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# Calculating the air-sea flux of any trace gas: transfer velocity, chemical enhancement and uncertainty

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Given to Geochemical Luncheon Club, UEA, autumn q

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### Calculating the air-sea flux of any trace gas: transfer velocity, chemical enhancement and uncertainty

1. 1. Calculating the air-sea flux of any trace gas: transfer velocity, chemical enhancement and uncertainty Motivation Classical air-sea flux theory Calculating temperature- and salinity-dependent diffusive transfer velocities for any gas Liss and Slater (1974) revisited rg/rl Solubilty &apos;threshold&apos; Chemical enhancement Previous studies Rate &apos;threshold&apos; Wider application Global K climatology for any gas The effect of bubbles Barry Huebert&apos;s DMS observations / NOAA COARE prediction Global analysis of potential error Other uncertainties... Calculating the air-sea flux of any trace gas: transfer velocity, chemical enhancement and uncertainty
2. 2. Motivation Lots of researchers need to calculate air-water exchanges from concentration difference measurements: Many not experts in gas exchange Many for poorly studied gases (i,.e. Not GHGs, noble gases, O 2 or DMS) Concentration uncertainty is large so simple (wind driven parameterised) approach to transfer velocity is probably sensible Serious mistakes are often made in calculations e.g. for CH 3 OH using kl rather than kg leads to factor of 20 overestimation of flux! When is it appropriate to consider either k l =K l or k g =K g ? Notwithstanding the need to choose the &apos;best&apos; transfer velocity parameterisations; solubility and diffusivity of the gas, and viscosity of the medium must be quantified for the gas of interest When is chemical enhancement potentially important? What else should we be worrying about?
3. 3. Two-layer model of gas exchange F = -K. Δ C = -K a (C g -C sg ) = -K w (C sl -C l ) C sg = K H . C sl Liss, P.S and Slater, P.G., 1974, Nature (247), 181-184
4. 4. J ä hne, B. (2009), Air-sea gas exchange in Encyclopedia of Ocean Science, second edition 147-156. Two-layer model of gas exchange F = -K. Δ C = -K a (C g -C sg ) = -K w (C sl -C l ) C sg = K H . C sl 1/K w = 1/K H .k a + 1/k w 1/K a = 1/k a + K H /k w R l = r l + r g (R g = r l &apos;+r g &apos;) R = r1+r2 V r1 r2
5. 5. Liquid phase transfer velocity, k l k l = f(u x ). (S c /S c 0 ) -0.5 S c = η/ρD k l commonly expressed as an exponential function of windspeed (u) scaled by the square root (or other negative exponent) of the ratio of the Schmidt number of the gas in question to a reference Schmidt number (S c 0 ) n – viscosity of seawater (T, S and composition dependent) p – density (T, S and composition dependent) D – diffusion coefficient of gas in question (dependent itself on the viscosity and also the molecular weight of the medium, and also the molcular weight and molecular volume of the gas in question).
6. 6. Liquid phase transfer velocity, k l
7. 7. In press, Ocean Science... Temperature Salinity Wind speed Solubility at STP T dependence of solubility Molecular structure Gas-specific data Physical forcings Henry solubility in water Diffusion coefficients in air and water Viscosity of air and water Schmidt numbers in air and water k w – Nightingale2000, Wanninkhof92, Woolf97 (bubbles) and various others k a – various schemes including Duce91, Jeffrey2010 K w and K a (1/K w = 1/k w + H/k a ) All parameters T dependent (and S dependent for water side) Outputs Temperature Salinity Wind speed Solubility at STP T dependence of solubility Molecular structure Gas-specific data Physical forcings Henry solubility in water Diffusion coefficients in air and water Viscosity of air and water Schmidt numbers in air and water k w – Nightingale2000, Wanninkhof92, Woolf97 (bubbles) and various others k a – various schemes including Duce91, Jeffrey2010 K w and K a (1/K w = 1/k w + H/k a ) All parameters T dependent (and S dependent for water side) Outputs
8. 8. Henry&apos;s law solubility and temp dependence mostly taken from Rolf Sanders compilation ( http://www.mpch-mainz.mpg.de/~sander/res/henry.html ), or primary literature where not compiled by Sander. Salinity dependence of K H determined from novel relationship derived from empirical data on gas solubilities in seawater V b calculated using &apos;Schroeder&apos; additive method Diffusivities of gases in air and water and viscosities of air and water calculated from best available paramterisations Transfer velocities: various parameterisations of k l and k g implemented. Nightingale et al 2000 (k l ) and Jeffrey et al 2010 (k g ) used here. Key assumptions: neutral bouyancy, all the assumptions made by the k l and k g parameterisations selected(!) For each compound the following data are required: Henry&apos;s law solubility (K H ) T-dependence of K H (- Δ soln H/R ) Molecular structure (in order to calculate liquid molar volume at boiling point, V b ) Wind speed, temperature, salinity Temperature Salinity Wind speed Solubility at STP T dependence of solubility Molecular structure Gas-specific data Physical forcings Henry solubility in water Diffusion coefficients in air and water Viscosity of air and water Schmidt numbers in air and water k w – Nightingale2000, Wanninkhof92, Woolf97 (bubbles) k a – various schemes including Duce91, Jeffrey2010 K w and K a (1/K w = 1/k w + H/k a ) All parameters T dependent (and S dependent for water side) Outputs
9. 9. Total transfer velocity K H k g k l u 10 T S K H 0 - Δ soln H/R Sc g Sc l D g D l ν g ν l η g T η l T,S Sensitivity analysis ρ g T ρ l T,S V b C D k g k l Estimated parameter /% uncertainty Highly soluble gas e.g. NH 3 Sparingly soluble gas. e.g CO 2 50 50 10 25 5 5 10 10 25 10 10 10 10 0.1 50 10 16 -0.04 4 0.05 -0.05 -1 10 1 -1 9 40 2 1 2 -0.2 2 4 4 -6 20 0.1 -0.1 1 Sparingly soluble gas. e.g CO 2 Highly soluble gas e.g. NH 3 Estimated parameter /% uncertainty D l D g 25 25 0.1 3 11 0.3 Table presents percentage change in total transfer velocity over range of parameter uncertainty
10. 10. Really important to know when to use k w or k a on their own rather than K l (or K a )
11. 11. Application of thin film model of interfacial mass exchange to the air-sea interface Early estimates of k g and k l for H 2 O and O 2 and some trace gases of interest: SO 2 , N 2 O, CO, CH 4 , CCl 4 , CCl 3 F, CH 3 I, DMS Showed that r g /r l was small (&lt;10 -1 ) for all except SO 2 , where chemical enhancement in the liquid phase was shown to be important
12. 12. log(r g /r l ) for a suite of trace gases Log (r g /r l ) = 0 -&gt; r g = r l -&gt; 50% contribution to total transfer from both phases Log (r g /r l ) = 1 -&gt; r g /r l = 10 -&gt; 10% of total resistance due to liquid phase Log (r g /r l ) = -1 -&gt; r g /r l = 0.1 -&gt; 10% contribution to resistance from gas phase Log (r g /r l ) = 2 -&gt; 1% contribution to transfer from liquid phase Log (r g /r l ) = -3 -&gt; 0.1% contribution to transfer from gas phase
13. 13. K H dependence of r g /r l For gases with solubility between 0.1 and 1000 mol/L/atm, both phases need to be considered in quantifying total transfer veloctiy
14. 14. H2S CH3Cl C6H5CH3 CH3Br C2H5I CH3I HI CHCl3 CHI3 CH2CL2 DMS DES 2Butylnitrate Br2 2Propylnitrate CH2ICl BrCl DMDS 1Propylnitrate 1Butylnitrate HBr CH2Br2 SO2 Ethylnitrate CH2IBr CHBr3 Methylnitrate CH2I2 PPN I2 methylmethanoate PAN TEA methylethanoate TMA HCN propanal ethanal butanone HCl NHCl2 acetone OH DEA DMA nitromethane HNO2 MEA CH3CN NH3 2Nitrophenol HOBr NH2Cl MMA ICl MeOH EtOH IBr methylperoxide ethylperoxide IO HOI Phenol methanal HO2 K H dependence of r g /r l
15. 15. r g /r l compared with Liss and Slater 1974
16. 16. Chemical enhancement of k l (and k g ?): Hoover and Berkshire 1969 α = τ / {(τ-1) + (tanh(x)/x)} where x = z(k hyd .τ/D) 1/2 z = layer thickness (inversely related to wind speed) D = molecular diffusivity of gas in medium k hyd = rate of (hydration) reaction of gas in seawater τ = 1+ ([unreacted gas]/[reacted products]) Tanh(x)/x When k hyd slow, x is small, tanh(x)/x=1, α = 1 When k hyd v fast, x is large, tanh(x)/x=0, α max = τ / (τ-1) = e.g. 1+ [XH 2 O] /[X] Hoover and Berkshire assume stagnant film model, which probably underestimates potential chemical enhancement for reversible reactions Assumptions: 1. Stagnant film model applies 2. reaction can be represented by pseudo-first-order rate constant – i.e. rate is proportional to concentration of gas of interest and independent of all other factors
17. 17. Chemically enhanced SO 2 transfer unenhanced enhanced
18. 18. Chemically enhanced SO 2 transfer k a k w K w Gas phase α Liquid phase α Total enhancement r a r w r a /r w
19. 19. Gases other than CO 2 and SO 2 , reactions other than hydration Reversible reactions i) undersaturation ii) supersaturation
20. 20. Gases other than CO 2 and SO 2 , reactions other than hydration Irreversible reactions (e.g. photolysis) i) understaturation 2) supersaturation For an irreversible reaction that produces the gas of interest in the surface layer, a flux out would be enhanced and a flux in would be inhibited... The physics is the same in the gas phase, so the Hoover and Berkshire equation will apply there too...
21. 21. Rate constants to give α = 2 in both gas and liquid phases (90 gases plotted)
22. 22. Rate constants required to give different α for a gas of &apos;average&apos; diffusivity
23. 23. Selected reaction rates Compound Gas phase reaction Rate constant / s -1 Liquid phase reaction Rate constant / s -1 NH 3 Uptake on acid sulfate aerosol 10 -5 protonation &gt;10 9 CH 2 I 2 photolysis 10 -4 photolysis 10 -3 SO 2 - - hydration 10 6 CH 4 Oxidation by OH &lt;10 -6 Biological turnover 10 -3 * CO 2 - - Hydration 0.04 Methanal (formaldehyde) ? ? Hydration 10 5 * estimated from bulk seawater bacterial methane turnover of 1 day -1 scaled up by factor of 100 for possible microlayer bacterial activity
24. 24. Chemically enhanced NH 3 transfer – seawater pH ~95% total NH 3 as NH 4 + -&gt; reasonable &apos;buffering&apos; of changes to NH 3 . Protonation reaction extremely fast, therefore max thermodynamically constrained enhancement possible: α max = 1 + ([NH 4 + ]/[NH 3 ]) = 20 rg/rl Liquid phase control Gas phase control unenhanced enhanced
25. 25. Chemically enhanced NH 3 transfer – pH 9.5 ~25% total NH 3 as NH 4 + -&gt; poor &apos;buffering&apos; of changes to NH 3 . Protonation reaction still extremely fast, therefore max thermodynamically constrained enhancement possible: α max = 1 + ([NH 4 + ]/[NH 3 ]) = 1.33 rg/rl Gas phase control Liquid phase control unenhanced enhanced
26. 26. Effect of chemical enhancement / inhibition on K for gases of different solubilities
27. 27. Application of chemical enhancement equation – care needed! Formaldehyde hydration reaction is very fast in water (k = 10 6 s-1) Reaction cannot easily be inhibited by e.g. changing pH Therefore Henry&apos;s law constants implicitly include hydration product and chemical enhancement is already accounted for in flux calculation!
28. 28. Global transfer velocity climatologies We can use the transfer velocity scheme to produce gridded K fields for any gas, using climatological T and S (WOCE) and windspeed (NCEP/NCAR reanalysis) e.g. DMS: Bell and Johnson, In Prep.
29. 29. Completely injected bubbles -&gt; drive relative supersaturation Incompletely injected bubbles -&gt; drive (slightly asymmetrical) enhanced transfer for insoluble gases David Woolf (1997), Bubbles and their role in gas exchange , in The Sea Surface and Global Change The effect of bubbles
30. 30. DMS relatively soluble, so bubbles don&apos;t have a big effect Therefore applying a typical k w paramaterisation may be innapropriate at high winds. Not much data for DMS so the Jury&apos;s still out. Johnson 2010 reproduces COARE DMS prediction and fits observations well, particularly at low/medium wind speeds. Using total K w rather than k w is better (i.e. air phase transfer velocity makes a significant contribution) Reproducing observations and COARE algorithm predictions
31. 31. Temporal / Spatial Variations in K DMS January July Bell and Johnson, In Prep. K cm hr -1
32. 32. Differences in K caused by bubbles (using Woolf et al. 1997) January K DMS – K DMS(inc. bubble) July Bell and Johnson In Prep. cm hr -1
33. 33. Concentration uncertainty is large Lana et al 2010: DMS database – extension of Kettle et al 1999 50000 data points Concentration uncertainty same OOM as transfer velocity uncertainty!
34. 34. Other uncertainties Parameterizations Drag coefficient (NOAA COARE predicts u* half that of classic empirical C D ) Whitecapping parameterization (3 orders of magnitude variations) Processes and Phenomena Alternative bubble effects (turbulence, adsorption) Microlayer effects Enrichment / depletion Viscosity Henry&apos;s law in microlayer Heat and water fluxes Irreversible thermodynamics Rainfall Cool / warm skin effect Averaging and extrapolation Wind-speed averaging and applying them in the correct way What is a representative concentration Non-linearities e.g. high winds mean low concentrations?
35. 35. Summary Using numerical scheme of Johnson (2010) users can get current best estimate of classical two-layer model transfer velocity for their gas of interest This doesn&apos;t account for effects outside of the two-layer model e.g. chemical enhancement, bubbles, microlayer effects, which are variable depending on gas properties / chemistry / biology Asymmetrical effects make generalising even for a particular gas difficult Nonetheless, for regional or global extrapolations, uncertainty in concentration difference is probably still larger