Lecture 7 Gases and Gas ExchangeComposition of the atmosphereGas solubility

Gas Exchange FluxesEffect of windGlobal CO2 fluxes by gas exchange

Emerson and Hedges: Chpts 3 and 10

Sarmiento and Gruber (2002) Sinks for Anthropogenic CarbonPhysics Today August 2002 30-36

Q. Was pre-industrial (PI) CO2 at steady state?Q. Is atm CO2 at steady state today?

Composition of the AtmosphereMore 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 (0°C)

N2 0.78080 22.391O2 0.20952 22.385Ar 9.34 x 10-3 22.386CO2 3.9 x 10-4 22.296Ne 1.82 x 10-5 22.421He 5.24 x 10-6 22.436

H2O ~0.013

Q. Why is dry air used?

Some comments about units of gases:

In Air In WaterPressure - 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 0C (= 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 LawGas concentrations are expressed in terms of pressures.

Total Pressure = SPi = Dalton's Law of Partial PressuresPT = 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) range = 32 to 25 inch

Hg

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)

Humidity Example:Say we have a humidity of 80% today and the temperature is 15C

Vapor pressure of H2O at 15C = Po = 12.75 mm Hg (from reference books)

Then, PH2O = 0.80 x 12.75 = 10.2 mm HgIf 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 398 (present) ppm.

In the table of atmospheric concentrations (see slide 3)fG,CO2 = 3.9 x 10-4 moles CO2/total moles = 390 x 10-6 moles CO2/total moles = 390 ppm

This can also be expressed in log form as:

= 100.59 x 10-4 = 10-3.41

Example: Units for Oxygen

Conversion from volume to molesUse 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 mol O2 / Lsw

SolubilityThe 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 ration using an equilibrium constant:

K = [A(aq)] / [A(g)]

There are two main ways to express solubility (Henry’s 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 K

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 0C):Partial Pressure = Pi = fG x 1atm total pressure

Gas Pi KH (0C , S = 35) Ci (0C, 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

ExampleThe value of KH for CO2 at 25C 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 20°C and Table 3A1.1 for regressions for all T and S

Example: What is the concentration of CO2 (aq) in equilibrium with the atmosphere?

For PCO2 = 350 ppm = 10-3.456 and T = 25°C

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

= 10+0.014 10-5 = 1.03 x 10-5 = 10.3 x 10-6 mol/l at 25C (0.5% of DIC)

The equilibrium concentration of CO2(aq) will be dependent only on PCO2 and temperature.

CO2(aq) is independent of pH.

But this is only the first step!

Summary of trends in solubility:1. Type of gas: KH goes up as molecular weight goes up (note that CO2 is anomalous)See solubility table.

2. Temperature: Solubility goes up as T goes downMajor effect

3. Salinity: Solubility goes up as S goes downMinor effect

Controls on Solubility

O2 versus temperaturein surface ocean

solid line equals saturationfor S = 35 at different temperatures

average supersaturation≈ 7 mmol/kg (~3%)

Temperature controlon gas concentrations

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 ExchangeStagnant Boundary Layer Model.

Depth (Z)

ATM

OCN

Cg = KH Pgas = equil. with atm

CSW

ZFilm

Stagnant BoundaryLayer – transport by molecular diffusion

well mixed surface SW

well mixed atmosphere

0

Z is positive downward

C/ Z = F = + (flux into ocean)

Flux of GasThe 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 d[Cg] / dZwhere 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)D[Cg] 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 (from 222Rn and 14C)

Example:D = 1 x 10-5 cm2 sec-1

Zfilm = 17 mm determined for the average global ocean using 14C dataThus Zfilm = 1.7 x 10-3 cm

The piston velocity = D/Z = k = 1 x 10-5 cm2 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

Liss and Merlivat,1986from wind tunnel exp.

Wanninkhof, 1992from 14C

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

~ 5 m d-1

One of main goals of JGOFS was to calculate the CO2 flux across the air-sea interface

Flux = F = - D/Zfilm (Catm - CSW) = - D/Zfilm (KHPatm - CSW)

= - D/Zfilm (KHPatm – KHPSW)

= -D/Zfilm KH (Patm – PSW)

See Boutin Figure

Expression of Air -Sea CO2 Flux

k-transfer velocity

From Sc # & wind speed

From CMDLCCGG network

S – Solubility

From SST & Salinity

From measurements and proxies

F = k s (pCO2w- pCO2a) = K ∆ pCO2

pCO2apCO2w

MagnitudeMechanismApply over larger space time domain

Global Map of Piston Velocity (k in m yr-1) times CO2 solubility (mol m-3) = Kfrom satellite observations (Nightingale and Liss, 2004 from Boutin).

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

∆pCO2 fields

Monthly changes in pCO2w

∆pCO2 fields:Takahashi climatology

JGOFS Gas Exchange Highlight #4 -

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

http://www.ldeo.columbia.edu/res/pi/CO2/carbondioxide/pages/pco2_flux_rate_maps.html

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

Wanninkhof&McGillis-98: 2.33 Pg C yr-1

Zemmelink-03: 2.45 Pg C yr-1

Yes!

CO2 Fluxes: Status

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

Solubilities of Gases in Seawater

Solubility increases with mole weight and decreasing temperature

KH = 29 x 10-3

= 2.9 x 10-2

= 10-1.53

Concentration ratio for equal volumes of air andwater.

Henry’s LawBunson Coefficient

from Broecker and Peng, (1982)

Gas Solubility - CFCs

Effect of El Nino on ∆pCO2 fieldsHigh resolution pCO2 measurements in the Pacific since Eq. Pac-92

Eq Pac-92 process study

Cosca et al. in press

El Nino Index

PCO2sw

Always greater than atmospheric