Air Phase: F= Kg(Csg-Cg) Csg α Csg=Csl Water Phase: F=Kl(Cl-Csl) Csl

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1 SOLAS Summer School Air-sea gas exchange lecture II Tuesday July 8, 3 Rik Wanninkhof, NOAA/AOML, Miami, USA rik.wanninkhof@noaa.gov FOUS - Exchange Processes at the Air-Sea Interface and the Role of Transport and Transformation in the Surrounding Boundary Layers Activity. - Exchange Across the Air-Sea Interface Activity. - Processes in the Marine Boundary Layer Activity.3 - Processes in the Atmospheric Boundary Layer FOUS 3 - Air-Sea Flux of arbon Dioxide Air-sea gas exchange from a waterside perspective Rik Wanninkhof, NOAA/AOML, Miami, USA rik.wanninkhof@noaa.gov. onceptual view of air-sea gas exchange of gases a. "Liss-Slater" model b. Gas dependence/schmidt number c. Liquid vs. air phase resistance * sidebar: solubilities. Basic measurement principles a. Natural radioactive decay b. Mass balances a. b. 4 -natural c. 4 - bomb d. Deliberate tracers a. laboratory tanks b. wind-wave tanks c. oceans Air-sea gas exchange from a waterside perspective, continued Basic Gas Flux Equation: Gas Flux (outward is positive): F = k L ( l - α g ) a. hemical reaction in the boundary layers (case study O ) b. Bubble enhanced exchange c. The causes and effects of supersaturation on fluxes 6. Global air-sea O exchange * side bar -natural versus anthropogenic fluxes a. cross correlation issues b. wind speed variability c. wind speed dependencies K L : l : g : Gas transfer velocity,piston velocity,gas exchange coefficient deposition velocity oncentration in water near the surface oncentration in air near the surface Time Scale considerations: -haracteristic time scale of gas transfer ( = h/k) is on order of weeks -Forcing function change on order of days. In order to get a global assessment of gas fluxes we must have continual global estimates of gas concentrations and forcing function. F = k L ( l - α g ) = k L K o (p w - p g ) Digression: Solubility relationships: α : Ostwald solubility coefficient [Volume of gas at system temperature T and partial pressure P dissolved per unit volume of solvent] β : Bunsen coefficient, β = α * (73.5/T) Henry Law (dimensionless), H = / β Solubility coefficient (mol/l/atm), K o = α /RT (for ideal gas) Solubility: d α/d T., except for helium and hydrogen Air Phase: F= Kg(sg-g) l sl sg α sg=sl Water Phase: F=Kl(l-sl) g

2 Air/water resistance: Solubilities of common gases and their temperature dependence Magnitude of typical Ostwald solubility coefficients: He. O.3 O.7 DMS H 3 Br PB's - H O Notes:. r g and r l are influenced in different ways by forcing functions. r g becomes important when α * ε Ostwald Solubility. Ostwald solubilities@ Temperature dependence of solubilities dβ/dt) [%] ε is large for molecules which react in the boundary layer (SO, NH 3 ).. SF 6 He Ne N H O O Ar H 4 Kr F- F- N O O H 3 Br DMS Gas - SF6 He Ne N H O O Ar H4 Kr F-B F-B NOA OA H3Br DMS Gas Dependence on Diffusivity Gas Transfer velocity of Insoluble Gases (α < ) k L : a. Function of environmental forcing of water boundary layer b. Function of thermodynamic property of gas and liquid k L = (ν/d) -n f(q,l) f(q,l) = function of turbulent velocity and length scale (ν /D) = Schmidt # - n = Schmidt # dependence D = 7 * -5 cm /s for He, D = * -5 cm /s for n = * - cm /s for water so: Sc - Increase temperature from to 3 o, D increases by factor of.5, n decreases by factor of -Sc varies by factor of 5 to 6 over oceanic temperature range -Gas transfer velocity is a strong function of temperature Hayduk, W. and H. Laudie (974). "Prediction of diffusion coefficients for non-electrolytes in dilute aqueous solutions." AIhE J. : Wilke,. R. and P. hang (955). "orrelation of diffusion coefficients in dilute solutions." AIhE J. : Normalization of gas transfer velocities to common temperature/environment (assuming f(q,l) is unaffected): k L / k L = (Sc / Sc ) -n ommon practice to normalize to Sc =6 (Schmidt number of O in fresh ) Sc= 66 (Schmidt number of O in ) Note: D is known to about 5 % D differs from seawater to fresh water by about 5 % Seawater ν is thought to differ from fresh water by about 5 % For most common gases Sc is known to ± % The normalization to Sc=6 can change k L by a factor of -3 if k L is measured using a gas with high diffusion coefficient (e.g. He) or if the measurement is done at an environmentally extreme temperature. Schmidt number dependence: Depending on model/environmental condition n varies from - to -.5. ommonly accepted Schmidt number dependency is -.5 Surface models used in gas transfer calculations. I. Lewis-Whitman stagnant film model (93): l sl α g=sl Water Phase: F=Kl(l-ag) g Lewis-Whitman stagnant film model (93): - k L = D/z - Film thickness is independent of gas - Gas transfer velocities only change as a function of diffusion coefficient -ommonly used in "historical work" - Generally viewed as incorrect. If so, we can introduce significant error in comparing gas transfer velocities of different gases (up to a factor of ). -Implies that k L is proportional to Sc -

3 II a. Film replacement model (Dankwerts, 97; Higbie, 935), k proportional to Sc -/ l sl III. Solid wall model (Deacon, 977) k proportional to Sc -/3 Exact solution in which k is related to Schmidt number and air friction velocity: K l =.8 (ρ a /ρ w ) / Sc -/3 u* a II b. Eddy impingement model (Ledwell, 984; oantic, 986; Mcready, 984; Kittagoroddski, 984; Asher, 989) k proportional to Sc -/ Experimental verification of gas transfer models: Measure gas transfer of several gases: only possible with gases with widely different diffusion coefficient. Torgersen (98): ELA lakes compare and 3 He: k = f(q,l) Sc -. Torgersen (98) revisited: ELA lakes compare and 3 He: k = f(q,l) Sc -.8 Holmen and Liss (984): (H, He, Xe); k = f(q,l) Sc -.5 Jähne (984): (Heat, noble gases): k = f(q,l) Sc -/3, smooth surface; k = f(q,l) Sc -.55 for wavy surface Methods to determine gas transfer velocities. Based on inventories: Example water column: M/(A t) = k, dm = V, V = h A, = w - β a so: V /(A t) = k V /(A t) = k /( t) = k/h - integrate: ln ( w / w ) = k/h t. Balance of (known) decay and invasion/evasion rates k/h = λ 3. Measuring fluxes in the atmosphere (discussed last week) Wanninkhof (993): (He and SF 6 ) k = f(q,l) Sc -/3, smooth surface; k = f(q,l) Sc -/ for wavy surface, k = f(q,l) Sc >-/ for breaking waves.. Basic measurement principles Bomb 4 Bomb 4 inventories Semi-infinite Half space Broecker and Peng (994) Transfer velocity k av = cm/hr u * = 7.4 m/s Adapted from olm Sweeney

R observed n+ 4 N 4 Natural 4 O exchange Natural 4 O / O in gassing Outgassing of Radon Decay: 4 4 N + e - 4 Pre-industrial assumption: 4 O in = 4 O out + Decay Solve for I 4 O / O out gassing atm 4

4 cm hr - Adapted from olm Sweeney [] - [] mixed layer [] no loss = [Ra] λ λ + λ gas exchange.6 mol m - yr - uatm - =.

4 R observed n+ 4 N 4 Natural 4 O exchange Natural 4 O / O in gassing Outgassing of Radon Decay: 4 4 N + e - 4 Pre-industrial assumption: 4 O in = 4 O out + Decay Solve for I 4 O / O out gassing atm 4 IA = surf 4 IA + mean [ TO] V seaλ.6 mol m - yr - uatm - =.4 cm hr - Adapted from olm Sweeney [] - [] mixed layer [] no loss = [Ra] λ λ + λ gas exchange.6 mol m - yr - uatm - =.9 cm hr - 6 Ra aq gas + 4 He 8 Po + 4 He Adapted from olm Sweeney Deliberate tracer techniques Sulfur hexafluoride: hemical and physical characteristics: Biologically and chemically inert & non-toxic M.W. = 46 gr./mol D = * -5 cm /s α = <. Min. detectable level 5 * -7 mol Syringe shake -3 mol/l Trapping -6 mol/l man made (>8 % use as gaseous insulator) urrent atm. level.5 pptv 9 % /year increase Atm. residence time 3 years Global Warming potential (wght) 5-4 Relative to O -4 It does not destroy O 3 Deliberate tracer methods Dual tracer method for gas transfer Best combination volatile/non-volatile tracer pair oncentration non-volatile tracer decreases due to advection oncentration volatile tracer decreases due to advection and gas transfer The ratio decreases due to gas transfer: k = h/ t ln (R i /R f ) We do not have a suitable non-volatile tracer Alternative use two volatile tracers with widely different Schmidt numbers (diffusion coefficients) k = h/ t ln (R i /R f ) (- (Sc /Sc ) -n ) For smooth surfaces n = /3, for wavy surfaces n = / He/SF 6 technique: Two gaseous tracers 3 He, and SF 6 injected into the ocean and determine the change in ratio over time: k 3He = h/ t [ln(( 3 He/SF 6 ) t / ( 3 He/SF 6 ) t )]/ [-(Sc 3He /Sc SF6 ) n ] 4 Southern ocean Deliberate tracers Robust method Measure gas transfer on -3 day timescales. Applicable for wide range of locations Lagrangian marker ( glorified marker buoy ) R modeled.3u R = ln( 3 He/SF 6 ) R modeled.34u R modeled.83u 3 R modeled.77u Note, the coefficients were determine for each pair of points, not the full fit Year Day

Locations: North Sea Georges Bank Equatorial Pacific North Atlantic South Pacific Southern Ocean South Atlantic Southern Ocean Deliberate tracers The effect of forcing on air-sea gas exchange

,gb General trend with wind in synthesis of all results Strong dependence of wind for individual studies Offsets between studies dirty Gas Exchange and Environmental Forcing Why?

Scaling Tank (wall artifacts) Gas Exchange and Environmental Forcing: Tanks Example: tank artifact- fetch Wind-wave and other laboratory tanks are ideal systems to study processes but absolute

3 U^ 4 6 8 U* a (cm/s) Ocean estimate -m long tank 3-m long tank -m long tank Wanninkhof et al.

5 Locations: North Sea Georges Bank Equatorial Pacific North Atlantic South Pacific Southern Ocean South Atlantic Southern Ocean Deliberate tracers The effect of forcing on air-sea gas exchange Grid stirred tanks: isotropic turbulence clean Nightingale et al.,gb General trend with wind in synthesis of all results Strong dependence of wind for individual studies Offsets between studies dirty Gas Exchange and Environmental Forcing Why?- Applying results to larger regions Wind-wave tank results: 3 regimes Smooth surfacek =f(u*) Sc -/3 Wavy surface k = f(u*) Sc -/ Breaking waves k = f(bubble, u*) Sc -x All bets are off Issues: Scaling Tank (wall artifacts) Gas Exchange and Environmental Forcing: Tanks Example: tank artifact- fetch Wind-wave and other laboratory tanks are ideal systems to study processes but absolute magnitudes generally cannot be applied to oceans k(6) cm/hr Delft (m) Wallops ( m) Delft (m) IW, 3 m.3 U^ U* a (cm/s) Ocean estimate -m long tank 3-m long tank -m long tank Wanninkhof et al., 9, Donelan and Drennan Gas Exchange and Environmental Forcing: Oceans Summary Ocean Data Most relationships of gas exchange use a subset of this data along with some a priori assumptions The choice of relationships has a large effect on estimates of global air-sea O flux k,6 (cm/hr) Tracer N- Tracer Wat-9-4bomb -4 nat Liss & Merlivat, 985: Assumed a functional relationship from wind-wave tanks and scaled it to a lake experiment at intermediate winds k, 6 (cm/hr) Tracer N- Tracer Wat-9-4bomb -4 nat k, 6 L&M U U

6 Smethie et al. 986: Linear fit through Radon TTO data forcing it through non-zero intercept based on wind-wave tank: low winds very little exchange ( ). High winds : no clue Use straight line. Later adapted downward through 4 point by Tans et al. 99 k, 6 (cm/hr) Tracer N- Tracer Wat-9-4bomb -4 nat S-86 Smethie et al. 986: Linear fit through Radon TTO data forcing it through non-zero intercept based on wind-wave tank: low winds very little exchange ( ). High winds : no clue Use straight line. Later adapted downward through 4 point by Tans et al. 99 k, 6 (cm/hr) Tracer N- Tracer Wat-9-4bomb -4 nat S U U Wanninkhof-9: Gas exchange related to wind stress ( U ) Use global 4 constraint Attempt to account for variability in wind k, 6 (cm/hr) Tracer N- Tracer Wat-9-4bomb -4 nat k, 6 W-9 Wanninkhof and McGillis, 999 Gas exchange related to energy input into waves (u 3 ) Scales as whitecap coverage (bubble-enhanced exchange) Attempt to account for variability Good fit to Gas Ex-98 data Meets global 4 constraint k, 6 (cm/hr) Tracer N- Tracer Wat-9-4bomb -4 nat W U U hemical enhancement Why are relationships different? (or why do observations scatter?) Experimental uncertainty Variability in forcing Other parameters influence air-sea gas transfer k, 6 (cm/hr) Tracer N- Tracer Wat-9-4bomb -4 nat k, 6 W-9 k, 6 L&M S-86 W-99 + A Air Phase: F= Kg(sg-g) (d/dx) = k B l sl sg α sg=sl Water Phase: F=Kl(l-sl) d/dx = k g k > k 5 5 U O hydration reactions: O + H O H O 3 O +OH - HO 3 -

7 omparison of enhanced and unenhanced fluxes along W in 99. Enhancement is function of rate constants of hydration and concentration of OH- Enhancement can be increased by catalysis (e.g. carbonic anhydrase). arbonic anhydrase is ubiquitous in the environment k enh (cm h - ) Predicted enhancement at 5 o and ph=9.8 po (µatm) Using the relationship of Liss and Merlivat (986): Solubility (mol kg - atm - ) k (cm h - ) αk (cm h - ) α F enhanced (mol m - yr - ) Spring 5 N Spring 5 S Fall 5 N Fall 5 S Average difference between F and Fenhanced: 8% 4 Using the Wanninkhof (99) relationship: k (cm h - ) Spring 5 N Spring 5 S Fall 5 N Fall 5 S Average difference between F and Fenhanced: 4% For open ocean chemical enhancement probably not important Bubble enhanced exchange Gas transfer is linearly related to whitecap coverage Lower solubility gases more affected Surfactants influence bubble mediated exchange Bubble Mediated Gas Exchange Alternate parameterizations of air-sea gas transfer:. Whitecap coverage and radiometry: k = k m + Wc k b Evasion under highly super saturated conditions: K α (D β) / Asher et al., 996 Schluessel, pers com. Supersaturation: auses: Bubble dissolution: p : surface tension (LaPlace pressure) α r - : average depth of dissolution Biological effects: For O : supersaturation = % (5 % biology; 5 % bubbles For some organics:> % If supersaturation is bubble mediated and in steady state (equilibrium saturation): F = (k + k b ) * ( w - S p a (+ )) Global Air Sea O fluxes:. Gas exchange wind speed relationships. Effect of wind speed variability Side bar: Anthropogenic and total air sea O flux Total Flux: F = k s (po w -po a ) po w keeps up with po a increases with about.5 year lag Except in regions of upwelling and deep mixed layers Anthropogenic flux: F anthro = urrent Flux- Preanthtopogenic Flux F anthro = k s ( [po wt - po wi ] - [po at - po i ]) (can only be estimated from models) po wt = current po levels po wi = the pre-anthropogenic O The regions of greatest anthropogenic flux uptake and natural release is the Equatorial Pacific. Other regions of anthropogenic flux into the ocean are high latitude. 6. Global air-sea O exchange

po fields:takahashi climatology The effect of gas exchange wind speed relationships on global air-sea O fluxes ommonly used wind speed relationships: k =.3 U and k =.

8 po fields:takahashi climatology The effect of gas exchange wind speed relationships on global air-sea O fluxes ommonly used wind speed relationships: k =.3 U and k =.83 U 3 Both meet the 4 constraint But many other relationships have been developed and have their own intrinsic merits (e.g. Liss and Merlivat; Smethie et al.; Nightingale et al.; Erickson et al.; McGillis et al.) All the relationships are non-linear and or do not intercept the origin such that wind speed variability is a mathematical contributing factor. Monthly changes in po w 6. Global air-sea O exchange ourtesy of Takahashi, Sweeney and McGillis 6. Global air-sea O exchange k 66 [cm hr - ] Quadratic vs. cubic dependence: Same average k Sensitivity to parameterizations and changes in U & po Release in Pg, changing one parameter Eq Pac 4 S- 4 N, Area =57.8 ( 6 km ) av po = 9.8 Flux (pg ) U+.5 po +6 U U N Atlantic= 6 E(8 W) to 6 E (=W) and > 5N, Area =9.3 ( 6 km ) av po = u [m s - ] Flux (Pg ) U+ po + U U Southern Ocean> 5 S, Area =38 ( 6 km ) av po = -6.9 Flux (per 4 o latitude band) [mol m - yr - ] band average u band average u 3 difference Global air-sea O exchange.5- Pg difference in O uptake Flux (Pg ) U+.8 po +.5 U U Global, Area =368.3 ( 6 km ) av po = -8. Flux (Pg ) U+ po + U U Global air-sea O exchange The effect of variable winds Variability of winds - mathematics.6.5 Weibull frequency distribution wind P(U) norm to fraction P(U)*u^3*.83 fraction P(U)*u^*.34 k inst =.3 U inst The average gas transfer velocity k av is thus expressed as: P(U) norm to U.39 U k av = (.3 U inst )/N =.3/N ( U inst ) If the instantaneous winds are not available and mean winds are used U mean : k av =.3 ( (/N) U inst / U mean ) U mean The "enhancement" is =( (/N) U inst / U mean )) 4.3 U The second moment defined as, M= ((U inst ) )/N The gas transfer velocity can be written as: k =.3 * M 6. Global air-sea O exchange 5 5 Similarly for a cubic expression of wind such as presented in Wanninkhof and McGillis [999]: k =.83 * 3 M 6. Global air-sea O exchange

The "enhancement" is =( (/N) U inst / U mean )) U av (995) (m s - ) 8 6 4-8 -6-4 - 4 6 8 The effect of wind speed distribution Enhancement factor Enhancement factor.3 Quadratic dependence.5..5..5-8 -6-4 - 4 6 8.

6-8 -6-4 - 4 6 8 Flux (mol m yr - ) - -4-6 -8 - Exact Weibull Weibull-Exact -8-6 -4-4 6 8 - - -3-4 -5 Flux difference (mol m yr - ) 6. Global air-sea O exchange 6.

9 The "enhancement" is =( (/N) U inst / U mean )) U av (995) (m s - ) The effect of wind speed distribution Enhancement factor Enhancement factor.3 Quadratic dependence ubic dependence.5 Weibull Assumption Exact Weibull/Exact k av (u ) cm hr - 8 cm hr -. k av (u 3 ) 4 cm hr - 7 cm hr -.4 F (u ) -. Pg yr - -. Pg yr -.5 F(u 3 ) -3.3 Pg yr Pg yr Flux (mol m yr - ) Exact Weibull Weibull-Exact Flux difference (mol m yr - ) 6. Global air-sea O exchange 6. Global air-sea O exchange Global uptakes Liss and Merlivat-83: Pg /yr Wanninkhof-9:.85 Pg /yr Wanninkhof&McGillis-98:.33 Pg /yr Zemmelink-3:.45 Pg /yr onstant Av. k (.4 cm/hr):.3 Pg /yr 6. Global air-sea O exchange 6. Global air-sea O exchange

Gas Exchange II. Air-Sea Gas exchange from a Waterside Perspective. outline continued. Why this lecture?

Gas Exchange II. Air-Sea Gas exchange from a Waterside Perspective. outline continued. Why this lecture? Gas Exchange II Why this lecture? Rik Wanninkhof, NOAA/AOML, Miami, SA rik.wanninkhof@noaa.gov Hi, Rik: A reviewer of my iron fertilization paper complained that I did not use the quadratic formula for