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Lecture 4 Gases and Gas Exchange

2009

Gas Exchange Fluxes Effect of wind Global CO2

fluxes by gas exchange

Composition of the atmosphere Gas solubility

Emerson and Hedges Chpts 3 and 10

Sarmiento and Gruber (2002) Sinks for

Anthropogenic Carbon Physics Today August 2002

30-36

Composition of the Atmosphere More than 95 of

all gases except radon reside in the atmosphere.

The atmosphere controls the oceans gas contents

for all gases except radon, CO2 and

H2O. Gas Mole Fraction in Dry Air (fG)

molar volume at STP (l mol-1 )

where fG moles gas i/total moles 22.414

for an ideal gas (0C) N2 0.78080 22.391

O2 0.20952 22.385 Ar 9.34 x

10-3 22.386 CO2 3.3 x 10-4 22.296 Ne 1.82

x 10-5 22.421 He 5.24 x 10-6 22.436 H2O 0.

013

Why is dry air used?

Some comments about units of gases In

Air In Water Pressure - Atmospheres

Volume - liters gas at STP / kgsw 1 Atm 760

mm Hg STP standard temperature and

pressure Partial Pressure of Gasi P (i) /760

1 atm and 0?C (

273ºK) Volume - liters gas / liters air

Moles - moles gas / kgsw (ppmv ml / l,

etc) Conversion lgas/kgsw / lgas / mole

moles/kgsw (22.4

l/mol)

Dalton's Law Gas concentrations are expressed in

terms of pressures. Total Pressure SPi

Dalton's Law of Partial Pressures PT PN2

PO2 PH2O PAr ......... Dalton's Law

implies ideal behavior -- i.e. all gases behave

independently on one another (same idea as ideal

liquid solutions with no electrostatic

interactions). Gases are dilute enough that this

is a good assumption. Variations in partial

pressure (Pi) result from 1) variations in PT

(atmospheric pressure highs and lows) 2)

variations in water vapor ( PH2O) We can express

the partial pressure (Pi) of a specific gas on a

dry air basis as follows Pi PT - h/100 Po

fg where Pi partial pressure of gas i

PT Total atmospheric pressure

h relative humidity Po vapor

pressure of water at ambient T fg

mole fraction of gas in dry air (see table above)

Example Say we have a humidity of 80 today and

the temperature is 15?C Vapor pressure of H2O at

15?C Po 12.75 mm Hg (from reference

books) Then, PH2O 0.80 x 12.75 10.2 mm

Hg If PT 758.0 mm Hg PTDry (758.0 - 10.2)

mm Hg 747.8 mm Hg Then fH2O

PH2O / PT 10.2 / 758.0 0.013 So for

these conditions H2O is 1.3 of the total gas in

the atmosphere. That means that water has a

higher concentration than Argon (Ar). This is

important because water is the most important

greenhouse gas!

Example Units for CO2 Atmospheric CO2 has

increased from 280 (pre-industrial) to 380

(present) ppm. In the table of atmospheric

concentrations (see slide 3) fG,CO2 3.3 x 10-4

moles CO2/total moles 330 x 10-6

moles CO2/total moles 330 ppm This

can also be expressed in log form as

100.52 x 10-4 10-3.48

Example Units for Oxygen Conversion from volume

to moles Use O2 22,385 L / mol at standard

temperature and pressure (STP) if O2 5.0 ml

O2/LSW then 5.0 ml O2 / Lsw x mol O2 / 22,385

ml 0.000223 mol O2 / Lsw 223 mmol O2

/ Lsw

Solubility The exchange or chemical equilibrium

of a gas between gaseous and liquid phases can

be written as A (g) ? A (aq) At

equilibrium we can define the familiar value K

A(aq) / A(g) There are two main ways

to express solubility (Henrys Law and Bunsen

Coefficients).

1. Henry's Law We can express the gas

concentration in terms of partial pressure using

the ideal gas law

PV nRT P pressure, V

volume, n moles R gas constant

8.314 J K-1 mol-1, T temp so that the number

of moles n divided by the volume is equal to

A(g) n/V A(g) PA / RT where PA

is the partial pressure of A Then K

A(aq) / PA/RT or

A(aq) (K/RT) PA A(aq)

KH PA units for K are mol kg-1 atm-1

in mol kg-1

for PA are atm Henry's Law states that

the concentration of a gas in water is

proportional to its overlying partial pressure.

KH is mainly a function of temperature with a

small impact by salinity.

Example (Solubility at 0?C) Partial Pressure

Pi fG x 1atm total pressure Gas Pi KH (0?C ,

S 35) Ci (0?C, S 35 P 760 mm

Hg) N2 0.7808 0.80 x 10-3 624 x 10-6 mol

kg-1 O2 0.2095 1.69 x 10-3 354 x

10-6 Ar 0.0093 1.83 x 10-3 17 x

10-6 CO2 0.00033 63 x 10-3 21 x 10-6

Example The value of KH for CO2 at 24?C is 29 x

10-3 moles kg-1 atm-1 or 2.9 x 10-2 or

10-1.53. The partial pressure of CO2 in the

atmosphere is increasing every day but if we

assume that at some time in the recent past it

was 350 ppm that is equal to 10-3.456 atm.

See Emerson and Hedges Table 3.6 for 20C and

Table 3A1.1 for regressions fpr all T and S

Example What is the concentration of CO2 (aq) in

equilibrium with the atmosphere? For PCO2 350

ppm 10-3.456 For CO2 KH 29 x 10-3 2.9 x

10-2 10-1.53 moles /kg atm then CO2 (aq) KH

x PCO2 10-1.53 x 10-3.456 10-4.986 mol kg-1

100.014 10-5 1.03 x 10-5

10.3 x 10-6 mol/l at 25?C The concentration of

CO2(aq) will be dependent only on PCO2 and

temperature. It is independent of pH.

- Summary of trends in solubility
- Type of gas
- KH goes up as molecular weight
- goes up (note that CO2 is anomalous)
- 2. Temperature
- Solubility goes up as T goes down
- 3. Salinity
- Solubility goes up as S goes down

Temperature control on gas concentrations

O2 versus temperature in surface ocean solid

line equals saturation for S 35 at different

temperatures average supersaturation 7

mmol/kg (3)

Causes of deviations from Equilibrium Causes of

deviation from saturation can be caused

by 1. nonconservative behavior (e.g.

photosynthesis () or respiration (-) or

denitrification ()) 2. bubble or air injection

() 3. subsurface mixing - possible

supersaturation due to non linearity of KH

or a vs. T. 4. change in atmospheric pressure -

if this happens quickly, surface waters

cannot respond quickly enough to reequilibrate.

Rates of Gas Exchange Stagnant Boundary Layer

Model.

well mixed atmosphere

Cg KH Pgas equil. with atm

ATM

0

OCN

Stagnant Boundary Layer transport by

molecular diffusion

ZFilm

Depth (Z)

CSW

well mixed surface SW

Z is positive downward ?C/ ?Z F (flux

into ocean)

Flux of Gas The rate of transfer across this

stagnant film occurs by molecular diffusion from

the region of high concentration to the region

of low concentration. Transport is described by

Fick's First Law which states simply that flux

is proportional to the concentration

gradient.. F - D dA / dZ where D

molecular diffusion coefficient in water ( f

(gas and T)) (cm2sec-1) dZ is the thickness of

the stagnant film on the ocean side

(Zfilm)(cm) dA is the concentration difference

across the stagnant film (mol cm-3) The water at

the top of the stagnant film (Cg) is assumed to

be in equilibrium with the atmosphere. We can

calculate this value using the Henry's Law

equation for gas solubility. The bottom of the

film has the same concentration as the

mixed-layer (CSW). Thus Flux F -

D/Zfilm (Cg - CSW) - D/Zfilm (KHPg - CSW)

Because D/Zfilm has velocity units, it has been

called the Piston Velocity (k) e.g., D cm2

sec-1 Z film cm Typical values are D

1 x 10-5 cm2 sec-1 at 15ºC

Zfilm 10 to 60 mm Example D 1 x 10-5 cm2

sec-1 Zfilm 17 mm determined for the average

global ocean using 14C data Thus Zfilm 1.7 x

10-3 cm The piston velocity D/Z k 1 x

10-5 cm s-1 /1.7 x 10-3 cm 0.59 x

10-2 cm/sec ? 5 m / d note 1 day

8.64 x 104 sec Each day a 5 m thick layer of

water will exchange its gas with the

atmosphere. For a 100m thick mixed layer the

exchange will be completed every 20 days.

Gas Exchange and Environmental Forcing Wind

Wanninkhof, 1992 from 14C

Liss and Merlivat,1986 from wind tunnel exp.

5 m d-1

20 cm hr-1 20 x 24 / 102 4.8 m d-1

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U-Th Series Tracers

222Rn Example Profile from North Atlantic

Does Secular Equilibrium Apply? t1/2 222Rn ltlt

t1/2 226Ra (3.8 d) (1600

yrs) YES! A226Ra A222Rn

222Rn

226Ra

Why is 222Rn activity less than 226Ra?

222Rn is a gas and the 222Rn concentration in the

atmosphere is much less than in the ocean mixed

layer (? mixed layer). Thus there is a net

evasion of 222Rn out of the ocean.

The 222Rn balance for the mixed layer, ignoring

horizontal advection and vertical exchange with

deeper water, is

d222Rn/dt sources sinks decay of 226Ra

decay of 222Rn - gas exchange to atmosphere

?ml l222Rn d222Rn/dt ? ml l226Ra 226Ra ?

l 222Rn 222RnML

D/Zfilm 222Rnatm

222RnML

Knowns l222Rn, l226Ra, DRn Measure ? ml,

A226Ra, A222Rn, d222Rn/dt Solve for Zfilm

?ml l222Rn d222Rn/dt ? ml l226Ra 226Ra

?ml l222Rn 222Rn

D/Zfilm 222Rnatm

222RnML ?ml dA222Rn/ dt ?ml (A226Ra

A222Rn) D/Z (CRn, atm CRn,ML)

atm Rn 0

for SS 0

Then -D/Z ( CRn,ml) ?ml (A226Ra A222Rn)

D/Z (ARn,ml/lRn) ?ml (A226Ra A222Rn)

D/Z (ARn,ml) ?ml lRn (A226Ra

A222Rn) ZFILM D (A222Rn,ml) / ?ml lRn (A226Ra

A222Rn) ZFILM (D / ?ml lRn) (

)

Stagnant Boundary Layer Film Thickness

Z DRn / ? 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?
- unrealistic physical model
- steady state assumption

One of main goals of JGOFS was to calculate the

CO2 flux across the air-sea interface

Flux F - D/Zfilm (Cg - CSW) - D/Zfilm

(KHPg - CSW)

- D/Zfilm (KHPo KHPSW)

-D/Zfilm KH (Po PSW)

Expression of Air -Sea CO2 Flux

- Magnitude
- Mechanism
- Apply over larger space time domain

k-transfer velocity From Sc wind speed

S Solubility From SST Salinity

F k s (pCO2w- pCO2a) K ? pCO2

pCO2a

pCO2w

From CMDL CCGG network

From measurements and proxies

Global Map of Piston Velocity (k in m yr-1) times

CO2 solubility (mol m-3) K from satellite

observations (Nightingale and Liss, 2004 from

Boutin).

?pCO2 fields

Overall trends known Outgassing at low

latitudes (e.g. equatorial) Influx at high

latitudes (e.g. circumpolar) Spring blooms

draw down pCO2 (N. Atl) El Niños decrease

efflux

JGOFS Gas Exchange Highlight 4 -

?pCO2 fieldsTakahashi climatology

Monthly changes in pCO2w

Fluxes JGOFS- Global monthly fluxes

Combining pCO2 fields with k F k s (pCO2w-

pCO2a)

- On first order flux and ?pCO2 maps do not look

that different

CO2 Fluxes Status

Do different parameterizations between gas

exchange and wind matter?

Global uptakes Liss and Merlivat-83 1 Pg C

yr-1 Wanninkhof-92 1.85 Pg C

yr-1 WanninkhofMcGillis-98 2.33 Pg C

yr-1 Zemmelink-03 2.45 Pg C yr-1

Yes!

Global average k (21.4 cm/hr) 2.3 Pg C yr-1

We might not know exact parameterization with

forcing but forcing is clearly important

Compare with net flux of 1.3 PgCy-1 (1.9 -

0.6) in Sarmiento and Gruber (2002), Figure 1

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- 2. Bunson Coefficients
- Since oceanographers frequently deal with gas

concentrations not only in molar units but also

in ml / l, we can also define - A(aq) a PA
- where a 22,400 x KH (e.g., one mol of gas

occupies 22,400 cm3 at STP) - is called the Bunsen solubility coefficient.

Its units are cm3 mol-1.

Solubilities of Gases in Seawater

from Broecker and Peng, (1982)

Bunson Coefficient

Henrys Law

Solubility increases with mole weight and

decreasing temperature

Concentration ratio for equal volumes of air

and water.

KH 29 x 10-3 2.9 x 10-2 10-1.53

Gas Solubility - CFCs

Is beer carbonated? Calculate the flux of CO2

(in mol m-2 s-1) out of your favorite, frosty,

carbonated beverage. The PCO2 in the beverage

0.125atm Assume the surface of the beverage is

in equilbrium with the PCO2 of the atmosphere

(375 x 10-6 atm.). Let DCO2 2 x 10-9 m2 s-1

and let the stagnant boundary layer thickness be

Zfilm 5 x 10-5 m. What is the flux? (ans

0.144 x 10-1 mol m-2 s-1) Which way does the CO2

flux go? (ans out of the beer)

Effect of El Nino on ?pCO2 fields High resolution

pCO2 measurements in the Pacific since Eq. Pac-92

Eq Pac-92 process study

PCO2sw

Always greater than atmospheric

Cosca et al. in press

El Nino Index