Lecture 8 Tracers for Gas Exchange
Examples for calibration of gas exchange using:
222Rn – short term
14C - long term
E&H Sections 5.2 and 10.2
Rates of Gas Exchange
Stagnant Boundary Layer Model.
ATM
OCN
Depth (Z)
CSW
well mixed atmosphere
Cg = KH Pgas = equil. with atm
0
Stagnant Boundary
Layer –
transport by
ZFilm
molecular diffusion
well mixed surface SW
Z is positive downward
see:
Liss and Slater (1974) Nature, 247, p181
Broecker and Peng (1974) Tellus, 26, p21
Liss (1973) Deep-Sea Research, 20, p221
C/ Z =
F = + (flux into ocean)
Expression of Air -Sea CO2 Flux
Need to calibrate!
k = piston velocity = D/Zfilm
S – Solubility
From wind speed
From Temperature & Salinity
F = k s (pCO2w- pCO2a) = K ∆ pCO2
pCO2w
From measurements
at sea
pCO2a
From CMDL
CCGG network
Gas Exchange and Environmental Forcing: Wind
Wanninkhof, 1992
from 14C
~ 5 m d-1
Example conversion:
20 cm hr-1 = 20 x 24 / 102 = 4.8 m d-1
Liss and Merlivat,1986
from wind tunnel exp.
U-Th Series Tracers
Analytical Method for 222Rn and 226Ra
Analyze for 222Rn immediately, then 226Ra later
(after 20 days)
5 half-lives
charcoal
liquid N2
222Rn
SW
226Ra
Apply the principle of secular equilibrium!
Activity is what
is measured. Not
concentration!
226Ra
profiles in Atlantic and Pacific
Q. What controls the ocean distributions of 226Ra?
226Ra
– Si correlation – Pacific Data
You can calculate
226Ra
from Si!
Q. Why is there a hook
at the end?
226Ra
source from the sediments
Edmond et al (1979) JGR 84, 7809-7826
222Rn
Example Profile from North Atlantic
Does Secular Equilibrium Apply?
t1/2 222Rn << t1/2 226Ra
(3.8 d)
(1600 yrs)
222Rn
YES! Then..
A226Ra = A222Rn
222Rn
Why is
activity
less than 226Ra?
226Ra
222Rn
is a gas and the 222Rn concentration in the atmosphere
is much less than in the ocean mixed layer (Zml mixed layer).
Thus, there is a net evasion (gas flux) of 222Rn out of the ocean.
The simple 1-D 222Rn balance for the mixed layer, with thickness Zml,
ignoring horizontal advection and vertical exchange with deeper water, is:
222Rn/dt = sources – sinks
= decay of 226Ra – decay of 222Rn - gas exchange to atmosphere
Zml l222Rn [222Rn]/t = Z ml l226Ra [226Ra] – Zml l 222Rn [222RnML]
- D/Zfilm { [222Rnatm] – [222RnML]}
Knowns: l222Rn, l226Ra, DRn
Measure: Zml, A226Ra, A222Rn, d[222Rn]/dt
Solve for Zfilm
Zml λ222Rn d[222Rn]/dt = Z ml λ226Ra [226Ra] – Zml λ222Rn [222Rn]
- D/Zfilm { [222Rnatm] – [222RnML]}
Zml δA222Rn/ δt = Zml (A226Ra – A222Rn) + D/Z (CRn, atm – CRn,ML)
atm Rn = 0
for SS = 0
Then
-D/Z ( – CRn,ml) = Zml (A226Ra – A222Rn)
+D/Z (ARn,ml/λRn) = Zml (A226Ra – A222Rn)
+D/Z (ARn,ml) = Zml λRn (A226Ra – A222Rn)
ZFILM = D (A222Rn,ml) / Zml λRn (A226Ra – A222Rn)
ZFILM = (D / Zml λRn
)
(
1
A226 Ra
1
A222 Rn
)
Note: diffusion is
expressed in terms of
concentrations not
activities
Stagnant Boundary Layer Film Thickness
Z = DRn / Zfilm l 222Rn
(1/A226Ra/A222Rn) ) - 1
Histogram showing results of film thickness
calculations from many stations.
Organized by ocean and by latitude
Average Zfilm = 28 mm
Q. What are limitations of
this approach?
1. unrealistic physical model
2. steady state assumption
3. short time scale
Cosmic Ray Produced Tracers – including 14C
Cosmic ray interactions produce a wide range of nuclides in
terrestrial matter, particularly in the atmosphere, and in
extraterrestrial material accreted by the earth.
Isotope
3H
14C
10Be
7Be
26Al
32Si
Half-life
12.3 yr
5730 yr
1.4 x 106 yr
54 d
7.4 x 105 yr
276 yr
Global inventory (pre-nuclear)
3.5 kg
54 ton
430 ton
32 g
1.7 ton
1.4 kg
Carbon-14 is produced in the upper atmosphere as follows:
Cosmic Ray Flux  Fast Neutrons  Slow Neutrons + 14N* 
(protons)
(thermal)
From galactic cosmic rays from
supernova, which are more energetic than
solar wind. So these are not from
the sun.
The overall reaction is written:
14N
+ n
(7n, 7p)

14C
+ p
(8n, 6p)
So the production rate from cosmic rays can be calculated
For more detail see: von Blanckenburg and Willenbring (2014) Elements, 10, 341-346
14C
(5730 yrs)
Bomb Fallout Produced Tracers
Nuclear weapons testing and nuclear reactors (e.g. Chernobyl) have been an
extremely important sources of nuclides used as ocean tracers.
The main bomb produced isotopes have been:
Isotope
3H
14C
90Sr
238Pu
239+240Pu
137Cs
Half Life
12.3 yrs
5730 yrs
28 yrs
86 yrs
2.44 x 104 yrs
6.6 x 103 yrs
30 yrs
Decay
beta
beta
beta
alpha
alpha
alpha
beta, gamma
Nuclear weapons testing has been the overwhelmingly predominant source of 3H, 14C, 90Sr and
137Cs to the ocean.
Nuclear weapons testing peaked in 1961-1962.
Fallout nuclides act as "dyes"
Another group of man-made tracers that fall in this category but are not bomb-produced and
are not radioactive are the chlorofluorocarbons (CFCs).
Atmospheric 14CO2 in the second half of the 20th century.
The figure shows the 14C / 12C ratio relative to the natural level in the atmospheric
CO2 as a function of time in the second half of the 20th century.
The bomb spike: surface ocean and
atmospheric Δ14C since 1950
• Massive
production in
nuclear tests ca.
1960 (“bomb
14C”)
• Through air-sea
gas exchange, the
ocean took up
~half of the bomb
14C by the 1980s
bomb spike in 1963
data: Levin & Kromer 2004; Manning et al 1990; Druffel 1987;
Druffel 1989; Druffel & Griffin 1995
Comparison of 14C in
surface ocean
Atlantic
Pre-nuclear (1950s)
and nuclear (1970s)
Indian
Pacific
Example – Use 14C to calculate ZFILM using the Stagnant Boundary Layer
Use Pre-bomb 14C – assume steady state
source = sink
14C from gas exchange = 14C lost by decay
1-box model
14C
atm
[14C]
14C
decay
Assume [CO2]top = [CO2]bottom = [CO2]surface ocean (e.g. no CO2 gradient,
only a 14C gradient)
Assume
D = 3 x 10-2 m2 y-1
Then:
h = 3800m
Zfilm = 1.7 x 10-5 m
l1 = 8200 y
[CO2]surf = 0.01 moles m-3
= 17 mm
-3
[DIC]ocean = 2.4 moles m
a14CO2/aCO2 = 1.015 (14C-CO2 is more soluble than CO2)(a equals solubility constant)
(14C/C) surf = 0.96 (14C/C)atm
(14C/C)deep = 0.84 (14C/C)atm
Example – 14C Deep Ocean Residence Time
vmix in cm yr-1; vC in cm yr-1 x mol cm-3
substitute for B
Rearrange and
Solve for Vmix
Use pre-nuclear 14C data when surface 14C > deep 14C
(14C/C)deep = 0.81 (14C/C)surf
Vmix = (200 cm y-1) A
for h = 3200m
A = ocean area
thus age of deep ocean box (t)
t = 3200m / 2 my-1 = 1600 years
Example:
What is the direction and flux of oxygen across the air-sea interface given?
PO2 = 0.20 atm
KH,O2 = 1.03 x 10-3 mol kg-1 atm-1
O2 in mixed layer = 250 x 10-6 mol l-1
The wind speed (U10) = 10 m s-1
(assume 1L = 1 kg)
Answer:
O2 in seawater at the top of the stagnant boundary layer
= KH PO2 = 1.03 x 10-3 x 0.20 = 206 x 10-6 mol l-1
So O2 ml > O2 atm and the flux is out of the ocean.
What is the flux?
With a wind speed = 10 m s-1, the piston velocity (k) = 5 m d-1
DC = (250 – 206) x 10-6 = 44 x 10-5 mol l-1
Flux = 5 m d-1 x 44 x 10-6 mol l-1 x 103 l m-3 = 5 x 44 x 10-6 x 103 = 220 x 10-3 mol m-2 d-1
Example
The activity of 222Rn is less than that of 226Ra in the surface water of the
North Atlantic at TTO Station 24 (western North Atlantic).
Calculate the thickness of the stagnant boundary layer (ZFILM).
A226Ra = 8.7 dpm 100 L-1
A222Rn = 6.9 dpm 100 L-1
Assume:
λ222Rn = 2.1 x 10-6 s-1
D222Rn = 1.4 x 10-9 m2 s-1
Zml = 40m
Answer: ZFILM = 40 x 10-6 m
Tritium (3H) is produced from cosmic ray interactions with N and O.
After production it exists as tritiated water ( H - O -3H ), thus it is an ideal tracer
for water.
Tritium concentrations are TU (tritium units) where
1 TU = 1018 (3H / H)
Thus tritium has a well defined atmospheric input via rain and H2O vapor
exchange.
Its residence time in the atmosphere is on the order of months.
In the pre-nuclear period the global inventory was only 3.5 kg which means there
was very little 3H in the ocean at that time. The inventory increased by 200x and
was at a maximum in the mid-1970s
Tritium in rain (historical record)
Tritium (3H) in rain
and surface SW
Tritium is a conservative tracer for water (as HTO)
– thermocline penetration
Eq
Meridional Section in the Pacific
Atmospheric Record of Thermocline Ventilation Tracers
Conservative, non-radioactive tracers (CFC-11, CFC-12, CFC13, SF6)
Time series of northern hemisphere atmospheric concentrations
and tritium in North Atlantic surface waters
226Ra
Distributions
Example 226Ra Profile
South Atlantic at
15°S ; 29.5°W
222Rn
as a tracer for gas exchange

222Rn/t = sources – sinks
= decay of 226Ra – decay of 222Rn - gas exchange to atmosphere