Composition and flux of groundwater from a California beach aquifer: Implications for nutrient supply to the surf zone

The coastal, unconﬁned aquifer at Huntington Beach, California contains saline groundwater (33 psu) adjacent to the water line, and a brackish groundwater (BGW) mixing zone (3–9 psu) approximately 50 m from the water line. According to salinity and water isotope analyses, the BGW composition varies spatially in the alongshore direction. Measurements obtained from two BGW wells indicate this water is a mixture of seawater and a freshwater end member (likely inﬁltrated runoff); results from a third more southerly well suggest the BGW is composed of seawater, freshwater, and water from the conﬁned Talbert Aquifer. Saline groundwater, on the other hand, shares similar salinity and water isotopic composition with seawater. The saline groundwater is enriched with short- and long-lived radium isotopes relative to the surf zone, which in turn is enriched relative to waters further offshore. We derive eddy diffusion coefﬁcients for the nearshore using 223 Ra and 224 Ra, and in conjunction with 226 Ra activities, estimate a submarine groundwater discharge (SGD) rate between 4.2 and 8.9 L min (cid:1) 1 m (cid:1) 1 of shoreline, respectively. Using analytical models, we estimate that between 74 and 100% of this discharge represents seawater than has been forced by tides and waves through the beach aquifer. Under one set of model assumptions, results indicate that a portion (up to 56%) of seawater pumped into the beach aquifer by waves and tides is not discharged suggesting salt water intrusion may be occurring. Because saline groundwater is enriched with dissolved inorganic nitrogen and soluble reactive phosphate relative to the coastal ocean, our results suggest that tidally and wave-driven seawater circulated through the beach aquifer represents an important mechanism for nutrient input to the nearshore environment in dry weather. Estimates of nutrient ﬂux to the coastal ocean via SGD along 16–17 km of shoreline are equivalent to nutrient ﬂuxes from two salt water wetlands near the study site during the dry season. 2005 rights


Introduction
Over the last two decades, researchers have come to recognize that submarine groundwater discharge (SGD, defined as the combined mixture of freshwater and recirculated seawater discharging to the www.elsevier.com/locate/csr

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0278-4343/$ -see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10. 1016/j.csr.2005.11.008 ocean from a coastal aquifer) can be a significant contributor of nutrients and freshwater to the coastal environment under certain conditions (Johannes, 1980;Valiela et al., 1990;Krest et al., 2000;Paytan et al., 2006;Shellenbarger et al., in review). Locally, groundwater inputs to the coastal zone can have major effects on geochemical cycles either through the discharge of fresh groundwater or the recirculation of seawater through shoreline aquifers (Buddemeier, 1996;Moore, 1997Moore, , 1999. SGD is now recognized as a potentially important pathway for pollution migration to the nearshore, particularly where agricultural or urban activities have impacted the groundwater (Cable et al., 1996;Corbett et al., 1999, Kelley andMoran, 2002;Boehm et al., 2004). Because 37% of the world's population lives within 100 km of the coastal zone (Cohen et al., 1997), understanding the increasing effects of the ever-growing human population on the coastal environment is critical to development of sound management principles. Moore (1999) characterizes the subsurface landward of the land-sea interface as a subterranean estuary where water is exchanged between the sea and aquifers. Tidal pumping of seawater through the beach aquifer causes constant inflow to and outflow from the beach aquifer (Nielson, 1990). Wave pumping also contributes to infiltration and discharge over shorter time scales than the tides (Longuet-Higgens, 1983). Terrestrial flows resulting from aquifer recharge, as well as seasonal exchange of saline groundwater and dispersive entrainment of saline groundwater along the freshwater-saltwater interface in the beach aquifer also drive exchange (Michael et al., 2005). The result of these processes is constant mixing and exchange of groundwaters of both terrestrial and marine origin, along with the interaction of these waters with aquifer substrate (rocks, sand, or sediment) (Church, 1996). In this study, we use the term SGD to describe groundwater of both terrestrial and marine origins.
The four naturally occurring radium isotopes, which vary in half-life (3.7 days to 1600 years), are useful as tracers of SGD and have also been used to study groundwater input and mixing processes on a wide range of time scales (Elsinger and Moore, 1983;Moore, 1997;Yang et al., 2002;Charette et al., 2001;Krest and Harvey, 2003). The divalent cation radium isotopes are bound to soil particles and rocks in low ionic strength water. They readily desorb via ion exchange in the presence of solutions of high ionic strength (e.g., Elsinger and Moore, 1983;Webster et al., 1994;Yang et al., 2002). In coastal aquifers where seawater with high ionic strength mixes and interacts with freshwater and aquifer rocks, respectively, high radium waters can result. On the other hand, open ocean seawater has relatively low radium activities. Therefore, excess radium in the coastal ocean (over the offshore seawater activities) suggests a coastal source that in many cases is the unconfined surficial aquifer (Moore, 1996(Moore, , 2003Moore et al., 2002).
In a previous study (Boehm et al., 2004), we used short-lived radium isotopes 223 Ra and 224 Ra as tracers of SGD at Huntington Beach, California ( Fig. 1) and investigated the correlation of SGD with microbial pollution in the surf zone. However, the study did not demonstrate to what extent the water in the coastal unconfined aquifer and SGD was composed of tidally and wave-pumped re-circulated seawater, meteoric water, water originating in a confined aquifer, or seawater pumped via other forcing mechanisms (Michael et al., 2005). Fig. 2 illustrates a conceptual model of the rockwater interactions in the subsurface of the field site, illustrating the potential contributions to SGD and beach groundwater. In the current study, we introduce new measurements of 226 Ra (half-life of 1600 yr) and isotopic ratios of hydrogen and oxygen from coastal waters and groundwater. The purposes of this study are to (1) explore the origin of the groundwater within the unconfined beach aquifer ARTICLE IN PRESS Fig. 1. Map of the field site. Background is from the USGS seamless database. TA is the location of the Talbert Aquifer well sample, TM is the mouth of the Talbert Marsh, SAR is the mouth of the Santa Ana River, stations 7 through 11 are sampling sites. Stations 9 and 10 represent the primary study area. and SGD, (2) determine the groundwater discharge rates to the coastal ocean using cross-shore eddy diffusivity coefficients derived from short-lived radium isotope activities (to compare to previous results obtained by a mass balance box model), and (3) apply the models of wave-driven groundwater circulation of Longuet-Higgens (1983) and tidally pumped groundwater circulation of Nielson (1990) to the study site to determine the proportions of SGD that result from wave and tidal pumping of seawater, and the proportion that is due to discharge of others waters (e.g., meteoric, water leaking from the confined aquifer, or seawater discharged under other forces).

Field sampling: surf zone
Four 3-day sampling excursions were conducted during the summer of 2003 during two neap tides and two spring tides. Two low tides and two high tides were sampled for a total of four sampling events during the majority of the sampling excursions. During each event, seawater was collected from the near surface of the surf zone in ankle and waist deep water adjacent to lifeguard stations 9 (33138.327 N, 117158.577 W) and 10 (33138.416 N, 117158.725 W) (Figs. 1 and 2). In addition, during each low tide, a groundwater sample was obtained from the unconfined aquifer by pumping from a shallow well (o1 m deep) in the intertidal zone, far enough from the swash zone so that no surface water contaminated the well. We also obtained (1) surface seawater samples from approximately 182, 608, and 1350 m offshore of station 9 during a neap and spring tide at low tide in conjunction with nearshore and groundwater sampling and (2) groundwater from shallow wells (o1 m deep) in the intertidal zone and seawater from the near surface of the surf zone at knee depth at stations 7, 8, and 11 (Figs. 1 and 2) during low tide under spring and neap tide conditions. All seawater samples were collected from a vertically well-mixed water column based on previous characterization of stratification in the nearshore .

Field sampling: other locations
To characterize other potential local water sources to the surf zone, we collected samples during spring and neap tidal conditions at the mouths of the Santa Ana River and Talbert Marsh when the tide was ebbing as well as groundwater from the Talbert Aquifer (TA in Fig. 1), a confined aquifer managed by the Orange County Water District (OCWD). The aquifer sample was collected from a well (#M31, OCWD) screened between 25 and 50 m deep, located 1000 m inland from our study site.
Samples from the mixing zone in the unconfined aquifer (located approximately 50 m from the mean low water line) were collected using screened PVC well-points. These were installed using a hand auger at stations 8, 9, and 10 (Figs. 1 and 2). Screens were positioned within the top 1 m of the aquifer, which was located approximately 3 m below the surface of the sand. A total of four groundwater samples were pumped from each well during two low tides and two high tides starting 12 h after well-point installation. Prior to sample collection, wells were purged for 5 min.
We obtained a sample of fresh groundwater (salinityo1 psu) from the surficial aquifer at station 9 during August 2005. Although not collected contemporaneously with the rest of the water samples, the fresh groundwater sample potentially represents a fresh end member in the surficial aquifer. The sample was obtained in the same manner as water from the mixing zone using a PVC well point installed approximately 60 m from the mean low water line. The single fresh groundwater sample was processed only for d 18 O for inclusion in a mixing diagram. Salinity was measured using a conductivity/temperature probe (YSI 30,Yellowsprings,OH). The limitations of including this sample in our analysis are discussed in the Results section.

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All samples obtained during these studies (unless otherwise stated) were analyzed for 226 Ra activities and salinity as described below. A subset of the samples were analyzed for water isotopic composition. 223 Ra and 224 Ra activities as well as nutrient concentrations (nitrate, ammonium, and soluble reactive phosphate (SRP)) for these samples were reported by Boehm et al. (2004).

Water analyses: radium isotopes
95, 76, and 38 L of water were collected for seawater, brackish groundwater (BGW), and saline groundwater (SGW) samples, respectively. Water was passed over manganese-impregnated acrylic fibers at a flow rate p1.5 L min À1 in the field immediately after collection (Moore, 1976). Plugs of untreated acrylic fiber were placed in the column to reduce the deposit of sediment and plankton from the sample on the impregnated acrylic fibers. 226 Ra activity was quantified using a Rad7 (Durridge Co. Inc., Bedford, MA) following the method described by Kim et al. (2001). This method provides quantification of 218 Po, the daughter of 222 Rn (a 226 Ra daughter). Fibers were moistened with MilliQ water to obtain constant recoil efficiency for radon, placed into air tight glass tubes, flushed with helium, and incubated for approximately three weeks to allow ingrowth of 222 Rn and secular equilibrium to be achieved. Measurement precision estimated by multiple analyses of several gravimetrically prepared samples was within 10%.
2.4. Water analyses: dD and d 18 O of water 30 mL of 0.2 mm filtered water were sub-sampled from the large volume samples, immediately stored on ice, and then frozen. Water samples for analysis of hydrogen isotopic composition were prepared using zinc reduction (Kendall and Coplen, 1985). Water samples for analysis of oxygen isotopic composition were prepared by equilibration with CO 2 at 25 1C (Epstein and Mayeda, 1953). Values are reported per mille (%) relative to Vienna Standard Mean Ocean Water (VSMOW). Precisions of dD and d 18 O are better than 71.0 and 0.05 %, respectively.

Water analyses: salinity
To obtain an accurate and precise estimate of salinity, 10 mL of water were sub-sampled from the large volume samples, filtered through a 0.2 mm filter, and stored at 4 1C for densiometric analysis (Anton-Paar model DMA 4500, Graz, Austria). Densities were converted to salinities with the UNESCO Equation of State (IES 80) (http://fermi.jhuapl.edu/denscalc.html). The precision of our salinity measurements are within 0.01 psu.

Sand analysis: hydraulic conductivity and porosity
The hydraulic conductivity of unconsolidated sand collected from the unconfined aquifer at the field site was assessed using a bench top combination permeameter (SOILTEST, Ele International, model K-605A, Pelham, Alabama). Because none of the sediment passed through a number 200 sieve, a constant head test was performed as per the manufacturer's directions. Two separate sand samples were tested using a range of configurations. A total of seven estimates was obtained, averaged, and compared to estimates obtained in situ within 1 km of the field site using aquifer pumping tests (Theis, Neuman and Distance-Drawdown methods, Komex H 2 O Science, 2000). The comparison with in situ estimates was necessary because it is well understood that removing sand from an aquifer can change its hydraulic conductivity. The porosity was estimated by measuring the volume of water needed to fill the pore spaces in a predetermined volume of sand.

Modeling: mixing coefficient and seepage rate
The seepage rate of groundwater from the coast was calculated using the offshore gradient of 226 Ra and eddy diffusivity coefficients K inferred from the exponential decrease of 223 Ra and 224 Ra with distance from shore following Moore (2003). In brief, the slope (m) of the line describing the decline of ln 223 Ra or ln 224 Ra with distance in the offshore direction (x) can be used to estimate K as follows: where l is the tracer's decay constant (0.061 and 0.19 day À1 for 223 Ra and 224 Ra, respectively). K is then used to estimate the flux F of 226 Ra from ARTICLE IN PRESS the shoreline: where dB/dx is the offshore gradient of 226 Ra. It should be noted that this model assumes no alongshore gradient in groundwater discharge, no net offshore advection, and steady-state conditions.
2.8. Modeling: wave-driven and tidally driven SGD SGD, as calculated with 226 Ra gradients, is composed of fresh and saline groundwater discharge to the coastal ocean. The outflow portion of tide-and wave-pumped seawater circulation is included in SGD, although these do not contribute to net discharge over longer time scales that may occur as a result of aquifer recharge (Li et al., 1999). Thus, total SGD (D) can be expressed as where D t and D w represent outflow from tidal-and wave-driven circulation of seawater through the beach aquifer, respectively, and D m represents all other contributors to SGD including meteoric waters (resulting from aquifer recharge) and seasonally discharged seawater as described by Michael et al. (2005).
The outflow seepage rate driven by waves per unit alongshore distance, D w , can be expressed as follows (Li et al., 1999): where K h is the hydraulic conductivity of beach sand, S w is the slope of the wave setup, and L is the surf zone width defined as the distance between the breaker line and the wave runup line. S w and L can be calculated from the local oceanographic and geologic conditions: and where H b is the breaker height, s b is the beach slope, and s is the breaking index where T w is the wave period and g corresponds to gravitational acceleration.
The tidally driven groundwater outflow seepage rate per alongshore distance (D t ) can be estimated as follows (Li et al., 1999): In the above equations, A corresponds to the tidal amplitude, T t the tidal period, o the tidal frequency, n e the effective porosity of the beach sand, and H the aquifer thickness.
Input parameters required for application of these models to our study site are given in Table 1. The slope of the beach was reported previously by Boehm (2003). The magnitude of the M 2 tidal harmonic is used for A as is its period (12.42 h) and frequency. According to the Huntington Beach Lifeguard records, breaking wave heights were on average 1 m (David Pryor, California State Parks, person. comm., 2004) during the study. Although records are not kept for wave period, we use 15 s as this is typical for the field site (personal observation). The effective porosity and hydraulic conductivity of the sand were measured in the lab with aquifer material, as described earlier. Komex H 2 O Science (2000) reports six measurements of K h for the unconfined aquifer within 1 km of the field site ranging from 3 Â 10 À5 to 7.4 Â 10 À4 m s À1 . The geometric mean of the Table 1 Parameters used for calculation of D w and D t

Parameter (units)
Value K h is the geometric mean of field observations. estimates is K h ¼ 1.5 Â 10 À4 m s À1 . The field measurements were determined with aquifer pumping tests using Theis, Neuman and Distance-Drawdown methods. Because hydraulic conductivity estimates span at least an order of magnitude, we present a sensitivity analysis for K h , incorporating the possible range of values expected based on lab and field analyses. H is estimated in the same report by Komex H 2 O Science for the unconfined aquifer 1000 m inland as 30.5 m. This agrees with subsurface mapping of the field site completed by the California Department of Water Resources (1966).

Results and discussion
3.1. 226 Ra distribution overview Fig. 3 shows the spatial distribution of 226 Ra activities integrated over alongshore space and time at the field site. The error bars (and errors mentioned in the rest of the paper) represent the 90% confidence intervals given the whole range of tidal variability of 226 Ra at each site and not the analytical error. Intertidal wells contained saline groundwater (hereafter referred to as SGW) (average salinity ¼ 33.2 psu) that had significantly (po0.1) higher 226 Ra (average of 12.071.3 dpm/ 100 L, n ¼ 12) compared to the surf zone samples (average of ankle and waist depth water 8.570.4 (n ¼ 29) and 8.770.3 (n ¼ 29) dpm/100 L, respectively). The average salinity of surf zone samples was 33.1 PSU. Samples collected offshore of the surf zone had lower activities relative to the surf zone samples (7.870.7 dpm/100 L at 182 m, 7.670.7 dpm/100 L at 608 m, and 8.470.9 dpm/ 100 L at 1350 m, n ¼ 2 for each average); the average salinity of all offshore samples was 33.2 psu. Although the differences between offshore and surf zone 226 Ra activities are not significant when all samples are pooled across the entire month of sampling over various tidal conditions, synoptic measurements during the offshore transects illustrate that there were notable trends of decreasing radium activities with increasing distance from shore (Fig. 4, bottom panel). Interestingly, samples collected at 1350 m offshore showed higher activities than the two offshore samples at 182 and 608 m. This could be explained by the offshore water being of different origin than the nearshore water, perhaps advected from another location. Other possibilities are that it is influenced by a seep or another aquifer discharging radium-rich groundwater offshore, or it is impacted by a potentially radium-rich anthropogenic waste stream released in the vicinity of the field site (thermal and wastewater outfalls shown in Fig. 1-note that radium activities have not been measured in these waste streams).
Groundwater collected from wells in the mixing zone (hereafter referred to as BGW) ranged in salinity from 3.1 to 9.5 psu, and activities of 226 Ra were significantly (po0.1) lower (4.771.0 dpm/ 100 L, n ¼ 12) than those measured in the SGW from the intertidal zone. These low activities are not surprising given the low salinities that would suppress radium desorption from sediment/soils within the aquifer (Webster et al., 1994). 226 Ra activities of Talbert Marsh and Santa Ana River ebb flow (salinities undistinguishable from surf zone salinities) were not significantly different from the activities measured in the surf zone  average). The two ebb flow samples for each site were obtained during neap and spring tidal conditions. Each time when these sites were sampled, there was at least one surf zone sample that exceeded or was within measurement error of the activities of both ebb flows supporting the conclusion that the ebb flow from these sources was not enriched with radium relative to the surf zone at the time of our study.
The confined Talbert Aquifer (salinity of 16.3 psu) had a 226 Ra activity of 944 dpm/100 L, much higher than other 226 Ra activities recorded at the field site. The elevated salinity of this water is a result of saltwater intrusion offshore of the field site where the confined aquifer intersects the ocean floor; the precise location where this occurs is not known (T. Sovich, OCWD, personal communication, 2005). As suggested by our conceptual model (Fig. 2), it is conceivable that water from the Talbert Aquifer leaks into the unconfined aquifer through breaches in the aquitard. A previous investigation of the subsurface at the field site suggests that such breaches exist and in some instances, the confined and unconfined aquifers are in direct hydraulic communication (California Department of Water Resources, 1966). We should point out that it is unknown whether water in the Talbert Aquifer directly below or near our sampling sites has a similar radium activity or salinity as the water collected at well M31.
There was not an obvious alongshore gradient in 226 Ra activities in the surf zone, SGW, or BGW based on our survey (data not shown). The observed cross-shore distribution of 226 Ra activities supports our previous results (Boehm et al., 2004) suggesting discharge of SGW from the unconfined surficial aquifer. An analysis of variance (Matlab, Natwick, MA) between 226 Ra activities in the surf zone and tide level (high or low) indicates that activities are significantly (po0.1) elevated during low tides compared to high tides (based on a Kruskal-Wallis non-parametric analysis of variance). This observation points to tidal pumping as an important mechanism for SGD. The reduced offshore gradient in 226 Ra activities compared to our previously reported 223 Ra and 224 Ra activities (Fig. 4) is not surprising since the time scale of mixing and transport in this region is short relative to the extremely long half-life of 226 Ra. In addition, the relatively low 226 Ra activities, relative to the short-lived isotopes, are likely due to the elemental composition source rock. Specifically, the regeneration rate of 226 Ra in the nearshore coastal aquifer where SGW interacts with uranium and thorium containing soil and rocks is slow; therefore, the standingstock of desorbable 226 Ra is small.

Groundwater composition
The activity ratios of the 223 Ra and 224 Ra to 226 Ra in the beach aquifer (1.9 and 39, respectively, Fig. 5) are different from the activity ratios in the Talbert Aquifer (0.18 and 2.0, respectively). If radium-enriched waters from Talbert Aquifer were the source of radium to the unconfined beach aquifer, then the ratios would be identical or the short lived isotopes would decay to some extent, effectively lowering the ratios. Since the ratios are higher in the beach aquifer compared to the Talbert Aquifer, the contribution of Talbert Aquifer groundwater to the beach aquifer is probably minimal overall, suggesting that if breaches exist, as shown in Fig. 2, they are small relative to other water inputs to the unconfined aquifer, or that radium adsorbs onto beach sediment, if experiencing a lower salinity regime, as leakage occurs.
We analyzed the hydrogen (dD) and oxygen (d 18 O) isotopic composition of a subset of representative water samples to further evaluate the vertical leakage of the Talbert Aquifer to the unconfined beach aquifer. Both BGW from the surficial aquifer and Talbert Aquifer waters fall on a local meteoric line (Yurtsever and Gat, 1981) but have distinct dD and d 18 O values (Fig. 6A). dD and d 18 O of SGW, on the other hand, cluster close to the seawater values (labeled surf zone and offshore) indicating a significant contribution of seawater. A plot of d 18 O versus salinity (Fig. 6B) shows that BGW samples collected from the unconfined aquifer at stations 9 and 10 fall on a mixing line (line 1) between the offshore seawater end member and the lowest salinity BGW sample (collected at station 9). This line has been extended to a hypothetical 0 salinity end member (which was not sampled during the summer of 2003). The isotopic composition of water collected from the mixing zone at station 8, falls on a mixing line (line 2) between the Talbert Aquifer and the hypothetical 0 salinity end-member obtained by extending mixing line 1 to 0 psu salinity. This suggests that BGW collected at station 8 may be composed of nearly 50% Talbert Aquifer water. No samples analyzed fell on the mixing line between the Talbert Aquifer and the seawater end member (line 3). However, it should be pointed out that we did not conduct water isotope analyses on any other samples from station 8.
The fresh groundwater sample collected from station 9 during August of 2005 is shown as a square in Fig. 6B (salinity of 0.1 psu, d 18 O of À6.06%). The sample lays directly at the intersection of mixing lines 1 and 2. If this fresh groundwater sample is representative of fresh groundwater present in the beach aquifer during the summer of 2003 when the rest of the samples were collected, its position on the diagram supports the mixing discussions above. However, there is no way to be certain that the fresh groundwater end member collected in 2005 is the same as one that was present in 2003. This freshwater end-member is likely infiltrated runoff or precipitation.
These results suggest that there is spatial heterogeneity in the composition of waters in the mixing zone of the unconfined aquifer. At stations 9 and 10, waters in the mixing zone (BGW) are composed of seawater and a freshwater end member; the Talbert Aquifer contributes negligibly. At station 8, the BGW may contain a more significant contribution of Talbert Aquifer origin (up to 50%). The results suggest that there may be vertical leakage of the Talbert Aquifer to the unconfined near station 8. Vertical leakage could occur through a breach in the aquitard, or alternatively, the aquifers could be in direct hydraulic connection in this area (T. Sovich and J. Dadakis, OCWD, personal communication, 2005). Interestingly, the 226 Ra activities in BGW from station 8 were not significantly higher than those of BGW collected at other stations, despite the fact that the water isotope data suggests it contains Talbert Aquifer water. This could be because 226 Ra re-adsorbs to particle surfaces as it moves from the higher salinity Talbert Aquifer to the lower salinity BGW.

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It should be noted that our interpretation of the water isotope data assumes that Talbert Aquifer discharge to the unconfined aquifer has the same salinity and water isotopic composition as Talbert Aquifer at well M31 (approximately 400 m inland, 900 m south-east from the study site). It is possible that the salinity and water isotopic composition spatially vary in Talbert Aquifer in the cross-shore direction as it mixes with seawater (T. Sovich, OCWD, personal communication, 2005), suggesting that the true salinity and isotopic composition of discharge could fall on any value along the mixing line between the Talbert Aquifer and seawater in Fig. 6B (line 3). If the salinity of Talbert Aquifer discharge to the unconfined aquifer near station 8 were much higher than 16 psu, then the BGW at station 8 could no longer be explained as a mixture of the Talbert Aquifer and hypothetical fresh groundwater end members. The presence of another freshwater end-member with lower d 18 O would need to be identified to explain the chemistry of BGW at station 8.  (Boehm et al., 2004). Given that cross-shore advection accompanies upwelling events, the assumption required to derive Eqs. (1) and (2) that cross-shore advection is minimal was violated. Thus, transect 1 was not used to derive mixing coefficients. Transect 2 (open and closed circles) was sampled during a low, spring tide under typical oceanic conditions. The decline in 223 Ra and 224 Ra follows the Moore (2003) model well within 608 m of the shoreline (Pearson's r ¼ À0.99 and À0.96, respectively). The farthest offshore sample at 1350 km had higher radium activities than would be expected due to cross-shore mixing at the rate described by the nearshore decline in radium activities with distance. Moore (2003) also observed a discontinuity in the decline of short-lived radium isotope activities with distance Each sample is labeled with the location from which it was collected. Numbers refer to the sampling site where brackish groundwater samples were collected; sz(h,n) and sz(l,s) refer to samples collected from the surf zone during high, neap and low, spring tidal conditions, respectively; offshore is the sample collected at the most offshore location during Transect 2; SGW is saline groundwater.

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offshore of the Florida coast and attributed it to different mixing rates in the nearshore relative to offshore. It should be noted that Moore looked at much larger scales than we have examined here (on the order of 10 km offshore). The relatively high offshore activities could be due to an additional source of radium (e.g., discharge from a confined aquifer, a submarine seep, or anthropogenic waste stream) or advection of high radium waters from another location.
To estimate cross-shore eddy diffusivities and the rate of SGD, we use only the activities measured during transect 2, within 1 km of the shoreline, as these are consistent with the model used to derive Eqs. (1) and (2). Using Eq (1), the eddy diffusivity coefficients estimated from 223 Ra and 224 Ra activities are K ¼ 0.12 and 0.26 m 2 s À1 , respectively. According to Okubo (1974), K increases as length scale to the 4 3 -power in marine systems. According to the 4 3 law, at a length scale of 1000 m, K may range from 0.1 to 1 m 2 s À1 . Approximately 45 km to the south of the field site in the coastal waters off San Onofre, List et al. (1990) measured K between 2 and 10 m 2 s À1 . The K values reported here are within the order of magnitude of the values predicted by the 4 3 law, but smaller than those reported by List et al. (1990). K surely varies with time at many scales in response to meteorological and oceanographic forcing, thus this estimate should be viewed as an approximation only.
The cross-shore 226 Ra gradient (À6.9 Â 10 À6 dpm L À1 m À1 , Pearson's r ¼ À0.96), obtained from a least-squares curve fit of activities measured in transect 2 within 1 km of the shoreline, is shown in Fig. 4 (bottom panel). Applying Eq. (2), the product of the gradient and K estimated from 223 Ra and 224 Ra yields a 226 Ra cross-shore flux of 0.0504 and 0.107 dpm m À2 min À1 , respectively. The area over which this flux occurs is the vertical cross section of the coastal ocean parallel to shore at the most offshore location (608 m), which in our case is approximately 2814 m 2 (assuming 10 m depth 608 m from shore, and an alongshore distance of 281.4 m, bathymetry in Boehm et al., 2002). Thus, the crossshore flux of 226 Ra is estimated at 142 (using 223 Ra K) or 300 (using 224 Ra K) dpm min À1 . Using the average 226 Ra activity of SGW measured in the beach aquifer (12.0 dpm/100 L), this corresponds to a discharge rate per alongshore distance of 4.2 and 8.9 L min À1 m À1 (based on estimates of K from 223 Ra and 224 Ra, respectively). These estimates are within the range reported for the site pre-viously during low, spring tide conditions of 3.1-16 L min À1 m À1 using a box model (Boehm et al., 2004).
It should be noted that we have assumed that the 226 Ra activity of SGD to the nearshore during the offshore survey is adequately represented by the 226 Ra activity of SGW (12.0 dpm/100 L). That is, we have assumed that there is no other important input of groundwater with different 226 Ra activities within 608 m of the shore during the survey. This is justified based on the following observations: (1) Boehm et al. (2004) showed that samples collected in the surf zone fell in a mixing line between an offshore end member and SGW based on shortlived radium activities and salinity, suggesting the SGW is a major component of SGD; (2) SGW was observed seeping from the beach (subaerially during extreme low, spring tides) indicating that this water does discharge to the coastal ocean; (3) discharge rates calculated with 226 Ra activities from SGW closely match discharge rates obtained from an independent technique (Boehm et al., 2004); and (4) there are no documented groundwater seeps within 608 m of the shoreline (T. Sovich, OCWD, personal communication, 2005). Moore (2003), who originally presented the analysis used in the present work to estimate flux, used 226 Ra activities of water captured in a seepage meter at his field site in Florida to calculate the flux of groundwater. Deployment of seepage meters was unreasonable at our study site because of the high degree of wave activity. If there is significant discharge of groundwater along the cross-shore transect that has a variable 226 Ra activity relative to SGW, then our estimate for SGD rates could be an under-or overestimate. As will be discussed next, however, the discharge rates we calculated are not only in close agreement with those obtained using an independent method (Boehm et al., 2004) but also are close to what would be expected due to tidaland wave-driven pumping of seawater through the beach aquifer.

Model of tidally driven and wave-driven discharge
The models for tidally and wave-driven driven SGD were applied to the study site to determine the proportions of discharge attributable to the outflow portion of wave and tidal pumping of oceanic water and discharge of waters of other origins (e.g., meteoric waters). Based on Eqs. (3) and (7), and the parameters reported in Table 1 (using the mean in situ measurement of K h ), D w ¼ 3.4 and D t ¼ 3.2 L min À1 m À1 . The sum of these values exceeds the minimum total discharge estimate of 4.2 L min À1 m À1 by 2.4 L min À1 m À1 , and is lower than the maximum estimate of total discharge by 2.3 L min À1 m À1 . The laboratory measurements of K h indicated K h ¼ 4.7 Â 10 À4 72.7 Â 10 À5 m s À1 (n ¼ 7). Using this value for K h in lieu of the one obtained from field estimates, the wave and tide pumped discharge estimates are higher: D w ¼ 10.5 and D t ¼ 5.5 L min À1 m À1 . Both sets of D w and D t estimates with realistic K h predict the rate of SGD due to wave pumping exceeds that due to tidal pumping at this beach, although they are within the same order of magnitude. D w and D t estimates based on in situ measurements of K h at the field site are probably more accurate because removing sediment from an aquifer for laboratory analyses causes resorting and reorganization of the grains which in turn impact the hydraulic conductivity. Fig. 7 shows D w , D t , and their sum (D w +D t ) as a function of K h . K h is chosen for our sensitivity analysis because it has the most uncertainty associated with it, with estimates spanning at least an order of magnitude. The x-axis spans the range of K h relevant to the field site (from 3.3 Â 10 À5 to 7.4 Â 10 À4 m s À1 ). The range of estimates for total discharge (D) (4.2-8.9 L min À1 m À1 ) obtained using the estimates of eddy diffusivity and 226 Ra gradient is highlighted with light gray. The dark gray band shows the range of estimates for discharge of waters other than wave and tide-pumped seawater (D m ). The band was developed by using both the minimum and maximum D estimates, and assuming D m makes up the difference between D and D w +D t . When D w +D t exceeds D, D m is negative indicating that there is some inflow of water to the aquifer that effectively reduces the outflow discharge from the value it would be under the action of waves and tides. On the other hand, if D w +D t is less than D, D m is positive indicating that some component of discharge is not comprised of wave and tide pumped seawater.
If our low-end estimate for D (4.2 L min À1 m À1 ) is accurate, then negative D m is predicted for all relevant values of K h . On the other hand, if our high end estimate for D (8.9 L min À1 m À1 ) is correct, then D m is predicted to range from À14 to 4.5 L min À1 m À1 over the range of K h . Given that removal of sediment from an aquifer causes sorting and rearrangement of grains, it is probably more accurate to use the field measurements of K h in the models for D w and D t . Assuming K h is best approximated with the mean of the field measurements (1.5 Â 10 À4 m s À1 ), D m is predicted to be between 2.4 and À2.3 L min À1 m À1 when D is at the maximum (8.9 L min À1 m À1 ) and minimum (4.2 L min À1 m À1 ), respectively. This corresponds to 26% and À56% of D, respectively.
Assuming that D m contains water with low salinities relative to seawater (i.e., freshwater or water originating in Talbert Aquifer), the lack of salinity depression in the coastal ocean suggests that a very low percentage of SGD is not tidally and wave pumped seawater, supporting the low end estimates of D m that indicate there is salt water intrusion. On the other hand, if D m consists of water with salinity near that of seawater (i.e., seawater infiltrating and exfiltrating at a seasonal time scale as described by Michael et al., 2005), then the highend estimate for D m could be consistent with our salinity observations. 4. Implications for nutrient supply to the surf zone SGD seepage rates calculated using nearshore eddy diffusion coefficients and 226 Ra gradients are Fig. 7. Discharge due to tides (D t ), waves (D w ), their sum (D t +D w ), and maximum discharge of other waters including meteoric water (D m , estimated from the difference between the sum of D t and D w and the total discharge at the field), as a function of K h . The light gray horizontal bar denotes the range of discharge calculated from the radium measurements. The x-axis spans the relevant range of K h at the field site based on laboratory and field measurements. within the rates previously estimated using an independent method (mass balance/box model) (Boehm et al., 2004). At our study site, SGW contains elevated levels of dissolved inorganic nitrogen (DIN, defined as the sum of nitrate and ammonium) and SRP relative to offshore waters with average concentrations of 11.5 and 0.49 mmol L À1 (compared to 1.00 and 0.05 mmol L À1 offshore), respectively (Boehm et al., 2004). Assuming that nutrient levels in SGW are representative of SGD and given a seepage rate of 7 L min À1 m À1 of shoreline (the average of our estimates), this implies a discharge of 116 mmol day À1 m À1 of shoreline DIN and 5 mmol day À1 m À1 of shoreline SRP. Taking into account that waters offshore contain an order of magnitude less of these nutrients than SGW, discharge induced by tides and waves could be an important source of nutrients to the coastal environment, especially during the dry season. This conclusion is supported by field work along the Gulf of Aqaba in Eilat, Israel (Shellenbarger et al., in review).

ARTICLE IN PRESS
The source of nutrients in SGW at the field site is not known. It is possible that dissolved nutrients are supplied by microbial re-mineralization of particulate matter that has infiltrated to the subsurface or regeneration from sediments. Also, elevated levels of DIN (average 343 mmol L À1 ) and SRP (average 1.2 mmol L À1 ) concentrations were measured in BGW from the mixing zone (Boehm et al., 2004), just meters from SGW (Fig. 2). We suspect nutrients in BGW emanate from nutrient-polluted (with fertilizer, sewage, and/or detergents) runoff from the surrounding watershed that has infiltrated the subsurface. Even small volumes of BGW mixed into nutrient-depleted SGW could raise nutrient levels over background seawater levels without necessarily causing an obvious salinity depression. Work continues at this field site to explore the origin of DIN via isotopic analysis and nutrient cycling in the subsurface (Santoro et al., in review).
Given that the stretch of open-ocean, sandy shoreline where the study site is located continues for over 20 km, the dry weather delivery of DIN and SRP via SGD is comparable, if not greater, than input of DIN and SRP from the tidal Talbert Marsh and Santa Ana River wetlands to the south-east during similar dry weather conditions. Previous studies documented average summer-time ebb flow rates from the Talbert Marsh of 8.37 m 3 s À1 (Grant et al., 2001) and Santa Ana River of 11.57 m 3 s À1 (Grant et al., 2002). Because these discharge a small amount of freshwater, and function as tidal wetlands, the discharge values are not expected to change dramatically year to year. Assuming that this flow rate is present during all ebb tides (approximately 12 h day À1 ), and assuming the DIN and SRP levels measured by us previously (Boehm et al., 2004) are representative of typical conditions (2.54 mmol L À1 DIN and 0.1 mmol L À1 SRP at the Talbert Marsh and 1.85 mmol L À1 DIN and 0.1 mmol L À1 SRP at the Santa Ana River), then these watershed outlets deliver to the coastal ocean, together, approximately 1890 mol DIN and 86 mol SRP per day. It should be pointed out that this represents a high-end estimate since the discharge is tidally modulated and is not constant throughout the ebb tides. In addition, some of the ebb flow is recirculated through the wetlands during the following flood tides. Our estimates indicate that DIN and SRP released by these wetlands during the dry season is equivalent to the amount delivered by SGD along 16 km (DIN) and 17 km (SRP) of shoreline. This estimate assumes no alongshore gradients in SGD and nutrient concentrations in SGD.

Conclusions
Based on data collected during the summer of 2003, SGD along the shoreline of Huntington Beach is primarily seawater that, under the force of tides and waves, is flushed through the surficial aquifer. We estimate that SGD could be composed of up to 26% water other than wave and tidally pumped seawater. However, our measurements did not identify a salinity depression in the surf zone that could be attributed to BGW discharge, indicating that BGW discharge was not traceable in the coastal ocean with our chemical tools. It is likely that during the wet season, when there is more infiltration of runoff to the unconfined aquifer, that a salinity depression would be observable, and BGW would compose more of the SDG.
Under a set of assumptions, the discharge estimated from radium isotopes is less than that estimated from models of wave and tidally pumped seawater through the aquifer. This result suggests that some of the seawater pumped by tides and waves into the aquifer is not discharged. The forcing mechanism for this influx could be seasonal recharge and evapotranspiration discussed by Michael et al. (2005).
The confined Talbert Aquifer does not appear to contribute significantly to radium (and thus other solutes) in the surficial unconfined beach aquifer at our main study site between stations 9 and 10, based on analyses of radium and isotopic composition of water. However, the water isotope data suggest that Talbert Aquifer communicates with the BGW in the unconfined aquifer at station 8 (to the south-east of our main study area). However, it does not appear to contribute radium. Communication between confined and unconfined aquifers may occur via breaches in the aquitard.