1. Characterizing CO 2 fluxes from oceans and terrestrial ecosystems Nir Krakauer PhD thesis seminar May 19, 2006

2. The atmospheric CO 2 mixing ratio Australian Bureau of Meteorology

3. Warming is underway Dragons Flight (Wikipedia) Data: Hadley Centre

5. The atmospheric CO 2 mixing ratio: A closer look 1990s fossil fuel emissions: 6.4 Pg carbon / year The amount of CO 2 in the atmosphere increased by 3.2 Pg C / year Where did the other half of the CO 2 go? Why the interannual variability?

6. Ocean CO 2 uptake The ocean must be responding to the higher atmospheric pCO 2 ; models estimate ~2 Pg C/ year uptake Hard to measure directly because air-sea CO 2 fluxes are patchy, depending on ocean circulation, biology, heating, gas exchange rate LDEO

7. CO 2 uptake on land Change in C content of biomass very patchy; hard to extrapolate from small-scale surveys… Uptake must make up for ~1.5 Pg C / year deforestation Land biomass might be growing because of longer growing seasons, CO 2 fertilization, N fertilization, fire suppression, forest regrowth… Buermann et al 2002

8. 1) Tree-ring evidence for the effect of volcanic eruptions on plant growth Henri D. Grissino-Mayer Chris Newhall, via GVP N. Y. Krakauer, J. T. Randerson, Global Biogeochem. Cycles 17, doi: 10.1029/2003GB002076 (2003)

9. Motivation Why did the atmospheric CO 2 growth rate drop for 2 years after the 1991 Pinatubo eruption? Changes in the latitudinal CO 2 gradient and in δ 13 C suggest that part of the sink was from northern land biota An enhanced carbon sink also followed the 1982 El Chichón and 1963 Agung eruptions

10. How would eruptions lead to a carbon sink? Roderick et al (2001) and Gu et al (2003): light scattering by aerosols boosts canopy photosynthesis for 1-2 years after eruptions Jones and Cox (2001) and Lucht et al (2002): soil respiration is lower because of cooling; boreal photosynthesis decreases Gu et al 2003 Lucht et al 2002 Harvard Forest (clear skies)

11. What I did What happened to tree ring widths after past eruptions? Large eruptions since 1000 from ice core sulfate time series 40,000 ring width series from the International Tree Ring Data Bank (ITRDB) 40,000 ring width series from the International Tree Ring Data Bank (ITRDB) Crowley 2000

12. Ring width anomalies by latitude

13. above 45°N: by genus

15. The 1990s: Harvard Forest

16. Part 1: Conclusions Northern trees (>45°N) had narrower rings up to 8 years after Pinatubo-size eruptions Eruptions had no significant effect on trees at other latitudes (few trees from the tropics though) From this sample, negative influences on NPP appear to dominate positive ones – respiration slowdown is likely to be responsible for the inferred carbon sink

17. Part 1: Research directions Are there niches where diffuse light does strongly enhance growth? – understory trees, tropical rainforest… Why are boreal rings narrower so long after eruptions? Can we tell what happens to trees’ physiology after eruptions (short growing season, nutrient stress…)? – tree-ring δ 13 C, δ 15 N

18. 2) Selecting parameters in inversions for regional carbon fluxes by generalized cross- validation Baker et al 2006 N. Y. Krakauer, T. Schneider, J. T. Randerson, S. C. Olsen, Geophys. Res. Lett. 31, doi: 10.1029/2004020323 (2004).

19. CO 2 fluxes from concentration differences: a linear inverse problem Ax ≈ b A transport operator that relates concentration patterns to flux magnitudes the (unknown) flux magnitudes Measurements of CO 2 concentrations, with error covariance matrix C b x ≈ x 0 A plausible prior flux distribution, with prior uncertainty covariance matrix C x

20. Ambiguities in parameter choice Solving the inverse problem requires specifying C b, C x, x 0 Adjustable parameters include: How much weight to give the measurements vs. the prior guesses? Weight CO 2 measurements equally or differentially? Different parameter values lead to varying results for, e.g., the land-ocean and America-Eurasia distribution of the missing carbon sink

21. Generalized cross-validation (GCV) Craven and Wahba (1979): a good value of a regularization parameter in an inverse problem is the one that provides the best invariant predictions of left-out data points Choose the parameter values that minimize the “GCV function”: GCV = T = effective degrees of freedom

22. The TransCom 3 inversion Estimates mean-annual fluxes from 11 land and 11 ocean regions Data: 1992-1996 mean CO 2 concentrations at 75 stations, and the global mean rate of increase Gurney et al 2002

23. Parameters varied λ: How closely the solution would fit the prior guess x 0 –controls size of the prior-flux variance C x higher λ: solution will be closer to x 0 (more regularization) –Weighting used in original TransCom inversion taken as λ=1 τ: How much preference to give data from low- variance (oceanic) stations –controls structure of the data variance C b 0: all stations weighted equally –TransCom value: 1

24. Results: the GCV function Function minimum Parameter values used in TransCom

25. Results: inferred CO 2 flux (Pg C/ yr)

26. Ocean

27. Equatorial land

28. overall inferred flux distribution TransCom parameter values GCV parameter values

29. (2) Conclusion and research directions Parameter choice explains part of the variability in CO 2 flux estimates derived from inverse methods GCV looks promising for empirically choosing parameter values in global-scale CO 2 inversions, e.g. weights for different types of information GCV-based parameter choice methods should also be useful for studies that try to solve for carbon fluxes at high resolution (e.g. NACP)

30. 3) Regional air-sea gas transfer velocities estimated from ocean and atmosphere carbon isotope measurements N. Y. Krakauer, J. T. Randerson, F. W. Primeau, N. Gruber, D. Menemenlis, submitted to Tellus GasEx

31. A conceptual model of gas exchange: the stagnant film Most of the air-sea concentration difference is across a thin (<0.1 mm) water-side surface layer F = k w (C s – C a ) –F: gas flux (mass per surface area per time) –C s : gas concentration in bulk water (mass per volume) –C a : gas concentration in bulk air (partial pressure * solubility) –k w : gas transfer coefficient (a “gas transfer velocity”) J. Boucher, Maine Maritime Academy 100 μm

32. Wu 1996; Pictures: WHOI Measured gas transfer velocities range widely… Gas transfer velocity usually plotted against windspeed (roughly correlates w/ surface turbulence) Many other variables known/theorized to be important: wave development, surfactants, rain, air-sea temperature gradient… Several measurement techniques have been used – all imprecise, sometimes seem to give systematically different results What’s a good mean transfer velocity to use?

33. ..as do parameterizations of k w versus windspeed Common parameterizations assume k w to increase with windspeed v (piecewise) linearly (Liss & Merlivat 1986), quadratically (Wanninkhof 1992) or cubically (Wanninkhof & McGillis 1999) Large differences in implied k w, particularly at high windspeeds (where there are few measurements) –Are these formulations consistent with ocean tracer distributions? Feely et al 2001

34. CO 2 isotope gradients are excellent tracers of air-sea gas exchange Because most (99%) of ocean carbon is ionic and doesn’t directly exchange, air-sea gas exchange is slow to restore isotopic equilibrium Thus, the size of isotope disequilibria is uniquely sensitive to the gas transfer velocity k w Ocean carbonate speciation (Feely et al 2001) O2O2 14 d N2ON2O17 d CFC-1121 d CO 2 295 d C isotopes2926 d Sample equilibration times with the atmosphere of a perturbation in tracer concentration for a 50-m mixed layer ppm μmol/kg

35. Optimization scheme Assume that k w scales with some power of climatological windspeed u: k w = (u n / ) (Sc/660) -1/2, (where <> denotes a global average, and the Schmidt number Sc is included to normalize for differences in gas diffusivity) find the values of, the global mean gas transfer velocity and n, the windspeed dependence exponent that best fit carbon isotope measurements using transport models to relate measured concentrations to corresponding air-sea fluxes

36. Windspeed varies by latitude SSM/I climatological wind (Boutin and Etcheto 1996)

37. The radiocarbon cycle at steady state 14 C (λ 1/2 = 5730 years) is produced in the upper atmosphere at ~6 kg / year Notation: Δ 14 C = 14 C/ 12 C ratio relative to the preindustrial troposphere Stratosphere +80 ‰ 90 Pg C Troposphere 0‰ 500 Pg C Shallow ocean –50‰ 600 Pg C Deep ocean –170‰ 37000 Pg C Land biota –3‰ 1500 Pg C Sediments –1000‰ 1000000 Pg C 14 N(n,p) 14 C Air-sea gas exchange

38. The bomb spike: atmosphere and surface ocean Δ 14 C since 1950 Massive production in nuclear tests ca. 1960 (“bomb 14 C”) Through air-sea gas exchange, the ocean took up ~half of the bomb 14 C by the 1980s bomb spike data: Levin & Kromer 2004; Manning et al 1990; Druffel 1987; Druffel 1989; Druffel & Griffin 1995

39. Ocean bomb 14 C uptake: previous work Broecker and Peng (1985; 1986; 1995) used 1970s (GEOSECS) measurements of 14 C in the ocean to estimate the global mean transfer velocity,, at 21±3 cm/hr This value of has been used in most subsequent parameterizations of k w (e.g. Wanninkhof 1992) and for modeling ocean CO 2 uptake Based on trying to add up the bomb 14 C budget, suggestions have been made (Hesshaimer et al 1994; Peacock 2004) are that Broecker and Peng overestimated the ocean bomb 14 C inventory, so that the actual value of might be lower by ~25%

40. Ocean 14 C goals From all available (~17,000) ocean Δ 14 C observations, re- assess the amount of bomb 14 C taken up, estimate the global mean gas transfer velocity, and bound how it varies by region The 1970s (GEOSECS) observations plus measurements from more recent cruises (WOCE) data: Key et al 2004

41. Modeling ocean bomb- 14 C uptake Simulate ocean uptake of bomb 14 C (transport fields from ECCO-1°), given the known atmospheric history, as a function of the air-sea gas transfer velocity Find the air-sea gas transfer velocity that best fits observed 14 C levels

42. Results: simulated vs. observed bomb 14 C by latitude – 1970s For a given, high n leads to more simulated uptake in the Southern Ocean, and less uptake near the Equator Observation-based inventories seem to favor low n (i.e. k w increases slowly with windspeed) Simulations for = 21 cm/h and n = 3, 2, 1 or 0 Observation-based mapping (solid lines) from Broecker et al 1995; Peacock 2004

43. Simulated-observed ocean 14 C misfit as a function of and n The minimum misfit between simulations and (1970s or 1990s) observations is obtained when is close to 21 cm/hr and n is low (1 or below) The exact optimum and n change depending on the misfit function formulation used (letters; cost function contours are for the A cases), but a weak dependence on windspeed (low n) is consistently found

44. Optimum gas transfer velocities by region As an alternative to fitting and n globally, I estimated the air-sea gas exchange rate separately for each region, and fit and n based on regional differences in windspeed Compared with previous parameterizations (solid lines), found that k w is relatively higher in low- windspeed tropical ocean regions and lower in the high- windspeed Southern Ocean (+s and gray bars) Overall, a roughly linear dependence on windspeed (n ≈ 1; dashed line)

45. Simulated mid-1970s ocean bomb 14 C inventory vs. and n The total amount taken up depends only weakly on n, so is a good way to estimate The simulated amount at the optimal (square and error bars) supports the inventory estimated by Broecker and Peng (dashed line and gray shading)

46. Other evidence: atmospheric Δ 14 C I estimated latitudinal differences in atmospheric Δ 14 C for the 1990s, using observed sea-surface Δ 14 C, biosphere C residence times (CASA), and the atmospheric transport model MATCH The Δ 14 C difference between the tropics and the Southern Ocean reflects the effective windpseed dependence (n) of the gas transfer velocity °N°N

47. Observation vs. modeling The latitudinal gradient in atmospheric Δ 14 C (dashed line) with the inferred and n, though there are substantial uncertainties in the data and models (gray shading) More data? (UCI measurements) Similar results for preindustrial atmospheric Δ 14 C (from tree rings) Also found that total ocean 14 C uptake preindustrially and in the 1990s is consistent with the inferred n (cm/hr) ( ‰ difference, 9°N – 54°S)

48. 14 C conclusions The power law relationship with the air-sea gas transfer velocity k w that best matches observations of ocean bomb 14 C uptake has –A global mean =21±2 cm/hr, similar to that found by Broecker and Peng –A windspeed dependence n= 0.9±0.4 (about linear), compared with 2-3 for quadratic or cubic dependences This is consistent with other available 14 C measurements

49. The ocean is now releasing 13 C to the atmosphere… Notation – δ 13 C: 13 C/ 12 C ratio relative to a carbonate standard The atmospheric 13 C/ 12 C is steadily declining because of the addition of fossil-fuel CO 2 with low δ 13 C; this fossil-fuel CO 2 is gradually entering the ocean Scripps (CDIAC) 1977-2003

50. …and the amount can be estimated… Budget elements –the observed δ 13 C atmospheric decline rate (arrow 1) –biosphere disequilibrium flux (related to the carbon residence time) (5) –fossil fuel emissions (6) –biosphere (4) and ocean (2) net carbon uptake (apportioned using ocean DIC measurements) I calculated that air-sea exchange must have brought 70±17 PgC∙‰ 13 C to the atmosphere in the mid-1990s, ~half the depletion attributable to fossil fuels Pg carbon PgC∙‰ carbon-13 Randerson 2004

51. …but the air-sea δ 13 C disequilibrium is of opposite sign at low vs. high latitudes Reflects fractionation during photosynthesis + temperature-dependent carbonate system fractionation The dependence of k w on windspeed must yield the inferred global total flux data: GLODAP (Key 2004) Sea-surface δ 13 C (‰) Air-sea δ 13 C disequilibrium ( ‰) Temperature-dependent air-sea fractionation (‰)

52. Simulated 1990s air-sea δ 13 C flux vs. and n At high n, the 13 C flux into the Southern Ocean largely offsets the 13 C flux out of the tropics The observed rate of decline of atmospheric δ 13 C, combined with the known fossil fuel emissions, suggests a large 13 C flux out of the ocean (dashed line and gray shading), which requires n < 2

53. The air-sea CO 2 flux is also of different sign at high vs. low windspeed regions Sea-surface pCO 2 is high in the tropics (→ flux out of ocean) and low in the midlatitudes (→ flux into ocean) Takahashi et al 2002

54. Implications for ocean CO 2 uptake We can apply the new parameterization of gas exchange to pCO 2 maps: –uptake by the Southern Ocean is lower than previously calculated (fitting inversion results better) –outgassing near the Equator is higher (reducing the required tropical land source)

55. 3) Conclusions 14 C and 13 C measurements constrain the mean air-sea gas transfer velocity and its spatial/windspeed dependence, averaged over large regions and several years The new parameterization promises to increase the usefulness of ocean pCO 2 measurements for answering where carbon uptake is occurring and how it changes with time (e.g. tropical land vs. ocean)

56. 3) Questions to pursue Might a polynomial match the relationship of the gas transfer velocity with windspeed better than a power law (e.g. k w is not expected to be zero in calm seas) ? Are there other easily measured quantities, such as mean square surface slope or fractional whitecap coverage, that predict gas transfer velocities better than windspeed? Does the dependence on windspeed change if we use the same high-resolution winds that drive model ocean mixing? What are the implications for trace gas budgets?

57. That’s all for now USRA

58. Acknowledgements Tapio Schneider and Jim Randerson Jess Adkins, Paul Wennberg, Don Burnett, Andy Ingersoll, Yuk Yung, Jared Leadbetter François Primeau, Stan Tyler, Sue Trumbore, Xiaomei Xu, John Southon Seth Olsen, David Noone, Carrie Masiello, Diego Fernández, Ross Salawitch, John Miller, Parvadha Suntharalingam, Moustafa Chahine, Qinbin Li Lisa Welp, Nicole Smith Downey, Zhonghua Yang Betty and Gordon Moore Foundation and NASA for graduate fellowships The Earth System Modeling Facility for computing support