Is submarine groundwater discharge predictable?

Authors


Abstract

[1] The contribution of submarine groundwater discharge (SGD) to the total hydrological discharges to the sea may be large but has been difficult to quantify. We have tested the applicability and generality of a suggested linear relationship between annual average total SGD and its fresh groundwater component against various SGD simulation results and field data. This relationship is found to constitute a general attractor for hydrologically simulated and directly measured SGD values across a wide range of conditions and world regions. But these consistent SGD quantifications differ systematically and largely from indirect SGD interpretations of tracers in seawater. This is an essential gap between inland- and sea-based methods of SGD estimation that needs to be bridged.

1. Introduction

[2] Near-coastal catchment areas can yield surprisingly large waterborne discharges of tracers and pollutants to the sea through a combination of unmonitored surface water discharges (near-coastal streams and river stretches) and submarine groundwater discharge (SGD) [Destouni et al., 2008a] (see Figure S1 of the auxiliary material). The contribution of SGD to this total, typically unmonitored near-coastal discharge may also be surprisingly large [Moore, 1996; Moore et al., 2008], but is debated [Younger, 1996; Moore and Church, 1996; Destouni et al., 2008a] and difficult to interpret and quantify [Mulligan and Charette, 2006; Destouni et al., 2008b].

[3] Site-specific steady-state SGD simulations [Destouni and Prieto, 2003] have indicated a possible linear relationship between annual average total SGD and its fresh groundwater component (QN), which could greatly simplify SGD quantifications and decrease their uncertainty, if found to be more generally applicable. This approximate linear relationship obtained by regression fitting to SGD simulation results for three Mediterranean coastal aquifer cases [Destouni and Prieto, 2003] is:

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The main aim of the present study is to test the applicability and generality of this simple linear SGD(QN) relationship against a wide range of different SGD simulation results and field data from different parts of the world reported in the literature.

2. Materials and Methods

[4] As a first step in testing the SGD(QN) line [Destouni and Prieto, 2003], we compared it with a wide range of steady-state SGD results compiled from the two independent and generic simulation studies of Smith [2004] and Kaleris [2006]. These studies used different numerical codes and investigated different hydrogeological aquifer conditions, geometries and scales, and types of seabed boundary conditions. The auxiliary material outlines how the QN and SGD implied by the studies of Smith [2004] (Figure S2 and Table S1) and Kaleris [2006] (Figure S3 and Table S2) were calculated from their reported non-dimensional variable values.

[5] However, SGD is not commonly at steady-state but varies in time across hourly to inter-annual time scales [Anderson and Emanuel, 2010] due to different types of temporal variability in its fresh groundwater discharge component QN and re-circulated seawater flow component QSW (Figure S1). We then compared the steady-state SGD(QN) line [Destouni and Prieto, 2003] against the transient SGD results of: 1) Prieto and Destouni [2005], Robinson et al. [2007] and Li et al. [2009] for diurnal and semi-diurnal tidal oscillations, 2) Prieto [2001] and Michael et al. [2005] for periodic seasonal variability in QN, and 3) Destouni and Prieto [2003] for a large step change in QN. However, these simulation results, as well as the steady-state simulation studies discussed above, and the tested SGD(QN) line were all based on a seawater salinity of about 35 g/L. Since groundwater dynamics in coastal aquifers and consequently also SGD are driven by differences in water density, different SGD(QN) relationships can be expected for different seawater salinities. To identify the effect of different seawater salinity, simulation results for the changing salinity conditions in the shrinking Aral Sea [Shibuo et al., 2006] were compared with the steady-state SGD(QN) line, which applies to a salinity of 35 g/L.

[6] Finally, the tested SGD(QN) line was compared with available direct seepage measurements of SGD (SGDm) [Lewis, 1987; Simmons, 1992; Kim et al., 2003; Burnett et al., 2006; Povinec et al., 2006], indirect SGD interpretations from radium (Ra) measurements in seawater (SGDRa) [Moore, 1996; Hwang et al., 2005; Paytan et al., 2006; Povinec et al., 2006; Moore et al., 2008; Windom et al., 2006], and calculated site-specific implications of the SGD(QN) line from independently reported QN data for the different measurement sites (SGDQ) [Younger, 1996; Jones et al., 2000; Grassa, 2001; Kim et al., 2003; Burnett et al., 2006]. The present study expresses these estimates in the same normalized form as the different simulation results of SGD, and compares them directly with each other and with the tested SGD(QN) line.

3. Results

[7] Figure 1 shows the generic SGD simulation results of Smith [2004] and those from Kaleris [2006] for hydraulic conductivity (K) values of the order of 10 to 100 m/d in comparison with the investigated SGD(QN) line [Destouni and Prieto, 2003]. Figure S3 extends the comparison to a wider range of hydraulic conductivity values. In general, all the independent SGD results fall around the SGD(QN) line, differing from it by a factor range of 0.35–12.33 for all K>1 m/d in spite of large differences in modeling code, aquifer type, geometry and parameterization among the different modeling studies. For K≤1 m/d, the associated relevant QN values are very small (≤3 m/d) as are all the associated SGD results, with the results by Kaleris [2006] being smaller than those of the SGD(QN) line (Figure S3).

Figure 1.

The linear SGD(QN) relationship [Destouni and Prieto, 2003] compared to different independent steady-state simulation results [Smith, 2004; Kaleris, 2006].

[8] Figure 2 illustrates the different simulation results for transient SGD. The results for tidal conditions [Prieto and Destouni, 2005; Robinson et al., 2007; Li et al., 2009] are shown in Figures 2a and 2b. For relatively small QN, the average SGD under tidal conditions is larger than the steady-state SGD according to the SGD(QN) line of Destouni and Prieto [2003], with this effect increasing with tidal amplitude and decreasing with QN. For QN≥12 m2d−1, the tidal average SGD values [Prieto and Destouni, 2005; Robinson et al., 2007; Li et al., 2009] converge to the tested steady-state line.

Figure 2.

The steady-state SGD(QN) line [Destouni and Prieto, 2003] is shown along with the following temporally variable SGD simulation results: (a) average SGD from tidal simulation results of Prieto and Destouni [2005] (with solid regression line) and Robinson et al. [2007] for different tidal amplitudes A (including also a non-tidal result, A=0), (b) average SGD from the tidal simulations of Li et al. [2009] for different tidal amplitudes A and the tidal regression line [Prieto and Destouni, 2005] from Figure 2a, (c) monthly SGD results from seasonally variable QN simulations of Prieto [2001] (unfilled squares) and Michael et al. [2005] (filled triangles); the numbers inside the symbols indicate the temporal sequence of change in SGD and QN, in terms of monthly results over a simulated year, with the insert explicitly showing their continuous temporal evolution, and (d) total SGD development after a step decrease in QN (from 18 m2/d to 1 m2/d for the Rhodes case study of Destouni and Prieto [2003]); the numbers inside the symbols indicate the temporal sequence of change in SGD and QN, with the insert showing the continuous temporal evolution of SGD.

[9] Figure 2c shows the simulation results for inland seasonal variability in QN [Prieto, 2001; Michael et al., 2005]. This variability does not significantly affect annual average SGD relative to the tested steady-state SGD(QN) line, but yields seasonal variations around it. The relative range of SGD variations is small compared to the relative range of seasonal QN variations. For instance, relative seasonal ranges in QN of 25 and 2.5 (i.e., maximum minus minimum seasonal values relative to its average) yield SGD variation ranges of 0.74 and 0.59 relative to average SGD, respectively.

[10] Simulation results for the transient SGD development after a step decrease in QN are shown in Figure 2d, specifically for the example of a QN decrease from 18 to 1 m2d−1 [Destouni and Prieto, 2003]. The SGD response to this step change is that a relatively fast and large decrease from 20 to 4 m2d−1 occurs during the first 13 years after the change, followed by a slow and small remaining decrease toward the new steady-state SGD of 2.5 m2d−1 after 192 years. For about a decade after a rapid QN decrease, SGD thus remains larger than the SGD value corresponding to the new QN value in the tested steady-state SGD(QN) line. However, SGD converges to that steady-state value during its rapid change in the first decadal period.

[11] Furthermore, Figure 3 illustrates the SGD simulation results for the changing QN and salinity of the Aral Sea during its shrinkage [Shibuo et al., 2006]. These results show that SGD values were smaller than the tested SGD(QN) line while the Aral Sea salinity was smaller than 35 g/L, converged to the line as salinity increased to around 35 g/L, and diverged from the line as the salinity continued to increase further.

Figure 3.

Effect on SGD of changing QN and seawater salinity. The steady-state SGD(QN) line [Destouni and Prieto, 2003] (derived for constant seawater salinity of 35 g/L) is shown along with simulated SGD while both QN and annual average seawater salinity change during the first 40 years of shrinkage of the Aral Sea [Shibuo et al., 2006].

[12] Figure 4 finally shows the comparison of the SGD(QN) line with: the direct seepage measurements SGDm [Lewis, 1987; Simmons, 1992; Kim et al., 2003; Burnett et al., 2006; Povinec et al., 2006], the indirect interpretations SGDRa from radium (Ra) measurements in seawater [Moore, 1996; Hwang et al., 2005; Paytan et al., 2006; Povinec et al., 2006; Moore et al., 2008; Windom et al., 2006], and site-specific implications SGDQ of the SGD(QN) line equation for independently reported QN data for the different measurement sites [Younger, 1996; Jones et al., 2000; Grassa, 2001; Kim et al., 2003; Burnett et al., 2006]. The SGDRa interpretations are shown as lines rather than points because the sea-based studies do not resolve the inland freshwater component QN related to their total SGD interpretation.

Figure 4.

SGD estimates by different methods for different coastal areas in the world. For each coastal area (south-eastern coast of Sicily (green) [Grassa, 2001; Povinec et al., 2006], upper Atlantic Ocean (pink) [Moore et al., 2008], Patos Lagoon (lilac) [Windom et al., 2006], southwest coast of Mauritius (brown) [Burnett et al., 2006; Paytan et al., 2006], Jeju Island (light blue) [Kim et al., 2003; Hwang et al., 2005], South Atlantic Bight (SAB, red) [Simmons, 1992; Moore, 1996; Younger, 1996; Moore et al., 2008] and Barbados (dark blue) [Lewis, 1987; Jones et al., 2000]), available direct seepage measurements of SGD (SGDm) [Lewis, 1987; Simmons, 1992; Kim et al., 2003; Burnett et al., 2006; Povinec et al., 2006] are shown along with the SGD(QN) line [Destouni and Prieto, 2003], the range of reported hydrological estimates of seaward fresh groundwater flow (QN) in the area [Younger, 1996; Jones et al., 2000; Grassa, 2001; Kim et al., 2003; Burnett et al., 2006], the SGD range corresponding to the QN range according to the SGD(QN) line [Destouni and Prieto, 2003] (SGDQ), and sea-based estimates for each area as interpreted from radium isotope content in seawater (SGDRa) [Moore, 1996; Hwang et al., 2005; Paytan et al., 2006; Povinec et al., 2006; Moore et al., 2008; Windom et al., 2006]. See Table S3 for different data sources and explanations regarding the estimates with different number indices for each coastal area in Figure 4.

[13] The direct seepage measurements (SGDm) are consistent with the implications of the SGD(QN) line (SGDQ) for all sites. However, the sea-based Ra interpretation estimates (SGDRa) are systematically larger than both SGDm and SGDQ. A large difference between land-based (SGDQ and SGDm) and sea-based (SGDRa) methods of SGD estimation has previously been noted [Younger, 1996] for the South Atlantic Bight (SAB) case study that is also included in Figure 4. The present study shows this gap to be general and systematic.

4. Discussion

[14] In all of the SGDRa interpretations in Figure 4, SGD was inferred from the extra water flow needed, besides the monitored river flow, to explain the measured Ra isotope content in the seawater. However, other studies [Destouni et al., 2008a; Jarsjö et al., 2008] have clarified the occurrence and magnitude of additional unmonitored discharges (from unmonitored near-coastal streams and river stretches), besides SGD, which are considerable and must also be accounted for when interpreting SGD from tracers in seawater [Destouni et al., 2008a] (Figure S1).

[15] The present study has identified an important transience effect for about a decade after a rapid decrease in QN, when SGD can be considerably larger than expected from the steady-state SGD(QN) line of Destouni and Prieto [2003] for the smaller new QN value (Figure 2d). Such transiently larger SGD should be detectable by sea-based tracer interpretation methods. However, this type of discrepancy from the SGD(QN) line cannot explain the equally large gap between these SGD interpretations and direct seepage measurements of SGD, which should detect the same SGD if the measurements and interpretations apply to the same time period.

[16] In general, it is essential to clarify whether SGD estimates represent annual average SGD or some particular temporal conditions. In the SAB case, for instance, one reason for the discrepancy between the implication of the tested SGD(QN) line and a sea-based SGD interpretation [Moore, 1996] was that the latter represented a period of particularly low river flow while the former represents annual average SGD conditions [Destouni et al., 2008a]. Furthermore, clarification of the spatial representativeness of local SGD measurements is also essential in view of the large variability of local fluxes found along coastlines [Destouni et al., 2008b; Jarsjö et al., 2008].

5. Conclusions

[17] Transience and spatio-temporal representativeness effects can to some degree contribute to a gap between land- and sea-based methods of SGD estimation. However, these effects cannot alone explain the systematic and large gaps found in this study (Figure 4), with for instance up to two orders of magnitude differences in the SAB and Sicily cases. Mulligan and Charette [2006] have noted a need for more careful SGD interpretations from Ra data in seawater and the present results further emphasize that conclusion. These results also strengthen and generalize previous site-specific conclusions [Destouni et al., 2008a] that seawater-based tracer interpretations must start accounting for the additional unmonitored discharges to the sea through near-coastal streams and river stretches (Figure S1) besides SGD.

[18] Moreover, the simple steady-state SGD(QN) line of Destouni and Prieto [2003] has here emerged as a general attractor, around or toward which SGD values move under various types of groundwater flow transience (for seawater salinity around 35g/L). Such an attractor offers a possibility for robust first-order quantification of total annual average SGD under transient and changing coastal groundwater conditions based on accurate estimates of the fresh groundwater discharge (QN). An example of QN quantification for unmonitored coastal areas with regard to flow has, e.g., been presented by Jarsjö et al. [2008].

Acknowledgments

[19] Financial support for this work has been provided by the Swedish Research Council (VR).