Biogeochemistry 10: 257-276, 1990© 1990 Kluwer Academic Publishers. Printed in the Netherlands

Groundwater seepage along a Barrier Island

HENRY BOKUNIEWICZ & BARBARA PAVLIK'Marine Sciences Research Center, State University of New York, Stony Brook, NY 11794-5000, USA ('present address: Delta Environmental Consultants, 4200 West Cypress, Suite500, Tampa, FL 33607, USA)

Key words: Barrier Island, freshwater lenses, stratigraphy

Abstract. Resistivity and water level measurements were made on a barrier island on the southshore of Long Island, New York to examine the distribution of fresh groundwater and thepotential for recirculation of saline groundwater. The depth to the base of the freshwater lenswas overpredicted by calculations of the static-equilibrium depth to a sharp interface ap-parently because of the sensitivity of the calculation to the low water-table elevations whichare in turn sensitive to variations in sea level because of the existence of a transition zonebetween fresh and saline groundwater. Mixing and recirculation of saline groundwater at thebase of the lens produced a transition zone up to 9.65 m thick. Measurements also supportmodel forecasts of a mean bay level several centimeters above sea level, augmented byatmospheric forcing and wave setup. A time lag of about 8 hours between the response of theocean level to longshore winds and the corresponding response of the bay level can result ina difference in elevation between the bay and the ocean that is up to four times that producedby other agents such as Stokes transport and density differences. In the presence of differentialhydraulic head, bay and ocean water may be exchanged via groundwater flow between thebase of the freshwater lens under the barrier beach and a deeper clay layer.

Introduction

Investigators attempting to quantify the groundwater coupling betweenwatersheds and the coastal ocean often rely on direct measurements of theseepage flux across the sea floor. The measured flux, however, is not neces-sarily comprised of only the freshwater discharge with its associatednutrients and contaminants. As we will discuss in this article, the seepageflux may also represent recirculated sea water at the saltwater/freshwaterinterface or the internal circulation of saline pore waters. Care must be usedto avoid overly simplistic representations of the flow through coastal aqui-fers when interpreting direct measurements of seepage fluxes.

This article describes the distribution of saline and fresh groundwaterunder a barrier island in order to illustrate some of the complexities ofcoastal seepage. Groundwater seepage in the study area plays only a minorrole in the biogeochemical cycles in adjacent marine waters, but the small,

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isolated site is a convenient one for a variety of observations. The principalmeasurements discussed here are the results of a resistivity survey but earliermeasurements of the seepage flux and some preliminary water level measure-ments are also included. Although the latter two data sets are somewhatincomplete, they are rare, if not unique, and may be of interest. The observa-tions illustrate that:- the size and shape of the freshwater lens can show substantial differences

from theoretical predictions,- the recirculation of saltwater could be an important component of the

total seepage across the sea floor and- water level differences between the bay and the ocean have the potential

for driving an independent flow of saline groundwater.

Background

The size and shape offreshwater lenses

The Ghyben-Herzberg relationship is based on the assumption that verticalhydrostatic equilibrium exists between the fresh groundwater and the under-lying seawater. Accordingly, the depth below sea level to the interfacebetween the freshwater and the saltwater is given by

z = hpf/(p 5 - pr) (1)

where h is the elevation of the water table, p, is the density of freshwater andp, is the density of saltwater. Typically, z = 40 h (Freeze & Cherry 1979).A more realistic formulation accounts for the flow of groundwater accord-ing to the Dupuit approximation in which the flow is assumed to be strictlyhorizontal and the hydraulic gradient is assumed to be equal to the slope ofthe water table. The resulting Dupuit-Ghyben-Herzberg analysis describesthe size and shape of the freshwater lens in terms of the rate at whichfreshwater is recharged to the aquifer, R; the width of the island, L; and thehydraulic conductivity, K (Vacher 1988a). For example, the maximumthickness of the lens is found to be

Hm = L[R(1 + Pr/(Ps - p,))/4K ] /2 (2)

(Vacher 1988a). When an allowance is made for the existence of seepageoutflow beyond the shoreline, the results of the Dupuit-Ghyben-Herzberganalysis is virtually indistinguishable from the solutions determined fromthe potential theory (Vacher 1988a; Henry 1964).

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Under equilibrium conditions the deepest part of the lens is beneath thegreatest elevation of the water table, but the shape can be distorted if thereis a difference in mean water level between the bay and the ocean. Water-table elevation will be displaced towards the shore with the higher mean sealevel and the deepest point of the lens will be displaced toward the shore withthe lower mean water level (Vacher 1988b). Tidal (Urish 1980) or wave(Harrison et al. 1971; Dominick et al. 1971) action on a sloping beach resultin mean groundwater levels in the beach that are higher than mean sea level.Mean water level can also differ between the bay and ocean across a barrierisland by four mechanisms:1. Wave setup. Shoaling waves produce a net shoreward transport of

energy which causes an increase in mean sea level from the line ofbreaking waves to the shore. (Longuet-Higgins & Stewart 1964). Theamount of setup depends on both the incident wave characteristics andthe geometry of the beach. Direct measurements are rare, but setup canbe a substantial fraction of the deepwater wave height and elevations onthe order of one meter have been measured (Holman & Sallenger 1985;Nielsen 1988).

2. Wind setup. The difference in response to winds between the bay and theocean could cause differences in mean sea level across the island.

3. Stokes transport into the bay. Correlation between tidal currents andtidal elevations through inlets produces a net flow of ocean water into thebay (Stokes transport; Pritchard 1980).

4. Density differences between the bay water and the ocean water.

In addition, short term differences in water level across an island can be dueto differences in the tidal amplitude and phase between the bay and theocean. Variations in sea level not only can distort the freshwater lens butmay also drive an independent flow of saline pore water beneath the island,as we will discuss later.

Recirculation of sea water

The transition from the freshwater lens to the underlying sea water is agradual one resulting from the mixing of fresh and saline groundwater at theinterface. This mixing can be driven by tidal motion, the adjustment of thelens to varying recharge or the infiltration of sea water over fresh ground-water due to wave run-up, storm surges or sea spray. Within the transitionzone there is a density-driven recirculation of saline groundwater into thetransition zone and back to the sea (Cooper 1959). The interface position

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predicted by the Ghyben-Herzberg relationship is usually taken to corres-pond to the midpoint of the transition zone (Vacher 1988a). Some observa-tions indicate that the top of the transition zone would be 25 times the watertable elevation (Keller & Frischknecht 1966). If this is the case the transitionzone thickness would be 30 times the water table elevation; its volume wouldbe about 15% larger than the volume of the freshwater lens and about halfof that volume would be recirculating sea water.

Flow of saline groundwater

The discharge of brackish groundwater along the fresh-saltwater interfacerequires undiluted saline groundwater to flow shoreward into the transitionzone. In addition, any or all of the mechanisms that produce a change in sealevel could establish an excess hydraulic head and drive a flow of salinegroundwater. Lee (1977), for example, found that the seepage flow acrossthe sea floor at Beaufort, NC varied inversely with the tide. At mean lowwater seepage velocities were about 1.2,um/sec, while at a maximum tidalelevation 0.9 m above mean low water, seawater was driven into the sedi-ment at a seepage velocity of about 0.1 m/sec. The tides here were sufficientto recharge seawater into the sediment at least part of the time.

Measurements of the seepage flux of groundwater across the sea floorcould include contributions from each of these types of flow especially nearthe shore and where the freshwater lens is small. This article will examine thegroundwater distribution on a barrier island (Barrett Beach/Talisman Na-tional Seashore on Fire Island, New York) to illustrate the potential impor-tance of these phenomena to the total seepage flux.

Study area

Fire Island is a microtidal barrier island on the south shore of Long Island.It is approximately 49 km long and ranges from 225 to 750 m wide. BarrettBeach and Talisman National Park are located about midway along thelength of Fire Island at its narrowest point (Fig. 1). Marshes were found onthe bay shore both to the east and west of the study area, but they wereabsent here, simplifying the task of surveying. The beach had a welldeveloped dune with a 6.7m crest. The beach berm elevation was 4.4m.Vegetation densely covered most of the central portion of the island. Earlierinvestigations of the seepage flux had also been done at this location.

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Fig. 1. Index map. Talisman National Seashore is immediately west of Barrett Beach.

Stratigraphy

The island is constructed on the surface of the Upper Glacial Aquifer whichincludes sediments of both Holocene and Pleistocene age and is between 36and 38 m thick (Doriski & Wilde-Katz 1983). The Holocene deposits consistof a layer of aeolian sand, less than 2 m thick, interbedded with washoverdeposits over a thick layer of sandy washover deposits with possible claylenses (Leatherman & Allen 1985). The Holocene beds overlie stratified bedsof fine to coarse sand and gravel of Pleistocene age which dip seaward at alow angle (Leatherman & Allen 1985; Perlmutter, Geraghty & Upson 1959).Salt marshes, buried as a result of barrier island migration, form peatdeposits in some areas of the Upper Glacial Aquifer, and these depositscould complicate the interpretation of electrical surveys. However, a series

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of vibracores taken in the Talisman area (Leatherman & Allen 1985) did notuncover any evidence of buried salt marshes.

The Upper Glacial Aquifer is the most homogeneous and isotropic of FireIsland's aquifers. The horizontal hydraulic conductivity is 60 m/day, and thevertical hydraulic conductivity is between 6 and 24 m/day (Bokuniewicz &Zeitlin 1980). The anisotropy of the aquifer varies between 1:10 and 1:2.5,but is locally as low as 1:1.8 (Getzen 1977).

The Upper Glacial Aquifer rests on the Gardiners Clay, which isapproximately 12 m thick (Doriski & Wilde-Katz 1983) with an estimatedhorizontal conductivity of 0.003 m/day and a vertical conductivity of0.0003m/day (Franke & Cohan 1972). It consists of gray-green clayeyglacial till and silt including some sand and gravel lenses and organicmaterials (Perlmutter, Geraghty & Upson 1959; Jensen & Soren 1971). TheGardiners Clay is relatively impermeable and confines the Cretaceous unitswhich lie unconformably below it (Perlmutter, Geraghty & Upson 1959).This study was limited to the Upper Glacial Aquifer.

Underlying the Gardiners Clay, the Cretaceous Monmouth Greensandextends to a depth of between 96 and 105 m (Doriski & Wilde-Katz 1983).It has a low permeability and acts as an additional confining layer for theMagothy Aquifer below it (Jensen & Soren 1971). The Magothy Aquifer isa major aquifer approximately 200 m thick. Much of the freshwater supplyfor communities on Fire Island is pumped from the Magothy. The MagothyAquifer is underlain by the Raritan Clay which extends to a depth of 365 m(Perlmutter, Geraghty & Upson 1959). The Raritan Clay is a low-permeabil-ity, confining unit (Jensen & Soren 1971). The lowermost aquifer is theCretaceous Lloyd Aquifer, extending to a depth of 550 m and underlain bybedrock (Perlmutter, Geraghty & Upson 1959).

Freshwater lens

There is no naturally occurring surface water in the study area. All of therecharge to the groundwater comes from precipitation. The mean annualprecipitation over Long Island is 1.12m/year (Perlmutter, Geraghty &Upson 1959), and 50% of the annual precipitation is lost to evapotranspira-tion (Miller & Frederick 1969), corresponding to a mean annual recharge of0.56 m/yr. The evapotranspiration rate on Fire Island is not known. It maybe substantially less than that on Long Island because of the shallow rootsystem of the barrier islands vegetation and the high percolation rate whichresults from the lack of soil cover and high permeability of the aquifer.

The water table on Fire Island is 0.3 to 0.6m above mean sea level(Perlmutter & Crandell 1959). The Ghyben-Herzberg depth [Eq. (1)] for a

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freshwater lens with a sharp interface should be between 12 and 24 m. If theevapotranspiration on Fire Island is the same as that on Long Island (i.e.,50%), then the recharge, R, is 0.56m/yr. With L = 242m and K = 60m/day, the maximum lens thickness would be predicted by Eq. (2) is 3.92 m.If, on the other hand, evapotranspiration is negligible the lens could be asmuch as 5.54 m thick. In any event, it seemed likely that the freshwater lenswould be contained entirely in the Upper Glacial Aquifer.

Tidal conditions and mean sea level

Because the flow into the bay is restricted to narrow tidal inlets, the tidalrange in the bay is less than 0.25 m while the range in the adjacent oceanexceeds 1 m. The bay level will therefore be substantially different from theocean level over a tidal cycle as they both oscillate around mean sea level.In addition, mean bay level is expected to be slightly higher than the staticmean ocean level. A finite-element numerical oceanographic model of thebay has been used to calculate water levels (Pritchard & Gomez-Reyes1986). It was found that the Stokes transport produced a bay level 0.031 mabove sea level and the supply of freshwater produced an additional0.041 m. The bay level predicted by the model is thus 0.072 m above sea level.

Subtidal water level variations in coastal oceans are produced by long-shore winds and these variations in the bay are highly coherent with regionalvariations in the ocean but lag behind changes in the adjacent ocean byabout 8 hours (Wong & Wilson 1984). As a result, temporary differences inwater level across Fire Island can be produced and differences in excess of0.2 m around a common mean sea level can be calculated from the availableobservations (Wong & Wilson 1984). The effects of local winds directly onthe bay have not been measured but they can be estimated using semi-empirical equations developed for enclosed basins (U.S. Army Corps ofEngineers 1977). For example, persistent winds of 30 mph directed down thelong axis of the bay should produce a local setup of as much as 0.25 m fromone end of the fetch to the other.

Groundwater seepage

Direct measurements of the seepage flux of groundwater across the bay floorwere made at Barrett Beach using an enclosed chamber vented to a plasticcollection bag. The details of these observations are presented inBokuniewicz & Zeitlin (1980), but they will be summarized briefly here. Themeasurement device was essentially that developed by Lee (1977). The bayfloor was sand and the water depth was only 0.7m at a distance of 184m

aBARRETT BEACH· 10-11 JUNE. 1979AAA II JUNE, 1979 80-

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Fig. 2. Seepage rates across the bay floor. The solid ornaments show the first set of measur-ments made on a particular day; the open ornament the second set; the half filled ornaments,the third and fourth sets. Where the outflow rates measured at one location were nearlyidentical, the ornaments representing them were displaced slightly to the right and left so theycould be seen (from: Bokuniewicz & Zeitlin 1980). (a) 10-11 June, 1979; (b) 10 July, 1979; (c)7-10 August, 1979.

from shore. Groundwater seepage measurements were made on each ofthree dates (10-11 June, 10 July, and 9-10 August 1979) chosen to corres-pond as closely as possible to times of maximum spring tides, when any tidalmodulation of the subaqueous seepage would be expected to be mostpronounced.

On 10-11 June, four sets of measurements were made (Fig. 2a) along atransect into the bay. The first set of measurements was made over an entiretidal period and showed the flow to be less than 5 /day-m 2out to a distanceof at least 98 m. The second set of measurements was made over a three-hourperiod centered on the time when the difference between the bay water leveland the ocean level was greatest with the ocean being higher than the bay.The flow rates measured at this time were slightly higher; the highest wasabout 22 I/day-m 2 at a distance of 75 m. The next two sets were taken attimes when the bay level was expected to be higher than the ocean level, but

264

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265

the outflow values of the third and fourth set of measurements were compar-able in magnitude to the second set and higher than the first.

Four sets of measurements were made on 10 July 1979 (Fig. 2b). The firstset was taken during a period when the ocean level was higher than the baylevel and the next three sets were made while the bay level was higher thanthe ocean level. No unequivocal, systematic changes in the outflows weredetected, although the highest flow rate (68 1/day-m2 at a distance of 10 m)was measured when the ocean level was higher than the bay. In addition, theonly negative seepage values, representing the recharge of bay water to thesediments, were measured at a time when the bay level was higher than theocean level.

On 9-10 August, two sets of measurements were done (Fig. 2c). Theresults of the first set represented the flow rates over an entire tidal periodwhile the second set was collected over the time when the ocean level washigher than the bay level. The average seepage flux over the tidal period wasconsistently lower than that measured while the ocean level was higher thanthe bay, but the results did not show a strong modulation of the seepage bytidal conditions.

The high flow values very near the shoreline are evidence of a dischargeof groundwater from the freshwater lens under Fire Island. With the as-sumption that the flow decreases exponentially with distance from the shore(McBride & Pfannkuck 1975), a total discharge of about 20001/day/meterof shoreline was calculated from these data (Bokuniewicz & Zeitlin 1980).Upward leakage from the Magothy is unimportant; the hydraulic head inthe Magothy under Fire Island is estimated to be 3.3 m (Doriski 1986) whichwould drive a flow of less than 0.1 I/day-m2. As we will discuss later however,some of the measured flux could be due to seepage of saline groundwateraffected by local sea level differences.

Methods

A standard resistivity survey was done to examine the distribution of freshand saline groundwater under the island and measurements were made ofthe difference in water level between the bay and the ocean. In addition,shallow temporary wells were used to measure the elevation of the watertable. These usually consisted of plastic tubes screened at the bottom andsunk to a depth just below the water table. The elevations were determinedto local mean bay level using a rod and level from a datum established at atide gage on the site. The estimated uncertainty in the relative elevations was

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2cm. In one case, a well was driven to directly measure the verticaldistribution of groundwater salinity.

Resistivity survey

Vertical electrical soundings were made between 30 April and 12 May 1988at nine stations using a Bison 2390 Signal Enhancement Earth ResistivitySystem. A Schlumberger electrode array was used with electrode spacingsbetween 0.5 and l00m arranged parallel to the shoreline. As recommendedby Mooney (1980), the current electrode spacings were progressivelyincreased by a factor of the square root of two to give good verticalresolution.

An additional check on the lateral homogeneity of the aquifer was madeby modifying the Schlumberger configuration to include a fifth electrode,commonly called the Lee electrode, at the center of the array. In addition tothe usual reading in which the potential drop between the two potentialelectrodes is recorded, two extra readings on the Lee electrode were takenfor each current electrode spacing. The potential drop between first the Leeelectrode and the left potential electrode and then between the Lee electrodeand the right potential electrode was recorded. The two sets of measure-ments were similar for seven of the nine stations indicating that the assump-tion of lateral homogeneity was valid. The measurement sets diverged at twostations indicating a lateral inhomogeneity which may have been caused bytopographic variation or cultural interference such as underground cables orburied metal objects. Measurements at these two stations were not used.

The interpretation of the resistivity data was done by computer assisted,interactive curve matching (Davis 1979; Ghosh 1971; Merrick 1977;Mooney 1980). Usually three layers were sought - an unsaturated zoneabove the water table, a zone of fresh groundwater and a transition zoneoverlying saline groundwater. Based on analyses of repeated surveys at onestation, the uncertainty in the interface depths was estimated to be + 0.1 m.

A four-layer model was used at one of the survey stations where a test wellwas also drilled. The well was a driven point screened at the bottom.Penetration was interrupted at sampling depths of 1.5, 3.0, 4.6, 5.5, 6.1, 7.6,9.1 and 10.7 meters and samples were withdrawn with a flexible impellerpump. The hoses were primed with distilled water and at least one well-volume, including the hose volume, was flushed out before a sample wastaken. Salinities were measured with a refractometer to 0.5 parts perthousand.

A four-layer model was also used at a station at the toe of the dune. Theinterpretation at this station was unreliable, however, apparently because of

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Fig. 3. Arrangement of hoses for measuring sea level differences between the bay and theocean.

the presence of local, shallow layers of high resistivity (peat?); data from thisstation were not used in the following interpretation.

Sea level measurements

The difference in elevation between the bay and the ocean was measured byrunning a hose from both the bay and the ocean to the center of the island(Fig. 3). These were attached to the bottoms of vertical transparent tubesabout 2 m long. The top ends of the tubes were fitted to a common vacuum.The hoses were then completely filled with water and a vacuum was appliedto the common connection at the tops of the transparent tubes until thewater levels from both the bay and the ocean were visible in their respectivetubes. This technique has been used to study wave set-up (Nielsen 1988). Itwas similar to that described by Lee & Cherry (1978) and Lee & Hynes(1978) in their study of hydraulic head distributions in lakes and rivers,although the system used at Barrett Beach was on a larger scale. Valveswithin the hoses allowed the cross-section to be reduced in order to dampenhigh frequency oscillations in the water level due to the passage of waves.The difference in water level between the bay and the ocean could then bedirectly measured by comparing the levels between the two tubes.

Results

Subsurface measurement

The salinity of the groundwater in a test well near the bay shore is shownin Fig. 4. Fresh water was encountered at a depth of 1.2 m below the surfaceor 0.3 m above the bay level. The groundwater salinity increased to 32 parts

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SALINITY (parts per thousand) STATION

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 R5

E

--

I

-

0

U.

N

3-

DRY

FW

TZ

SW

Fig. 4. Salinity as a function of depth in a test well (see Fig. 5 for the location of the well). Thecolumn to the right shows the thickness of the dry, freshwater (FW), transition zone (TZ) andsaline groundwater (SW) as interpreted from the electrical resistivity survey at this site.

per thousand over the next 6.4 m to a depth of 6.1 m. Groundwater with asalinity of 32 parts per thousand was found to the bottom of the well, 10.7 mbelow the surface. Groundwater at the water table was also sampled at sixlocations across the ocean beach. The salinity ranged from 25 parts perthousand to 33 parts per thousand. The freshwater lens does not extendunder the beach probably because salt is contributed to the groundwatereither by tides, waves or sea spray.

The resistivity data is listed in the Appendix and the results are shown inFig. 5. The resistivity of the first layer, or unsaturated zone, ranged from43.6ohm-meters to 10,000ohm-meters. The low resistivities of the un-saturated zone in some places are probably caused by a combination ofpartial saturation and salt infiltration. The second layer, which wouldrepresent the freshwater lens, had a resistivity ranging from 85.0 to 304 ohm-meters, and thickness between 1.05 and 4.84m. The third layer in thetransition zone had resistivities ranging from 7.33 to 80.1 ohm-meters, andthe resistivity in the saltwater-saturated layer ranged from 0.585 to 2.1 ohm-meters. These values are reasonable; typical values for freshwater-saturatedsand, for example, are between 48 and 150 ohm-meters although highervalues are possible. For sand saturated with brackish water, typical valuesare between 5.0 and 80 ohm-meters, and for sand saturated with saltwater,between 0.1 and 60 ohm-meters (Jones & Skibitzke 1956). The great range

I

269

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CEAN

(UNSATURATED)

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SALTWATER)

LOCATIONS

Fig. 5. Interpreted cross-section of the distribution of fresh and saline groundwater under FireIsland with comparisons to predictions of the Ghyben-Herzberg relation and the modifica-tions proposed by Keller & Frischknecht (1966) and Vacher (1988a).

of resistivities found in the transitional zone is most likely due to the factthat the transitional zone contains water of different salinities. What theinstrument senses as the boundary between the fresh and transitional zonesor the transitional and saltwater zones depends on the thickness and resistiv-ity of the unsaturated zone, among other things, because an overburden ofextremely high resistivity, as is present in most of the study area, canpartially mask the effects of subsurface layers (Flathe 1955).

A four-layer analysis done at the site of the test well yielded a dryoverburden 1.23 m thick having a resistivity of 3700 ohm-meters. A secondlayer, representing the freshwater lens was found to be 1.05 m thick with aresistivity of 97.1 ohm-meters. The transitional zone, taken as a single unit,was found to be 6.43 m thick with a resistivity of 7.33 ohm-meters. Theresistivity of the saltwater layer was 0.6 ohm-meters. This independentinterpretation was in good agreement with the direct measurements ofsalinity in the well (Fig. 4).

On the beach, the resistivity of the unsaturated zone increased away fromthe ocean. It was 43.6ohm-meters nearest the ocean, and progressivelyincreased to 89.9ohm-meters, 1032ohm-meters, and 3161ohm-meters. Asimilar trend was seen on the bay beach. The unsaturated zone resistivitynearest the bay was 3147 ohm-meters, and ranged between 3703 and10,000ohm-meters inland. The resistivity of the unsaturated zone in thecenter of the island seemed anomalously low at 1010 ohm-meters. Possiblefactors affecting the cross-island distribution of unsaturated sediment resis-tivity included variations in salt infiltration, grain-size and composition ofthe aquifer or the effect of buried telephone cables which were known to bein the vicinity of the station.

The measured water table elevation ranged from 0.2m above mean bay

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100

80E2 60o

40To

20

O0Eo -20C-

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-80

-Irfn

10 12 14 16 18 20 22 24 2

Time, hours

Fig. 6. Measured relative water levels between the bay and ocean across Barrett Beach.

level to 0.54 m above mean bay level. The greatest elevation was found underthe dune crest. The greatest thickness of the freshwater lens was 4.84 beneaththe dune crest. Here, the freshwater lens had a resistivity of 122 ohm-meters.There was no freshwater lens at either the ocean beach or the bay beach.

Water levels

The measured relative water levels in the bay and the ocean, and theobserved differences in elevation are shown in Fig. 6. The measured differen-ces in the water level between the bay and the ocean showed a clear andsmooth tidal variation even though the first few measurements containedsome uncertainty which is most likely due to the formation of bubbles in thehoses. Bubbles may have formed because of leaks or initial temperatureequilibration but did not seem to be a problem after 2 hours when the systemwas tightly sealed and well flushed. From the measured tidal elevations inthe bay, and the difference in elevation between the bay and the ocean, thetide in the ocean was calculated to be 1.07 m while a range of 1.02 m waspredicted from the tide tables. The phase of the calculated oceanic tide wasabout 14.5 ° (30 min) in advance of the predicted tide. The inflection point onthe calculated oceanic tidal curve, which corresponds to local mean sea levelwas about 0.11 m above local mean water level in the bay. The bay levelreached a maximum elevation of 0.69 m above the ocean level about one

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hour after the calculated low tide in the ocean. It reached a minimum levelof 0.46m below the ocean level about 45 minutes before high tide in theocean.

Discussion

The freshwater lens was asymmetrical with the maximum thickness occur-ring beneath the dune crest. North of the dune, toward the bay, the lensbecame thinner, and the interface depth remained between one and twometers until the lens pinched out within about 12m of the shore. Theinterface depth was less than that predicted by Keller and Frischknecht(1966; Fig. 5). The calculation is sensitive to the elevation of the water tableover a long-term average sea level position. The deviation from the expectedvalue could be due in part to the relatively large percentage errors associatedwith determining the elevation of the water table and in part to the departureof local sea level from the relevant average value over the residence time ofwater in the lens.

The formulation based on the amount of recharge (Eq. 2) is not dependenton the measurement of the water table elevation and avoids the complica-tions due to sea level variations. The maximum lens thickness of 4.84 metersis intermediate between the values predicted from Eq. (2) with 50%evapotranspiration and that without evapotranspiration (3.90 and 5.54meters, respectively). The measured lens thickness implies a net annualrecharge of 0.85 m/yr, or a mean annual evapotranspiration of 0.27 m/yr or24%.

The lens was calculated to contain 184 cubic meters of fresh water permeter length of shoreline (assuming 50% porosity). This corresponds to aresidence time of 316 days for freshwater in the lens, or typical flow speedsof about 0.4 m/day.

The transition zone

Near the bay the transitional zone reached a thickness of 5.4 meters. Thetransitional zone becomes less than one meter thick toward the center of theisland where the tidally enhanced mixing should be diminished. It thickensagain near the ocean shore reaching a maximum thickness of 9.65 meters.If the transitional zone were considered to be comprised of all water of asalinity intermediate between fresh water and water of ocean salinity, thetransitional zone on the ocean side would span the entire beach. On the bayside, where the tidal range is less, the transitional zone would be less than12 meters wide under the beach.

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The maximum thickness of the lens to the midpoint of the transition zonewas about 7.5m. This was less than predicted by the Ghyben-Herzbergrelation (Fig. 5). The overprediction implies that the lens was not in equi-librium with the present bay levels but would be in equilibrium with a sealevel 0.20 to 0.40 m higher than measured. Wave setup is capable of produc-ing such an increase in elevation over the longer term.

If the porosity of the aquifer is assumed to be 50%, the transition zonecontains 463 cubic meters of water per meter length of shoreline or about230 cubic meters each of freshwater and saltwater per meter of shoreline.The freshwater would require 395 days of recharge to be replaced and, sincethe commingled waters are flowing seaward together, we might reasonablyassume that the seawater has the same residence time in the transition zone.Flow speeds in the transition zone would be comparable to those in thefreshwater lens. Recirculating seawater may account for between 30 and40% of the total seepage of groundwater across the sea floor.

Water level differences between the bay and the ocean and implications forthe flow of saline groundwater

On the day of the measurements the mean water level in the bay was 0.11 mhigher than mean sea level. This difference was due to a combination ofmechanisms:

1. The water temperature was the same in both hoses but the bay salinitywas 29.5% while the ocean water salinity was 34.0%. The watercolumns in the hoses and the tubes were held by the vacuum at anelevation of about 7.5m so the difference in salinity alone would ac-count for a difference in the measured water levels of about 0.03 m withthe bay side being higher than the ocean side of the device. The differ-ence in salinity between the bay water and the ocean could explain 27%of the observed difference in mean water levels.

2. As mentioned earlier, a numerical hydrodynamic model of the bay hasbeen used to determine that the increase in the bay level due to Stokestransport should be approximately 0.031m and the freshwater inputshould account for an aditional 0.019 m exclusive of changes due to thedifference in salinity and temperature between the bay waters and theocean. These two mechanisms therefore might explain 45% of theobserved difference.

3. Tilting of the bay surface by the local winds was probably negligible.The winds during the study period blew approximately along the long

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axis of the bay from the west or southwest at speeds of about 4.4 m sec-'(8.7 knots). Under these conditions the difference in water level betweenthe two ends of the fetch would be less than 0.03 m (U.S. Army Corpsof Engineers, 1977) and at Barrett Beach, which is about midway alongthe fetch, the water level should be near the mean bay level being tiltedhigher to the east and lower to the west.

4. Set-down of the ocean surface due to the longshore component of thiswind cannot be ignored. Longer-term water level records which includethe study period are not available to quantify this effect. The magnitudeof the change, however, may be estimated empirically from regionalwind data collected at Kennedy Airport, 64 km to the west of the studyarea, and the relationships described by Wong & Wilson (1984). Fromthe wind records the longshore component of the wind stress wascalculated using a drag coefficient of 10- 3 (Wong & Wilson 1984). Thesubtidal changes in water level corresponded to the longshore windstress in a roughly linear manner over the range of interest at a rate ofabout 0.40m/dyne-cm - 2. With these approximations, mean sea levelshould have been falling at a rate of about 0.005 m/hr during theexperiment. Bay level is assumed to fall at the same rate but to lagbehind the ocean levels by 8 hours (Wong & Wilson 1984). The differ-ence between the ocean and the bay, therefore, due to this mechanismwas estimated to be about 0.05m with the non-tidal bay level beinghigher throughout the period. This mechanism can explain about 45%of the observed difference in mean water level between the bay and theocean. An examination of the records presented by Wong & Wilson(1984) for December 1984 showed that the longshore winds couldproduce subtidal differences in elevation between the bay and the oceanranging from a bay level 0.23 m above the ocean level to 0.11 m belowocean level.

5. At the ocean shore, there may be a displacement of mean sea level dueto wave set-up. The measurements reported here were purposely madewhen wave heights were small, about 0.3 m, to facilitate the installationof the equipment. The water level difference was measured with respectto mean sea level in the ocean regardless of wave conditions, but thesetup at the time of the measurements was estimated to be 0.05 m.

The conditions under which the measurements were made may not neces-sarily be typical. Nevertheless, the elevation difference was substantial andcould reasonably be explained in principle. Such a sea level difference acrossthe island could drive a flow of saline groundwater that does not depend on

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the freshwater hydraulic head. For this case, the flow would be from the bayto the ocean under the freshwater lens. In the absence of more detailedinformation, only a very rough estimate of the rate of flow can be made. Theconduit for the transport between the freshwater lens and the GardinersClay was about 24 m thick and 225 m long. The discharge rate would be 7001of water per m length of shoreline per day.

Setup due to waves or transient subtidal water level motions would reduceor reverse these conditions. The average wave height here is about 0.6 m, forexample, so a setup of 0.1 and 0.2 m might be expected on the average andregularly exceeded. It appears that such a change has the potential forsubstantially influencing seepage measurements with a flow of salinegroundwater.

Conclusions

The seepage of groundwater across the sea floor not only includes thatcontributed from the freshwater aquifer but also recirculated sea water aswell as a flow of saline groundwater depending upon the water level con-ditions.

The dimensions of the freshwater lens could be explained as a function offreshwater recharge and hydraulic conductivity. Under Fire Island, thefreshwater lens had a maximum thickness of 4.84m. The lens was out ofequilibrium with the bay level at the time, but sea level variations arerelatively large and the lens might be expected to be in equilibrium with anaverage sea level over the residence time of water in the lens or about 10months. Where the lens is small, or very near the shoreline, the contributionof sea water to the seepage may be substantial. This island's freshwater lensextended to within 12m of the bay shore and to within 30 m of the swashlimit at high tide on the ocean shore. The lack of freshwater under the beachis probably due to seawater infiltration by tides, waves and spray. Tidalmixing at the base of the freshwater lens produces a transition zone up to9.65 m thick under the island. Seawater being recirculated in this zone mayaccount for as much as 40% of the seepage along the shoreline of FireIsland.

In restricted bays there are several mechanisms for maintaining unequalsea levels between the bay and the ocean which may drive a flow of salinegroundwater independent of the freshwater hydraulic head. The long-termexchange under Fire Island depends on the prevailing wind conditions butthe rate of saline groundwater seepage through the barrier may be compar-able to the discharge of freshwater across the sea floor.

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Acknowledgements

We greatly appreciate the cooperation of the National Parks Service, theU.S. Geological Survey and the Town of Islip. This project was supportedin part by grants from the East Hampton Beach Preservation Society, Dr.Harry H. Carter, Sigma Xi, and the New York Community Trust.

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