Surface-Water Radon-222 Distribution along the 

West-Central Florida Shelf

By C.G. Smith and L.L. Robbins

Open-File Report 2012-1212

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

Kenneth Salazar, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director 

U.S. Geological Survey, Reston, Virginia 2012

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Suggested citation:

Smith, C.G., and Robbins, L.L., 2012, Surface-water radon-222 distribution along the west-central Florida shelf: 

U.S. Geological Survey Open-File Report 2012-1212, 26 p.

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Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted material contained within this report.
i

Table of Contents

Abstract ....................................................................................................................................................... 1

Introduction ................................................................................................................................................. 1

Methods....................................................................................................................................................... 3

Radon-222 Mapping............................................................................................................................... 3

Water-Column Radon-222 Flux and Mass Balance ............................................................................... 5

Results and Discussion ............................................................................................................................... 7

Spatial and Temporal Radon Mapping Data........................................................................................... 7

Radon-222 Production and Decay ....................................................................................................... 10

Radon-222 Evasion.............................................................................................................................. 12

Radon-222 Cross-Shelf Mixing ........................................................................................................... 13

Radon-222 Benthic Fluxes .................................................................................................................. 16

Summary ................................................................................................................................................... 19

Acknowledgments .................................................................................................................................... 20

References Cited....................................................................................................................................... 20

Figures

1. Map showing tracklines for the February 2009 and August 2009 cruises. ............................................4

2. Map showing surface-water radon-222 activity for the February 2009 and August 2009 

cruises.................................................................................................................................................... 8

3. Radon-222 activity plotted as a function of distance from the shoreline for the February 2009 and 

August 2009 cruises............................................................................................................................... 9

4. Wind speed normalized to 10 meters above sea-level from NOAA Buoys 42036 and 42013 

for the February 2009 and August 2009 cruises .................................................................................. 10

5. Regression analysis of atmospheric evasion rates of radon-222.........................................................12

6. Map showing atmospheric radon-222 flux for the February 2009 and August 2009 cruises.................13

7. Atmospheric radon-222 flux plotted as a function of distance from the shoreline for the 

February 2009 and August 2009 cruises.............................................................................................. 14

8. Evasion-corrected excess radon-222 inventories plotted as a function of distance from the shoreline for 

the February 2009 and August 2009 cruises........................................................................................ 17

Tables

1. Summary of the boundary conditions and optimal parameters determined for the cross-shelf 

mixing and benthic flux model of evasion-corrected excess radon-222 inventory as a function of 

distance offshore.................................................................................................................................. 15

2. Summary of radon-222 fluxes (Bq m-2 d-1) from several studies along the eastern and 

northeastern Gulf of Mexico. ................................................................................................................ 18
ii

iv 

Conversion Factors

SI to Inch/Pound 

Multiply By To obtain 

Length 

centimeter (cm) 0.39370 inch (in.)

meter (m) 3.28083 feet (ft)

kilometer (km) 0.62137

Volume 

milliliter (mL) 0.03382 ounce, fluid (fl. oz)

liter (L) 0.26417 gallon (gal)

cubic meter (m3) 35.31446 cubic foot (ft3) 

Mass 

gram (g) 0.03527 ounce, avoirdupois (oz)

Radioactivity 

becquerel (Bq) 27.02703 picocurie (pCi) 
1

Surface Water Radon-222 Distribution along the 

West-Central Florida Shelf

By C.G. Smith and L.L. Robbins

Abstract

In February 2009 and August 2009, the spatial distribution of radon-222 in surface water 

was mapped along the west-central Florida shelf as collaboration between the Response of Florida 

Shelf Ecosystems to Climate Change project and a U.S. Geological Survey Mendenhall Research 

Fellowship project. This report summarizes the surface distribution of radon-222 from two cruises 

and evaluates potential physical controls on radon-222 fluxes. Radon-222 is an inert gas produced 

overwhelmingly in sediment and has a short half-life of 3.8 days; activities in surface water ranged 

between 30 and 170 becquerels per cubic meter. Overall, radon-222 activities were enriched in 

nearshore surface waters relative to offshore waters. Dilution in offshore waters is expected to be 

the cause of the low offshore activities. While thermal stratification of the water column during the 

August survey may explain higher radon-222 activities relative to the February survey, radon-222 

activity and integrated surface-water inventories decreased exponentially from the shoreline during both cruises. By estimating radon-222 evasion by wind from nearby buoy data and accounting 

for internal production from dissolved radium-226, its radiogenic long-lived parent, a simple onedimensional model was implemented to determine the role that offshore mixing, benthic influx, and 

decay have on the distribution of excess radon-222 inventories along the west Florida shelf. For 

multiple statistically based boundary condition scenarios (first quartile, median, third quartile, and 

maximum radon-222 inshore of 5 kilometers), the cross-shelf mixing rates and average nearshore 

submarine groundwater discharge (SGD) rates varied from 100.38 to 10-3.4 square kilometers per 

day and 0.00 to 1.70 centimeters per day, respectively. This dataset and modeling provide the first 

attempt to assess cross-shelf mixing and SGD on such a large spatial scale. Such estimates help 

scale up SGD rates that are often made at 1- to 10-meter resolution to a coarser but more regionally 

applicable scale of 1- to 10-kilometer resolution. More stringent analyses and model evaluation are 

required, but results and analyses presented in this report provide the foundation for conducting a 

more rigorous statistical assessment. 

Introduction 

Radon-222, which has a half-life of 3.82 days (t1/2 = 3.82 d), is a naturally occurring radionuclide that originates from the uranium-238 decay series through the alpha decay of radium-226. 

Radon (Rn) behaves conservatively in most chemical reactions in nature (except weak van der 
2

Waal bonds). Dissimilar geochemical behaviors of radium (Ra) and Rn provide for a unique system 

where the daughter elements can easily decouple, and depending on the environment and processes 

(turbulent mixing, groundwater flow), either enrichment or deficiencies of the daughter isotopes 

relative to their radiogenic parents are likely. Due to its utility more so than its ease of measurement, radon-222 has been used to quantify benthic exchange (Broecker and others, 1967; Clements 

and Wilkening, 1974; Hammond and others, 1977; Gruebel and Martens, 1984; Hoehn and others, 

1992; Bertin and Bourg, 1994; Cable and others, 1996a). The recent advent of continuous radon-inair monitoring devices has allowed for increased continuous monitoring of radon-222 in coastal and 

shelf waters (Dulaiova and others, 2005). Because radon-222 is produced primarily by ingrowth 

from sediment-bound radium-226 (hereafter referred to as sedimentary production) in the natural 

environment, the enrichment of radon-222 in coastal waters has been linked to a phenomenon commonly referred to as submarine groundwater discharge (SGD), a form of enhanced benthic fluid 

flux. Submarine groundwater discharge has been implicated as a major vector, delivering trace metals, nutrients, and a variety of other dissolved constituents to the coastal region. In this study, we 

examine the spatial distribution of radon-222 along the west Florida shelf (WFS) and evaluate its 

spatial distribution in terms of potential benthic fluxes. 

Submarine groundwater discharge is defined as any and all fluids discharged from benthic 

sediments into coastal water bodies (Burnett and others, 2003) and consists of both marine (recirculated) and terrestrial fluid sources. Submarine groundwater discharge has long been recognized 

as a potential vector for ecologically important and deleterious constituents to the coastal oceans 

(Johannes, 1980). However, it has not been until the last decade, with the advent of reliable SGD 

measurement techniques, that quantification of material fluxes and suggested subsequent ecological impacts have been possible. Of the two SGD components, the terrestrial fraction represents the 

allochthonous contribution and is the most provocative source when investigating the interactions 

between the ecology and hydrology in coastal systems. Human activities onshore, including on-site 

waste disposal and agriculture, can contribute allochthonous nutrients to the shallow coastal waters. 

Several studies have linked SGD to coastal nutrient loading (Hwang and others, 2005; Kroeger and 

others, 2007), but it has not been quantitatively determined whether SGD is directly linked to specific events such as harmful algal blooms (HABs). 

Along the west Florida coast, three aquifers are exposed at or near land surface and are hydrologically connected to the coastal ocean; they are, from north to south, the Floridan aquifer, the 

Surficial aquifer, and the Biscayne aquifer. North of Tampa, the Floridan aquifer crops out and is 

recharged directly by precipitation. The Surficial aquifer is exposed at or near the land surface from 

south of Tampa to almost the southern tip of Florida within the Everglades National Park. The Biscayne aquifer underlies the southern portion of the Everglades National Park. Where these aquifers 

are exposed at the land-sea margin, they provide a potential source of submarine groundwater to the 

coastal ocean. In addition to this shoreline connection, several studies have shown that appreciable 
3

SGD occurs from submarine springs sourced primarily by the Floridan aquifer (Fanning and others, 

1987). Thus, submarine groundwater may represent a formidable vector for new nutrients to the 

west Florida shelf.

Recent studies conducted in the Tampa Bay region of Florida have examined submarine 

groundwater discharge and its role in nutrient delivery to this coastal embayment (Kroeger and 

others, 2007; Swarzenski and others, 2007). Swarzenski and others (2007) surveyed the entire bay 

and found that SGD-derived total dissolved nitrogen (TDN) was on the same order of magnitude as 

local riverine inputs. Similarly, Kroeger and others (2007) looked at SGD-derived nutrient fluxes 

from the southern tip of Pinellas County into the adjacent nearshore region. Based on their results, 

fresh SGD delivered comparative quantities of allochthonous TDN and PO4

3- as do local streams, 

while saline SGD delivered approximately 70 percent and 223 percent of TDN and PO4

3-, respectively, as compared to local streams (Kroeger and others, 2007). These studies show that SGD plays 

an important role in the nutrient delivery to this embayment and further indicate that SGD may be 

an important vector for nutrient delivery to the shallow WFS.

In this study, we utilize a previously unpublished dataset of over 1,000 radon-222 activity 

measurements made during two separate cruises (600+ in February 2009 and 400+ in August 2009) 

along the WFS. The objectives were to determine (1) whether the data provide insight to the physical and potentially geologic controls on radon-222 distribution across a broad shelf and (2) whether 

a simple parameterized model can be used to quantitatively extract meaningful rates of benthic 

radon-222 flux (analogy for SGD) and cross-shelf mixing. Previous investigations that utilized radon-222 to quantify these processes have been restricted to relatively small, linear scales (generally 

represented as a function of distance from the shoreline). Here, we build upon previous models to 

evaluate if and how radon-222 observations can be scaled up. 

Methods

Radon-222 Mapping

Radon-222 surveys along the WFS were conducted February 23-28 and August 16-21, 

2009, in collaboration with the U.S. Geological Survey Coastal and Marine Geology Program 

(CMGP)-funded project Response of Florida Shelf Ecosystems to Climate Change. Tracklines 

are shown in figure 1. Radon extraction and measurement followed the procedure of Dulaiova and 

others (2005). Briefly, surface water was continuously pumped (2 to 5 liters per minute; L min-1) 

from a through-hull opening at approximately 1.5 meters (m) below the sea surface to an air-water 

equilibration chamber. Radon was separated from the water into the headspace of the chamber. 

Using three commercially available radon-in-air detection devices with internal air pumps (RAD7, 
4

Durridge, Inc.), radon-222 in the air phase was circulated and analyzed via its short-lived decay 

product, polonium-218. Count integration time for both trips was 10 min. Chamber temperature 

was monitored to accurately convert in-air concentrations to in-water concentrations. Based on system background count rates measured before, during, and after the cruises, the minimum detectable 

activity (MDA) in the system was 2.7±0.5 becquerels per cubic meter (Bq m-3) (n=6). All errors are 

reported to one standard deviation unless otherwise noted. In addition to radon-222, salinity and 

temperature were measured continuously using a flow-through conductivity and temperature probe 

system (YSI 6600).

Sampling density (~0.3 to 1 sample per kilometer) was governed by the speed of the boat 

(2.5 to 5 meters per second, m s-1) and integration time (10 min). These measurements are much 

Figure 1. Map showing tracklines (black arrowheads) for the (A) February 2009 and (B) August 2009 cruises. Warmer 

colors on land indicate higher elevations that decrease down-gradient to greenish-blue. Colored lines beyond the 

shoreline (solid black line) are bathymetry, increasing from blue (shallowest) to red (deepest). Abbreviations: m, meter; m 

asl, meters above sea level.
5

coarser than observed in other coastal mapping studies. Position was continuously recorded at 

2-min intervals (datum WGS84) and integrated with the radon data during post-processing. Once 

integrated, the data were analyzed using GIS software (ESRI ArcGIS). The distance between midpoint sampling locations and shoreline (NOAA, 2012a) was determined using the built-in ArcToolbox function NEAR (ESRI). The NEAR function computes the shortest distances between two 

vector datasets and records the distance and angle. Given the irregularity of the shoreline, not all 

measurements were orthogonal to the shoreline. Assessment of potential error due to non-orthogonal measurements was determined to be less than or equal to 20 m. Depth was extracted for each 

radon measurement from the National Geophysical Data Center bathymetric model for the Gulf of 

Mexico (NOAA, 2012b).

Water-Column Radon-222 Flux and Mass Balance

Processes affecting water-column radon-222 have been defined for a variety of coastal 

and deep marine settings (Broecker and others, 1967; Broecker and Peng, 1971; Peng and others, 

1974; Fanning and others, 1982; Cable and others, 1996b; Colbert and others, 2008). Assuming 

water-column radon-222 inventories are in steady state, the balance between sources and sinks 

must equate to the decay-corrected water-column inventory (Craig, 1969; Cable and others, 1996b; 

Corbett and others, 1997). The model is often represented for a known water-column thickness ( z ; 

m) and unit area (m2) such that the 222Rn inventory ( IRn ; Bq m-2) in steady state is

 

In well-mixed, shallow-water systems, benthic flux ( benthic J ; advection and diffusion) from 

sediments is the primary source of radon-222 in the water column. Additional sources of radon-222 

to the offshore surface layer include mixing fluxes from the coastal zone and production from dissolved radium-226 (Cable and others, 1996b; Burnett and Dulaiova, 2003). Losses of radon-222 

from the surface layer include atmospheric evasion, decay, and (or) mixing loss. While this model 

is fairly simplistic, the utility of modeling radon-222 exchange and its relationship to benthic fluxes 

has proven quite robust. 

dIRn

dt = 0 = Jbenthic − Jatm ± Jmix + ⎡z(λ RnARa − λ RnARn ) ⎣ ⎤

⎦ (1)

where losses due to water-column mixing ( mix J ; becquerels per square meter per day, Bq m-2 d-1), 

atmospheric evasion ( atm J ; Bq m-2 d-1), and depth-integrated in-situ decay (zλ RnARn ; Bq m-2 d-1) 

are balanced by benthic flux of 222Rn ( benthic J ; Bq m-2 d-1), depth-integrated production from 226Ra 

(  Az RaRn ; Bq m-2 d-1), and lateral inputs ( benthic J ; Bq m-2 d -1). Solving the equation for benthic J provides a direct estimate for total benthic fluxes, provided estimates of the other sources and sinks are 

available.
6

Atmospheric evasion ( atm J ) can represent a formidable loss term with respect to both coastal 

and open-ocean surface-water radon-222 (Peng and others, 1979; Burnett and others, 2007; Smith 

and others, 2011). Models of radon evasion (or atmospheric flux, atm J ) have been well represented 

in the literature and are of the form:

  atm Rnw Rnair  AAkJ (2)

where k is the gas transfer coefficient (m s-1), Rnw A and Rnair A are the radon content in the water and 

the air (Bq m-3), and  is the Ostwald solubility coefficient. In most coastal and open-ocean settings, atmospheric concentration is negligible (Burnett and others, 2007). Thus, a first-order estimate of atmospheric flux is

Jatm = kARnw

(3)

Estimates of the gas transfer coefficient [ k(600)] generally rely on empirical formulas that are 

functions of wind velocity at (u10 ; m s-1) (MacIntyre and others, 1995): 

6.1 2/1

10 (600 .0) 45 ( 600)

 k  u Sc (4)

where Sc is the Schmidt number (ratio of molecular diffusion and kinematic viscosity). The dependence of the Sc on temperature and salinity allows for relating the transfer to variable in-situ conditions. Wind velocity was not measured shipboard; instead, wind velocity acquired at two offshore 

buoys and data distributed by the National Data Buoy Center (NOAA, 2012c) were used to assess 

atmospheric evasion. Locations of the two buoys used in this study (Station 42021 at 28.500o N.

and 84.417o W. and Station 42013 at 27.169o N. and 82.926o W.) are presented in figure 1. All data 

were normalized to a measurement height of 10 m using the power-law function presented by Hsu 

and others (1994).

Equations describing the offshore turbulent mixing ( Kh ; m2 d-1) of a conservative, short-lived 

radioactive tracer have been presented by Moore (2000). The general form is 

  0 

 



 x

x

h A

dx

dA K

dx

d  (5)

with the general solution for the boundary conditions 0 0( ) == AxA and  0

L

x

dx

dA

 

    x 0   KxAA h lnln (6)

where Ax and A0 are specific activities (Bq m-3) at some x distance offshore (m) and at the shoreline, respectively, and λ is the decay coefficient of the radionuclide (d-1). Since atmospheric evasion can enhance radon-222 loss across the shelf, non-gaseous tracers are typically used (for exam-
7

ple, radium-223 and radium-224) to determine the mixing coefficient and then subsequently applied 

to radon-222 gradients. However, since the radium isotopes were not measured in this study, the 

mixing coefficient ( Kh ) could not be determined in this manner. As an alternative, we used an 

advection-diffusion equation similar to that presented by Hancock and others (2006):

 

 d

dx

Kh

dIRn

dx

⎛

⎝

⎜ ⎞

⎠

⎟ − λIRn = −Bx (7)

where Bx (Bq m-2 d-1) is a benthic source term written as a function of distance offshore. Equation 

7 was modified to examine excess inventory as opposed to specific activity. Excess inventory was 

determined by correcting for atmospheric evasion and water-column production prior to modeling. 

For this study, Bx was written as an exponential function based on trends observed by Smith and 

Swarzenski (2012):

Cx

x eBB   0 (8)

where B0 is the flux at x = 0 (Bq m-2 d-1) and C is a decay constant (m-1 or km-1). Equation 7 was 

solved numerically using a fully implicit, central difference approach. Boundary conditions for 

equation 7 were chosen as a fixed inventory (Dirichlet type) at the coastal boundary and a no-flux 

boundary (Neumann type) beyond 80 km offshore. The first quartile, median, third quartile, and the 

maximum of the ln-transformed nearshore inventories (< 5 km offshore; n = 46 for February 2009 

and n = 53 for August 2009) were used to evaluate dependence on the variance of the nearshore 

data. The model was optimitized for h 0 ,, CBK using the Nelder-Mead simplex algorithm (Nelder 

and Mead, 1965; Press, 1992) and a modified 2  goodness-of-fit parameterization:

χ2 = IRni ,meas − IRni ,calc(Kh ,B0 ,C)

σ Rni ,meas

⎛

⎝

⎜

⎞

⎠ i=1 ⎟ n

∑ + t

IRni ,meas − IRni ,calc(Kh ,B0 ,C)

σ Rni ,meas

⎛

⎝

⎜

⎞

⎠ i=1 ⎟ n

∑ (9)

where Rn meas i I , and IRni ,calc are the measured and calculated radon inventories, respectively; Rn meas i  ,

is the error in the measured inventory, and t is a weighting factor to ensure fitting parameters are 

greater than 0. 

Results and Discussion

Spatial and Temporal Radon Mapping Data

Total radon-222 activities measured during the February and August 2009 cruises are presented in figure 2. The data show inherently higher radon-222 activities closer to the shoreline and 

decreasing activities farther offshore. Two general areas that have consistently high radon-222 ac-
8

tivities are offshore Indian Rocks Beach and Venice, Fla. In these regions, radon-222 activities are 

two times higher than similar shallow-water sections of the survey. Offshore activities are consistently low. The two-dimensional context of the data provides some insight to the regional heterogeneity of surface radon-222 distribution; however, converting the data into one dimensional (that is, a 

function of distance offshore) provides more generic yet quantitative trends at the entire shelf scale. 

During the February 2009 cruise, 662 individual surface-water radon-222 activities were 

determined with only 6 samples falling below the MDA. Radon-222 activities for the remaining 

656 measurements ranged between 3.21 and 120 Bq m-3. Activities decrease exponentially with 

respect to both distance offshore (r2

 = 0.70) and water depth (r2 = 0.45; not shown). In both cases, 

radon-222 activities merged to an asymptotic activity of 8.0±3.3 Bq m-3 (n = 209), which corresponds to approximately 40 km offshore or approximately 20-m water depth (fig. 3). Inshore of the 

Figure 2. Map showing surface-water radon-222 activity for the (A) February 2009 and (B) August 2009 cruises. 

Warmer colors on land indicate higher elevations that decrease down-gradient to greenish-blue. Colored lines beyond 

the shoreline (solid black line) are bathymetry, increasing from blue (shallowest) to red (deepest). Abbreviations: m, 

meter; m asl, meters above sea level; Bq m-3, becquerels per cubic meter.
9

20-m isobath, radon-222 activities were more variable, having a range of 4.34 to 117 Bq m-3, with 

approximately 96 percent of the nearshore data greater than the offshore mean radon activity. 

During the August 2009 cruise, 454 measurements of individual surface water radon-222 

activities were determined with only 5 samples falling below the MDA. Radon-222 activities for 

the remaining 449 measurements ranged between 3.50 and 178 Bq m-3. Radon-222 activities decrease offshore; however, regression with distance (r2

 = 0.45) and water depth (r2 = 0.25; not shown) 

are less robust than during the February cruise (fig. 3). Offshore radon-222 activities merge at approximately 40 km offshore or approximately 20-m water depth. The asymptotic radon-222 activity 

is 11.5±6.0 Bq m-3 (n = 70). Nearshore data (that is, inshore of the 20-m isobath) range from 4.17 

to 178 Bq m-3, with approximately 88 percent of the nearshore data greater than the offshore mean 

radon activity.

Time-series wind-velocity data from two offshore buoys are presented in figure 4. In general, the winds were on average slightly calmer during the August (2.79 m s-1) cruise than during the 

Figure 3. Radon-222 activity plotted as a function of distance from the shoreline for the (A) February 2009 and (B) 

August 2009 cruises. Solid red line indicates the mean offshore radon-222 activity, which is interpreted as the supported 

radon-222 in secular equilibrium with radium-226. Dashed red lines are one standard deviation about the mean. Green line 

is an exponential regression of the data. Abbreviations: km, kilometer; Bq m-3, becquerels per cubic meter; SD, standard 

deviation. 
10

February cruise (3.22 m s-1). However, temporal variation (range) during each sampling trip was 

quite large, with higher wind velocities observed during the first day of each cruise and slowly dying down thereafter. The wind velocities observed at two buoys during each cruise were regionally 

coherent, with only slight differences in the overall wind velocity at any point in time between the 

two buoys (fig. 4).

Radon-222 Production and Decay

Estimates of radon-222 production from the natural decay of radium-226 at the shelf scale 

were made through careful examination of total radon-222 data. Previous investigations (Fanning 

and others, 1981, 1982; Smith and Swarzenski, 2012) along the WFS have found relatively constant radium-226 values at least at the shelf scale. Fanning and others (1982) found that cross-shelf 

distribution of radium-226 was fairly uniform (9.67±4.67 Bq m-3; n = 12) in the surface mixed layer 

between Tampa Bay and Charlotte Harbor, Fla. Smith and Swarzenski (2012) observed similar 

activities (6.33±3.00 Bq m-3; n = 10) along the inner WFS north of Tampa Bay. Considering the 

extent of this study, we felt it reasonable to assume that the radium-226 activity of the surface water 

was spatially homogeneous. Building from this assumption, total radon-222 values beyond approxFigure 4. Wind speed normalized to 10 m above sea level from the NOAA Buoys 42036 (northern) and 42013 

(southern) for the (A) February 2009 and (B) August 2009 cruises. Abbreviations: m, meter; m s-1, meters per second.
11

imately 40 to 60 km (20-m isobath) were fairly constant. In fact, average total radon-222 measured 

beyond 40 km during the February and August 2009 cruises were 8.00±3.33 Bq m-3 and 11.5±6.0 

Bq m-3, respectively, and were within the same range as previously published radium-226 activities. 

Hence, it seemed reasonable to interpret these asymptote total radon-222 activities as the marine 

background and sourced solely by the decay of dissolved radium-226 in the water column. By assuming secular equilibrium with radon-222 and radium-226 across the shelf, radon-222 production 

rates were computed as  ARaRn . Thus, the shelf-wide production rates of radon-222 for February 

and August were 1.45±0.60 Bq m-3 d-1 and 2.09±1.09 Bq m-3 d-1, respectively.

Radon loss (decay flux) in the water column due to radioactive decay was determined using 

λ RnARn . Since the fluxes are linearly related to the specific activity, the same two- and one-dimensional patterns were observed in the data. During the February cruise, radon decay flux ranged 

between 0.58 and 21.3 Bq m-3 d-1, with a mean flux of 3.90±3.58 Bq m-3 d-1. Like specific activity 

during the August cruise, average radon decay flux was higher (6.59±5.28 Bq m-3 d-1) than during 

February but with a similar range (0.63 to 32.29 Bq m-3 d-1). 

As shown in equation 1, production and decay fluxes must be integrated over the thickness 

of the mixed layer / water column in order to compare with other sources (benthic fluxes, mixing) 

and sinks (mixing, atmospheric evasion). Unfortunately, vertical hydrographic profiles of salinity, temperature, and depth were not performed on either of the cruises. However, the decrease of 

radon-222 activities to near-shelf background activities at approximately the 20-m isobath provides 

an interesting observation. In general, stratification along the WFS is quite variable throughout the 

year (Morey and O’Brien, 2002). During winter months, warmer Gulf of Mexico and cooler shelf 

waters mix relatively isotropically across the shelf, with horizontal stratification occurring out to the 

shelf – slope break. During the summer months, increased heat flux and relaxed local wind forcing 

create a vertical stratification across much of the shelf and slope system. However, vertical summer- and winter-density gradients within the 20-m isobath are less defined than for the rest of the 

WFS. Water-column profile data collected as part of the National Oceanic and Atmospheric Administration (NOAA)-funded study (that is, Ecology and Oceanography of Harmful Algal Blooms or 

ECOHAB:WFS) show nearly horizontal thermal and salinity gradients inshore of the 20-m isobath 

for both the summer and winter seasons (Liu and Weisberg, 2007). Based on this observation, we 

computed an initial radon-222 water-column inventory by assuming radon is evenly distributed 

throughout the entire water column inshore the 20-m isobath. Smith and Swarzenski (2012) showed 

this assumption is fairly reasonable between the 5- and 20-m isobath. When water depths exceed 

20 m, we assume a 20-m-thick mixed upper water column. Moore and Shaw (2008) made similar 

observations and assumptions for the Atlantic Ocean offshore from Georgia and Florida. 
12

Radon-222 Evasion

Atmospheric fluxes were computed using equation 2 and the assumption that the atmospheric radon concentration was negligible. To test the validity of this assumption, we compared 

the atmospheric fluxes for the February cruise assuming radon-in-air concentrations of 0.00 and 10 

Bq m-3

air (or 0.00 and 2.67 Bq m-3water at 25 o

C, respectively). Regression analysis between the two 

datasets indicated a nearly 1:1 relationship and a regression coefficient of 1 (fig. 5). 

Similarly, the average absolute difference between these datasets is 0.0019 Bq m-2 d-1, which 

is six orders of magnitude less than the average atmospheric flux (16.7 Bq m-2 d-1) and two orders of 

magnitude less than the minimum atmospheric flux (0.55 Bq m-2 d-1). Thus, for a background atmospheric concentration exceeding the average coastal ocean value of 17 Bq m-3

air, the use of equation 

2 holds. 

The atmospheric fluxes for the February and August cruises are presented in figures 6 and 

7. Atmospheric fluxes varied by approximately four orders of magnitude during both cruises (0.45 

to 202 Bq m-2 d-1) with slightly higher individual fluxes during August (maximum = 202 Bq m-2 d-1) 

Figure 5. Regression analysis of atmospheric evasion rates of radon-222 assuming atmospheric radon-222 activity of 0 

and 10 Bq m-3. Abbreviations: Bq m-2 d-1, becquerels per square meter per day; Bq m-3, becquerels per cubic meter. 
13

relative to February (maximum = 128 Bq m-2 d-1). The mean flux and overall variability were both 

higher during August (26.3±35.0 Bq m-2 d-1) compared with February (16.7±19.5 Bq m-2 d-1) despite 

slightly higher wind velocities in February. This reflects the linear dependence of equations 2 and 3 

on the surface-water concentration, which on average was higher during the August cruise. 

Radon-222 Cross-Shelf Mixing 

Evasion-corrected excess radon-222 inventories (hereafter, just “inventories”) and model results 

are presented in figure 8. Much like radon-222 activity, inventories computed from direct 

measurements were highest near the shoreline and decreased offshore. Inventories for February 

2009 were between 58.7 and 1,820 Bq m-2 with a mean of 363±257 Bq m-2. August 2009 

inventories were slightly higher and were between 67.4 and 2,980 Bq m-2 with a mean of 574±460 

Figure 6. Map showing atmospheric radon-222 flux for the (A) February 2009 and (B) August 2009 cruises. Warmer 

colors on land indicate higher elevations that decrease down-gradient to greenish-blue. Colored lines beyond the 

shoreline (solid black line) are bathymetry, increasing from blue (shallowest) to red (deepest). Abbreviations: m, meter; m 

asl, meters above sea level; Bq m-2 d-1, becquerels per square meter per day.
14

Bq m-2. 

The boundary conditions set by the first quartile, median, third quartile, and maximum inventory for the nearshore data are presented in table 1 for both seasons along with optimized values 

of h 0 ,, CBK . Mixing coefficients ( Kh ) derived from the radon-222 data varied by almost three 

orders of magnitude (10-0.38 – 103.4 km2 d-1). For the median coastal boundary condition scenarios, 

the mixing coefficients were 101.8 and 100.7 km2

 d-1 for the February and August cruises, respectively. 

The mixing coefficients have a negative correlation with both the coastal boundary condition and 

benthic radon-222 flux at the shoreline. 

Despite the seemingly large variation in the mixing coefficients, the range and average of 

these values compare well with the range and average mixing coefficients obtained by radium-223 

and radium-224 (Smith and others, 2011). Based on 13 independent studies using short-lived radium isotopes, mixing coefficients generally range from 10-2 to 103.7 km2

 d-1 (Smith and others, 2011). 

More locally, Smith and Swarzenski (2012) reported radium-based mixing coefficients of 101.2 to 

101.9 km2

 d-1 for the coastal region (within 15 km of the shoreline) offshore from Pinellas County, 

Fla., which lies in the domain of our larger-scale study. Although radon and radium are geochemically different, correcting radon-222 inventories for evasion normalizes the two elements to similar 

(assumed) conservative geochemical behavior. Also, since short-lived radium isotopes (radium-223 

Figure 7. Atmospheric radon-222 flux plotted as a function of distance from the shoreline for the (A) February 2009 and 

(B) August 2009 cruises. Abbreviations: km, kilometer; Bq m-2 d-1, becquerels per square meter per day. 
15

Table 1. Summary of the boundary conditions and optimal parameters determined for the cross-shelf mixing and benthic flux model of evasion-corrected excess radon-222 inventory as a function of distance offshore. Submarine groundwater discharge estimates are based on two separate end-members: 7,000 Bq m-3 (footnote 

1) and 37,000 Bq m-3 (footnote 2).

[Bq m-2, becquerels per square meter; Bq m-3, becquerels per cubic meter; Bq m-2 d-1, becuerels per square meter per day; km2 d-1, square kilometers per day; km-1, per kilometer; cm d-1, 

centimeters per day]

Month in 

2009

Statistical nature 

of the nearshore 

boundary 

condition

Nearshore 

boundary 

condition 

(Constant 

inventory), I0 

(Bq m-2)

Offshore 

boundary 

condition 

(Constant 

flux) 

(Bq m-3)

Mixing 

coefficient, Kh 

(km2 d-1)

Shoreline benthic 

radon-222 flux, B0 

(Bq m-3 d-1)

Benthic 

flux decay 

function, sig 

(km-1)

Submarine 

groundwater 

discharge, SGD 

(cm d-1)

Submarine 

groundwater 

discharge, SGD 

(cm d-1)

February First Quartile 479 0 102.9 0.00 11.49 0.00 0.00

February Median 683 0 101.8 45.8 2.07 0.65 0.12February Third Quartile 959 0 101.3 59.8 3.02 0.85 0.16February Maximum 1824 0 10-0.38 73.21 7.65 1.05 0.20

August First Quartile 546 0 103.4 0.00 89.87 0.00 0.00

August Median 778 0 100.70 64.8 5.52 0.93 0.18

August Third Quartile 1591 0 101.2 85.7 4.26 1.22 0.23August Maximum 2520 0 10-0.35 118.7 10.59 1.70 0.32
16

and radium-224) have a similar decay rate ( λ 223 is 0.0582 d-1 and λ 224 is 0.190 d-1) to radon-222 ( λ 222 

is 0.181 d-1), we feel the comparison to be quite reasonable. 

Radon-222 Benthic Fluxes 

Optimized values of the benthic radon-222 flux ( B0 ) at the shoreline were between 0.00 

(~10-5) and 118 Bq m-2 d-1 for the two trips. The median cases for February and August cruises 

were 45.8 and 64.8 Bq m-2 d-1, respectively. While benthic radon-222 fluxes increased log-linear 

(r2

 = 0.85) with the nearshore boundary condition, the overall variability (excluding the first quartile) was fairly low (average (SD) = 74.7 (25.4) Bq m-2 d-1). The benthic flux decay function coefficient (C ) values were quite variable, with a range of over an order of magnitude for both seasons 

(2.07 and 89.87 km-1). There was no apparent relationship between the decay term (C ) and the 

boundary conditions or the other parameters. The large decay coefficients indicated rapid decay of 

benthic radon-222 fluxes across the shelf.

The benthic radon-222 fluxes (74.7±25.4 Bq m-2 d-1) obtained from the model are at 

the low end of previously reported fluxes for the eastern and northeastern Gulf of Mexico (0.00 to 

3,330 Bq m-2 d-1; table 2; compare with Cable and others, 1996b). Differences in scale (spatial) of 

observation and the framework (hydrogeologic) best explain these “lower” estimates. For example, 

high benthic radon-222 fluxes tend to be focused at sites proximal to the shoreline, whereas studies focused farther offshore have generally lower fluxes. This fits reasonably well with previous 

models for SGD – assuming that SGD is the dominant process driving radon-222 flux – where SGD 

rates decay rapidly offshore (Bokuniewicz, 1992). Furthermore, our study integrates over large 

spatial scales and reduces the ability to resolve true nearshore fluxes. Although the model indicates 

benthic radon-222 fluxes at the “shoreline” (x = 0), our estimates pertain to fluxes as much as 5 km 

from the shoreline. While ideally at a small scale, refinement of fluxes in nearshore studies would 

be on the order of tens of meters; however, when the study area is almost 50,000 km2

, then the need 

to refine to a 5-km resolution is adequate and substantial. 

Also contributing variability of our large-scale estimates to other synoptic studies are 

hydrogeologic controls. Smith and Swarzenski (2012) data originate from an area where the adjacent onshore topographic gradient is large, the Floridan aquifer is very near the seafloor, and potential outwelling of groundwater to the coastal zone is high. Similarly, the high benthic fluxes Santos 

and others (2009) observed correspond to a region in the northeastern Gulf of Mexico where significant fresh groundwater discharge influences the coastal zone. In contrast, the bulk of the measurements obtained as part of this study were focused between Tampa Bay and Charlotte Harbor, Fla., 

in a region where the Floridan aquifer is much more deeply confined and topographic gradients are 

generally small. 
17

In small-scale studies, conversion of benthic radon-222 fluxes to SGD is relatively 

straightforward, as the relationship between the two is linear. Groundwater radon-222 end-members used to convert the fluxes to fluid rates are often derived from equilibration studies or regional 

groundwater radon-222 activities. Only a few studies have investigated radon-222 activities in 

either deep submarine groundwater or shallow-marine pore waters. In submarine spring fluids discharging to the WFS off the Charlotte Harbor region, Fanning and others (1981) reported radon-222 

activities on the order of 14,300±2,000 Bq m-3. Radon-222 activities were enriched almost an order 

of magnitude over dissolved radium-226 (1,550±330 Bq m-3) in the submarine spring groundwater and almost six orders of magnitude greater than offshore Gulf of Mexico seawater (10±15 Bq 

m-3). Offshore from Indian Rocks Beach, shallow porewater radon-222 (7,340±1,400 Bq m-3) is 

similarly enriched relative to the overlying surface water (94±38 Bq m-3; Smith and Swarzenski, 

2012). At the same location, marine groundwater collected from 1.5 to 3.5 m below the seafloor 

had radon-222 an order of magnitude greater (31,600±8,200 Bq m-3; Smith and Swarzenski, 2012) 

than the pore waters and about twice that of spring water observed to the south. In comparison, 

radon-222 values from water-supply wells on land adjacent to the surveys average 37,000 Bq m-3

(FDEP, 2000). While there is no reason to think that radon-222 activities should be constant across 

the region, it is quite impressive that radon-222 activities among terrestrial groundwater, deep-marine groundwater, and shallow pore water vary by a factor of only five over such a large geographic

Figure 8. Evasion-corrected excess radon-222 inventories plotted as a function of distance from the shoreline for the 

(A) February 2009 and (B) August 2009 cruises. Colored lines show modeled data fit for the scenario where the inshore 

boundary condition is the first quartile (blue), median (green), third quartile (red), or maximum (cyan) of the radon-222 

inventories within 5 km of the shoreline. Abbreviations: km, kilometer; Bq m-2, becquerels per square meter.
18

Table 2. Summary of radon-222 fluxes (Bq m-2 d-1) from several studies along the eastern and northeastern Gulf of Mexico.[Bq m-2 d-1, becquerels per square meter per day]

Location within 

Gulf of Mexico

Site Description Measurement Type Radon-222 Flux Source

Minimum Average Maximum

(Bq m-2 d-1) (Bq m-2 d-1) (Bq m-2 d-1)

Northeastern Shelf < 24 km offshore Benthic chambers 30.8 42 53.2 Cable and others, 1996b

Northeastern Shelf < 24 km offshore Mass balance model 90 Cable and others, 1996bNortheastern Beach < 200 m offshore Mass balance model 0 237 3330 Santos and others, 2009

Eastern Shelf < 15 km offshore Mass balance model 190 527 1280 Smith and Swarzenski, 2012

Eastern Shelf < 120 km offshore Mass balance model 0 74 118.7 This study
19

and geologic region. Since the measurements were conducted independently over a time period of 

almost three decades, it is unlikely that chance would account for this small variability (table 2). In 

other words, it seems reasonable that given long enough residence time in the aquifer, the radon-222 

will reach a secular equilibrium activity between 7,000 and 37,000 Bq m-3, and will more likely 

approach 37,000 Bq m-3. Using this range in potential radon-222 sources, the regionally averaged 

SGD rates would be between 0.12 and 1.70 cm d-1, depending on the radon-222 end-member used 

(table 1). 

The approach of addressing SGD from regional radon-222 measurements is simplistic and 

averages over a number of different spatial (thousands of square kilometers) and temporal (days to 

seasons) scales. However, the results are interesting in the sense that the estimates of groundwater 

discharge at the shoreline for this regional shelf scale are comparable (within an order of magnitude) 

to synoptic studies carried out over various spatial and temporal scales. For example, seepagemeter measurements along the northeastern Gulf of Mexico by Cable and others (1996b) showed 

an average advection rate of 1.21±0.49 cm d-1 at a distance of 24 km from the shoreline. Smith and 

Swarzenski (2012) found that within a region of the cruise domain that SGD rates declined from 

15.6 to 0.7 cm d-1 from the shoreline to 15 km offshore. As with these fluxes, given the proposed 

resolution of the radon-222 measurement (1 – 3 km) and the lumping of radon-222 activities within 

5 km of the shoreline, the data are consistent.

Summary

Radon-222 data collected as part of two shelf-wide cruises provide insight to the large-scale 

spatial distribution of a commonly used groundwater and oceanographic tracer along the WFS. 

Using a number of physically reasonable assumptions, the large datasets can be reduced to a more 

simplistic one-dimensional cross-shelf (that is, distance from shoreline) dataset that can be used 

to evaluate marine background radon-222 activities, atmospheric fluxes, and decay fluxes. Coupling the reduced spatial data with a physical-based offshore mixing model provided insight to the 

mechanism, timing, and intensity of both cross-shelf mixing of radon-222 and the benthic supply of 

radon-222, predominantly at the shoreline. The optimization parameters obtained from the model 

for mixing and benthic inputs made physical sense, because the model appeared to be less sensitive to benthic radon-222 flux than it did to mixing. The three orders of magnitude variability in 

the mixing coefficient, while consistent with global and even local observations, is reflected in the 

nearshore radon-222 gradient. Further work is required to provide reasonable brackets of certainty 

and confidence on the various modeled parameters and their physical relationships. Refined studies 

at local scales, such as those presented by Smith and Swarzenski (2012), provide the means to corroborate a large-scale dataset such as this and to aid in scaling between these types of studies.
20

Acknowledgments 

We especially thank Jonathan B. Martin of the University of Florida in Gainesville for 

access to the radon-in-air monitoring devices used during the cruises. We thank Paul Knorr, Sherwood Liu, Mark Hansen, Gary Hill, and Captain Mike Lawrence for their assistance during the 

cruise. This cruise was funded by the U.S. Geological Survey Coastal and Marine Geology Program, and data analysis and interpretation were part of a U.S. Geological Survey Mendenhall Research Fellowship Program awarded to Christopher G. Smith. 

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Additional Digital Information

For additional information on the instrument deployments, please see: 

For an online PDF version of this report, please see:

http://pubs.usgs.gov/of/2012/1212/ 

For more information on the U.S. Geological Survey St. Petersburg Coastal and Marine Geology 

Team, please see:

http://coastal.er.usgs.gov/

Direct Contact Information

General Project Information: Christopher G. Smith (cgsmith@usgs.gov)

Regarding this Report: Christopher G. Smith (cgsmith@usgs.gov)