Horizontal mixing of Great Barrier Reef waters: Offshore diffusivity determined from radium isotope distribution

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2006jc003608, 2006 Horizontal mixing of Great Barrier Reef waters: Offshore diffusivity determined from radium isotope distribution Gary J. Hancock, 1 Ian. T. Webster, 1 and Thomas C. Stieglitz 2,3 Received 28 March 2006; revised 24 July 2006; accepted 1 September 2006; published 23 December [1] The Great Barrier Reef (GBR), northern Australia, is the largest coral reef system in the world and provides habitat for highly diverse tropical marine ecosystems. Mixing in the coastal waters of the GBR is an important parameter influencing the health of these ecosystems. We have used the distribution of the four naturally occurring radium isotopes to determine the rate of mixing of nearshore waters of the central part of the GBR lagoon with water from the Coral Sea. The observed radium distribution is modeled using a onedimensional diffusion model. The model improves on previous radium offshore mixing models by incorporating the benthic flux of radium diffusing across the sediment-water interface and offshore changes in water column depth. We find that the inner lagoon diffusivity (<20 km offshore) is best estimated using the short-lived isotopes 224 Ra and 223 Ra. The concordance of K x estimated using the two different isotopes and the apparent consistency between measured riverine inflows to the lagoon and inflows inferred from the modeled salinity distribution provide confidence in the results. The mean value of K x for the inner lagoon region of the southern central zone between latitudes 15.8 S and 19.0 S (265 ± 36 m 2 s 1 ) is more than twice that in the northern central zone (14.3 S to 15.8 S). This difference likely reflects the different reef matrix density in the two zones. The distribution of the longer-lived isotope 228 Ra indicates more rapid mixing in the middle and outer lagoon. These results indicate that central GBR water within 20 km of coast is flushed with outer lagoon water on a timescale of days, with the flushing time increasing northward. Citation: Hancock, G. J., I. T. Webster, and T. C. Stieglitz (2006), Horizontal mixing of Great Barrier Reef waters: Offshore diffusivity determined from radium isotope distribution, J. Geophys. Res., 111,, doi: /2006jc Introduction [2] Increasing attention in marine science is being focused on the seaward fluxes of terrestrially derived particles and solutes and their effects on marine ecosystems. In the Great Barrier Reef (GBR) region, there is concern that land-use changes over the last century have altered the sediment and nutrient status of ecosystems that were previously in balance. Specifically, it has been estimated that sediment delivery to the GBR lagoon has increased substantially since European settlement due to increased erosion rates in the GBR catchments resulting from clearing of forested slopes for grazing and cultivation [Neil et al., 2002; Furnas, 2003]. The increased delivery of fine sediments, along with particle-bound and dissolved loads of nutrients and other contaminants has lead to the identification of various water quality issues in the GBR lagoon [Hutchins et al., 2005]. Higher contaminant loads have 1 CSIRO Land and Water, Canberra, ACT, Australia. 2 School of Mathematical and Physical Sciences, James Cook University, Townsville, Queensland, Australia. 3 Also at Australian Institute of Marine Science, Townsville, Queensland, Australia. Published in 2006 by the American Geophysical Union. been linked to reductions in coral growth and a shift in the relative abundance and composition of coral species [van Woesik et al., 1999; Fabricius et al., 2003]. [3] One of the most important parameters required by scientists and managers aiming to predict and control the effects of terrestrially derived particles and solutes on the health of coastal ecosystems is the rate at which these contaminants are mixed with ocean water and transported offshore. Solutes and fine particles entering coastal waters from the land are diluted with an efficiency that depends on the driving physical processes, as well as on the degree of restriction of exchange with other water bodies. The use of hydrodynamic modeling to predict contaminant transport near the coast and through coral reefs is problematical due to the complex spatial variability of the coastal shoreline, the reef bathymetry, and the dynamic nature of driving forces such as tides, wind and large-scale oceanic currents. Direct measurement of solute dilution and transport using chemical tracers has the potential to overcome some of these problems. In particular, the distribution of naturallyoccurring radium isotopes with half-lives ranging from 4 days to 1620 years have the ability to provide the time constants required for mixing, transport and residence time estimation in nearshore environments [Moore, 2000, 2003; Charette et al., 2001; Kelly and Moran, 2002]. 1of14

2 Figure 1. Sample sites in the central GBR lagoon. The dashed line at latitude 16.5 S represents the latitude where the outer reef matrix density changes. The section north of latitude 15.8 S (transect RP) comprises transects traversed in April 2003, including Barrow Point (BP), Cape Flattery (CF), and Cape Bedford (CB). The section south of latitude 15.8 S (April 2004) comprises transects at Cape Grafton (CG), Cooper Point (CP), Bingil Bay (BB), and Halifax Bay (HB). The Rattlesnake Point (RP) transect at 15.8 S was traversed on both cruises Study Site [4] The GBR is the largest coral reef ecosystem on earth, and spans the continental shelf of the tropical North Queensland coast of Australia for 2000 km in an approximately northwest-southeast direction (Figure 1, inset). Although the term lagoon is used to describe the zone between the coast and the outer shelf coral reefs the GBR lagoon is in fact a partially enclosed water body and is connected to the Coral Sea via passages between the reefs. The lagoon contains inshore reefs fringing the coast and islands, midshelf submerged reefs, and outer shelf barrier reefs. The nearshore areas also host a large variety of other marine habitats such as mangroves and seagrass beds. The South Equatorial Current impinges on the outer section of the reef and bifurcates, with one branch flowing northward and the other southward as the East Australian Current (EAC) [Burrage et al., 1994]. Water from the Coral Sea penetrates into the lagoon through the reef gaps and contributes to water renewal on the shelf [Wolanski, 1994]. Although the EAC is dominantly a slope current, a portion of it appears to be associated with southward water motion within the reef matrix. A more detailed discussion on the complex nature of water movement in the GBR lagoon is provided by P. V. Ridd et al. (unpublished manuscript, 2006). [5] The section of the GBR lagoon investigated in this study covers a 550 km length of reef from latitudes 14.3 S to 18.6 S representing the central third of the latitudinal expansion of the GBR lagoon. The inner lagoon is characterized by the presence of a zone about km wide adjacent to the coast which is fairly clear of islands and reefs. Farther offshore runs a string of coral reefs that are separated by relatively deep channels that connect to the deeper waters past the shelf edge. North of latitude 16.5 S (dashed line, Figure 1) the reef matrix on the outer shelf is relatively dense in comparison to the lagoon farther south. Few deep channels exist in this region. [6] Despite the importance of solute transport to the ecology of the GBR zone, or perhaps due to the complex nature of water movement in the lagoon, there are few quantitative estimates describing water transport across the GBR. The work presented in this paper seeks to improve on current knowledge by determining the large-scale diffusivity for the central zone of the GBR lagoon. In conjunction with P. V. Ridd et al. (unpublished manuscript, 2006) these are the first detailed estimates of GBR cross-shelf mixing rates based on experimental observations Radium Isotopes as Tracers [7] Four radium isotopes occur in nature. All are radioactive with wide-ranging half-lives: 224 Ra (t 1/2 = 3.7 days), 223 Ra (t 1/2 = 11.4 days), 228 Ra (t 1/2 = 5.8 years), 226 Ra (t 1/2 = 1620 years). In freshwater, Ra is tightly bound to the sediment grains, but in seawater, Ra attached to the surface of sediment grains is desorbed by ion exchange with dissolved cations. Thus the delivery of terrigenous sediment to estuaries and coastal waters leads to nonconservative increases in dissolved Ra activities in these areas. Also, because Ra is continually produced in sediments by the decay of insoluble thorium (Th) parents terrigenous sediments deposited along the coastal fringe provide a continuous source of Ra to nearshore marine waters [Moore, 1992; Rama and Moore, 1996; Hancock and Murray, 1996]. The sources of nearshore Ra include Ra desorbed from suspended riverine sediment, Ra desorbed from bottom sediments, and Ra advected into coastal waters by groundwater discharge. The importance of each of these sources depends on the physical, chemical and biological processes operating in the coastal zone [Moore, 1992]. [8] The release of Ra by coastal sediments generates a seaward flux of Ra as coastal water is mixed with low-ra water from the open ocean. Because dissolved Ra in seawater is essentially unsupported by its Th parents the 2of14

3 [12] We model the Ra distribution using the onedimensional advection-diffusion equation [Fischer et þ H @x K þ la ¼ H 1 B; ð1þ Figure 2. A schematic showing features of the diffusivity model. Black arrows represent Ra flux terms; F 0 and F e denote the Ra flux at the coast and the shelf edge; B denotes the Ra benthic flux; H is water depth. concentration (activity) of each Ra isotope is determined primarily by its rate of decay (its half-life) and by the transport processes of advection and mixing. Knowledge of the isotope decay time constants in conjunction with measurements of the offshore distribution of the four isotopes allows the estimation of the rate of offshore mixing [Moore, 2000, 2003]. [9] In this paper we use Ra isotopes to determine mixing rates for seawater in the central GBR. Moore [2000, 2003] used Ra isotopes to determine mixing rates in the South Atlantic Bight and the Gulf of Mexico. This study expands on Moore s approach by including the introduction of Ra into the water column through a diffusive bottom (benthic) flux across the lagoon, and by allowing for variation in the water column depth. These parameters were not required in the South Atlantic Bight and were not considered important in the Gulf of Mexico due to the low-activity quartz-rich nature of the bottom sediments and the relatively low water depth gradient across the gulf. For coastal waters that have a comparatively steep offshore depth gradient and which overlie fine-grained sediments rich in clay minerals we show that benthic flux and variable water column depth are two parameters that are required to correctly estimate mixing rates. 2. Theory [10] The factors controlling offshore distribution of dissolved Ra in the water column are shown schematically in Figure 2. In modeling the Ra distribution we assume that dissolved Ra in the GBR zone has three major sources: (1) an input at the shore which includes river inputs, nearshore groundwater discharge and Ra flushed from intertidal sediments and mangrove forests; (2) a diffusive benthic flux emanating from bottom sediment across the shelf; and (3) the open ocean. In reality the ocean is only a significant source for the long-lived isotopes 226 Ra and 228 Ra. [11] We also assume that all parameters are uniform in the longshore direction; that is, within each of the two study sections the overall characteristics of the reef lagoon such as its width and reef density are approximately uniform. The third assumption of our model is that the water column is well mixed vertically on a timescale short compared to the half-life of the shortest-lived isotope, 224 Ra; i.e., a few hours. This assumption is supported by CTD, 224 Ra and 222 Rn measurements, which all show little or no variation through the water column. where A is radium activity (in effect the concentration), t is time, x is offshore distance (perpendicular to the coast), u is offshore advection velocity, H is water depth, K x is the offshore coefficient of solute diffusivity, l is the isotope decay rate (given by ln 2/t 1/2 ), and B is the Ra benthic flux. The variation of H and B with x is determined from measurements and laboratory experiments. [13] To solve equation (1), we take u = 0; that is, we assume that diffusive-like processes dominate offshore transport and that offshore advection is negligible. Later, we consider the possible effects of offshore advection introduced by riverine input at the coast and by evaporation and precipitation over the shelf. We further assume eddy diffusivity to be a function of x in the governing equation and look for the steady state solution; that =0. With these assumptions, equation K þ lha ¼ [14] To solve equation (2) between the coast and the outer edge of the GBR lagoon requires equations describing H and B and two boundary conditions. For the two short-lived isotopes, 223 Ra and 224 Ra, one boundary condition sets the flux of Ra activity across the coastline to be F 0. The other boundary condition sets the flux at the outer limit of the lagoon near the shelf edge (F e ) to be zero; ¼ 0 x ¼ x e: ð3þ [15] Integration of equation (2) with respect to x yields K x xe x¼0 Z xe x¼0 ðb lhaþdx: ð4þ [16] The left-hand side of equation (4) is just F 0 F e, but since F e = 0 at the offshore boundary, then F 0 ¼ Z xe x¼0 ðlha BÞdx: ð5þ [17] The integral on the right-hand side of equation (5) is evaluated for each isotope using the measurements of radium activities and the functions used to describe the benthic flux and water depth. The eddy diffusivity is estimated by varying the form and magnitude of K x until we obtain optimal agreement between measured and modeled Ra activities across the shelf. [18] Isotopes 226 Ra and 228 Ra have half lives that are sufficiently long (1620 years and 5.8 years) that on the timescales of mixing across the GBR lagoon (weeks to months, see discussion in section 5.6) the decrease in Ra 3of14

4 activity by radioactive decay in the water column is negligible. Thus equation (2) K ¼ B: [19] In effect, the divergence in the offshore flux of activity equals the benthic flux. The condition of zero offshore flux at the outer edge of the reef is no longer valid as the flux there is equal to the flux across the coast augmented by the benthic flux. For 226 Ra and 228 Ra we will assume that K x is known from the 223 Ra and 224 Ra analysis, and we will treat the coastal flux (F 0 ) and the outer reef activity (A e ) as the parameters to be determined by fitting the model to the measurements. 3. Methods 3.1. Sample Collection [20] Depth profiles of salinity and temperature were recorded using a conductivity-temperature-depth (CTD) profiler (Seabird SBE19). Surface water samples were collected for Ra analysis along nine transects. Sampling distance from shore varied from 0.5 to 60 km. Transects BP, CF, CB, RP were sampled during a 7-day period spanning the end of March to early April 2003 (Figure 1). Transects RP, GI, CG, CP, BB, HB were sampled over a similar time frame in March April Both sampling periods occurred during the spring phase of the spring-neap tidal cycle, i.e., during the maximum tidal excursions. The dominant wind direction during both sampling periods was southeasterly, 20 knots, and was typical for April. Two additional water samples were collected in the Coral Sea in late 2005 at about km offshore in water more than 1000 m deep. [21] Water samples for Ra were pumped from about 2 m depth through a 10-inch cartridge filter (CUNO Micro Wynd; nominal pore size 0.5 mm). The volumes of samples collected for short-lived isotope analysis varied between 20 L and 200 L depending on the expected Ra activity; that is, greater volumes were required farther offshore. Dissolved Ra was extracted from the filtered seawater by gravity feeding the water through a plastic tube containing MnO 2 -coated acrylic fiber (Mn fiber [Moore, 1976]) at a flow rate of less than 0.5 L min 1 The efficiency of Ra adsorption was tested using two columns of Mn fiber in series and measuring the breakthrough of Ra into the second column. The adsorption efficiency of the first column was found to be >98%. At some sites, 1000 L of filtered seawater was pumped through a MnO 2 impregnated cartridge (CUNO Micro Kleen II) at a flow rate of L min 1. The adsorption efficiency of Ra by this method was also tested using two cartridges in series and found to be 90 95%. [22] A frame-mounted Smith-MacIntyre grab sampler was used to collect bottom sediments. The sampler retrieved sediment to a depth of 20 cm, retaining the integrity of the sediment profile. The top 2 cm of the sediment was collected for analysis. A total of eight sediment pore water samples were obtained by squeezing wet sediment (0 2 cm) through a fine woven cloth and filtering the water extruded. The samples were filtered within 2 3 hours of collection Sample Analysis [23] Activities of the short-lived radium isotopes, 223 Ra and 224 Ra, were measured in the shipboard laboratory shortly after sample collection. The Mn fibers were partially dried and placed in a closed-loop air circulation system connected to photomultiplier tubes. The nuclides were detected by the a decay of their respective daughter nuclides, 219 Rn and 220 Rn, and identified with a delayed coincidence circuit [Moore and Arnold, 1996]. The respective daughters were flushed from the fiber into the tubes where counters discriminate the decay of the 224 Ra daughters ( 220 Rn and 216 Po) from the 223 Ra daughters ( 219 Rn and 215 Po) by electronically gating the registered counts with high detection efficiencies. The efficiency of the system was calibrated using fibers containing a known amount of 232 Th (for 224 Ra) and 227 Ac (for 223 Ra) in secular equilibrium with its decay products. [24] Activities of the long-lived radium isotopes, 226 Ra and 228 Ra, were determined either by alpha spectrometry after leaching the radium from the Mn fiber with dilute HCl or by gamma spectrometry after ashing the fiber or cartridge to a powder. For alpha spectrometry, radiochemical separation using coprecipitation and ion exchange techniques was used to purify the Ra which was finally electroplated onto a stainless steel disc [Hancock and Martin, 1991]. A tracer isotope ( 225 Ra in equilibrium with its 229 Th parent) was added at the beginning of the leaching process to measure the overall efficiency of the process. The 226 Ra activity was determined from its direct a decay lines at 4.60 and 4.78 MeV. The 228 Ra activity was determined via its 228 Th and 224 Ra daughters in the zone MeV after an ingrowth period of 6 12 months. Alternatively, 226 Ra and 228 Ra were determined using gamma spectrometry [Murray et al., 1987] on the MnO residue after ashing the fiber and cartridges at 450 C. [25] Sediment samples were dried in an oven to determine porosity and then homogenized by grinding in a ring mill. The samples were then analyzed by gamma spectrometry ( 226 Ra, 228 Ra, 228 Th) as described above. A subsample was digested in acid (HNO 3, HF, and HClO 4 ) and analyzed for Th isotopes ( 232 Th, 230 Th, 228 Th) using alpha particle spectrometry following radiochemical separation [Martin and Hancock, 2004]. [26] Desorption experiments [Webster et al., 1995] were carried out to determine the amount of sediment-bound Ra available for ion exchange between sediment and pore water, a parameter required for benthic flux estimation. Duplicate amounts of wet sediment, equivalent to 20 g dry weight, were equilibrated for 2 hours with 1 L of seawater. One duplicate was spiked with a known activity of 223 Ra. The activity of the 223 Ra spike was such that it dwarfed the natural 223 Ra activity. After equilibration, the solution was centrifuged, the supernatant filtered through a 0.45-mm filter membrane, and the 223 Ra activity of the filtrate measured by a spectrometry. The fraction of 223 Ra tracer adsorbed by the sediment was determined from its loss from solution. This fraction was used in combination with the filtrate activities of all isotopes in the unspiked duplicate 4of14

5 Table 1. Radionuclide Activities of Bottom Sediment and Parameters Used to Model Ra Benthic Flux a Transect Site Distance Offshore, km f Q f 232 Th North CB ± ± ± ± ± 0.6 BP ± ± ± ± ± 0.3 CF ± ± ± ± ± 0.3 BP ± ± ± ± ± 0.2 BP ± ± ± ± ± 0.2 RP ± ± ± ± ± 0.2 South RP ± ± ± ± ± 0.4 CP ± ± ± ± ± 0.6 RP ± ± ± ± ± 0.4 RP ± ± ± ± ± 0.4 HB ± ± ± ± ± 0.2 CG ± ± ± ± ± 0.2 CP ± ± ± ± ± 0.3 CG ± ± ± ± ± 0.2 CP ± ± ± ± ± 0.1 BB ± ± ± ± ± 0.2 a Bottom sediment activities are in units of Bq kg 1 dry weight; f is fraction of sediment-bound Ra available for ion exchange; Q is desorption function; f is porosity. The uncertainties in radionuclide activities correspond to ±1 SE. 228 Ra 228 Th 230 Th 226 Ra to determine their total ion exchangeable (adsorbed + dissolved) activities Benthic Flux Estimation [27] We define the Ra benthic flux as the rate of diffusion of dissolved Ra ions from bottom sediment pore water into the overlying water column. This is estimated using the procedures and methods described by Hancock et al. [2000] whereby the distribution of ion exchangeable Ra in the sediment column is modeled using a one-dimensional transport equation. The benthic flux (B) of Ra across the sediment-water interface is derived from equations (17) and (18) of Hancock et al. [2000], which, when sedimentation is assumed to be negligible, reduces to rffiffiffiffiffiffiffiffiffiffiffi D s lf B ¼ g c w Qg Q l ð1 fþ ; ð7þ where g is the rate of production of ion exchangeable Ra in bottom sediment, f is the sediment porosity, D s is the effective diffusion coefficient for Ra in bottom sediment pore water, l is the Ra decay constant, c w is the water column activity, and Q is a volume-based ratio measuring the fraction of exchangeable Ra which has desorbed from bottom sediment into surrounding pore water. The value of Q is determined from Q = c p /c e where c p is the pore water Ra activity and c e is the total ion exchangeable activity of Ra per unit volume of wet sediment [Webster et al., 1994; Hancock et al., 2000]. Both c p and c e have units of Bq m 3. [28] The diffusivity of dissolved Ra in sediment (D s )is lower than its molecular diffusivity in seawater (D 0 = m 2 d 1 [Li and Gregory, 1974]) and is estimated by dividing D 0 by the tortuosity squared. The tortuosity was estimated from the porosity using [Boudreau, 1996] q 2 1 2lnðfÞ: [29] The values of g and c e are estimated using the methods described by Hancock et al. [2000]. Briefly, the ð8þ production rate (g) of exchangeable 223 Ra and 224 Ra is estimated from g ¼ lc e 1 f with the values of c e for 223 Ra and 224 Ra being estimated using desorption experiments carried out 60 days after sample collection, i.e., after a period of more than five halflives of 223 Ra and 224 Ra had elapsed at which time production-decay equilibrium had been established. The production rate of exchangeable 226 Ra and 228 Ra is estimated by determining the amount of Ra that is easily desorbed (ion exchanged) from the sediment; i.e., g ¼ fa Th lr; ð9þ ð10þ where f is the fraction of Ra available for desorption from the sediment, a Th is the total Th activity of the sediment, and r is the sediment dry density. The term f is <1, and reflects the fact that not all parent isotopes bound to the sediment produce ion exchangeable Ra; some parents are located within the sediment grains in internal lattice sites and their Ra progeny are not always available for desorption into pore water. We estimate f using the 232 Th- 228 Ra pair rather than 230 Th- 226 Ra as was used by Hancock et al. [2000] and Rama and Moore [1996], as it is possible that 230 Th has been added to offshore sediment from ocean water. We estimate f from one minus the 228 Ra/ 232 Th activity ratio of the bottom sediment, and its values range from 0.48 for fine-grained sediment near the coast to 0.26 for coarse grained sediment in the GBR lagoon. Table 1 lists the Ra and Th activities of GBR sediment and the parameters required for benthic flux estimation. 4. Results 4.1. Model Application [30] Because of differences in bathymetry and reef density between the northern transects (2003 cruise) and 5of14

6 H = 49.1(1 e 0.051x ) for the southern zone data and H = 40.3(1 e 0.110x ) for the north, where units of depth are meters and units of offshore distance are kilometers Benthic Flux Across Lagoon [33] In describing the relationship between benthic flux and distance offshore we consider the distribution of fine-grained terrigenous sediment as represented by the 232 Th activity of the sediment. Fine-grained sediment of terrigenous origin is usually enriched in 232 Th series radionuclides compared to quartz and carbonate-rich marine sediments. In fact, virtually all 232 Th in marine sediment is of terrigenous origin. A plot of 232 Th and distance offshore is shown in Figure 4. In this plot we have included measurements of sediment samples collected from many different transects in both northern and southern zones. Figure 4 shows a nearshore zone 8 10 km wide where the highest 232 Th activities are seen and where the activity of the sediment is approximately constant. These results correspond to the findings of numerous studies [Orpin and Woolfe, 1999; Woolfe et al., 2000; Brunskill et al., 2002] which conclude that the nearshore zone to the 20 m isobath (10 km offshore) is the region where most of the fine-grained terrigenous sediment is deposited. Figure 4 shows that 232 Th activity of sediment declines farther offshore. Figure 3. Plots of water depth and distance offshore for the northern and southern transects. the southern transects (2004 cruise), and to minimize the effects of possible differences in weather conditions in 2003 and 2004 that may have affected mixing, we have separated the Ra data into southern and northern zones. Grouping the data in this way allows the examination of broad-scale differences in diffusivity. The Rattlesnake Point transect (RP) was collected during both the 2003 and 2004 cruises, and so one RP transect is included in both the northern and southern analyses. At latitude 15.8 S, RP represents the southernmost of the northern transects, and the northernmost of the southern transects, and so can be considered a common boundary between the two zones. In terms of bathymetry and reef structure, the RP transect represents a transition zone between the northern and southern zones, and although it is included in both data sets, the RP data do not significantly influence model fitting in either case. [31] To apply the model described in section 2, we determine two functions representing the offshore variation of water column depth (H) and benthic flux (B) Water Depths Across Lagoon [32] A plot of water column depth and offshore distance (Figure 3) shows that depth can be approximated by a saturating exponential function. The northern transects (2003 cruise) and southern transects (2004 cruise) are plotted separately and reflect the changing bathymetry of the GBR lagoon latitude. Northward the lagoon becomes narrower with a steeper nearshore gradient. We use the function Figure 4. Plots of (top) the 232 Th activity of sediment and (bottom) the calculated 224 Ra flux against distance offshore. The trend shown by the 224 Ra flux-distance relationship is typical of the other Ra isotopes. 6of14

7 Table 2. Parameters Describing the Benthic Flux Relationship With Distance Offshore Isotope B 0,Bqm 2 s 1 C,Bqm 2 s 1 b 224 Ra ± Ra ± Ra ± Ra ± [34] Not surprisingly the trend shown by the 224 Ra benthic flux (also shown in Figure 4) closely matches the trend of sediment-bound 232 Th, its great grandparent. Other Ra isotopes behave similarly to 224 Ra, although the absolute values of their fluxes vary considerably, the variations being due to the different half-lives (and hence regeneration rates) of the isotopes, and the variation in the sediment activity of the Th parents. We model the benthic flux as being constant up to 10 km offshore (B 0 ), and declining exponentially thereafter; i.e., B ¼ B 0 B ¼ Ce bx x < 10 km x 10 km where the parameters B 0, C, and b are determined using a squares fitting procedure to the data (solid line, Figure 4). The values of the parameters determined for each Ra isotope are listed in Table 2. the eddy diffusivity increases from zero at the coast to asymptote to K 0 farther offshore. The length scale for this increase is D. We develop solutions for a prescribed K x = K 0 by discretizing equation (2) [Roache, 1982] in massconserving form with a cell size of 500 m. The resulting discretized equation with its two boundary conditions was solved using Gaussian elimination [Lindzen and Kuo, 1969]. Optimal K x were estimated by minimizing in a least squares sense the difference between model simulation and measurements. For the first diffusivity formulation only a single parameter estimation was required, but the second formulation required that both K 0 and D be estimated simultaneously. [36] Table 3 presents the best estimates of K x for the southern measurements of the two short-lived isotopes. The plots of the best fits to the measurements are shown in Figure 5. The values of K 0 vary from 256 to 331 m 2 s 1, and the two values of D were 0.87 and 1.3 km. These values of D suggest that if K x does diminish near the shore the length scale of this variation is 1 2 km which is small compared to the shelf width. Also presented in Table 3 are the standard errors (d) for the best fits to the measurements. The standard errors of the fits for the one-parameter and two-parameter fits are similar to each other for each isotope with the two-parameter fit having a slightly smaller d. With 4.4. Determination of K x Using 223 Ra and 224 Ra [35] In remainder of section 4 we first present results for the short-lived isotopes ( 223 Ra and 224 Ra) and use them to estimate eddy diffusivities (K x ). The time frames for these estimates of K x correspond to the mean lifetime of the isotopes, 16.5 and 5.3 days for 223 Ra and 224 Ra (given by 1/l). These time frames span the spring-neap tidal cycle, averaging over the potentially variable currents associated with this cycle [Wolanski and Spagnol, 2000]. We then apply our estimate of K x determined using short-lived Ra isotopes to the 226 Ra and 228 Ra distributions and assess how well the modeled distribution fits the data. In determining K x we investigate two possible representations: (1) K x = K 0 and (2) K x = K 0 (1 exp ( x/d)). In both formulations, K 0 is constant. In the second formulation, Table 3. Results of the Least Squares Analysis for the Southern and Northern Diffusivities Using One-Parameter and Two- Parameter Fits Ra Isotope Number of Parameters K 0, m 2 s 1 D, km d, Bq m 3 Minimum Negative Log Likelihood Southern Northern Figure 5. Measurements of 224 Ra and 223 Ra (solid circles) in surface water of the southern zone. The lines show various model interpretations. 7of14

8 Figure 6. Plots of 228 Ra and 226 Ra in the northern and southern zones. See text for details of the enhanced diffusivity model output. The dotted line in the 226 Ra plot presents the Coral Sea activity (1.05 Bq m 3 ). more parameters than the one-parameter fit, the twoparameter fit would be expected to have a smaller d, but the question is whether the higher-order fit is really a better representation in the statistical sense considering the likely error in the measurements. Hilborn and Mangel [1997] outline techniques for undertaking such an analysis by estimating negative log likelihoods for the best fit for diffusivity. Using this analysis we show that the exponential fit to the variable diffusivity is not significantly better than a uniform diffusivity at the 5% confidence level (Appendix A). This result is not surprising considering the similarities between the cross-shelf profiles of radium activities determined using the uniform and exponential diffusivity functions (Figure 5). [37] For the one-parameter fit we also consider the probability that diffusivities derived from the two analyses using 223 Ra and 224 Ra are consistent with the same value of K 0 (hereafter termed K x ). This can be readily calculated from their joint probabilities (Appendix A) and is found to be 96% (Figure A1). This high value indicates that the two analyses have produced the same result for K x, and we therefore assume that the best estimate of K x is the average of the least squares fit for 223 Ra and 224 Ra (265 m 2 s 1 ). The uncertainty associated with this value (±1 SE, 67% confidence interval) is determined to be ±36 m 2 s 1. [38] The same approach has been applied to the 223 Ra and 224 Ra distribution of the northern zone. As for the southern zone, the calculated values of K x (K 0 ) for the one-parameter and two-parameter fits for both isotopes were virtually the same and including the extra parameter is not justified (Table 3). The fits for 223 Ra and 224 Ra were similar to one another being 96 and 112 m 2 s 1, respectively. There is a 35% probability that these represent the same value. The mean of the 223 Ra and 224 Ra determinations is 104 ± 6 m 2 s 1. The analysis presented in Appendix A shows this value is significantly lower than the diffusivity obtained for the southern zone (Figure A1) The 228 Ra and 226 Ra Distributions [39] Figure 6 shows the distributions of 226 Ra and 228 Ra. The distribution of 226 Ra in the northern zone is similar to the south, and is not shown. The activities of both isotopes decrease toward the outer shelf boundary approaching values measured in the Coral Sea, km offshore. The two Coral Sea samples gave a mean value of 226 Ra = 1.05 Bq m 3 and 228 Ra = 0.11 Bq m 3. The 226 Ra Coral Sea activity is represented by the horizontal dashed line in Figure 6, and the solid lines show the modeled 226 Ra and 228 Ra activity distribution calculated using the diffusivities determined from 224 Ra and 223 Ra data (one-parameter fit). The fitted parameters, namely the coastal fluxes (F 0 ) and the activities at outer lagoon edge (A e ) are presented in Table 4. [40] The model for both isotopes provides a reasonable fit for measurements less than 30 km offshore, but for 228 Ra in both the northern and southern zones the measurements suggest a different trend to the modeled activities in the outer lagoon. The measurements show that the 228 Ra activity in the southern zone declines across the shelf to a distance of 35 km and thereafter remains in the range 0 to 1Bqm 3 as the shelf boundary is approached. The decline predicted by the model is somewhat steeper; in fact, the model solution for 228 Ra would become negative for Table 4. Results of the Least Squares Analysis for 226 Ra and 228 Ra Isotope F 0,Bqm 1 s 1 A e,bqm 3 d,bqm 3 Southern Northern of14

9 middle and outer lagoon are mainly supported by benthic fluxes (see section 5). Figure 7. Salinities measured in the southern zone of the lagoon during 2004 and the model fit obtained using K x = 265 m 2 s 1. distances greater than 60 km which is physically impossible. For the northern zone, the model predicts negative 228 Ra activities at around 40 km. [41] Visual inspection suggests that the measured southern zone activities of 226 Ra also level out at about 35 km offshore at 1.1 Bq m 3 or so (Figure 6). However, the modeled activities of 226 Ra continue to decrease farther offshore in a similar fashion to 228 Ra, reaching values lower than the Coral Sea (<1 Bq m 3 ). To address these irregularities, we postulate that the values of K x determined using 223 Ra and 224 Ra are too low at offshore distances greater than 20 km, and that in the middle and outer lagoon the eddy diffusivity increases due to the increased complexity of flow within the reef matrix (see section 5). The dashed lines in Figure 6 show the effect of assuming K x is constant to 20 km offshore (the approximate width of the inner lagoon and the distance at which reef density starts to increase), and then increasing K x linearly to the edge of the outer lagoon reaching a value that is twice its value near the coast. Increasing the diffusivity in this way has the effect of causing the modeled activity to be greater than zero for 228 Ra, and greater than 1.05 for 226 Ra, and to decrease in a way which is qualitatively more similar to the measurements in the offshore half of the GBR lagoon. On the basis of our measurements of inner lagoon diffusivity, K x in the middle and outer lagoon varies from 265 to 530 m 2 s 1 in the south, and from 104 to 208 m 2 s 1 in the north. These upper limit values are indicative only as our Ra measurements do not permit precise estimates of diffusivities in the outer lagoon. In fact our scaling of K x in the outer lagoon so that its value is doubled at the outer edge of the lagoon is the minimum increase in K x required to produce positive modeled Ra activities. It is possible that K x is significantly higher than our lagoon edge values across much of the outer lagoon. Note also that increasing diffusivity in the outer lagoon has little effect on activities of 223 Ra and 224 Ra whose activities in the 5. Discussion 5.1. Effect on K x of Neglecting Advection Application of K x to the Offshore Salinity Distribution [42] Salinity measurements taken during the 2004 sampling period (southern transects) are shown in Figure 7. River discharge data for March 2004, the month immediately preceding sampling, showed above average freshwater input for the southern zone and yielded significantly decreased salinities near the coast. Here we test our value of K x, which was determined using Ra data and assuming advective flow is zero, by considering the salinity distribution arising from the effects of river discharge at the coast, cross-shelf evaporation and precipitation causing a net advective movement of water away from the coast. For this analysis we shall assume that the freshwater input (Q 0 ) is spread uniformly along the coast, although we recognize that most of it will occur as discrete river discharges. In addition to freshwater discharge, the water balance across the shelf is modified by evaporation and precipitation having rates of E and P. These rates are assumed to be uniform across the GBR Lagoon although it is certain that precipitation will be higher near the coast due to orographic effects. Thus the volume of water moving offshore at distance x will be Q = Q 0 + (P E)x and the water velocity associated with this transport will be: u ¼ Q H ¼ Q 0 þ ðe PÞx : ð11þ H [43] With an analysis similar to that employed for radium we estimate Q 0 from the measured salinity distribution. If salinity (S) is substituted for A, then equation (1) can be K x ¼ @x ð12þ [44] From Bureau of Meteorology climatic charts for the month of March we estimate E = 150 mm mo 1 and P = 500 mm mol 1. Equation (12) requires two boundary conditions: (1) the salt flux through the coast is zero and (2) the salinity at the offshore boundary is S e. For solution we vary Q 0 and S e to obtain an optimal least squares fit to the observed salinity. [45] Using K x = 265 m 2 s 1, we obtain the model fit shown in Figure 7 and a value of Q 0 = 4.7 ± 2.3 m 3 s 1 per kilometer of coast. This value of Q 0 agrees well with the freshwater input calculated from river discharge data for March 2004 for the southern zone (5.1 m 3 s 1 per kilometer). Solving for the cross-shelf distributions for 223 Ra and 224 Ra with u 6¼ 0, gives K x = 250 m 2 s 1 for 223 Ra and 270 m 2 s 1 for 224 Ra. Thus the inclusion of advection results in a reduction in K x of just 2% for the southern zone. For the northern zone, river discharges for the month of March 2003 were well below average. The calculated freshwater input from river discharge is 1.2 m 3 s 1 per 9of14

10 kilometer, a factor of 4 lower than the south, and indicates that advection due to freshwater input was likely to be even less significant in the northern zone Oceanic Inflow [46] Brinkman et al. [2001] have shown how oceanic inflow from the Coral Sea can penetrate into the GBR Lagoon and cause cross-shelf flows there. They suggest that the magnitude of this flow is 0.58 Sv spread over 500 km north and south of the separation point. In a water depth of 40 m, which is approximately the water depth of the offshore boundary of our model domain, such a transport would cause a current of 0.03 m s 1. A current of this size would significantly affect the cross-shelf radium distribution. However, Brinkman et al. also suggest that the majority of this transport would occur along the zone where the offshore reef matrix is relatively sparse. All our transects are to the north of Brinkman et al. s study zone where the reef matrix is relatively thick and so would be less subject to the effects of onshore advection. In any event, an onshore flow of this sort must necessarily turn to longshore transport with the likelihood of longshore variations in radium concentrations becoming important in the transport equation. An analysis which describes this behavior must be two-dimensional, which is beyond the scope of the analysis that we have undertaken One-Parameter and Two-Parameter Fits [47] The agreement between the one-parameter diffusivities estimated using 223 Ra and 224 Ra, together with the salinity modeling undertaken in section 5.1, suggest that the inner lagoon values of K x derived in this work are robust results. Further, the two-parameter results for the case where the diffusivities increase from zero away from the coast are also consistent with one another with length scales of diffusivity variation both being 1 2 km, even though the two-parameter fits are not superior to the one-parameter fits in a statistical sense. The two-parameter fits ought to provide a better fit to the data because their major assumption, that eddy diffusivity must decline to zero as the coast is approached, is realistic. In effect, if one presumes that eddy diffusivity is due to fluctuating flows then the condition that there be no flow through the coast implies that diffusivity must reduce to zero there. The onshoreoffshore component of the tidal volume flux must necessarily approach zero as the coast is approached, and so we might expect that diffusivity associated with tidal shear would also diminish to zero as x! 0[Ou et al., 2003]. [48] Webster [1990] estimated that the surface shoreward flow due to an onshore wind decelerates to zero over a distance of 25H from the land boundary in unstratified flow. Using a scale depth of H 10 m for the shelf in the study zone, one might expect that the proximity of land would not significantly decrease shear in a wind-driven flow closer inshore than several hundred meters. However, freshwater discharging from rivers significantly reduced salinities near the coast (Figure 7) and the resulting horizontal density gradients are likely to have altered the dynamics of flow there. Moore [2003] inferred reduced diffusivities in a 3-km-wide nearshore zone on the Florida coast which he attributed to freshwater discharge there. Although the assumption of uniform diffusivity must break down as the coast is approached at some distance, our results suggest that the assumption is reasonable over much of the shelf. The one-parameter and two-parameter representations of diffusivity yield similar cross-shelf activity profiles of radium, and in statistical terms both representations are consistent with the measurements Effect of Ra Benthic Flux and Variable Depth on K x [49] Our model has allowed for the variability of the benthic Ra flux as a function of offshore distance. To examine the importance of bottom flux on the analyses, we first compute the cross-shelf activity profile for the southern zone using the optimal fitted K x while assuming zero bottom flux. Figure 5 shows that the water column activities are significantly reduced. However, in order to maintain the measured amount of radium in the water column, the coastal flux (F 0 ) needs to be increased. For 223 Ra, F 0 is increased from to Bq m 1 s 1, and for 224 Ra it is increased from 1.53 to 2.69 Bq m 1 s 1. When the least squares fitting procedure is applied with zero bottom flux and revised coastal flux, the optimal diffusivities are calculated to be 206 and 215 m 2 s 1 for the two isotopes. These values represent a 20% and 22% decrease over the diffusivities calculated using the nonzero bottom flux. Thus the neglect of bottom flux would induce a considerable distortion in the results. [50] The effect of including variable water depth (H) in the model is demonstrated by solving equation (1) without the benthic flux and depth terms. As Moore [2003] showed, by neglecting advection, assuming steady state and applying suitable boundary conditions the one-dimensional advection-diffusion equation reduces to " sffiffiffiffiffi# l A x ¼ A 0 exp x ; ð13þ where A 0 is the Ra activity at the coast (x = 0), and K x is constant. This approach implicitly assumes that depth is constant and that benthic flux is negligible; i.e., the offshore distribution of Ra is primarily controlled by longitudinal mixing and radioactive decay. By plotting log A x against offshore distance it can be shown that the slope (m) ofthe best fit linear regression is related to diffusivity by sffiffiffiffiffi l m ¼ : ð14þ [51] Application of this method to Ra data in the southern zone inner lagoon yields K x = 163 m 2 s 1 for 224 Ra and 73 m 2 s 1 for 223 Ra. When compared to our model-derived values of K x these values are 40% lower for 224 Ra and 70% lower for 223 Ra. These values of K x are also significantly lower than the values determined when benthic flux alone is neglected, and show that the inclusion of variable depth has had a major effect on the determination of K x by our model. Moreover, agreement between the 223 Ra and 224 Ra determinations of K x without consideration of benthic flux and depth variation is poor, and indicates that the assumption that the offshore distribution of Ra in GBR water is primarily controlled by radioactive decay and longitudinal mixing is too simplistic. K x K x 10 of 14

11 5.4. Variation of K x Within the GBR Zone [52] As noted above, the agreement between the values of K x estimated using two different Ra isotopes provides confidence in our results. The results show an approximately 2.5 times enhancement of the southern inner lagoon diffusivity compared to the north, a result which may reflect the greater reef density in the north, although other factors such as bathymetry, tidal currents and the wind speeds and directions may also be important. However, reef density and connectivity to the Coral Sea are two factors which differ markedly between the two study sections, with the major outer reef complex in the northern zone (named ribbon reefs ) forming a closed ribbon of coral with no major passages for exchange with the Coral Sea. These ribbon reefs have been shown to limit exchange between the GBR lagoon and Coral Seawater [Brinkman et al., 2001; Drew, 2001]. By contrast the coral reef in the southern zone of this study is far more open to exchange with the Coral Sea. [53] It should be noted that our data are most sensitive to the estimation of nearshore mixing (x < 20 km) using shortlived 223 Ra and 224 Ra. Our estimates of K x in the middle and outer lagoon (x > 20 km) are based on 228 Ra measurements which show considerable scatter, especially in the midlagoon zone, and are therefore subject to higher uncertainties. Nevertheless, the measured 228 Ra distribution is best modeled by invoking enhanced mixing in the outer lagoon, and our inner lagoon estimates of eddy diffusivity can therefore be used confidently as a lower limit farther offshore. Enhanced mixing within the middle and outer lagoon is a reasonable conclusion, given the greater connectivity with the Coral Sea via deep channels, and the fact that coral reefs can enhance mixing by generating eddies, convergence and divergence zones, tidal jets and stagnation zones [Wolanski, 1994] Comparisons With Other Eddy Diffusivity Measurements on the Continental Shelf [54] Our values of K x = m 2 s 1 for the inner lagoon, and K x ranging up to over 500 m 2 s 1 at the edge of the outer lagoon are well within the range of diffusivities inferred from measurements of other continental shelves using large-scale mass balance techniques. Using 223 Ra and 224 Ra to determine cross-shelf mixing rates in the South Atlantic Bight, Moore [2000] estimated diffusion coefficients to fall in the range m 2 s 1. An analysis of the salinity regime in the Spencer Gulf in Australia yielded diffusivities that ranged from less than 10 m 2 s 1 to almost 400 m 2 s 1 at the mouth of the gulf 150 km away [Nunes and Lennon, 1986]. Salinity measurements in the Mersey Estuary [Bowden, 1965] suggested a diffusivity of 170 m 2 s 1. Other estimates of cross-shelf diffusivity include 80 m 2 s 1 for the California shelf [Davis, 1985] and 500 m 2 s 1 for the Delaware coast [Münchow and Garvine, 1993]. [55] P. V. Ridd et al. (unpublished manuscript, 2006) used salinity gradients to estimate GBR diffusivities from a salinity transect about 100 km farther south than our southernmost transect. They varied their diffusivity linearly from the coast to the shelf, obtaining values ranging from m 2 s 1 at the coast to m 2 s 1 at the outer edge of the lagoon, 100 km offshore. Their value of diffusivity at 20 km offshore, corresponding to the width of our inner lagoon, is m 2 s 1, a value which compares favorably with our values for the inner lagoon. Although our values for the outer edge of the lagoon (maximum 500 m 2 s 1 in the southern zone) appear significantly lower than Ridd et al. s, the agreement is reasonable when one considers the uncertainty in our outer lagoon estimates using 228 Ra (noted above) and the decreasing north-south trend in diffusivity evident from our observations. Overall, we consider the agreement between methods to be good Lagoon Flushing Time [56] The flushing time (Dt) of the water in the lagoon is an important parameter influencing physical, biological and chemical processes because it gives an indication of the duration of exposure to solutes delivered to that part of the reef. We define it as the time required for diffusive mixing to reduce the solute concentration of the inner lagoon to 1/e (0.37) of its initial value. It can be estimated from Dt ¼ L 2 =K; ð15þ where K is a representative value of diffusivity for the area of interest, and L is the width of the inner lagoon from the coast to the inner edge of the reef. Using a distance of 20 km for the inner lagoon and values of 104 and 265 m 2 s 1 for K, Dt is found to be 45 days for the northern zone and 18 days for the south. These values relate to mixing of inner lagoon water with outer lagoon water. To estimate the flushing of the outer lagoon with Coral Seawater, we take the diffusivity of the outer lagoon to be the average of the inner lagoon value and our estimate of K at the outer lagoon edge. This gives K = 150 and 400 m 2 s 1 for the northern and southern zones. Using values of L taken as the average width of the outer lagoon (20 km in the north and 40 km in the south), an outer lagoon flushing time of 30 days is calculated in the north and 47 days in the south. As for inner lagoon flushing times, these values pertain to offshore mixing between two adjacent water bodies, in this case the outer lagoon and the Coral Sea. [57] Figure 8 summarizes flushing time estimates. Although we acknowledge the high uncertainty of our outer lagoon estimates of K, we nevertheless consider we have taken a conservative approach to the estimation of Dt by using values of K which represent lower limits (see discussion above). The fact that we have erred toward low values of K in the outer lagoon is supported by the results of P. V. Ridd et al. (unpublished manuscript, 2006). Thus our outer lagoon estimates of Dt should be considered upper limits for each zone. 6. Conclusions [58] 1. The distribution of short-lived Ra isotopes ( 223 Ra and 224 Ra) has been used to determine inner lagoon (<20 km offshore) diffusivities for northern and southern zones of the central GBR lagoon. The concordance of K x estimated using two different isotopes and the apparent consistency between measured riverine inflows to the lagoon and inflows inferred from the modeled salinity distribution provide confidence in the results. 11 of 14