The effect of groundwater advection on salinity in pore waters of permeable sediments

Transcription

1 Limnol. Oceanogr., 54(2), 2009, E 2009, by the American Society of Limnology and Oceanography, Inc. The effect of groundwater advection on salinity in pore waters of permeable sediments John P. Rapaglia 1 School of Marine and Atmospheric Science, 195 Endeavour Hall, Stony Brook University, Stony Brook, New York ; National Research Council of Italy, Institute of Marine Science, Castello 1364/a Venice 30122, Italy Henry J. Bokuniewicz School of Marine and Atmospheric Science, 211 Endeavour Hall, Stony Brook University, Stony Brook, New York Abstract Measurements of the upward advection and pore-water profiles of salinity were made at three coastal settings (the Venice Lagoon, Italy; Jamaica Bay, New York; and Mattituck, New York). Coincident measurements of seepage rates using vented benthic chambers and profiles of salinity in pore water collected with a piezometer are used to quantify the coefficient of dispersive mixing. Three mathematical methods were used to quantify this coefficient: a simple, linearized salt balance and two analytical solutions to the steady-state, one-dimensional, advection-diffusion equation in either a slab or a semi-infinite medium. The majority of dispersive mixing coefficients in fine- to medium-grained silty sand were calculated to be between 0.04 and 0.8 m 2 d 21. In some cases, the dispersive mixing seemed to involve small-scale preferred pathways for vertical transport, such as would be the case for bioirrigation, gravitational convection, or salt fingering. An impetus behind the study of submarine groundwater discharge (SGD) has been to determine the role the process plays in transporting chemical constituents to the coastal ocean (Johannes 1980; Slomp and Van Cappellen 2004). Since nutrients and other chemical constituents are often elevated in groundwater relative to surface waters (Christensen et al. 2001; Manning and Hutcheon 2003), even if SGD does not represent a substantial proportion of the volume flux of water into the sea, SGD may be a primary or major input pathway for dissolved chemical constituents. Indeed, it is likely that SGD is the main source of nutrients to at least some coastal regions and responsible for any associated effects. For example, nitrate supplied by SGD can cause a shift in the phytoplankton community by driving the system toward phosphate limitation and may be responsible for harmful algal blooms (Gobler and Sañudo- Wilhelmy 2001). To calculate chemical fluxes, investigators multiply SGD by concentrations of chemical species measured in nearby wells (Oberdorfer et al. 1990). Defining the proper end 1 Present address: Christian Albrechts University, Cluster of Excellence The Future Ocean, Institute of Geography, Ludewig- Meyn Str. 14, Kiel 24098, Germany ( john.rapaglia@gmail.com). Acknowledgments The authors acknowledge Kirk Cochran, Sergio Sañudo- Wilhelmy, Teng-Fong Wong, and Luca Zaggia for the thoughtful comments on this manuscript. In addition the authors thank Aaron Beck for his help in the collection of the data in all three study sites. An acknowledgement is given to Andrea Pesce and Italo Ongaro for their help in Venice. Support in Venice was provided by the Aluminum Company of America (ALCOA) Foundation and the Agenzie per il protezione dell ambiente e per i servizi tecnici (APAT). Support in Jamaica Bay was provided by New York State Sea Grant. We thank Ronnie Nøhr Glud and two anonymous reviewers; their constructive comments greatly improved the manuscript. 630 member can be problematic, however, and it is complicated by the fact that nutrients do not behave conservatively along flow lines (Kaplan et al. 1979; Moore 1999). Regardless of chemical transformation, the composition of SGD should be expected to reflect the site pore-water concentration at the sediment water interface. In addition, improvements to the estimation of chemical fluxes associated with SGD have been made by directly measuring chemical constituents in the sediment where discharge appeared to be occurring (Bone et al. 2006). Difficulties remain, however, even for conservative tracers, as a result of the mixing of fresh groundwater with overlying seawater. SGD is composed of both fresh groundwater and recirculated seawater, and the recirculated component may comprise over 95% of the total SGD (Li et al. 1999). Here we attempt to use simultaneous measurement of flow rates taken with vented, benthic chambers and profiles of the salinity of sediment pore water collected with a piezometer to determine the magnitude of downward dispersive mixing in sandy coastal sediments. Possible mechanisms involved are also considered. Previous work The flux of a dissolved chemical species across the sediment water interface represents a balance between vertical rate of advection of pore water out of the sediment, referred to as submarine groundwater discharge or SGD, and the rate of downward dispersive mixing into the sediment. The molecular diffusivity of salt in water is about m 2 d 21, and diffusivity in a porous medium is one to two orders of magnitude less than this (Freeze and Cherry 1979). In the face of upward advection, the presence of salt from the overlying water at depth in the sediment cannot be accounted for by molecular diffusion. Even in the presence of small SGD, molecular diffusion could not bring salt into the sediment more than a millimeter; salinity would be expected to be zero just below

2 Permeable sediments pore-water salinity 631 the sediment water interface with even moderate values of SGD. However, in areas where SGD exceeds 50 cm d 21, pore water in the upper few centimeters of the sediment may have a measurable salt content (Bokuniewicz et al. 2004; Rapaglia 2005). The penetration of the salt into the sediment from the overlying water requires efficient downward mixing of salt from the open water into the pore water. This mixing is usually represented by a dispersion coefficient, although the exact mechanism is variously described (Ullman et al. 2003). Because of vertical dispersive mixing, the incremental chemical flux due to SGD should, therefore, not be measured at the sediment water interface but rather at the base of the mixed layer within the sediment pore water. This is indeed necessary, as we will discuss later, in the presence of preferred conduits that more easily allow water to discharge from a depth below the interface. In principle, groundwater supplying SGD should approach perpendicular to the sediment water interface (Hubbert 1940). Hydrodynamic or mechanical dispersion in the direction of the flow is one physical process that controls the flux into and out of the sediment. The coefficient of hydrodynamic dispersion can be expressed by multiplying dispersivity with the advective velocity and adding molecular diffusion (Freeze and Cherry 1979). It is commonly between and 0.01 m 2 d 21 (Gelhar 1993). Hydrodynamic dispersion should go to zero as the sediment water interface is reached. Martin et al. (2007) used an analytical solution to the advection-diffusion equation in conjunction with measurements of SGD and pore-water salinity profiles to estimate dispersion coefficients as high as m 2 d 21 at sites in the Indian River Lagoon, Florida. They showed that the expected, hydraulic dispersion is too low to account for the observed salinity profiles in the presence of the measured SGD (Martin et al. 2007). Ground-water flow paths can cross isohalines in the pore water, and several other mechanisms have been suggested for the process by which salt may enter into the surficial layers of sediment (Martin et al. 2006). These include wave pumping (Riedl et al. 1972), tidal pumping (Cooper 1964; Li et al. 1999), density-driven mixing (Bokuniewicz et al. 2004), changes in the terrestrial water table (Michael et al. 2005), and bioirrigation (Martin et al. 2004). Cooper (1964), for example, considered additional dispersion within the aquifer due to the tides. Modulation of the local hydraulic gradients by the diurnal tides causes oscillations of the groundwater through the pore space. Although displacements are small, the differential movement coupled with molecular diffusion disperses salt in the groundwater. Relating the tidal range to the amplitude of the displacement of water in a coastal aquifer caused by the tides, Cooper (1964) calculated values of dispersion up to 0.01 m 2 d 21 near a shoreline. Other, previous estimates of dispersion coefficients range up to 0.2 m 2 d 21. Using profiles of electrical conductivity as a surrogate for salinity, for example, Bokuniewicz et al. (2004) calculated dispersion coefficients of between 0.03 m 2 d 21 and m 2 d 21 by fitting the data to a steady-state, one-dimensional solution to the advectiondiffusion equation in a semi-infinite medium with a constant salinity at the surface. Density-driven interfingering, or salt fingering, was suggested as the mechanism of dispersive mixing (Bokuniewicz et al. 2004). Denser, overlying salt water can penetrate into less dense and less saline pore water as columns of saline water a centimeter or two in diameter. The process was first studied in permafrost (Gosink and Baker 1990). There is some experimental evidence that salt fingering can occur even in the presence of a vertical advection of water at rates up to at least 45 cm d 21 (Seplow 1991). However, field evidence is sparse. Vertical profiles of pore-water temperature at a site in Delaware Bay (Dale and Miller 2007) showed time lags of between 0.1 to 0.3 h cm 21 between the temperature events at the surface and those at depth. Interpretation of the observed time lag, in terms of conductive heat transfer in the presence of advection, yields effective dispersion coefficients between 0.02 and 0.2 m 2 d 21. Bioirrigation has also been implicated as a mechanism capable of producing dispersion coefficients of 0.05 m 2 d 21 under the assumption that exchange occurred to a depth of 0.4 m within 46 h (Martin et al. 2006). Vertical burrows in the sediment can provide conduits through which overlying salt water can be actively pumped to depth in the sediments by organisms. Alternatively, if the organisms are absent but their burrows remain, the burrows may still provide conduits for higher density, saline water to penetrate the sediments at depth or to provide low-permeability pathways for groundwater to escape past the sediment water interface. Site description Measurements were made at a total of five locations in three sites. Mattituck Beach on the Peconic Bay in New York was a sandy site with low anthropogenic influence, while sites in Jamaica Bay, New York, and the Venice Lagoon represented urbanized, coastal lagoons. Peconic Bay: The Peconic Bay, an estuary at the east end of Long Island, New York (Fig. 1A), is underlain by a sequence of glacial outwash and thin (,10 m) clay confining units. These all rest upon the Magothy Aquifer, which is about 150-m thick and overlies the Lloyd Sand Member Aquifer. SGD has been measured at various sites around the bay shore to occur at rates as large as 170 cm d 21 (Paulsen et al. 2004). SGD is an important factor controlling the ecosystem structure of the bays (Paulsen et al. 2004; Stieglitz et al. 2007). Measurements were made at one site on the north shore of Peconic Bay, Mattituck Beach. Mattituck Beach is a sheltered, gently sloping sand beach where the tidal range is 0.75 m. Preliminary measurements at the site have shown a tidally modulated SGD at rates up to 200 cm d 21. Jamaica Bay: Jamaica Bay is a lagoon covering 52 km 2 located entirely within the boroughs of Brooklyn and Queens in New York City (Fig. 1B). The bay has been extensively altered by dredging, landfill construction, and bulkhead installation (Swanson et al. 1992). The bay s drainage basin covers 344 km 2. The annual average rainfall

3 632 Rapaglia and Bokuniewicz Fig. 1 (A) Peconic Bay, New York. Mattituck Beach site is represented by the star. (B) Jamaica Bay, New York. Canarsie Pier and Canarsie Pol are represented by stars. (C) The Venice Lagoon. Punta Sabbioni and Treporti are represented by stars. The insets show the location of benthic chambers, which are demarcated by circles. is about 1160 mm, but the bay receives little, if any, surface water input. Almost all freshwater enters as effluent from four major sewage treatment plants. Jamaica Bay sits atop the Upper Glacial Aquifer, which is more than 200-m thick. The Upper Glacial Aquifer is composed of highly permeable glacial till and outwash deposits interbedded with marine clays (Busciolano 2002). It overlies the Jameco Aquifer, which is 170-m thick and composed of fine-to-

4 Permeable sediments pore-water salinity 633 coarse gravel. The Jameco Aquifer is underlain in turn by the Magothy and Lloyd Aquifers to bedrock at a depth of 550 m (Busciolano 2002). The majority of the bay bottom consists of silty clay sediment of reworked glacial outwash and salt marsh deposits. Sixty-six percent of the bay is covered by marshland. The mean tidal range in Jamaica Bay is about 1.5 m (Beck et al. 2007). Measurements were made at two gently sloping, sandy beaches in Jamaica Bay, Canarsie Pier and Canarsie Pol (Fig. 1B). The Canarsie Pier site is a sand beach located on the northern shore of Jamaica Bay. Canarsie Pol is the largest uninhabited island in Jamaica Bay, with an area of about 1 km 2 and a relief of up to 4 m. The island is covered with terrestrial vegetation. It is bordered by marshes along much of its shores to the north and east and has intermittent marshland and sandy beaches to the south and west. Measurements were made on the south shore of Canarsie Pol. Venice Lagoon: The Venice Lagoon extends over 550 km 2 on the northwest coast of the Adriatic Sea (Fig. 1C). It has an average depth of 0.8 m and a tidal range of about 1 m. Its waters are home to a major fishing industry as well as host to many urban and industrial activities. Perhaps no lagoon in the world has been subject to a longer and more continuous history of human modification. The lagoon is underlain by a series of nine aquifers, some of which are artesian, with a total thickness of 1000 m (Carbognin et al. 1977). Only the uppermost aquifer is known to intercept the seafloor. The surrounding land has little, if any, relief. The lagoon s drainage basin covers 1850 km 2 and has an annual average rainfall of 950 mm (Zonta et al. 2005). Previous measurements of SGD in this lagoon average 30 cm d 21 in the northern lagoon and 6 cm d 21 in the central lagoon (Rapaglia 2005; Garcia-Solsona et al. 2008). Maximum SGD reaches 200 cm d 21 (Rapaglia 2005). Measurements were made at two beaches in the Venice Lagoon, Treporti and Punta Sabbioni, both located along the western shore of the barrier peninsula (Fig. 1C). The substrate at Treporti consisted of silty sand and that at Punta Sabbioni of fine to medium sand. Both beaches were backed by bulkheads. Although both sites are located adjacent to one of the major channels in the lagoon with fast-flowing currents, they were protected by jetties and an anchorage. Methods At each location, vented benthic chambers, commonly known as manual seepage meters (Lee 1977), were used to determine SGD. These devices consisted of benthic chambers (0.25 m 2 in area) vented to plastic bags. Except when samples were collected for measurements of salinity, collection bags were prefilled with 500 ml of ambient water to reduce artifacts (Cable et al. 2006) and to allow for the calculation of negative SGD (saltwater intrusion). Seepage meters were placed between 10 and 15 cm into the sediment, leaving a head space of 5 to 10 cm. The devices were left in place for 30 min before measurement began in order to allow for settling into the sediment to occur. Samples were collected every 30 min for 3 to 12 h depending on the situation. At Mattituck Beach and Treporti measurements of SGD were sometimes taken at more frequent intervals to obtain a better resolution of high flow rates. Although these devices have been criticized for possibly altering the process they are intended to measure (Shinn et al. 2002), they have been used extensively in diverse settings (Burnett et al. 2006). As we have done, precautions can be taken to reduce artifacts. Seepage meters have been shown to be reliable when SGD is larger than a few centimeters per day under calm conditions (Cable et al. 2006). There are several lines of evidence that lend confidence to measurements made with vented benthic chambers. First, the cross-shore distribution of SGD often shows a decrease with distance from shore (Cable et al. 2006), as would be expected of SGD driven by a terrestrial hydraulic gradient. Second, in some cases, the flow rate has been shown to agree well with SGD calculated via Darcy s Law from independent measurements of the vertical hydraulic gradient and the vertical hydraulic conductivity at the site (Bokuniewicz et al. 2004). Third, measured SGD often shows a tidal modulation as expected in response to tidal changes in the hydraulic gradient (Li et al. 1999; Paulsen et al. 2004). Fourth, the water collected from the chambers shows a decrease in salinity over time as the head space of the chambers is flushed with fresher pore water from below (Stieglitz et al. 2007). Fifth, independent estimates of SGD by using geochemical tracers in open water and from in situ dye injections have been found to be in good agreement with measurements using seepage meters (Burnett et al. 2006). For example, at a study site on Shelter Island, New York, which is near Mattituck Beach, seepage meters recorded SGD at rates between 2 and 37 cm d 21, while independent calculations of SGD made from simultaneous radon concentrations ranged from 0 to 30 cm d 21 (Burnett et al. 2006). Sufficient measurements to calculate uncertainty estimates have been rare, but Zeitlin (1980) found that 50% of the duplicate measurements from vented benthic chambers and 70% of the replicate measurements fell within a variation of less than 20%. An analysis of 32 duplicate measurements from diverse sites, including the ones investigated here, yielded a standard deviation of 9.0 cm d 21 around a mean of 73.2 cm d 21, or 612% (Rapaglia 2007). Pore-water samples were collected with a retractable-tip piezometer (Charette and Allen 2006) consisting of a screened stainless steel tip connected to Teflon tubing. Samples of about 500 ml were collected at intervals of about 50 cm to a depth of up to 4 m along the same profile. In some cases (23 March 2006 at Canarsie Pier) pore water was sampled from a piezometer emplaced directly below the seepage meter. At Mattituck Beach, 60-mL samples were collected every 4 cm after flushing the tubes with at least 30 ml of water (Beck 2007). Samples in Jamaica Bay and Mattituck were measured immediately with a YSI, version 556, conductivity, salinity, and temperature meter. It is important to recognize that the pore-water profiles represent average pore-water salinities. Assuming a porosity of 0.45, if 90 ml of water was withdrawn every 4 cm, then water has been pumped from a 200-mL volume, which

5 634 Rapaglia and Bokuniewicz may correspond to a sphere with a radius of 4 cm. Each sample depth could overlap with two adjacent sampling regions, thereby averaging the variation of salinity within that sampling volume. The average salinity measured in the pore water may include, for example, higher salinity pore water from centimeter-sized burrows or salt fingers averaged with lower salinity pore water between the burrows or salt fingers. Results Direct measurements of SGD We considered three characteristics of the measured SGD: the magnitude, the variation with the tide, and the change in salinity of the collected water. There was only one site in Mattituck Beach. SGD at Mattituck Beach was measured on 09 May 2006 using three seepage meters (Fig. 1A). Two sites were visited in Jamaica Bay Canarsie Pier and Canarsie Pol. Three seepage meters were deployed at Canarsie Pier on 23 March 2006, and one seepage meter was deployed on 23 August 2005, 10 February 2006, and 04 May 2006 (Fig. 1B). Two seepage meters were used at Canarsie Pol on 20 April 2006 (Fig. 1B). Two sites were visited in the Venice Lagoon Treporti on 24 October 2005 and Punta Sabbioni on 03 November Three seepage meters were deployed at each site. Magnitude: The greatest seepage rates were measured at Mattituck Beach, where SGD reached 174 cm d 21. SGD as high as 141 cm d 21 was seen at Treporti in the Venice Lagoon. At the other site in the Venice Lagoon, Punta Sabbioni, the average values of SGD were 4.0 cm d 21, 8.8 cm d 21, and 14.7 cm d 21 in seepage meters SABB1, SABB2, and SABB3, respectively (Fig. 1C). SGD of similar, low magnitudes was measured at Canarsie Pier in Jamaica Bay, New York, where the average SGD was 3.0 cm d 21 on 23 August 2005, 1.0 cm d 21 on 10 February 2006, and 1.8 cm d 21 on 04 May The highest SGD at Canarsie Pier reached 18 cm d 21 on 23 March 2006; at Canarsie Pier, as well as at Mattituck Beach and Punta Sabbioni, SGD near zero and even recharge (i.e., negative values of SGD) were observed at times near high tide. SGD at Canarsie Pol never exceeded 5 cm d 21. If SGD is driven by the onshore water table hydraulic gradient, it should be expected to decrease with increasing distance from shore. Even though the three seepage meters at Mattituck Beach were clustered within an area of 4 m 2, SGD decreased by 20% to 50% between the device closest to shore (M1; Fig. 2) and the device farthest from shore (M3; Fig. 2). At Canarsie Pier an off-shore decrease may have been detected at a tidal elevation below 45 cm (Fig. 2). We did not detect a trend of decreasing SGD with distance from shore at Canarsie Pol; SGD was, perhaps, too low to resolve any changes. Though no distinct offshore decrease was seen at Treporti, a slight offshore increase in SGD was seen at Punta Sabbioni between SABB1 at 5 m from shore and SABB3 at 15 m from shore (Fig. 2). Tidal modulation: Measurements at many other sites (but not all) show a modulation of SGD with the tide Fig. 2. SGD as measured in seepage meters vs. tidal elevation at all five locations. In sites where the SGD is controlled by the local water table hydraulic gradient, SGD often has an inverse relationship with tide. Indeed this can be clearly seen at Canarsie Pier and Mattituck Beach.

6 Permeable sediments pore-water salinity 635 (Paulsen et al 2004; Burnett et al. 2006), with the highest rates of SGD occurring near times of low tide. Tidal modulation of SGD has been interpreted to indicate SGD driven by a terrestrial hydraulic gradient that does not change with the tide, so that the falling tide increases the hydraulic gradient offshore (Taniguchi 2002). At two of the sites (Canarsie Pier on 23 March 2006 and Mattituck Beach; Fig. 2) the tidal modulation suggests that the flow is driven by a terrestrial hydraulic gradient. On 23 March 2006, for example, SGD at Canarsie Pier reached a maximum value of 17.8 cm d 21 at low tide, significantly above its average value of 2.7 cm d 21 (Fig. 2). On the other dates at Canarsie Pier, however, SGD was too low to resolve any tidal modulation. At Mattituck Beach, SGD had inverse correlation with tidal elevation in all three seepage meters (Fig. 2). SGD as high as 174 cm d 21 was recorded at low tide, while negative values of SGD (i.e., recharge) were recorded at high tide. At Punta Sabbioni, measurements were made from high to low tide over a total tidal excursion of about 90 cm, but no consistent pattern in discharge with tidal variation was seen. Neither were systematic tidal changes in SGD seen at Canarsie Pol or Treporti (Fig. 2). Any changes may have been too small to be resolved, or the hydraulic gradients driving SGD here were insensitive to changes in the tidal elevation in open water. Salinity: In the presence of a vertical gradient in the pore-water salinity, groundwater approaching the sediment water interface must change its salinity by dispersive mixing along its flow path. The groundwater that crosses the sediment water interface should be expected to have the salinity of the pore water just below the sediment surface, but this does not necessarily have to be the same as the salinity of the ambient, open water trapped in the chamber. Other studies have found that the salinity of the water sampled within the chambers decreases over time, as the chamber is flushed with pore water from below (Stieglitz et al. 2007). Samples from Mattituck Beach and Canarsie Pol (Fig. 3) showed the greatest absolute decreases in salinity, but measurements at all of our sites except Treporti, which will be discussed below, showed some tendencies for the salinity to decrease as the chambers were flushed. At Mattituck Beach, for example, the open-water salinity was about 28.8, but over time salinity in the seepage meters decreased to about 17 (Fig. 3). It is interesting to note that high densities of the snail Ilyanassa obsoleta were found at Mattituck Beach in a thin, shore-parallel band of the seafloor along the seepage face, possibly indicating their preference for brackish salinities (Beck 2007). The seepage meters may not have been fully flushed, but the freshwater fraction of SGD was at least 41% at Mattituck Beach, 12% at Canarsie Pier, 10% at Canarsie Pol, and 3% at Punta Sabbioni. The salinity increases at Treporti because the end-member water at depth was more saline than the open water above the sediment water interface. In this case the groundwater at depth was estimated to comprise about 30% of the SGD. Pore-water profiles Pore-water salinity profiles are shown in Figs. 4 and 5. All profiles, with the exception of Fig. 3. Salinity as measured within the seepage meters vs. the cumulative discharge of groundwater through the meters in all five study locations. In some instances a clear change in salinity can be seen.

7 636 Rapaglia and Bokuniewicz Fig. 4. Profiles of salinity measured within the pore water collected at Canarsie Pol, Mattituck Beach, Punta Sabbioni, and Treporti. the profile at Treporti, which will be discussed later, showed a decrease of salinity with depth in the sediment. Mattituck Beach: Over a 3-h period of falling tide at Mattituck Beach, the pore-water salinity was nearly constant at two levels (Fig. 4). At a depth of 5 cm, salinity stayed constant at a value of about 26 and, at a depth of 25 cm, salinity remained at about 5. When the SGD reached 110 cm d 21 near the time of low tide (15:00 h; Fig. 4), pore-water salinity decreased from 26 at the sediment water interface to 4 at a depth of 25 cm along a Fig. 5. Profiles of salinity measured within the pore water collected at Canarsie Pier on 23 August 2005 and 10 February, 23 March, and 04 May concave profile. At a lower rate of SGD (10 cm d 21 )at Mattituck Beach, salt was able to penetrate deeper into the sediment. Jamaica Bay: Pore-water salinity profiles were taken at Canarsie Pier on four different dates (Fig. 5). The deepest

8 Permeable sediments pore-water salinity 637 profile was taken to a depth of 4 m (Fig. 5; 04 May 2006). SGD at Canarsie Pier on this date was low, being always below 4 cm d 21, and the salinity profile showed a rapid decrease from 28 at the sediment surface to 22 at 40-cm depth. This is followed by an increase to 27 at 100 cm, but below 100 cm the salinity showed a fairly uniform decrease to 19 at 270 cm, and finally to a value of 8 at a depth of 315 cm (Fig. 5). On 23 August 2006, SGD was as high as 17.8 cm d 21 at low tide at Canarsie Pier. The pore-water salinity profile at low tide showed a decrease in salinity from 25 to 16 at a depth of 200 cm (Fig. 5). The instantaneous SGD at this location was lowest on 10 February 2006, averaging 1 cm d 21, which could be disregarded as within the error uncertainty of the seepage devices. The pore-water salinity within the upper 2 m decreased in salinity from about 26 at the surface to 17 at depth, which is similar to that seen on 23 August 2006; below 40 cm salinity increased from 19 at 40 cm to 22 at a depth of about 100 cm, similar to the profile seen on 04 May On 23 March 2006, the salinity profiles disclosed a local, subsurface maximum with a decrease from 26 at the surface to a salinity of between 16 and 20 at a depth of 10 cm (Fig. 5) while SGD was between 5.3 and 2.1 cm d 21 near high tide. At Canarsie Pol, SGD was measured to be between 3 and 5 cm d 21 on 20 April 2006, and pore-water salinity decreased only slightly, from 28.8 at a depth of 40 cm to 27.7 at 120 cm, but reached a value of 24 at a depth of 195 cm (Fig. 4). Venice Lagoon: At Punta Sabbioni, a pore-water salinity profile was collected alongside of SABB3 (Fig. 4). The pore-water salinity decreased from 34 to about 26 in the upper 70 cm (Fig. 4). It then fluctuated between 25.5 and 28 to a depth of 280 cm. The pore-water salinity profile taken at Treporti (Fig. 4) shows a small decrease from a surface salinity of 33.9 to 32.5 at a depth of 30 cm. Below 30 cm pore-water salinity increased to 42 at a depth of 270 cm. The salinity at 270 cm is higher than either the average salinity in the lagoon or open Adriatic Sea salinity. The higher salinity at depth may be due to a local evaporite layer buried at depth because buried high-salinity salt marsh sediments have frequently been found in the lagoon (Marani et al. 2004). Treporti will be the exception throughout this discussion because in all other cases the pore-water salinity at depth was less than that of the overlying (denser) open water above the sediment water interface. Discussion Interpretation of the salinity profiles The salinity profiles provided evidence that the pore-water salinities were being controlled by rapid, downward dispersive mixing in the face of vertical upward advection. In each of the salinity profiles except at Treporti, salt penetrates downward into the sediment in the face of upward SGD. At Mattituck Beach, for example, salt penetration occurred as deep as 25 cm even though the upward advection was as high as 174 cm d 21. At both Canarsie Pier and Canarsie Pol, saline pore water also was observed to depths of at least 100 cm. As discussed earlier, molecular diffusion of salt through the pore water is insufficient to move salt downward against even a small upward SGD, so other, more efficient mixing processes must be operative. Salinity gradients in the upper meter of sediment would be indicative of downward dispersion of salt from the sediment water interface on a small scale of 1 m. The process at the sediment water interface, however, seemed to be complicated by the existence of lateral inhomogeneities providing preferred pathways vertically through the sediment as we will discuss. (At any of these locations, nonzero salinity end members at depth in the sediment most likely indicate the influence of large-scale recirculation of seawater, on a scale of 10s to 100s of meters, although we have no site-specific evidence that this was the case.) Advection and mixing: At Mattituck Beach, the porewater salinity within 5 cm of the sediment water interface was temporally invariant even though the upward advection of pore water due to SGD changed by an order of magnitude. In the upper few centimeters of sediment, the downward dispersion must be large enough to dominate the transport over the upward advection. Each of the profiles collected on 23 March 2006 at Canarsie Pier (Fig. 5) also showed little change in salinity with depth below 80 cm as would be expected if dispersive fluxes dominated over the process of upward advection. In the absence of vertical, upward advection, simple mixing between a high, pore-water salinity end member at the sediment water interface and a low-salinity end member at depth would produce a linear gradient. Within the resolution of measurements, near-linear gradients would also be seen if the flux due to vertical mixing was much greater that that due to advection. This seemed to be the case for several of the profiles measured here. For example, at the time of high tide at Mattituck Beach (Fig. 4, 12:00 h), when SGD was low, the salinity profile was approximately linear between depths of 5 and 25 cm, as would be expected due to simple mixing between two end-member concentrations with little advective SGD. The profile of salinity from the Treporti site under an average SGD of 50 cm d 21 might also be an approximation to linearity, suggesting, more or less, simple mixing between the surface and the deep, high-salinity end member (Fig. 4). As the difference between the upward, advective flux and the downward dispersive mixing becomes smaller, a concave profile should be seen. Several of the profiles showed this characteristic. A concave profile was recorded at Mattituck Beach at the time of low tide, when SGD was largest (15:00 h, Fig. 4). At Punta Sabbioni, a concave profile could also have been the result of the combined effects of upward advection and downward dispersive mixing of comparable magnitude between end-member concentrations. On 23 August 2006 at Canarsie Pier too, the profiles showed concave form characteristic of a profile generated by downward dispersion of salt superimposed on upward advection (Fig. 5). Comparisons of the pore-water salinity profiles at Punta Sabbioni and Treporti suggest to us that the effective

9 638 Rapaglia and Bokuniewicz dispersion coefficient may have been controlled by the rate of advection because a more linear profile was seen at Treporti where the SGD was high, while a more concave profile was found at Punta Sabbioni where SGD was lower. The dispersive mixing seemed to be directly related to the rate of SGD, increasing with larger SGD. This would be the behavior of classical, hydrodynamic dispersion in an aquifer (Freeze and Cherry 1979). Lateral inhomogeneities: The seepage meters themselves served to disrupt the dispersion process in the sediment immediately below the meter, allowing for end-member pore water to reach the surface without significant mixing. At Mattituck Beach, the pore-water salinity was invariant at a depth of 25 cm, apparently representing the endmember salinity of the advective pore water. The salinity of samples collected within the chambers, however, reached levels of between 14 and 19 (Fig. 3), even though the salinity just below the sediment water interface remains constant at 25. Groundwater flowing vertically across these isohalines should be expected to cross the sediment water interface and enter the seepage meter at a salinity of 25. It seemed that the water entering the chambers originated instead at a depth between 10 and 15 cm and, somehow, resisted an increase in salinity to 25 as it moved up in the sediment column to cross the seafloor. This could only happen if the lateral distribution of upward flow was not uniform but rather confined to channels, columns, or other preferred, vertical conduits that allowed pore water from a depth of between 10 and 15 cm to reach the seafloor without adjusting to the average salinity profile observed in the piezometer samples (Beck 2007). The average salinity measured with the piezometer near the sediment water interface could be a mix of lower salinity pore water in the preferred conduits and higher salinity pore water in the intervening spaces. Because the piezometer was estimated to draw pore water from a diameter of 4 cm around the sampling port, conduits must be on the order of a centimeter in diameter. Gravitational salt fingers or burrows would be the appropriate size. In Canarsie Pol, salinity in the seepage meter also had decreased with time as compared with the surface salinity (Fig. 3). Again a mechanism is needed to allow this lower salinity pore water to reach the surface from depth without the intervening mixing that was seen in the pore-water average salinity profile. Conceivably, salt fingering or bioirrigation could produce this effect (see fig. 11.9, Aller 2001). A middepth maximum, as was seen at Canarsie Pier on 10 February 2006 (Fig. 5), cannot be explained by uniform advection and dispersion. The subsurface maximum may be caused by either lateral transport or small-scale lateral variations in this vertical transport. Such a distribution could be due to stratification of sedimentary layers with different permeability or bioirrigation or burrow geometry may be a cause, but we had no further evidence that this was the case. Magnitude of dispersion determined by the mass balance of salt Although the pore-water salinity profiles have been observed to vary in time, as, for example, at Mattituck Beach (Fig. 4), the data are sparse and not well resolved. To make further progress with the available data we might assume, as is commonly done, that the profiles adjust quickly enough to be in steady state with the instantaneous conditions. If one assumes that the pore-water salinity profile is in steady state and, as an initial simplification, that it can be approximated by a linear gradient with depth in the sediment, then the profile can be used with the measured SGD to estimate the dispersion coefficient. The mass of salt in a volume of sediment with pore-water salinity S 0 and porosity F is FS 0 /1000. For example, a pore-water salinity of 27 corresponds to a mass concentration of grams of salt per cubic centimeter of water. In sediment of porosity 0.5 with pore-water salinity at the sediment water interface of 27, there would be grams of salt per cubic centimeter of sediment. Assuming that the salinity gradient is linear and that the salinity reaches zero at a depth z 1, then the gradient is FS 0 / 1000z 1. Continuing the example above, if the pore-water salinity gradient is such that the salinity is zero at a depth, z 1, of 540 cm, the gradient is /540 grams of salt per centimeter cubed of sediment per centimeter depth, or g cm 24, approximating the salinity profile at Canarsie Pier taken on 04 May 2006 (Fig. 5). Now in the presence of an upward advective (volume) discharge of pore water, or SGD, the advective velocity (v) of the pore water is SGD/F, and the rate at which salt is flushed from the sediment, S-dot, is S-dot ~ WS 0ðSGD=WÞ 1000 ~ S 0SGD 1000 For this example, if the SGD is 4 cm d 21 (that is, 4 cubic centimeters of water per square centimeter per day) then, assuming 0.5 is the porosity, 8 cm of the sediment would be flushed every day carrying out or g salt cm 22 d 21. To maintain steady state, this same amount of salt must be brought down into the sediment by mixing. As a result the dispersion coefficient, D, must equal the advective daily loss of salt divided by the mass concentration gradient of salt per unit volume of sediment, or D ~ 1000S 0SGD ~ SGDz 1 or vz 1 ð2þ 1000S 0 W=z 1 W For this example, D is 0.43 m 2 d 21. If the deep, endmember salinity is not zero, but, instead, some value S 2 reached at a depth z 2, then the dispersion coefficient is D ~ SGDz 2S 0 ð3þ S 0 { S 2 where z is zero at the sediment water interface. For the data taken at Canarsie Pier with an average SGD of 1.5 cm d 21, the dispersion coefficient was calculated to have been 0.16 and 0.17 m 2 d 21. Applying the same method to the profile of salinity measured at Canarsie Pol, assuming a zero salinity groundwater end member and using the average SGD flow of 3.5 cm d 21 yields a dispersion coefficient of 0.84 m 2 d 21. For the two sites studied in the Venice lagoon, assuming that the end-member salinity is 26 at Punta Sabbioni and 42 at Treporti, then both sites have a profile in which the salinity changes by 8 over a depth of ð1þ

10 Permeable sediments pore-water salinity cm. Because of the difference in SGD, the dispersion coefficients were calculated to be 0.23 m 2 d 21 and 2.8 m 2 d 21 in Punta Sabbioni and Treporti, respectively. Apart from the dispersion coefficient found at Treporti, which is very high, coefficients were within the range or only slightly higher than those measured elsewhere. Unlike Jamaica Bay and Venice, however, Mattituck had large temporal variation in SGD, ranging from 210 to 174 cm d 21. Although the end points of the profile are invariant (Fig. 4), the shape of the profile seemed to be affected by the flow rates. Using Eq. 2, the dispersion coefficient at Mattituck could be as high as 0.8 m 2 d 21 depending on the value of SGD. Magnitude of dispersion: steady-state, one-dimensional analytical solutions A slab solution (Martin et al. 2007): The steady-state, one-dimensional equation governing the advection-dispersion of salt (S) is 0 ~ vls Lz { DL2 S Lz 2 where v, as before, is SGD/F. To describe measured, porewater salinity profiles, Martin et al. (2007) applied this relationship to mixing in a slab of sediment with constant but different salinity at its upper and lower faces. They assumed that hydraulic dispersion was operative within the slab. In the sediment above the slab, bioirrigation was actively mixing the sediment. The salinity on the lower boundary was taken to be the asymptotic salinity deep in the sediment column. The solution presented by Martin et al. (2007) to Eq. 4 is 1 n h S(z) ~ 1 { exp v S L 1 { exp v i D L D z ð5þ h z S u exp v Z { exp v io D D L where S is salinity, v is the advective velocity of pore water, D is the dispersion coefficient, L is the lower limit of the salinity profile, S L is the salinity at the lower limit, z is the depth of sample, and S u is the salinity at the upper limit of the salinity profile. Martin et al. (2007) calculated a dispersion coefficient of m 2 d 21 from the molecular diffusion coefficient (Li and Gregory 1974) modified for tortuosity. To reproduce the measured salinity profile with this coefficient, SGD was required to be more than an order of magnitude lower than the SGD measured directly using seepage meters. Alternatively, to reproduce the measured SGD, a much larger dispersion coefficient would be needed (Martin et al. 2007). This conclusion is consistent with both earlier investigations at other sites and with the results presented here. Figure 6 shows the results of the application of (Eq. 5) to the data from Jamaica Bay, Mattituck Beach, and Venice, respectively. In Mattituck, the high-flow profile could be well represented using a dispersion coefficient of 0.84 m 2 d 21 (Fig. 6A), while the low-flow profile required a dispersion coefficient of m 2 d 21 (Fig. 6A). In Jamaica Bay, Eq. 5 reproduced the curves at Canarsie Pier ð4þ and Canarsie Pol using dispersion coefficients of 0.3 and 0.5 m 2 d 21, respectively (Fig. 6B). At Punta Sabbioni, on the other hand, the dispersion coefficient was much lower (0.04 m 2 d 21 ) using this method than when using the simplified salt balance. At Treporti, a dispersion coefficient of 3.0 m 2 d 21 was needed to match the profile of salinity in the face of a high SGD, which is similar to the coefficient calculated using the simplified salt balance above (Fig. 6C). All of the calculated dispersion coefficients are much higher than those calculated by Martin et al. (2007) but correspond well with the coefficients calculated using the simplified salt-balance method. A steady-state, one-dimensional, semi-infinite analytical solution Although a slab solution as suggested by Martin et al. (2007) may be more appropriate in some situations (Mattituck) or, perhaps, in layered sediment, there is no a priori reason to prefer it. Solutions to a steady-state, onedimensional, advection-dispersion equation in a semiinfinite medium were found to be practically indistinguishable from the slab solution in the region of interest. The distribution of the concentration of salt S(z), with depth in the sediment, assuming a constant salinity, S 0, at the surface, (z 5 0) is then governed by F ~ Sv { D Ls ð6þ Lz or D Ls v Lz ~ S { F ð7þ v Where F isaconstantfluxofsalt,v is the advective velocity of pore water, and D is the dispersion coefficient. Note that, in the sediment column, the convention is to have z increasing downward from the surface, so a value of v greater than zero is in the downward direction. Because the convention for SGD is to have SGD greater than zero (positive), in the upward direction v 52SGD/W, wherew is porosity. The boundary conditions for the advection-diffusion equation in a semi-infinite medium are S 5 S 0 at z 5 0andS remains finite as z R. Changing the variables such that q ~ S { F ð8þ v then L S { F Lq Lz ~ v Lz ~ LS Lz since F/v is a constant. So, in terms of the new variable D Lq v Lz ~ q ð10þ with the boundary conditions q 5 (S 0 2 F/v) atz 5 0andq remains finite as z R. The solution to this equation is q ~ S 0 { F exp v v D z ð11þ ð9þ

11 640 Rapaglia and Bokuniewicz Fig. 6. (A) Profiles of salinity and matching dispersion coefficients during high- and lowflow regimes at the Mattituck site. (B) Profiles of salinity and matching dispersion coefficients at both Jamaica Bay sites. (C) Profile of salinity and matching dispersion coefficient at both Venice Lagoon sites. Coefficients were determined using the relationship described in Martin et al. (2007). In these sites, actual data are designated by hollow insignia, calculated profile designated by filled insignia.

12 Permeable sediments pore-water salinity 641 Table 1. Calculated dispersion coefficients, in m 2 d 21, using different techniques. Location Hydrodynamic dispersion (Freeze and Cherry 1979) Tidal mixing (Cooper 1964) Salt balance Analytical (slab) solution (Martin et al. 2007) Canarsie Pier Canarsie Pol Mattituck low SGD Mattituck high SGD Punta Sabbioni, Venice Treporti, Venice Hydrodynamic dispersion is calculated as a function of the advection velocity. Tidal mixing was calculated using the technique from Cooper (1964) with site-specific tide data. Explanation of the calculation of the dispersion coefficients in the other three columns are found within the discussion section of this chapter. Substituting relationship Eq. 10 into Eq. 11 D Lq v Lz ~ D v S 0 { F v exp v v D D z ð12þ q 5 (S 0 2 F/v)atz50as required and, if SGD is upward (in the negative z direction), v is a value less than zero so q remains finite as z R, as required. F is the constant flux of salt, not water, so if the end-member salinity of the pore water advecting into the system is zero, then F can be taken as zero. Figure 6C shows that in Jamaica Bay, Eq. 11 and Eq. 4 essentially yield the same distribution; their differences are not great enough to be resolved in the data. Mechanisms of dispersion Further research is needed to demonstrate the actual mechanisms of vertical mixing in the field. As we have discussed, several candidates have been implicated as mechanisms for downward mixing from the sediment water interface. These all tend to occur over small scales and include hydraulic dispersion, salt fingering, wave or tidal dispersion, and bioirrigation. Any or all of the proposed mechanisms could be active at any particular site. For the conditions at our study sites, various estimates of the dispersion coefficients calculated here are compared in Table 1. Hydraulic dispersion, calculated as a function of the advection velocity, seemed insufficient to explain the pore-water salinity distributions in any case. This same conclusion was reached by Martin et al. (2007). Theoretically, tidal mixing would seem to be of the appropriate magnitude to explain the salinity distribution at Mattituck Beach, at least under low SGD, but the other situations required even more effective mixing mechanisms. The situation at Treporti remained the exception. At Treporti, gravitational convection or salt fingering could not have been the mechanism because the pore-water salinity at depth was greater than that at the sediment water interface giving a stable, pore-water density profile. Vertical mixing could have been due to bioirrigation or hydraulic dispersion. The profile at Treporti goes to a depth of 2.8 m (Fig. 4), which is much larger than normally seen in benthic sediments (Aller 2001). Because of this and because of the high value of SGD hydraulic dispersion seemed like the most likely, dominant mechanism. Implications for the calculation of chemical budgets The occurrence of large dispersion coefficients, whatever the mechanism, would have important implications in the calculation of any dissolved chemical budget. The estimation of SGD based on radium fluxes, for example, hinges on the ability to quantify all possible sources of Ra into the system under investigation, including the diffusion (or dispersion) of radium from sediments. In some investigations, this source is calculated as the product of a diffusion coefficient and the gradient of pore-water Ra profiles (Charette et al. 2003; Beck et al. 2007). Diffusion coefficients of m 2 d 21 are assumed (Charette et al. 2003; Beck et al. 2007). These are orders of magnitude lower than the dispersion coefficients calculated here and would result in a substantial underestimation of the importance of this component of the Ra budget. Indeed, dispersion from the sediments is often disregarded as negligible (Rama and Moore 1996), but this might not be the case if the dispersion coefficients are several orders of magnitude larger than commonly assumed. A second method used to calculate the diffusion component is by extracting cores from the study site and incubating them in a laboratory setting (Beck et al. 2007). This method should directly quantify true, molecular diffusion across the surface of the core. However, mechanisms of vertical mixing considered herein (i.e., wave pumping), would not occur in the laboratory as they would in nature. By shutting off some dispersion mechanisms, the laboratory incubation could underestimate the flux, perhaps by orders of magnitude. For example, based on laboratory incubations of large diameter sediment cores, it was estimated that diffusion of 224 Ra from sediment in Jamaica could supply disintegrations per minute (dpm) d 21, representing between 5% and 11% of the total excess 224 Ra in Jamaica Bay (Beck et al. 2007). Most of the rest is assumed to be due to SGD. Alternatively, if a dispersion coefficient of 0.15 m 2 d 21,as calculated from the pore-water salt balance at Canarsie Pier, is multiplied by a pore-water radium gradient between and dpm L 21 cm 21 (Beck et al. 2007), the diffusive flux would be recalculated between 2.0 and dpm d 21, increasing the apparent importance of the sediment flux to the radium balance. In coastal environments, investigators should expect SGD to show large spatial and temporal variability, which will alter chemical gradients in the pore water, and vertical dispersion coefficients might approach 1 m 2 d 21. Evidence from salinity profiles made at several locations suggests