# Isotopes and Gases. Isotopes as constraints to air sea gas exchange, gas exchange time scales, the various time scales of carbon (isotope) exchange

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1 Isotopes and Gases Isotopes as constraints to air sea gas exchange, gas exchange time scales, the various time scales of carbon (isotope) exchange Isotope effects in gas solution and molecular diffusion Where did this number come from?? 1

2 Using the natural radiocarbon budget A long term, large scale average Natural radiocarbon is very slow exchanger ( T ~ 10 y)* globally distributed produced by cosmic rays in the atmosphere only basic premise: flux in = decay of inventory Challenges: 1. Gas exchange model?. Isotope effects a) In solution b) During gas exchange *more later F Loss N A gas exchange model Gas exchange is a first order process flux proportional to degree of disequilibrium Slabs of water presented to atmosphere to be removed in time T before reaching equilibrium volume filled = Area x thickness L reached by diffusion (D ) depth reached in time T related to molecular diffusion rate L Scales like a random walk effect mass flux related to frequency of slab replacement () times the volume replaced each time D * F DT C C C CC frequency of slab replacement is related to viscosity of water ( ) D F k C (where k is a constant of proportionality) Define the Schmidt Number: S c D So now the G.E.R. becomes 0. 5 DT F k Sc C

3 A gas exchange model F k Sc Premises 0. 5 C ksc 0.5 is commonly called a piston velocity and is modeled as a function of U 10 (wind speed at 10 m height above ocean)* A first order process Usually plotted for Sc = 600 Separate water (k, T) and gas (Sc, C ) dependencies So you can derive a general relationship and predict for various gases Generally formulate k as a non linear function of wind speed Also dependent on surfactants, fetch, wave spectra, etc. Schmidt number for various gases and temperatures T(C) He Ne Kr Xe Rn H CH 4 CO *Wanninkhof, 199. Journal of Geophysical Research 97, In more general terms n F ksc C Range of physical models & situations dependent on wind speed (a) Beaker: stagnant film n=1 (b) Weak turbulence n=/3 (c) Normal oceanic n=1/ (d) Strong forcing: bubble dynamics & spray (all hell breaks loose) Beware: 1. Wind speed measured at 10 m above sea level. Choice of paremeterization depends on whether instantaneous or average wind speed 3

4 The Radon Deficit Technique Gas Exchange Flux = Production Decay F= H(A 6 A ) ----H F k Sc C 1/ H A A ksc 6 A T What is the characteristic timescale of this determination??? Warning: original literature (1974) used stagnant film model (n=1), which is morally incorrect and punishable by revocation of J.P. PhD If determined k using Rn at 10 C, using n=1 6 Ra flux of CO would differ by 5% flux of N would differ by a factor of 1.9 flux of He would differ by a factor of.6 Gas exchange timescales Adjustment time w.r.t. a change T GE =H/K where K is piston velocity = ksc 0.5, H is mixed layer depth a physical time scale examples U 10 = 10 m/s, H = 100 m, Temp = 0 C He (Sc = 150), T GE ~ 11 days O z (Sc = 450), T GE ~ 18 days CO (Sc = 600), T GE ~ 3 days???* CO is actually much longer due to chemical inertia of huge buffer system effect H CO H TGE R ksc pco ksc R is Revelle Factor and is a function of pco and carbon system parameters, as well as temperature ~ 10 So T GE ~ 0.7 years for CO 4

5 CO Gas Exchange and Radiocarbon CO has an even larger isotopic inertia to change p CO you have to flux much more CO into the water due to huge CO reservoir T H ksc CO this Broecker Factor arises because you have to move C throughout the entire carbon reservoir (unlike CO and the Revelle factor) the gas exchange residence time for CO is 180 X 3 days ~ 10 years!!! H pco ksc 180 Observation of the Broecker Factor? Surface ocean response to bomb C transient seen in coral records Long time scale related to reservoir age Atmospheric Forcing Surface Ocean Response Druffel, E. R. M. and Suess, H. E., Journal of Geophysical Research 88,

6 Isotope effects in solution and diffusion Gas Solubility Dalton s Law of Partial Pressures: individual partial pressures are additive gases behave independently Henry s Law: gas concentration in water proportional to partial pressure of gas above the water Keq A Aq PA RT [A aq ] = aqueous activity (gas concentration) expressed in molar units Solubility expressed in terms of Bunsen Solubility Coefficient* A Aq APA Relates concentration directly to partial pressure in gas phase *sometimes referred to as α heat of solution depends on 1. work required to create cavity in solvent. work required to contain solute in the cavity 3. energy gained from solutesolvent attraction Gas Solubilities Unlike in rocks, smaller atoms or molecules are less soluble than the larger ones! Gas solubility generalities: heavier, more polar gases are more soluble (3 rd ) all gases are more soluble at lower temperatures * more soluble gases have greater temperature dependence Increasing salinity depresses solubility ln 0 k S S S * unlike salts, for example 6

7 Gas Solubility Solubilities determined in the laboratory under controlled conditions reported in quasi thermodynamic equations, e.g., 1 ln A1 A A3 lnt S B1 BT B3T T just a convenient form to calculate solubility as a function of T& S Isotope Effects in Solution Heavier isotopes are more soluble (enriched in water) Due to nd (solute) and 3 rd (solute solvent) energy terms (former more important?) Gas Molecular Wt Isotope Ratio Mass Difference Isotope Effect Helium 4 3 He/ 4 He -8.6% -1.5% Neon 0. Oxygen 3 Argon 40 0 Ne/ Ne -9.5% -0.5% 18 O 16 O/ 6.1% +0.1% 16 O 40 Ar/ 36 Ar 10.5% +0.05% Proportional to fractional mass difference, inversely to solubility (more soluble gases less affected) CO / CO 1.5% 7

8 Isotope Effects in Diffusion Heavier isotopes move more slowly Related to but not explicable by kinetic gas theory (complicated reduced mass effect with multiple water molecules) Gas Molecular Isotope Mass Isotope Wt Ratio Difference Effect Helium 4 3 He/ 4 He -8.6% 5.0% m m Neon 0. Oxygen 3 Argon 40 0 Ne/ Ne -9.5% 1.4% 18 O 16 O/ 6.1% -0.3% 16 O 40 Ar/ 36 Ar 10.5% -0.8% Proportional to fractional mass difference, inversely to solubility (more soluble gases less affected) CO / CO 0.% Bourg and Sposito (008) GCA, 7, 37 47* Knox et al (199) JGR, Revisiting the global ocean radiocarbon mass balance calculation Using an appropriate Sc number for area weighted average ocean surface temperature Fin 0.07kC Or Fin 0.07kC Surf C0 Substituting what we now know : 0.07k0.95 This becomes C C C C Fin Surf Atm Atm CO CO C Which must balance decay in the ocean interior Fin k CO C Surf Atm Surf 8

9 Global ocean radiocarbon mass balance C Fin k CO C Surf Atm F Loss N C FLoss CO C Oceans Atm 9