Lecture 7 Gases and Gas Exchange 2011 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. GasMole 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 22.391 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 AirIn 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 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 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) 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)
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 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 (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 = nRTP = 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 GasPiKH (0C , S = 35)Ci (0C, S = 35; P = 760 mm Hg) N2 0.7808 0.80 x 10-3 624 x 10-6mol 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 24C 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 andT = 25C 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 = 10-4.986mol kg-1 = 10+0.014 10-5 = 1.03 x 10-5 = 10.3 x 10-6mol/l at 25C 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) • See solubility table. • 2. Temperature: • Solubility goes up as T goes down • Major effect • 3. Salinity: • Solubility goes up as S goes down • Minor effect
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 d[A] / 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) d[A] 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
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 measurements and proxies From CMDL CCGG network
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 fields:Takahashi 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 http://www.ldeo.columbia.edu/res/pi/CO2/carbondioxide/pages/pco2_flux_rate_maps.html
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 Wanninkhof&McGillis-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
Solubilities of Gases in Seawater from Broecker and Peng, (1982) Bunson Coefficient Henry’s 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
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