EPSL ELSEVIER Earth and Planetary Science Letters 144 (1996) 591-604

Estimating groundwater discharge into the northeastern Gulf of Mexico using radon-222

Jaye E. Cable * , William C. Burnett ‘, Jeffrey P. Chanton, Georges L. Weatherly

Drpartrwrr~ of Ocrano,~raphy. Flwida Stutv Unircrsit\, Tallahassre. FL 32306-3048. USA

Received 28 June 1996; revised 26 August 1996; accepted 3 September 1996

Abstract

Submarine groundwater discharge (SGD) may provide important chemical constituents to the ocean, but the dispersed nature of this process makes locating and quantifying its input extremely difficult. Since groundwater contains 3-4 orders of

magnitude greater radon than seawater, ‘?‘Rn may be a useful tracer of this process if all other sources of radon to bottom

waters can be evaluated. We report development of a SGD tracing tool based on radon inventories in a coastal area of the

northeastern Gulf of Mexico. We evaluated factors that influence the concentration of radon in the water column (i.e., production-decay, horizontal transport, and loss across the pycnocline) using a linked benthic exchange-horizontal transport model. Total ““Rn benthic fluxes (2 2420 dpm mm2 day- ’ ) measured with in situ chambers are of the magnitude required

to support measured sub-pycnocline ‘22Rn inventories, while estimates of molecular diffusion show that this input is

relatively small (I 230 dpm m-’ day- ‘1. Using this model approach, together with measurements of the radon inventory, we estimated a regional subsurface fluid flow ranging from 180 to 710 m3 set _’ into the 620 km2 study area. This

discharge, equivalent to an upward advective velocity of approximately 2-10 cm day- ’ dispersed over this entire study area,

is equivalent to approximately 20 first magnitude springs.

Keykvrds: ground water: discharge; Gulf of Mexico; Rn-222

1. Introduction

River discharge to the world’s oceans is widely recognized as an important contributor to oceanic chemistry [ 1,2]. Water recirculation through the

seafloor caused by macrofaunal irrigation [3,4], hy- drothermal vent activity [5], and along continental

margin brine seeps [4] also affect oceanic chemicai

mass balances. Other poorly understood but poten- tially significant oceanic sources of chemical compo-

nents are submarine groundwater discharge (SGD) and recirculated seawater along continental shelves.

These as yet unquantified sources include groundwa-

ter seepage through sediments as well as submarine spring discharge.

The occurrence of groundwater discharge into the

* Present address: Department of Fisheries and Aquatic Sci-

ences, 7922 NW 71st Street, University of Florida, Gainesville.

Florida 32653. E-mail: ievoune@nervm.nerdc.ufl.edu *< _ ’ E-mail: wburnett@mailer.fsu.edu.

ocean has been discussed for decades [7] but until recently its role in coastal ecosystems was little appreciated. Geochemical and hydrologic budgets usually neglect groundwater contributions to the

00 12-82 I X/96/$12.00 Copyright Q 1996 Elsevier Science B.V. All rights reserved. PII S0012~821X(96100173-2

592 J.E. Cable et al. /Earth and Planetaryv Science Letters 144 C 19961 SYI-604

coastal zone due to difficulties associated with locat-

ing and quantifying its input. Fanning et al. [S]

measured unsupported “‘Rn bottom water concen- trations on the West Florida Shelf ranging from 0.5

to 2.5 dpm 1-l and suggested groundwater discharge

or diffusion from underlying phosphorite deposits

might be responsible for these relatively high con- centrations. We compared Fanning’s “‘Rn contour

plot to a map of known submarine spring distribu- tions along the Florida coastline [9] and found that

the highest ‘*‘Rn activities are clearly found in

regions of greatest submarine spring density. Radon concentrations are often 3-4 orders of magnitude

greater in groundwater than in coastal seawater, and

this qualitative relationship suggests that radon should be a useful tracer of submarine groundwater dis-

charge. Development of tracer techniques to quantify

groundwater discharge would greatly enhance our

ability to assess its potential effect on coastal ecosys-

tems. Previous studies have employed ‘*‘Rn to ex- amine atmospheric evasion [lo], sediment-water ex-

change [4], submarine spring discharge chemistry

[I I], water column mixing rates [ 121, and other

processes. For example, 222Rn and salinity have been

used to calculate hydraulic mixing rates between

surface seawater and interstitial waters in a lagoonal

patch reef in Kaneohe Bay, Oahu [13]. We report results of a study in a small area of the northeastern

Gulf of Mexico evaluating the use of “‘Rn as a

tracer of submarine groundwater discharge. The

overall goal was to establish a quantitative relation-

ship between the regional flow of SGD and the inventory of water column ‘*‘Rn. Since inventories

are relatively easy to determine, this approach allows

a regional assessment of subsurface fluid flow which could, in principle, be applied to other areas.

2. Geologic setting, sample collection and analysis

The Floridan Plateau is a broad, flat limestone and dolomite platform separating the Atlantic Ocean from the Gulf of Mexico. Florida, the emergent part of this plateau, contains one of the United States’ largest freshwater reservoirs, the Floridan Aquifer [9]. The field portion of this investigation took place in a 620 km* section of the inner continental shelf

Fig. I. The study area (box; - 620 km’) is located south of

FSUML in the northeastern Gulf of Mexico. K-Tower, the site of

seasonal water column sampling and benthic flux measurements.

is about 24 km southeast of FSUML.

(Fig. 1) south of the Florida State University Marine

Laboratory (FSUMLI. Hydrographic characteristics were obtained from

conductivity, temperature, and pressure readings us- ing a CTD profiler (Seabird Electronics) at each

water collection station in the study area. In addition, long-term, burst-sampling current meters were

moored in 18 m of water at K-Tower (29”40.72N,

84O22.71 W), located about 24 km south of the FSUML, to determine average current flow charac-

teristics within the area. Shallow (10 meters above

bottom; mab) and bottom (1 mab) current meters were deployed in an array on 3 occasions: (I) De-

cember 199 1 to April 1992 [ 141; (2) July to October

1992; and (31 July to August 1993. During these sampling periods, current velocity, current direction,

current meter inclination. and temperature were mea-

sured every 1.5 min in 32 set sampling bursts. All tidal frequencies were suppressed in the current me- ter data using a Gaussian filter (full width-half maxi-

mum of 24 h). From July 1992 to December 1994, 135 bottom

water samples and 71 water column profiles were collected [15]. Water samples for 222Rn (t,,? = 3.82

day) and “6Ra (t,,? = 1620 yr) analysis were col- lected in 4-l evacuated glass sampling bottles using a submersible pump that drew water from depth di- rectly into the bottles. All samples were analyzed for “‘Rn (and later for ‘I6 Ra) using a standard approach

for “‘Rn extraction from seawater by sparging with helium [ 16,171. The unsupported radon (total “*Rn at time of analysis minus 226Ra) was decay-corrected back to time of sampling to obtain the in situ excess

J.E. Cable et al./ Earth and Planetary Science Letters 144 (1996) S-604 593

“‘Rn. All “>Rn concentrations are reported as un- supported and corrected to time of collection.

Pore waters were sampled at K-Tower by SCUBA

divers using a sediment pore water ‘sipper’, which consisted of a depth-calibrated 53.5 cm long, 6.4 mm

I.D. stainless steel tubing with a perforated bottom

copper tip. Pore water was collected by inserting the screened copper tip into the sediments to the desired

depth and drawing water into a syringe. Each pore

water sample was transferred from the syringe to an evacuated 125 ml glass sampling bottle for analysis

at the water surface. Radon-222 sediment-water exchange rates were

determined by benthic flux measurements using in situ chambers [ 181. Divers deployed four seepage

meter-style steel drums (90.7 1; 0.255 m’) by care-

fully pushing each chamber about 3 cm into the sediments. The water inside the chambers was stirred

gently using manually operated propellers to simu-

late a mixed water column. Initial and final (4-5 h later) water samples were collected from the benthic

chambers and analyzed for ““Rn and “bRa. The

“‘Rn concentrations were corrected for decay, and

the benthic flux was calculated as shown in Martens et al. [ 191. Advective seepage rates from the sedi-

ments were measured from the benthic flux cham- bers or using a seepage meter technique [20].

Sediment equilibration experiments were per- formed to estimate the amount of pore water ‘“Rn at

equilibrium with the solid phase sediments. Each

experiment consisted of slurrying approximately 85 g wet sediment aliquots with 300 ml of seawater in

500 ml Erlenmeyer flasks for 30 days. After this

period, radon in the water is assumed to be equili- brated with sediment 2’6Ra, and the activity CC,,) is

calculated using the porosity (4) and wet bulk den-

sity ( p,,,) of the sediments.

3. Results and discussion

3.1. Hydrographic characteristics of the inner conti- nental shelf ti’aters

For the purpose of this study, the inner shelf is defined as being seaward from the coastal barrier islands to the 20 m isobath. The circulation on the West Florida inner shelf is dominated by surface

winds, tides, and density gradients. Although outer

shelf currents such as the Loop Current may influ- ence this circulation, their effects are small and uncertain. Winter (December-April) hydrographic

profiles displayed a well-mixed water column which

is attributed to atmospheric forcing when cold conti-

nental air masses move over the Gulf [14.2 I I. Re-

sults showed that temperature, salinity, and density contours were uniformly distributed with depth, while

temperature and salinity values increased slightly with increasing distance from shore. Net (non-tidal

or low frequency) u and u current velocities show

that surface layer currents were strongest to the east

with an average II velocity of 3.2 cm set-’ between

December 199 1 and April 1992 [ 14,151. Duplicate

current meter moorings at 17 m deep ( 1 mab) and 50 m apart were highly coherent, showing that currents

moved north-northeast at more than 2.2 cm set _’

during the winter deployment period.

During the summer (June-August), the inner con-

tinental shelf waters develop a strong pycnocline and

are characterized by estuarine-like circulation [2 1,221. Surface currents (10 mab) measured between July

and October, 1992, were weak and variable in direc-

tion, while in July and August, 1993, the surface currents had a strong easterly component at 2.2 cm

see-‘. The mean u current velocity for the summers

of 1992-93 was 1.0 cm secY’ with a significant

minimum (LJ = 0.5 cm set- ’ ) found in the bottom

waters during July and August, 1992. A progressive vector diagram (Fig. 2) demonstrates the calculated

time-series bottom water movement t 1 mab) for this 1992 time period remained confined to a region

similar in scale to the study area until the summer

stratification broke down in the fall. These data

provide additional documentation that the most qui- escent, stable water column in this part of the north-

eastern Gulf of Mexico occurs during the summer months.

3.2. Water column distributions of “‘Rn and 2’6Ra

The formation and degradation of the pycnocline

has a significant effect on the water column distribu- tions of ‘“Rn (Fig. 3). During the summer, the waters are clearly stratified and “‘Rn activities in the bottom water reach the relatively high level of 4.10 & 0.13 dpm 1-l (Fig. 3B). The mean summer

594 J.E. Cable et al. /Earth and Planetar? Science Letters 144 t 1996) 591-604

bottom water “‘Rn concentration between 1992 and 1994 was 3.2 & 1.8 dpm ll’ (n = 234; [15]). Compa-

rable bottom water enrichment has been documented

for CH, in the same area [23]. During the summer stratification, the bottom waters become efficient

collectors of “*Rn with a source on or under the seafloor. Without this stratification, the waters would

quickly lose the trace gas signal due to atmospheric

evasion. Based on ‘*‘Rn depletion in surface waters,

Fanning et al. [24] reported an intense sea-air gas

exchange occurring in the waters of the West Florida shelf due to frequent storm fronts in the Gulf of

Mexico. Thus, a distinct advantage exists in using the summer, sub-pycnocline “‘Rn inventories to

quantify groundwater flow, since an important loss

term can be neglected. Radium-226 activities are also shown on these

profiles to illustrate the extent of *“Rn enrichment

or depletion relative to its radioactive parent. Activi- ties of 226Ra measured within our study area between

1992 and 1994 averaged 0.44 + 0.22 dpm 1-l (n =

"*lo-i1

-..

564), significantly greater than average open Gulf of

Mexico values of 0.106 f 0,028 dpm 1-l reported in

1984 [25]. These higher 226Ra activities provide ad-

ditional support that another source, such as ground-

water, supplies radium and radon to the coastal

ocean. In the following section, we present a model

which links advective-diffusive benthic exchange to horizontal water column transport for conservative

“‘Rn. This model is designed to test the importance

of water column transport on ‘“Rn concentrations

and to estimate the subsurface fluid flux from the seafloor based on comparisons of measured and modeled inventories of “‘Rn in the overlying wa-

ters.

3.3. Two-dimensional mass balance model

3.3. I. General approach The water column inventory of ‘**Rn represents a

balance between its sources and sinks: (1) benthic

,140

100 “...,

KM

Fig. 2. A progressive vector diagram shows net bottom water (1 mab) movement during the July-October 1992 current meter deployment at

K-Tower. Calculated water mass movements over consecutive 24 h periods are depicted as distance (km) between dots on the diagram.

J.E. Cable et al. / Earth and Planetary Science Letters 144 (I%61 591-604 595

diffusive-advective exchange; (2) ‘*‘Rn water col-

umn production and decay; (3) horizontal water col- umn advection; (4) eddy diffusion along and across

the pycnocline; and (5) air-sea exchange. Benthic diffusive-advective exchange processes can be fur- ther divided into molecular diffusion, sediment irti-

gation and resuspension by biological organisms or

wave pumping, fluid flow through sediments, and

submarine spring discharge. Results of molecular diffusion experiments are given in the next section

and demonstrate that this process has a minor effect

on summertime water column *‘*Rn inventories. Al-

though macrofaunal irrigation can enhance exchange

from the sediments, active macrofauna communities were not observed in this study area or in sediment

cores. Based on control experiments made with seep-

age meters in the near-shore region of the study area [26], wave pumping is not thought to have a signifi-

cant effect on interstitial fluid transport. Some sub-

marine springs are known to occur in the region, but

Activity (dpm.L.t) Activity (dpmL_l)

Fig. 3. Representative water column profiles at K-Tower demon-

strate seasonal “‘Rn distributions with depth (m). Activities (dpm

I-’ ) of total “‘Rn (open squares) and 226Ra (closed diamonds)

are given for: (A) 25 May 1993; (B) 10 August 1993; (C) 16

Septemebr 1993; and (D) 24 February 1994.

u c. SL

Fig. 4. An incremental mass balance of “‘Rn in the sub-pycnoc-

line water column was applied using this box model, which allows

the sub-pycnocline water column to change with distance up the

continental shelf.

they tend to be small - groundwater seepage ap-

pears to be the dominant process delivering SGD

into this area [15]. Since a strong pycnocline devel- ops in the summer, use of a sub-pycnocline box

model to predict fluid flow from the sediments avoids

the necessity of including air-sea exchange (Fig. 4).

As a water mass moves horizontally from an

initial boundary to some reference point across the

continental shelf (a Lagrangian approach), three pro-

cesses will affect the water column radon activities: (1) decay of initial water column ‘Z’Rn; (2) incre-

mental addition and decay of radon from benthic

advection and diffusion; and (3) exchange of radon across the pycnocline. All three of these processes

are addressed in the model which links benthic fluxes

to the horizontal water column transport. The “‘Rn flux balance can be written as:

‘\‘iAo + Jben + (Ga)Vn - vsC,A, - Jpyc

-(*C,“)V”-(~,,C,~)At=O (1) where TV, is the low frequency current velocity; C, represents the initial radon activity entering the re-

gion from offshore; A, is the area of the offshore

side of the study area; Jben is the total advective-dif- fusive benthic flux; A is the “‘Rn decay constant

(1.25 X lo-” min-‘); AC,, and AC,, represent

water column radon production and decay, respec- tively; V, is the volume of water in individual box segments; C, is the final radon activity horizontally exiting the box inshore; A, is the area of the exit side (inshore) of the lz* box; JPYc is the radon eddy

596 J.E. Cuble et al. /Earth and Planetaq Science Letters 144 (1996) B-604

diffusive flux across the pycnocline; uuP is the water

velocity across the pycnocline; and A, is the area of

the upper surface of the pycnociine. Most of the

parameters described in the flux balance were mea-

sured or easily calculated (Table 1).

Eddy diffusive fluxes across the pycnocline were calculated from Fick’s first law using the observed

“‘Rn concentration gradient across the pycnocline

(dC/dz) as a function of depth and the estimated

vertical eddy diffusivity (K,):

JPYc = K, $ i i

(2)

The inversely proportional relationship reported

between the local buoyancy gradient and vertical eddy diffusivity from 14 GEOSECS profiles of “‘Rn

and “‘Ra demonstrated K, values ranged from 5 to

440 cm” set- ’ near the seafloor [27]. Using their

oceanic buoyancy flux (-4 X 1O-6 cm’ sece3>, K, values of 3.4 (* 1.8) X lop4 cm2 set- ’ (mean i

1 a; Table 1) were calculated from the depth of the

greatest density gradient in seven hydrographic pro-

files collected in our study area. Horizontal eddy diffusivities (K, > can also affect

Table I Mass balance input parameters for the linked model

the distribution of “‘Rn in near-bottom ocean wa- ters. Lietzke and Lerman [28] report “‘Rn K, val- ues ranging from 10” to lo6 cm’ set ’ for a

borderland basin off California. We estimated hori- zontal “*Rn exchange between the study area and

adjacent coastal segments and offshore waters and

found the exchange to be very small, due to the low concentration gradients observed in the area. This

low exchange rate implies that SGD occurs even

further offshore, and our groundwater discharge re-

sults represent a minimum. Horizontal exchange is estimated to be the same order of magnitude as

molecular diffusion from bottom sediments.

First, the benthic exchange model used to obtain J ben is described. Jhen is estimated from the upward fluid velocity advecting across the sediment-water

interface necessary to balance measured 222Rn inven- tories. The linked model approach uses four simpli-

fying assumptions: (1) benthic fluxes are spatially and temporally uniform; (2) 2’2Rn activities are ver-

tically uniform within the deep layer; (3) the sub-

pycnocline water column geometry is a simple wedge

shape; and (4) horizontal fluid flow in sediments is

small relative to vertical flow.

Description Input parameters n Reference

Slope of the continental shelf

Eddy diffusivity, K, (lOel cm’ see- ‘)

Porosity of sediments, 4 (ml cm- ‘) ’

Sediment wet bulk density. pwrt (g cm-‘) b

Mean study area sediment 5’s (lOJ dpm rne3) ‘ K-Tower sediment, C,, (10 dpm m-j) ’

Overlying bottom water, C, (IO4 dpm m-‘1 d

Upper pycnocline “‘Rn (IO” dpm m-‘)

Sub-pycnocline ““Rn, C, (10” dpm mm’)

Submarine spring “‘Rn, C,, (IO’ dpm m-“1

Aquifer ‘*‘Rn, C,, (10’ dpm m--r)

-4.5 x 10-j

3.4 i. 1.8

0.42 t 0.04

1.9 f 0.1

7.1 f 2.6

4.4 f 0.7

0.46 + 0.11

0.11 +0.07

0.21 i 0.13

54.3 + I.0

55.7 i 8.7

7

13

13

13

3

12

34

31

I [I51 48 [ISI

Water column and sediment I” Rn concentrations (mean i 1 D ) were measured from 1992 to 1994.

a Porosity. 4 = ((A X W,/p,, ))/((A X We/p,,) + (1 - Wo X A/pdry )) where ps, is the density of seawater; A = [ 1000/((1000 -

35.174X3/35))] corrects for the salt content of interstitial fluids: S is the measured salinity of the overlying bottom waters; pdry is the dry

grain density as measured by volume displacement of a weighed aliquot of sediment in a known volume of water; and Wn = [(wet sediment

weight-dry sediment weight)/wet sediment weight] is the fraction of water present in sediment.

b Wet bulk density, p,,( =[~xP,,l+[(l-~)Xpdryl. ’ Sediment equilibration activities are in units of disintegrations per minute (dpm) per cubic meter of wet sediment.

d Overlying bottom water “‘Rn used in the benthic exchange model is specific for each sediment equilibration station. The summer

sub-pycnocline “‘Rn mean concentration inside the study area was 0.32 (50.18) X IO” dpm m-j (n = 234; [I5]).

J.E. Cable et al./ Earth and Planetar? Science Letters 144 (1996) 591-604 591

3.3.2. Betlthic exchange model A one-dimensional, vertical advection-diffusion

model presented by Craig [29] may be adapted to estimate radon exchange from sediments:

dC a?c ac -= dt

K,-- i)Z’ +w7z+P+hc

(3)

where C is the radon concentration in the sediments;

z is depth positive downwards; K, is the vertical

diffusivity; (a’C)/(az’) and (aC)/(az) are the ‘“‘Rn concentration gradients across the sediment-

water interface for diffusion and advection, respec- tively; o is vertical advective velocity; P is a zero-

order production term; and hC is radioactive decay.

To model radon activity in sediments, K, is set

equivalent to D,, the effective wet sediment diffusion coefficient, after correcting for temperature ( - log

D,, = (980/T) + 1.59; [30]) and sediment tortuosity

<D, = $D,; [3 I]). The ‘I2 Rn molecular diffusion co- efficient (D, = 1.14 X 1 O-5 cm’ set- ’ at 18°C; [32])

becomes 6.0 X 1O-6 cm’ set-’ for a sediment

porosity of 0.42 and a typical summer bottom water

temperature of 28S”C. For ‘2’Rn in the sediments, P is the result of radon present in pore fluids due to

recoil after production by decaying ?26Ra in mineral

grains (P = AC,,). The C,, term is an experimental “‘Rn sediment equilibration activity (dpm me3 wet

sediment; Table 1) which can be converted to pore

fluid concentrations by dividing by the fractional

porosity. Advection, w, and radioactive decay, h,

represent losses from the sediments and are defined as negative terms in the model. For “‘Rn, the solu-

tion to Eq. (3) reduces to:

c=

(C, - C,,q)[esjsinh( A’:z r ‘) j

+ C,,

(4)

where C, is the overlying bottom water radon activ-

ity (dpm rne3); z,s is a depth in the sediments much deeper than the depth where C,, initially occurs; z * is a one-dimensional mixing parameter described by Ds/w; and A = [l + 42 * (A/w)]~.~. which includes radioactive decay and advection [29]. This equation was used to model the radon concentration versus

depth for theoretical diffusion (w = 0 m min- ’ ) profiles of radon deficiency in the sediments using experimentally determined C,, values. When advec-

tion in the sediments is considered, information re- garding the subsurface fluid radon concentration is

necessary to estimate the fluid flux across the sedi-

ment-water interface based on radon inventories.

We will estimate upper and lower limits of subsur-

face advective flow based on field measurements and

the benthic exchange model.

3.3.3. Water column transport model The effect of horizontal water column transport

on “2Rn concentrations was estimated from mea- sured current velocities and sub-pycnocline “‘Rn

concentrations. Solving the mass balance equation

(Eq. (1)) for C, allows the final radon concentration

to vary as a function of current velocity (7,~) across

the shelf:

c, = YC,- ,A, + Jben + (AC,,)V, - (K,$C/dz)A

YA,+ I + A,v,, + AV,

(5)

Values for Jbeo from the benthic exchange model are linked to Eq. (5) so that C, may vary as a

function of advection through sediments (w). Initial offshore water column ‘2’Rn CC;), which is trans- ported into the study area, decays at a rate dependent

on A,, and time.

In addition, because the dominant current direc- tion in the study area is to the north (shoreward), the

model conserves mass by allowing the sub-pycnoc- line water column height to decrease as a function of

the average slope of the continental shelf (Table I).

The volume of the individual segments in the box

model are incrementally decreased to account for the decreasing water column height (Fig. 4). The water balance for this model is written as:

WA, + v,A, = pupA, + u,A, (6)

where this balance is solved for uuP, the velocity of

water moving across the pycnocline:

oA, + v,(A, - A,,) V up =

A, (7)

and is incorporated into the mass balance (Eq. (5)) to

598 J.E. Cable et al. /Earth and Planetarv Science Letters I44 (1996) 591-604

account for the change in water volume as the water

moves up-slope and the sub-pycnocline water col-

umn height decreases. This volume conversion is not

incorporated into the benthic flux terms because they are not volume dependent. Thus, the water column

incrementally gains radon from benthic fluxes and

loses radon to decay and vertical diffusivity across

the pycnocline during its transit across the shelf.

This Lagrangian approach allows simulation of

the final deep layer water column “‘Rn inventories after accounting for all known sub-pycnocline sources

and sinks. The radon inventories in the bottom layer can be converted easily to concentrations since the

geometry of this layer is known. In the following

sections, mass balance results are presented for diffu-

sive and advective-diffusive conditions. These model

results are then compared to observational data to

make estimates about the quantity of groundwater entering the study area.

3.4. Measured benthic fluxes and “‘Rn incentories

Diffusion of radon into overlying waters causes a

deficiency in sediments which is greatest near the

surface and decreases progressively downward from

the sediment-water interface. A theoretical profile of

K-Tower ‘**Rn versus depth using Eq. (4) demon-

strates the effect of radon diffusion in an undisturbed sedimentary environment (solid line; w = 0; Fig. 5).

The diffusional loss of radon into the overlying

waters near the sediment surface creates the near-in- terface deficiency, while the ‘equilibrium’ value at

depth represents a balance of radon decay with input

via recoil and other processes from the 226Ra present in the solid phase sediment. Although diffusion can

provide a significant contribution of radon to overly- ing waters, advective processes can greatly enhance

these diffusional inputs. For example, macrofaunal

irrigation of sediments can mix pore waters to greater

depths and release additional dissolved constituents to the overlying waters, as was shown for several

California borderland basins of the western Pacific Ocean [4].

The sandy, shell-hash sediments near K-Tower contain an average dry sediment 226Ra activity of 0.80 f 0.20 dpm gg’ (n = 5). Based on many obser- vations made by divers, the shelf sediments in the

study area do not appear subject to much macrofau-

Activity (dpm.L.’ wet sediment)

0 20 40 60 80 0.00

Fig. 5. A theoretical profile of “‘Rn concentrations (solid line:

w=O; dpm I-’ wet sediment) in K-Tower sediment calculated

using the benthic exchange model (Eq. (4)) shows the “‘Rn

deficiency near the sediment-water interface. Sediment core equi-

libration activities (squares) and pore water profile activities (#I,

circles; #2, triangles) from K-Tower are also shown for compari-

son

nal irrigation. Setting the advective velocity to zero

in Eq. (4) and using the C, and K-Tower sediment

C,, parameters previously described (Table 1). a diffusive flux of 133 & 7 dpm m-’ day-’ is esti-

mated for this site. In addition, equilibration of the

K-Tower sediment core sections yielded activities similar to the C,, theoretical value (squares, Fig. 5)

confirming the use of this approach. The flux from

Eq. (4) also compares well with a diffusive flux of 128 f 8 dpm m-’ day- ’ calculated from these re- sults using a Martens et al. [19] depth-independent

equation:

J = (D,h)““(C,, - C,) (8) where J is the flux calculated for the change in concentration between the sediments CC,,> and the overlying water column CC,). Sediment analyses were also performed at numerous other stations within the study area. The mean (_+ 1 CT> diffusive flux for the entire study area based on C,, determi- nations from sediment equilibration experiments (n = 13) and Eq. (8) was 230 & 110 dpm rnp2 day-‘.

Pore water profiles also collected in K-Tower

J.E. Cable et al. /Earth and Planetary Science Letrem 144 (1996) S-604 599

sediments about 5 m apart confirmed that diffusion

into the overlying waters is relatively small. These profiles are shown with the sediment core equilibra- tion activities in Fig. 5 (circles, #l; triangles. #2).

Pore water profile #2 displays a trend similar to the

theoretical curve. while profile #l may indicate

excess ‘“Rn. The excess activity could be due to a

number of factors, including the presence of advect-

ing fluids containing high “‘Rn or sediment inho-

mogeneity. Both pore water profiles demonstrated “‘Rn con-

centrations lower than expected near the sediment-

water interface based on the theoretical considera-

tions. This greater deficiency suggests that a physical

process (irrigation or wave pumping) may be affect- ing the sediments in the upper 7 cm. The total radon deficiency was estimated in the sediments by first

taking the difference between the K-Tower sediment

C,, and these pore water “‘Rn concentrations. These

deficiencies were then integrated to the depth at

which pore water “‘Rn approximately equalled sedi- ment C,,. If one assumes that these profiles are

steady-state, fluxes to the overlying water can be estimated in the same way that estimates are made

by integrating the unsupported “‘Rn water column

activities. These fluxes (350-450 dpm mm’ day- ‘1

indicate that even an external process such as wave pumping cannot account for the observed water col-

umn “‘Rn inventories. They would only support an

inventory of approximately 2,200 dpm m-‘, while measured summertime inventories in this area were

typically around 30,000 dpm m-‘. Some other pro-

cess must be contributing significant amounts of “‘Rn to this system.

Measured benthic fluxes and calculated diffusive fluxes did not yield similar results. Benthic flux

chamber measurements showed a mean “‘Rn flux of 2520 + 670 dpm mm2 day-’ (&la; n=6> at K-

Tower between August and October, 1993. Several ports on these chambers were open to allow seepage

and provide a measure of the total benthic flux. Advective fluxes appear to be a very important part of the total Jhen estimate. The mean seepage velocity at this site, measured via seepage meters. was 1.2 1 k 0.49 cm day _ ’ ( -t 1 (T; n = 8; equivalent to 8.5 f 3.3 ml rnp2 mini ‘), confirming that advective pro- cesses enhance the material flux across the sedi- ment-water interface.

Inventories of “*Rn measured in the overlying

water column vary seasonally (Fig. 3). During the summer, radon is significantly more concentrated in

the bottom waters. with a typical summer sub- pycnocline inventory of 30,000 dpm m-‘. Assuming

the seafloor is the only significant input, these water

column inventories would require a benthic flux of

5.400 dpm rn-’ day-’ - over one order of magni-

tude higher than the estimated diffusional inputs. It is clear from these measurements and calculations that

diffusion accounts for a minor portion of the ob-

served water column “‘Rn activities.

The dispersed nature of groundwater flow through

sediments makes precise identification of seepage

areas difficult. Even though this flow may be very slow and its occurrence ‘patchy,’ its widespread

distribution could result in a significant regional

input of groundwater and recirculated seawater. Ad- vective fluxes from sediments were estimated from

the linked benthic exchange-horizontal water col-

umn transport model presented above. An initial

water column radon concentration CC,) was defined as a mean of several offshore measurements outside

the study area. Average surface layer “‘Rn activities

measured immediately above the pycnochne during the summer months were used to calculate the diffu-

sive flux across this density gradient.

The physical limits of the study area were set at 2 1 X 30 km, and we chose a 10 km reference point

for modeling, because it is approximately centered

along any north-south (onshore-offshore) tract in the study area. An upper limit for current velocities

(3.2 cm sect’ ) used in the model was based on

winter velocities measured at K-Tower between 199 1

and 1993 [ 141. One drawback to our approach is the requirement that estimates of benthic advective fluxes must be considered uniform across the shelf. It is

likely that seepage velocities will be underestimated in one location and overestimated in others. Point sources, such as submarine springs, would be inte-

grated with areas where little or no actual flow may be occurring. However. this approach does allow estimates of regional submarine fluid discharge, the overall objective of this study.

Our analysis shows that the main factor control-

600 J.E. Cable et al. /Earth and Planetary Science Letters 144 (1996) 591-604

ling the *“Rn concentration in a water mass moving

north (shoreward) on the continental shelf for a

given distance (I 0 km) is the magnitude of benthic

inputs. Net current velocities do have a smaller, but

noticeable, effect. When “‘Rn sediment diffusion is

the only benthic contribution (w = 0) to the water

column, the dominant control on the water column “‘Rn activity is the balance between radioactive

decay and this diffusive input. Thus, the model

allows determination of the average seepage veloc-

ity, assuming one can estimate or measure: (1) net horizontal current velocity; (2) “‘Rn concentrations

in the advecting fluids; (3) sediment porosity; and

(4) water column “‘Rn inventories. By assigning

values for the sediment fluid radon concentration and the current velocity, the seepage velocity may be

estimated by successive approximation until an ap- propriate balance is established with the measured water column ‘*‘Rn inventory.

The concentration of “’ Rn in the advecting fluids

is an important yet difficult parameter to evaluate

precisely. Several approaches may be taken to obtain

estimates of “‘Rn in these advecting fluids. For

example, the “‘Rn concentration of waters discharg-

ing from a submarine spring located in the near-shore

portion of our study area may be representative of

the groundwater flowing offshore. The relatively high “‘Rn activities associated with groundwater and

springs should provide a minimum estimate of SGD,

since this concentration is at the upper limit of what might actually be encountered. Actual pore water

concentrations are lower because of mixing with

infiltrated seawater. Lanark Spring, located about

100 m offshore, is characterized by a “‘Rn activity

of about 540 dpm I-’ [15]. In addition, groundwater collected along the coastline from shallow private wells in the same area showed that 95% of the

measured “‘Rn activities (n = 48) were less than

4000 dpm I-‘, with a geometric mean value of

560 k 90 dpm I-’ [ 181. Since the radon concentra- tion in groundwater probably changes by mixing as well as decay during transit, lower concentrations are likely to occur offshore. An alternative to these spring or aquifer values would be sediment equilibra- tion radon values. These lower limit estimates for radon in the advecting fluids should give an upper estimate of the quantity of groundwater entering the region through the sediments. In areas where dissem-

?_ _____..._0=~.~

________.__...-.-~~ ___._____.-------

I-

O I 0 0.5 I 15 2 25 3 :

Onshore Current Velocity kmmx-1)

Fig. 6. Simulations of “‘Rn concentration (dpm I-’ )

5

“tYS”S

horizontal (onshore) current velocity (cm set-’ ) under various

benthic advective conditions demonstrate the influence of these

processes on “‘Rn concentrations. Radon in the subsurface pore

fluids are assumed to be equal to C,, (solid lines; 7.1 +2.6X IO”

dpm m-j) and C,( (dashed lines: 54.3 + 1 .O X 10’ dpm m-j). All

other conditions set for this simulation are given in Table I.

inated seepage flow or recirculated seawater are

thought to be the main process by which subsurface

fluids enter continental shelf waters, C,, is probably the best estimate of subsurface “‘Rn. Direct mea-

surements of seepage performed in the area have

suggested that seepage is probably the dominant process here [ 151.

The combined effects of horizontal transport and

benthic advection on the final water column “‘Rn

concentration are observed when the final concentra-

tion CC,) is plotted versus current velocity (Fig. 6). Typical observed sub-pycnocline “‘Rn activities (2-4 dpm I-’ ) and summer current velocities (0.5-

1.5 cm set- ’ ) are also shown for comparison. Sedi-

ment equilibration CC,,; solid lines) and submarine

spring CC,,; dashed lines) concentrations were both used for these simulations. At current velocities less than 0.5 cm set-‘. “’ Rn inputs are balanced almost exclusively by decay. As the current velocity in-

creases, 222Rn from benthic inputs has less time to

accumulate in the water column, and these net veloc- ities play a more active role in controlling the radon concentrations in the water column. Using both C,, and C,, scenarios, this model demonstrates that ob-

J.E. Cable et al./ Earth and P1anetar.v Science Letters 144 119961 S-604 601

served “’ Rn values can be predicted easily, and that

the required upward advective velocities may thus be estimated.

Using field measurements of radon inventories and current velocities as a guide, we estimated the magnitude of advective flow into the study area

(Table 2). Benthic advective velocities, based on

sediment equilibration and groundwater activities,

must range between 2 and 10 cm day- ’ to maintain

a typical summertime water column “‘Rn inventory

of about 30,000 dpm mm ‘. The evidence presented by the observed water column and benthic flux

measurements strongly suggests that advective trans-

port of “‘Rn through sediments is an important

process in this area.

offshore area, we recognize that such a process could

result in significant loss of “‘Rn by atmospheric

degassing. Should this actually occur, however, our discharge results would be underestimated because

of the unaccounted for loss.

Based on the range of modeled seepage velocities

and a study area size of 620 km’, a regional flux of subsurface fluids into the study area is estimated to

range between 180 and 7 IO m3 set- ‘. This input is

of the same magnitude as the Apalachicola River. the largest river in Florida, which has an average fresh-

water flow of 720 m’ see- ’ [33]. Wakulla Springs, one of the largest freshwater springs in Florida.

discharges about 1 IO m3 set- ’ of water into the

Wakulla River [9] and ultimately into the northeast-

em Gulf of Mexico. We estimated the flow from Lanark Submarine Spring at 0.041 m3 set- ’ [ 151,

while the estimated discharge from a single vent at

Mud Hole Submarine Springs south of Tampa Bay

was only 0.025 m3 set- ’ [I I]. Thus. the regional benthic fluid flux entering this area, estimated by balancing the radon inventories in the overlying wa-

ter column. is clearly significant - perhaps 50-250

times the size of a first magnitude spring ( 2 IO0 cfs;

2.8 m3 set- ’ ). Although submarine springs were not observed or reported to discharge as ‘boils’ in this

It is important to note that much of the advecting fluid is probably a mixture of groundwater and recir-

culated seawater driven by groundwater discharge

processes. This model cannot distinguish the differ- ence in the ultimate sources. However, comparison

to estimated fluxes of known submarine springs sug- gests that disseminated seepage and recirculated sea-

water are much more important in this area. AI-

though seepage fluid flux velocities (cm day-‘) may

seem small in comparison to the velocity of water exiting a river or spring, the large spatial distribution

can provide a volumetrically important source of

fluids and dissolved constituents to the coastal ocean.

The coastal waters in the South Atlantic Bight are

significantly enriched in Z2hRa and groundwater is

the likely source of this excess radium [34]. Based on a mass balance approach. Moore calculated that the

groundwater flow may represent up to 40% of the river flow into this region. A similar discharge esti- mate based on the “hRa inventory of the sub-

pycnocline waters from the Gulf of Mexico study area is given here.

The average summertime lZhRa concentration in

these waters is 0.46 + 0.17 dpm I-’ (n = 168). Since

open Gulf of Mexico waters contain an average of

0. I 1 dpm I - ’ [27], we have an excess of 0.35 dpm I-’ to account for. River flow in this area is domi-

nated by the Apalachicola River, which has a total

Table 2

Estimates of the benthic advective fluid flow into the 630 km’ study area -7, --- Rn source “‘Rn in advecting Current velocity Velocity of pore Total subburface fluid

fluids (dpm I-’ ) (cmsec-‘1 fluids (cm day ’ ) flow cm3 set- ’ )

C,, . Groundwater 560 f 90 0.5 2.5 180

Wells 1.5 2.7 190

C,,, , Sediment 169 5- 62 0.5 9.3 670 Equilibration 1.5 10 710

The two different estimates used for the fluid “’ Rn concentrations were: (1) groundwater wells: and (7) sediment equilibration experiments.

The estimates are also made for both 0.5 and I .5 cm set- ’ current velocities and are based on a typical summer sub-pycnocline ‘“Rn inventory of 30.000 dpm rn- ‘,

602 J.E. Cable et al./ Earth and Planeta? Science Letters 144 (19961 591-604

radium discharge of 8.08 X 10’ dpm day-’ [35]. charge, a stable sub-pycnocline system must be pre- Dividing that discharge by the volume of the study sent and some information on current flow and 2’2Rn area (620 km’ X 10 m bottom layer thickness = 6.2 concentrations in the coastal aquifer, sediment pore X 10” 1) results in a radium flow per day into the waters, water column, and sediments must be avail- study area of 13 X 1O-4 dpm 1-l dayy’. We esti- able. The radon approach works well in our inner mate the average residence time for water in the shelf environment because the density stratification study area at about 24 days, based on the average prevents significant transport of benthic-derived summertime net flow (N 1 cm set-‘> from the species through the pycnocline and the slow circula- current meter data. The river contribution to the tion ensures that there is little net flow over a time

radium balance is thus 13 X lop4 dpm 1-l day-’ X period comparable to the mean life of *“Rn. As is

24 days = 0.03 1 dpm 1~ ’ , less than 10% of the common in many coastal areas, the major loss term ‘excess’ 226Ra observed. for 2”Rn becomes radioactive decay, which can be

The net excess that remains to be balanced is thus easily modeled. 0.35 dpm 1-l minus the river contribution (N 0.031

dpm 1-l) or about 0.32 dpm 1-l. We convert this to

a required radium activity per time estimate by scal-

ing the excess to the entire volume of the sub- pycnocline waters (6.2 X 10” 1) and dividing by the

24 day residence time. This results in an estimate of

8.2 X 10” dpm day-‘, which must be balanced by another source, most likely subsurface fluid flow.

Diffusion of ‘26Ra from bottom sediments can only

account for approximately l-3% of this excess for the time scale being considered. At this point, one

may calculate the discharge by estimating the ‘26Ra

concentration of the advecting fluids. Taking the

calculated excess 2’6Ra to be balanced (8.2 X 10”

dpm day- ’ ) and dividing by the geometric mean for

‘26Ra in Florida groundwater (excluding the phos-

phate mining district) of 2 dpm 1-l [36], we arrive at

an estimated discharge into the study area of 500 m3

set-’ - very close to the middle of the range

(180-710 m3 set-‘) based on the *“Rn model.

Hydrographic measurements of the inner shelf

waters in a small area of the Gulf of Mexico showed that a two-layered, estuarine-like system develops in

the summer in which the bottom layer moves in a shoreward direction while the surface mixed layer

moves offshore. This two-layered structure allowed

us to construct a mass balance for 222Rn for just the

sub-pycnocline layer, eliminating the need to con-

sider atmospheric losses. Based on measured current

velocities and the size of our study area, radon transport to or from adjacent coastal areas was unim- portant under normal flow conditions. The magni-

tude of horizontal eddy diffusivity is low, similar to

molecular diffusion from sediments, and does not significantly influence the “‘Rn budget. During

sluggish summer circulation, advective transport of water masses across the continental shelf influences.

but does not control, the measured water column “‘Rn concentrations. Entry of lower-concentration

offshore waters into the region is accounted for in the model and exchange with adjacent coastal areas

will not result in any significant variation in radon

inventories. We demonstrated that water column transport and diffusion from sediments are insuffi-

cient to support the measured “‘“Rn inventories. The

only other reasonable source for this radon is via sediment pore fluids, relatively concentrated in radon, advecting from the seafloor, as supported by benthic flux experiments and direct seepage measurements. This fluid flow, probably a combination of ground- water and recirculated seawater, is thought to be driven by the hydraulic head on the coastal aquifers. Estimates of the magnitude of this flow indicate that this source is volumetrically important - compara- ble in discharge to the major rivers of Florida.

4. Summary and conclusions

Radon-222 is a useful natural tracer of groundwa-

ter discharge into the coastal zone because: (1) it is chemically conservative and easily measured; (2) it is 3-4 orders of magnitude more concentrated in groundwater than seawater; and (3) it decays at a rate comparable to the time scale of many coastal processes. Regional estimates of coastal subsurface discharge may be made by application of a box model based on deep water ’ 2Rn inventories. In order to apply this model for estimating fluid dis-

J.E. Cable et al. / Earth and Planetary Science Letters 144 (19961591-604 603

Acknowledgements

Project funding was provided by the National Science Foundation (OCE-9 I-01 797) and Earth-

watch, Inc. to WCB, JPC. and GLW. The efforts of

Capt. S. Wilson of the R/V Semiptole, G. Bugna, P.

Cable, R. Corbett, and M. Shultz, and many Earth- watch volunteers are gratefully acknowledged for

their help in completing this work. D. Hunley and J. Ritch of the FSU Current Meter Facility built, pro-

grammed, and deployed the current meters. R.

Harkema compiled the current meter data after ex-

periments were complete. The FSU support staff and facilities of the Academic Diving Program, Marine

Laboratory, and Oceanography Machine Shop were essential to our research. We thank W. Sturges, J.

Carroll, and W.S. Moore for their helpful comments

on earlier versions of this manuscript. [MKI

References

[ll

[21

[31

I41

151

J. Carroll, K. Falkner, E. Brown and W. Moore, The role of

the Ganges-Brahmaputra mixing zone in supplying barium

and ZZhRa to the Bay of Bengal, Geochim. Cosmochim. Acta

57. 29x1-2990, 1993.

P. Swarzenski, B. McKee and J. Booth. Uranium geochem-

istry on the Amazon shelf: Chemical phase partitioning and

cycling across a salinity gradient, Geochim. Cosmochim.

Acta 59. 7-1X. 1995.

R. Aller. Experimental studies of changes produced by de-

posit feeders on pore water. sediment, and overlying water

chemistry. Am. J. Sci. 278, 11X5-1234, 197X.

W. Berelson. D. Hammond and C. Fuller. Radon-222 as a

tracer for mixing in the water column and benthic exchange

in the southern California borderland, Earth Planet. Sci. Lett.

61, 41-54, 1982.

J. Edmond, C. Measures, R. McDuff, L. Chan. R. Collier, B.

Grant, L. Gordon and J. Corliss, Ridge crest hydrothermal

activity and the balance of the major and minor elements in

the ocean: The Galapagos data, Earth Planet. Sci. Lett. 46.

l-18. 1979.

[6] J. Chanton, C. Martens and C. Paul], Control of pore water

chemistry at the base of the Florida escarpment by processes

within the platform, Nature 349, 229-231. 1991.

[7] F. Kohout, Submarine springs: A neglected phenomenon of

coastal hydrology. Hydrology 26. 39 I-41 3, 1966. [X] K. Fanning. L. Torres and J. Breland II, ‘a6Ra and “‘Rn

along Florida’s coasts, in: Symp. on Natural Radiation and

Technologically Enhanced Natural Radiation in Florida. pp. 203-209. Florida Chap. Health Phys. Sot.. 1987.

[9] J. Rosenau, G. Faulkner, C. Hendry and R. Hull, Springs of

Florida, US Geol. Surv. Bull. 31. l-461. 1977.

[IO] R. Wanninkhof, P. Mulholland and J. Elwood, Gas exchange

rates for a first-order stream determined with deliberate and

natural tracers, Water Resour. Res. 26. 1621-1630, 1990.

[ 1 I] K. Fanning. R. Byrne. J. Breland II, P. Betzer. W. Moore, R.

Elsinger and T. Pyle. Geothermal springs of the West Florida

shelf: Evidence for dolomitization and radionuchde enrich-

ment. Earth Planet. Sci. Lett. 52. 345-354, 1981.

[I 21 Y.-C. Chung. Excess radon in the Santa Barbara Basin. Earth

Planet. Sci. Len. 17. 319-323. 1973.

[13] G. Tribble, F. Sansone. R. Buddemeier and Y.-H. Li. Hy-

draulic exchange between a coral reef and surface sea water,

Geol. Sot. Am. Bull. 104. 12X0-1291, 1992.

[I41 D. Thistle, G. Weatherly. A. Wonnacott and S. Ertman,

Suspension by winter storms has an energetic cost for adult

male benthic harpacticoid copepods at a shelf site, Mar Ecol.

Prog. Ser. 125. 77-86. 1995.

[ !5] J. Young, Tracing groundwater Flow into the northeastern

Gulf of Mexico using naturally occurring radon-222. Ph.D.

Thesis, Florida State Univ.. Tallahassee, FL. 330 pp.. 1996.

[ 161 W. Broecker. The application of natural radon to problems in

ocean circulation, in: Symp. on Diffusion in Oceans and

Fresh Waters. T. lchiye. ed.. pp. 116-145. Lamont-Doherty

Geol. Observatory, Pahsadea. NY, 1965.

[17] G. Mathieu, P. Biscayne. R. Lupton and D. Hammond.

System for measurement of “‘Rn at low levels in natural

waters, Health Phys. 55. 9X9-992, 1988.

[18] J. Cable, G. Bugna. W. Burnett and J. Chanton. Application

of “‘Rn and CH, for assessment of groundwater discharge

to the coastal ocean, Limnol. Oceanogr. 41(6). l437- 1444,

1996.

[19] C. Martens. G. Kipphut and J. Klump. Sediment-water

chemical exchange in the coastal zone traced by in situ

radon-222 flux measurements, Science 208, 285-288, 1980.

[20] D. Lee. A device for measuring seepage flux in lakes and

estuaries, Limnol. Oceanogr. 22, 140- 147. 1977.

[21] G. Marmorino. Variability of current. temperature, and bot-

tom pressure across the West Florida continental shelf, win-

ter 1981-1982. J. Geophys. Res. XX. 4439-4457, 1983.

[22] G. Marmorino, Summertime coastal currents in the northeast-

ern Gulf of Mexico, J. Phys. Oceanogr. 13. 65-77. 1983.

[23] G. Buena. J. Chanton, J. Cable. W. Burnett and P. Cable.

The importance of groundwater discharge to the methane

budgets of nearshore and continental shelf waters of the

northeastern Gulf of Mexico, Geochim. Cosmochim. Acta 60

(23). in press, 1996.

K. Fanning. J. Breland and R. Byrne, Radium-226 and

radon-222 in the coastal waters of West Florida: High con-

centrations and atmospheric degassing. Science 215, 667-

670, 1982.

[241

[251

[361

D. Reid, Radium variability produced by shelf-water trans-

port and mixing in the western Gulf of Mexico. Deep-Sea

Res. 31. 1501-1510. 1984.

J. Cable, W. Burnett. J. Chanton, R. Corbett and P. Cable.

Field evaluation of seepage meters in a coastal marine env-

ronment. Estuarine Coastal Shelf Sci., in press.

604 J.E. Cable et al./Earth and Planetary Science Letters 144 (1996) 591-604

1271 J. Sarmiento, H. Feely, W. Moore. A. Bainbridge and W.

Broecker, The relationship between vertical eddy diffusion

and buoyancy gradient in the deep sea, Earth Planet. Sci.

Lett. 32, 357-370, 1976.

[28] T. Lietzke and A. Lerman. Effects of bottom relief in two-di-

mensional oceanic eddy diffusion models, Earth Planet. Sci.

Lett. 24, 337-344, 1975.

[29] H. Craig, Abyssal carbon and radiocarbon in the Pacific, J.

Geophys. Res. 74, 5491-5506, 1969.

[30] T.-H. Peng, T. Takahashi and W. Broecker, Surface radon

measurements in the north Pacific station Papa, J. Geophys.

Res. 79, 1772-1780, 1974.

[31] W. Ullman and R. Aller, Diffusion coefficients in nearshore

marine sediments, Limnol. Oceanogr. 27, 552-556, 198 1.

[32] E. Rona, Diffusionsgrosse und atomdurchmesser der radi-

umemanation, Z. Physikal. Chem. 92, 213-218. 1917.

[33] E. Fernald and D. Patton, Water Resources Atlas of Florida,

291 pp., Florida State Univ. Tallahassee, FL, 1985.

[34] W. Moore, Large groundwater inputs to coastal waters re-

vealed by “‘Ra enrichments, Nature 380, 612-614, 1996.

[35] W. C. Burnett, J. Cowart and S. Deetae, Radium in the

Suwanee River and Estuary - spring and river input to the

Gulf of Mexico, Biogeochemistry 10, 237-255, 1990.

1361 R. Kaufman and J. Bliss, Effect of phosphate mineralization

and the phosphate industry on Ra-226 in groundwater of

central Florida, 114 pp., EPA Publ. 520-6-77-010, 1977.