-controlled systems have reported an overshoot phenomenon, whereby the freshwater-saltwater interface temporarily extends further inland than the eventual steady state position. In this study, we have carried out physical sand tank modeling of SLR-SWI in a flux-controlled unconfined aquifer setting to test if SWI overshoot is a measurable physical process. Photographs of the physical SLR experiments show, for the first time, that an overshoot occurs under controlled laboratory conditions. A sea-level drop (SLD) experiment was also carried out, and overshoot was again observed, whereby the interface was temporarily closer to the coast than the eventual steady state position. This shows that an overshoot can occur for the case of a retreating interface. Numerical modeling corroborated the physical SLR and SLD experiments. The magnitude of the overshoot for SLR and SLD in the physical experiments was 24% of the change in steady state interface position, albeit the laboratory setting is designed to maximize overshoot extent by adopting high groundwater flow gradients and large and rapid sea-level changes. While the likelihood of overshoot at the field scale appears to be low, this work has shown that it can be observed under controlled laboratory conditions.

1. Introduction

[2] Changes in the hydrology of the coastal zone can cause landward movement of seawater, a process referred to as seawater intrusion (SWI). Recently, the impact of sea-level rise (SLR) on SWI has received considerable attention. SLR and SWI have been assessed using steady state sharp interface analytic modeling by Werner and Simmons [2009] and Werner et al. [2012]. They found the inland boundary condition to be important in determining SLR-induced SWI, with greatest change occurring for head-controlled conditions, compared to flux-controlled conditions. Transient numerical modeling of SLR and SWI by Watson et al. [2010] encountered an overshoot in SWI. That is, the freshwater-saltwater interface moved temporarily inland beyond the final steady state position. Chang et al. [2011] also observed an overshoot in SWI; however, they needed to use unrealistically high specific storage values to simulate the overshoot phenomenon within field-scale settings.

[3] A flux-controlled inland boundary condition was applied by Watson et al. [2010] and Chang et al. [2011], whereby the change in hydraulic head at the coast (due to SLR) is followed by a rise of the water table throughout the domain, meaning that the pre-SLR seaward flux of fresh groundwater is eventually restored. Watson et al. [2010] and Chang et al. [2011] linked the overshoot to this rise in the water table and the time it takes to occur, with overshoot being largest in systems where water table rise is slowest.

[4] While SWI overshoot has been observed for a selection of cases involving numerical simulations of transient SLR-SWI, it has not been confirmed by physical measurements. We address this gap using physical sand tank modeling of SLR-SWI.

[5] The objective of this work is to test whether SWI overshoot is a physical phenomenon that is reproducible under controlled laboratory conditions. Given this objective, laboratory conditions were designed to be especially conducive to SWI overshoot, based on indications from previous modeling studies [Watson et al., 2010; Chang et al., 2011] regarding the propensity for overshoot to occur. Flux-controlled conditions were employed because the foregoing literature suggests that head-controlled conditions may preclude SWI overshoot. Additionally, the case of a sea-level drop (SLD) was examined to ascertain whether overshoot occurs for the situation of a retreating interface. Overshoot associated with a SLD (i.e., involving the interface retreating further toward the coast than the steady state position) has not been considered previously, although Goswami and Clement [2007] have considered transport processes associated with intruding and receding SWI under varying hydraulic gradients using sand box experiments. We carried out numerical modeling of both the SLR and SLD physical experiments to provide confidence in the results of the physical experiments and additional diagnostics.

2. Experimental Methods and Materials

2.1. Physical Model

[6] The apparatus used for the physical modeling was essentially the same as that used by Stoeckl and Houben [2012] in their investigation of flow dynamics in freshwater lenses, except the setup was modified for the situation of SLR in an unconfined aquifer with fixed inland flux (Figure 1). A transparent acrylic box of 2.0 m length, 0.5 m height, and 0.05 m width was used. An unconfined aquifer cross section was simulated by placing quartz sand homogeneously into the box, with a sloping beach face (slope of 37°) at the left side of the box. The sand body was 32 cm high and 183 cm in length. The grain size distribution of the medium sand (d10 = 0.44 mm and d50 = 0.62 mm) was optically determined using a Camsizer® (Retsch Technology, Germany), with a measurement range of 30 µm to 30 mm. A hydraulic conductivity (K) value of 0.0022 m s−1 was obtained using the grain size distribution and Hazen's equation [Fetter, 2001]. In addition, a mean K of 0.0015 m s−1 (± 0.0001 m s−1) was obtained using Darcy constant-head conductivity tests. Porosity ne [-] was calculated based on densities determined using a helium pycnometer (Micromeritics®, Germany) and found to be 0.45. Water densities were obtained using a DMA 38 density meter (Anton Paar, Austria). Freshwater density was determined to be 996.9 kg m−3 at 25°C. Freshwater was colored yellow using uranine. Saltwater, with a density of 1015.1 kg m−3, was colored red using eosine. Both uranine and eosine tracer concentrations were 0.3 g L−1.

Figure 1.

Schematic diagram of the physical model.

[7] A fixed-flux inland boundary condition was imposed using four tubes attached to a peristaltic pump. The tube outlets were at the right-hand edge of the sand box, and were equally spaced in the vertical direction below the water table. The flow was distributed equally between the tubes, with a total flux of 5.7 × 10−3 m3 d−1. This gave rise to a head of 3.8 cm at the inland boundary. A small saturated thickness was used in the physical experiments in order to achieve a relatively large aquifer length to thickness ratio. Watson et al. [2010] found (numerically) that a large aspect ratio was more likely to produce an overshoot. A constant water level was maintained in the saltwater reservoir at the left side of the sand box, simulating the sea. Freshwater discharge from the aquifer into the ocean formed a thin layer in the saltwater reservoir, and this was removed using skimming tubes, fixed in position. The saltwater reservoir was supplied continuously with additional saltwater to maintain the water level and avoid dilution.

[8] Initially, constant boundary conditions were maintained for 12 h to achieve a steady state interface. Steady state conditions were confirmed by monitoring the interface position for a 1 h period, over which time it remained stationary. The interface was visually approximated as the midpoint of the transition zone between saltwater and freshwater in the aquifer. SLR was simulated by augmenting the inflow rate of saltwater for a period of 6 min, raising the sea level from 2.4 cm to 4.8 cm. A slow rate of SLR was implemented so as not to disturb the stability of the sloping beach face. Photographs showing the interface location, wedge toe position, and piezometric head at the inland boundary were taken every 3 min for the first 2 h, and every 15 min for the following hour, using a Canon Ixus 220 HS camera. The wedge toe position (the intersection of the interface with the base of the aquifer) was marked along the base of the sand tank at regular time intervals during the experiment and measured using a scale along the horizontal base of the sand box, with the left-hand edge of the sand tank as the datum. The piezometric head was measured from the photographs using a scale adjacent to the piezometer, with the aquifer base as the datum.

[9] A SLD experiment was performed using the same general sand tank configuration as described above. After 12 h of equilibrium at a sea level of 4.6 cm, the sea level was dropped from 4.6 cm to 2.4 cm. This was achieved by readjusting the skimming tubes to a height of 2.4 cm above the model base and increasing the pumping rate over a time period of approximately 3 min.

2.2. Numerical Model

[10] The physical SLR and SLD experiments were simulated using the finite-element code FEFLOW 6.0, which considers variably saturated, density-dependent flow, and solute transport processes [Diersch, 2005]. The numerical model was assumed to be a unit-width aquifer (2-D) and hence the flux at the inland boundary Q0 was scaled to 0.114 m3 d−1. The coast was simulated using Dirichlet boundary conditions for head and concentration. A constraint was applied to the Dirichlet-type concentration boundary such that seawater concentration (C = 1) occurred only at inflow sections. The concentration of inflows through the inland boundary was C = 0 (representing freshwater). Inflows at the inland boundary were applied using a Neumann boundary condition for flux. A seepage face was expected to occur in the physical model and was implemented in the numerical model using a seepage face boundary condition along the sloping beach face, whereby the model determined the exit face for discharging groundwater. The seepage face boundary was realized by the application of a fixed head boundary (with head equal to the elevation of each node) that is only active if there is flow out of the model. Otherwise, the sloping beach face was a no-flow boundary above the seepage face.

[11] A trapezoidal mesh with 19,737 elements and 10,118 nodes was used. The grid was refined in the region close to the ocean (i.e., where the interface is located) to avoid numerical dispersion and oscillation, and to increase the accuracy of simulating sharp concentration gradients. Grid discretization in this region was Δx ≈ 2 mm and Δz ≈ 2mm. Automatic time-stepping was used with an upper step size limit of 0.0002 d. The unsaturated zone was modeled using van Genuchten [1980] functions, with a curve fitting parameter (α) of 30 m−1 and a pore size distribution index (n) of 3. These parameters are similar to those adopted by Jakovovic et al. [2011], who also used medium sand. A K of 0.0015 m s−1, ne [-] of 0.45 and density ratio δ [-] of 0.018 were applied, according with physical modeling values. δ is defined as inline image, where ρf and ρs are freshwater and saltwater densities [ML−3], respectively. Longitudinal and transverse dispersivities were set to 5 × 10−3 m and 5 × 10−4 m, respectively. The molecular diffusion coefficient was set to 10−9 m2s−1.

[12] Following the establishment of steady state conditions, an instantaneous change in sea level was applied in the SLR and SLD numerical models. This is a simplification of the physical experiments, where the same sea level changes were considered, but were not instantaneous. This simplification is expected to result in a shorter time to maximum and minimum SWI extent for SLR and SLD, respectively. However, the effect is not expected to be large given that the rates of SLR and SLD in the physical experiments are reasonably rapid. The wedge toe was defined as the point of intersection of the 50% seawater isochlor with the aquifer basement.

3. Results and Discussion

3.1. Physical Model

[13] The approximate interface location was traced on the front glass of the sand tank after 0, 9, 21, and 120 min (Figure 2). After SLR, the shape of the interface was temporarily more concave than at steady state (Figure 2b). The degree of concavity reduced after about 21 min (Figure 2c). There was a reduction in interface sharpness for about 45 min following SLR, as expected given the increased dispersion for moving interfaces observed by Werner et al. [2009]. A seepage face was evident, whereby freshwater discharged through the face of the sloping beach face above sea level.

Figure 2.

Images from the SLR physical experiment: (a) 0 min, (b) 9 min, (c) 21 min, and (d) 2 h. The portion of the sand tank shown above is from x = 17 to 35 cm (where x = 0 cm is at the left-hand edge of the sand tank) and from z = 0 to 6.5 cm.

[14] As shown in Figure 2, an overshoot was observed within the physical experiment. The interface moved inland following the commencement of SLR and reached a maximum inland extent of 33 cm (i.e., toe position) after around 30 min (Figure 3). The movement of the interface then reversed and moved back by 2 cm toward the coast, to the eventual steady state position of 31 cm (after 120 min). The SWI overshoot in this experiment was therefore 2 cm, or 24% of the change in steady state toe position (the steady state pre-SLR toe position was 22.5 cm). The water level in the piezometer at the inland boundary rose 2.1 cm (from 3.8 cm to 5.9 cm) in response to the 2.4 cm rise in sea level (Figure 3). The water level in the piezometer had re-equilibrated after about 30 min. Water level rise at the inland boundary was less than SLR, as expected, because the relationship between flux and head difference in an unconfined coastal aquifer is nonlinear [Strack, 1976].

Figure 3.

Wedge toe position and piezometric head (at the inland boundary) for the SLR physical modeling experiment and FEFLOW numerical simulation.

[15] An overshoot was also observed in the SLD experiment (see Figure 4). The steady state toe position was 29.4 cm prior to SLD. The wedge toe reached a minimum value of 21 cm after 12 min and then increased to a steady state value of 22.6 cm after 75 min. A 1.6 cm overshoot was therefore observed. The SLD overshoot is commensurate with the SLR overshoot, i.e., both being 24% of the change in steady state wedge toe location. The water level in the piezometer at the inland boundary dropped 1.9 cm (from 6.0 cm to 4.1 cm) in response to the 2.2 cm SLD (Figure 4). As with the SLR experiment, the water level at the inland boundary re-equilibrated after around 30 min.

Figure 4.

Wedge toe position and piezometric head (at the inland boundary) for the SLD physical modeling experiment and FEFLOW numerical simulation.

3.2. Numerical Model

[16] Transient wedge toe positions obtained from the numerical model were compared to the results of the physical experiments and a reasonable match was obtained (Figures 3 and 4). An overshoot of 1.2 cm was simulated in the SLR numerical model, which was 20% of the change in steady state wedge toe position. A 2.4 cm overshoot was simulated in the SLD numerical model, representing 43% of the change in steady state wedge toe position. Time to maximum SWI extent for the SLR simulation (32 min) and time to minimum SWI extent for the SLD simulation (14 min) were similar to results from the physical experiments.

[17] The numerical modeling results show that time to maximum SWI extent for an instantaneous SLR is longer than time to minimum SWI extent for an instantaneous SLD. Temporal asymmetry of the overshoot was expected, given that Watson et al. [2010] previously found response times under SLR to be greater than SLD for instantaneous changes in sea level (although only for a single pair of SLR and SLD simulations). Also, Chang and Clement [2012] have reported temporal asymmetry for intrusion and recession processes under changes of flux at the inland boundary, with intrusion taking longer than recession.

[18] Additional numerical modeling was carried out to explore the influence of the unsaturated zone on the overshoot in the SLR physical experiment. This was achieved through varying the van Genuchten [1980] curve fitting parameter, α. A larger value of α (i.e., 50 m−1, which applies to medium sand [Jakovovic et al., 2011]) reduced the capillary fringe thickness and increased the overshoot (from 1.2 cm to 1.7 cm). A smaller value of α (i.e., 10 m−1, which applies to a sandy loam [Carsel and Parish, 1988]) increased the capillary fringe and resulted in negligible overshoot. Changes in overshoot extent with α are attributed to changes in the capillary fringe thickness, which in the case of α equal to 10 m−1 effectively doubled the saturated thickness, thereby reducing the aspect ratio by approximately 50%. The lower aspect ratio produced a smaller overshoot, in agreement with the numerical simulations of Watson et al. [2010]. Numerical modeling was also used to explore the influence of the sloping beach face on the overshoot in the SLR physical experiment. An overshoot of 1 cm was simulated using a vertical beach face, indicating that the sloping beach face does not control the extent of overshoot, as expected given that overshoot in previous numerical modeling studies [Watson et al., 2010; Chang et al., 2011] occurred with vertical coastal boundaries.

[19] Although the cause of SWI overshoot has not been systematically explored within this study, the numerical modeling results indicate that overshoot is associated with a time lag in the response of the flow field following SLR. Velocity vectors showed that reversal of the wedge toe movement occurs as freshwater outflow at the coast approaches equilibrium. It follows that overshoot will be larger in systems where it takes longer for freshwater outflow to re-equilibrate. This agrees with the previous results of Watson et al. [2010] and Chang et al. [2011].

4. Conclusions

[20] Physical sand tank experiments have been undertaken to assess SWI overshoot observed previously in numerical modeling studies of SLR-SWI by Watson et al. [2010] and Chang et al. [2011]. An overshoot was observed in the SLR physical experiment and images of the overshoot are presented. A SLD experiment was also carried out and the overshoot was again observed. These are the first documented cases of overshoot in a laboratory setting, and the first time overshoot for a retreating interface has been reported.

[21] The transient wedge toe position obtained from the physical experiments was compared to numerical modeling results, and a reasonable match was obtained, with an overshoot simulated numerically for both the SLR and SLD cases. This provides confidence in the results of the physical experiments.

[22] The magnitude of the overshoot was 24% of the change in steady state wedge toe for both SLR and SLD physical experiments. As such, SWI overshoot was found to be relatively large, albeit the laboratory setting is designed to maximize overshoot extent by adopting high groundwater flow gradients and large and rapid sea-level changes. Using field-scale simulation results, Chang et al. [2011] concluded that it is difficult to observe overshoot in realistic aquifers. Hence, it is unlikely that overshoot would be a concern in real field-scale problems. Nevertheless, we demonstrate that overshoot is physically plausible, and can be produced in controlled laboratory experiments.

Acknowledgments

[23] Thanks to Georg Houben for the helpful comments. The support of Jan Bockholt for the experimental work is gratefully acknowledged as well as Ulrich Gersdorf for his help with the elaboration of Figure 1. Thanks also to Mothei Lenkopane for helpful discussions on the seepage face boundary condition in FEFLOW. We also wish to thank Prabhakar Clement, Christian Langevin, and three anonymous reviewers whose helpful suggestions have improved this work. This work was part funded by the National Centre for Groundwater Research and Training, a collaborative initiative of the Australian Research Council and the National Water Commission.

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