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

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Emery Robinson
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1 Gas Exchange II Why this lecture? Rik Wanninkhof, NOAA/AOML, Miami, SA Hi, Rik: A reviewer of my iron fertilization paper complained that I did not use the quadratic formula for air-sea O exchange.źi thought the cubic form is your latest replacing the quadratic.źan I have your opinion on which one should be used and the field experiment like GASEX providing new insight into the cubic. Thank you. See you in Boulder O conference. heers, S hi-shing Wong Ph.D.(SIO/SD), FRSŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹhi-Shing Wong Ph.D.(SIO/SD), FRS Senior Scientist/Team LeaderŹŹŹ ŹŹŹŹŹ ŹŹŹŹŹŹŹŹŹŹŹScientifique Ź Principal / hef D'quipe limate hemistry LaboratoryŹŹŹ Laboratoire De himie Du limat / /entre for Ocean limate hemistryźźź/entre pour la himie du limat de l'ocˇ an Science and Productivity Division ŹŹŹŹ ŹŹŹŹŹ ŹŹŹŹŹ Ź ŹŹŹŹŹScience Ź de la mer et productivitˇ Institute of Ocean SciencesŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹInstitut des sciences de la mer Fisheries and Oceans anada ŹŹ ŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹPches et Ocˇan s anada P.O. Box 6, Sidney, B.. V8L 4BŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹ. P. 6, Sidney, (.-B.) V8L 4B 986 W. Saanich Road, Sidney, B..,anada V8L 4BŹŹŹŹŹŹ 986, chemin Saanich ouest, Sidney,.- B., anadaź V8L 4B SOLAS Summer School Friday Sept 9, 5 ŹŹŹŹŹŹ ŹŹŹŹphone/ tˇ lˇph one ŹŹŹŹŹ(5) ŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹŹ acsimile f / tˇ lˇ copieur ŹŹŹŹŹ(5) wongcs@pac.dfo-mpo.gc.ca Air-Sea Gas exchange from a Waterside Perspective Rik Wanninkhof, NOAA/AOML, Miami, SA rik.wanninkhof@noaa.gov Outline 1. onceptual view of air-sea gas exchange of gases a. "Liss-Slater" model b. Different models and the Schmidt number dependence c. Liquid versus air phase resistance. Basic measurement principles a. Natural radioactive decay b. Mass balances Air-Sea Gas exchange from a Waterside Perspective outline continued 5. Global air-sea O exchange * side bar -natural versus anthropogenic fluxes a. wind speed variability b. sensitivity to uncertainty in wind and po c. dependencies on gas transfer velocity a. b. -natural c. - bomb d. Deliberate tracers a. laboratory tanks b. wind-wave tanks c. oceans

2 Basic Gas Flux Equation Gas Flux (outward is positive): K L : l : g : Time Scale considerations: F = k L ( l - α g ) Gas transfer velocity, also called piston velocity, gas exchange coefficient or deposition velocity oncentration in water near the surface oncentration in air near the surface -haracteristic time scale of gas transfer ( = h/k) is on order of weeks -Forcing function change on order of hours. In order to quantify gas fluxes on a regional or global scale we must have synoptic and co-located estimates of gas concentrations and forcing function. Basic onceptual Model Air Phase: F= Kg(sg-g) l sl sg α sg=sl Water Phase: F=Kl(l-sl) g Air/water Resistance Magnitude of typical Ostwald solubility coefficients: He.1 O.3 O.7 DMS 1 H 3 Br 1 PB's 1-1 H O Notes: Water side resistance Air and water side resistance of importance Air side resistance 1. r g and r l are influenced in different ways by forcing functions. r g becomes dominant when α * ε 1 ε is large for molecules which react in the boundary layer (SO, NH 3 ) Dependence on Diffusivity Gas Transfer velocity of Insoluble Gases (α ε < 1) k L : a. Function of environmental forcing of water boundary layer b. Function of thermodynamic properties 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 Sidebar: D = 7 * 1-5 cm /s for He D = 1 * 1-5 cm /s for ν = 1 * 1 - cm /s for water so: Sc 1-1 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

3 Normalization of Gas Transfer Velocities to ommon Temperature/Environment onceptual Models sed to Relate Gas Transfer to Flux (assuming f(q,l) is unaffected): k L1 / k L = (Sc 1 / Sc ) -n ommon practice to normalize to Sc =6 (Schmidt number of O in fresh ) Sc= 66 (Schmidt number of O in ) Sidebar: D is known to about 5 % D is about 5 % less in seawater to fresh water Seawater ν is about 5 % greater than for fresh water For most common gases Sc is known to ± 1 % 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. I. Lewis-Whitman stagnant film model (193): l sl α g=sl Water Phase: F=Kl(l-ag) g Implications of Lewis-Whitman stagnant film model: -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 -1 II. Solid wall model (Deacon, 1977) k proportional to Sc -/3 Provides an exact solution in which k is related to Schmidt number and air friction velocity: K l =.8 (ρ a /ρ w ) 1/ Sc -/3 u* a Relationship holds for exchange over smooth surfaces without waves

4 III a. Film replacement model (Danckwerts, 197; Higbie, 1935), k proportional to Sc -1/ l Gas exchange related to replacement time III b. Eddy impingement model (Ledwell, 1984; oantic, 1986; Mcready, 1984; Kittagoroddski, 1984; Asher, 1989) k proportional to Sc -1/ if all eddies reach surface sl Which Model is orrect? - probably none The thermal signature of the surface suggest fine scale structure with different processes affected the transfer across the interface QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Gas exchange related to turbulent length scales Zappa, 3, Zappa et al., 5 The visualization of the small scale structure has led to the notion that different parts of the surface have different exchange processes IV. The Hybrid model (Asher, APL) Methods to Determine Gas Transfer Velocities 1. Based on inventories: water column: Flux = M/(A t) = k, dm = V, V = h A, = w - β a QuickTime and a TIFF (LZW) decompressor are needed to see this picture. so: V /(A t) = k V /(A t) = k /( t) = k/h - integrate: ln ( w1 / w ) = k/h t.4.3. y = x R= k = h t -1 ln ( w1 / w ) ln() 1.9 Slope =.16 day -1 h = 1 m 1.8 gas transfer velocity = 1.6 m/day (Asher, personal com.) time ( day). Basic measurement principles

5 Methods to Determine Gas Transfer Velocities, continued. Balance of (known) decay and invasion/evasion rates k/h = λ Bomb Inventory Method 3. Measuring fluxes in the atmosphere (discussed by McGillis) Semi-infinite Half space Broecker and Peng (1994). Basic measurement principles Historic Inventories are being challenged! Peacock,4 Key,4 Transfer velocity k av = cm/hr u * = 7.4 m/s Note, several recent revised estimates of inventory that will affect the global k calculation! Adapted from olm Sweeney Bomb Inventories n+ N Natural Exchange: Decay Method Natural O / 1 O in gassing Solve for I O / 1 O outgassing atm IA = surf IA + mean [ TO ] V seaλ Decay: N + e - Pre-industrial assumption: O in = O out + Decay.61 mol m - yr -1 uatm -1 =1.4 cm hr -1 Adapted from olm Sweeney

Outgassing of Radon: Decay Method Deliberate Tracer Methods: Mass Balance Dual tracer method for gas transfer Best combination volatile/non-volatile tracer pair oncentration non-volatile tracer

6 Outgassing of Radon: Decay Method Deliberate Tracer Methods: Mass Balance 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: [] [Ra] 6 Ra aq gas + 4 He 18 Po + 4 He 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) which yields: - k = h/ t ln (R i /R f ) (1- (Sc 1 /Sc ) -n ) [] mixed layer [] no loss = λ λ + λ gas exchange For smooth surfaces n = /3, for wavy surfaces n = 1/.6 mol m - yr -1 uatm -1 =1.9 cm hr -1 Adapted from olm Sweeney 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 ) t1 / ( 3 He/SF 6 ) t )]/ [1-(Sc 3He /Sc SF6 ) n ] R = ln( 3 He/SF 6 ) Southern ocean Wanninkhof et al, 4 R observed R modeled.31 R modeled.34 R modeled.83 3 R modeled 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: Summary 3 He/SF 6 Tracer release Experiments Open symbols = coastal ocean; Solid symbols = open ocean Ho, 5 General increasing trend with wind in synthesis of results Strong dependence of wind for individual studies Offsets between studies

7 From Ho, 5 Open symbols = coastal ocean; Solid symbols = open ocean Why Establish Relationships between Gas Exchange and Wind? Ability to apply results to larger region Wind-wave tank results: 3 regimes Smooth surfacek =f(u*) Sc -/3 Wavy surface k = f(u*) Sc -1/ 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 Delft1 (1m) Wallops (1 m) Delft (1m) IW, 3 m.31 ^ * a (cm/s) Ocean estimate 1-m long tank 3-m long tank 1-m long tank Gas Exchange and Environmental Forcing: Oceans 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 Variability if wind is frequently not taken into account k,6 (cm/hr) Tracer N- -bomb - nat Summary Ocean Data Wanninkhof et al., 91, Donelan and Drennan

8 Gas Exchange and Environmental Forcing: Wind Gas Exchange and Environmental Forcing: Wind Liss & Merlivat, 1985: Assumed a functional relationship from wind-wave tanks and scaled it to a lake experiment at intermediate winds k, 6 (cm/hr) Tracer N- -bomb - nat k, 6 L&M Smethie et al. 1986: 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 se straight line. Later adapted downward through point by Tans et al. 199 k, 6 (cm/hr) Tracer N- -bomb - nat S Gas Exchange and Environmental Forcing: Wind Gas Exchange and Environmental Forcing: Wind Smethie et al. 1986: 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 se straight line. Later adapted downward through point by Tans et al. k, 6 (cm/hr) Tracer N- -bomb - nat S-86 Wanninkhof-9: Gas exchange related to wind stress ( ) se global constraint Attempt to account for variability in wind k, 6 (cm/hr) Tracer N- -bomb - nat k, 6 W

9 Gas Exchange and Environmental Forcing: Wind Gas Exchange and Environmental Forcing: Wind Wanninkhof and McGillis, 1999 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 constraint k, 6 (cm/hr) Tracer N- -bomb - nat W-99 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- -bomb - nat k, 6 W-9 k, 6 L&M S-86 W The effect of variable winds on global O exchange Variability of Winds - mathematics 1 k inst = a inst The average gas transfer velocity k av is thus expressed as: 8 k av = ( a inst )/N =.31/N ( inst ) 6 Bi-modal winds.39 = variable winds (Rayleigh) If the instantaneous winds are not available and mean winds are used mean : k av =.31 ( (1/N) inst / mean ) mean.31 = steady winds The non-linearity effect" is =( (1/N) inst / mean )) The second moment defined as, M= (( inst ) )/N The gas transfer velocity can thus be written as: k = a * M Similarly for a cubic expression of wind such as presented in Wanninkhof and McGillis [1999]: k = b * 3 M

10 Global Air Sea O fluxes: Details of the Wanninkhof gas exchange-wind speed relationship: Scaled to: total bomb inventory (Broecker & Peng, 1985) global mean wind of 7.4 m/s (Hellerman) k =.39 1 If global wind speed or global inventory is incorrect- the relationship is incorrect Index based relationship: k =.31* (bomb- inv /3*1 6 )* nd moment *(7.4/ mean ) Sidebar: sing recent estimates of global wind and 1 global = 7.7 m/s ( NEP 41-yr) Bomb- inv =. *1 6 (Hessheimer, 1994) nd moment = 1.16 k =.7 1 Global Air Sea O fluxes 1. Gas exchange wind speed relationships. Effect of errors in wind and po 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 1.5 year lag except in regions of upwelling and deep mixed layers Anthropogenic flux: F anthro = urrent Flux- Preanthtopogenic Flux Preanthtopogenic flux: F pre +.3 to +.5 Pg ( continental runoff) so: F anthro > urrent flux The regions of greatest anthropogenic flux uptake and natural release is the Equatorial Pacific. Other regions of high anthropogenic flux into the ocean are high latitude. The Effect of Gas Exchange Wind Speed Relationships on Global Air-Sea O Fluxes ommonly used wind speed relationships: k =.31 and k =.83 3 Both meet the 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. Global, Area =368.3 (1 6 km ) av po = -5. µatm Sensitivity to hanges in 1 & po Takahashi 1 climatology Global Flux (Pg ) Flux (Pg ) Flux (Pg ) +1 po w + K =.31 * R * =.83 * R 3 * So: Increase in global wind speed of 1 m/s increases global flux by.3 to.6 Pg /yr Increase in po w by µatm decreases global flux by.3 to.4 Pg /yr This is approximately the uncertainty in these parameters indicating the uncertainty in global air-sea O fluxes by this method

Effect of Gas Transfer Parameterization on Global O Fluxes Global uptakes Liss and Merlivat-83:.8 Pg /yr Wanninkhof-9: 1.6 Pg /yr Wanninkhof&McGillis-98: 1.9 Pg /yr Zemmelink-3:.45 Pg /yr onstant Av.

11 Effect of Gas Transfer Parameterization on Global O Fluxes Global uptakes Liss and Merlivat-83:.8 Pg /yr Wanninkhof-9: 1.6 Pg /yr Wanninkhof&McGillis-98: 1.9 Pg /yr Zemmelink-3:.45 Pg /yr onstant Av. k (1.4 cm/hr):.3 Pg /yr Summary Gas transfer of non-reactive gases is a first-order rate process and basic physicals laws can be applied Gas exchange is controlled by processes in the molecular boundary layer Many gases of environmental interest are liquid phase controlled Gas transfer can be measured from mass balances and/or decay balances of opportunistic or deliberate tracers Determining the processes in the boundary layer that control gas exchange is a hot research topic To estimate global and regional fluxes we need to scale up gas exchange processes though empirical relationships often bounded by global constraints Errors in global (O ) fluxes are due to: Systematic biases in near surface concentration estimates Failure to account for small scale variability and cross-correlations Incorrect parameterizations

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

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