Martha Peirce Butler March 5, 2010

1. Reducing the Uncertainty of North American Carbon Flux Estimates Using an Extended Atmospheric CO2 Measurement Network Martha Peirce Butler March 5, 2010

2. Presentation Outline • Global Carbon Cycle Overview • Global Atmospheric Inversion • North American Results for 2001-2003 • Future North American Networks • Conclusions 2

3. Global Carbon Cycle Units are PgC/yr IPCC TAR (2001) 3

4. Variability in Carbon Sources/Sinks Gray bars are annual increases in global mean atmospheric CO2. Solid black and red lines are 5-year mean annual growth rates (for 2 different networks of observations). Top line is what the atmospheric CO2 growth rate would be if all the fossil fuel emissions stayed in the atmosphere. The difference is in land and ocean sinks. My task is to improve the spatial and temporal diagnosis of the carbon sources/sinks, with an emphasis on North America. Figure TS3, IPCC AR4 TS (2007) 4

5. Evidence for a Northern Hemisphere Sink Fit to observations, 1981-87, adjusted to 1987 • Where is that sink? • Land or Ocean? • North America or Europe or Asia? • It depends on the analysis? • Time period • Method Tans et al. (1990) Forward simulations of fossil fuel emissions, neutral biosphere flux, tropical deforestation, and multiple versions of air-sea fluxes 5

6. Forest inventory Global Tower flux year Time Scale month Chamber flux Airborne flux day hour 2 2 2 2 2 (1m) (1km) (10km) ( 100km) (1000km) R earth - 4 2 4 6 8 = 10 ha = 10 ha = 10 ha = 10 ha = 10 ha Spatial Scale Summary of Diagnostic Methods Atmospheric Inversions Regional After K.J. Davis 6

7. What is this “Atmospheric Inversion”? • Assume: • CO2 is unreactive in the atmosphere. • All changes to atmospheric CO2 are the result of exchanges at the land and ocean surface. • An atmospheric observation of CO2 (mixing ratio) is the result of the transport of CO2 from (many) source and sink regions. • Given: • Atmospheric CO2 observation time series at locations globally • Modeled responses at these locations to surface exchanges (with known spatial and temporal resolution) • Infer (or attempt to infer): • The linear combination of sources/sinks in space and time that best explain the observation time series 7

8. Air Parcel wind wind Sinks Air Parcel Air Parcel Sources Sample Sample Blowing in the Wind Changes in CO2 in the air tell us about sources and sinks 8

9. Source/Sink Partitioning in Contemporary Global Atmospheric Inversions How is the global sink split between land and ocean? [Units are PgC/yr] North American Carbon Program, Interim Synthesis Activity (Jacobson et al., in preparation) T3IAV Atmospheric Tracer Transport Model Intercomparison (TransCom) (Baker et al., 2006) 9

10. The Problem is Not Well Constrained • The observations are predominantly in marine boundary layer. • The variability is predominantly over land. • Typical solutions involve: • Solving for adjustments to given background fluxes • Using estimates of adjustments and uncertainties as first guesses (priors) • Choosing prior fluxes and uncertainties is an art form. • The Bayesian Synthesis Inversion method • Create transport fields: samples from a transport model at the observation stations from forward runs of background and “pulse” tracer emissions. • Do a matrix inversion to adjust the background fluxes (plus any prior estimates) to better explain the real observations. 10

11. Bayesian Synthesis Inversion Method 11

12. Spatial and Temporal Resolution of the Inversion Estimate monthly carbon sources/sinks for each of these 47 regions for 2001-2003. To enable comparisons to other contemporary inversions: Ocean regions are the same 11 used in TransCom. Land regions are conformable to the 11 TransCom land regions. 12

13. Bayesian Synthesis Inversion Method 13

14. Fluxes for Forward Transport • Background Fluxes • Terrestrial: SiB3 hourly flux, annually neutral, with interannual variability (Baker et al., 2007; N. Parazoo) • Ocean: monthly climatology for the mid-1990s (Takahashi et al.,2002), with 1.6 PgC annual uptake • Fossil Fuel Emissions: monthly with seasonal variability (Erickson et al., 2008), scaled to global emissions from Marland et al. (2007) • Biomass Burning: GFED2 monthly fluxes (van der Werf et al.,2006, and Giglio et al., 2003) • Alternative background fluxes tested: • Terrestrial: CASA monthly mean flux with no interannual variability • Fossil fuel emissions: with no seasonal variability • “Pulse” Fluxes • Known flux emitted for 1 month from each region/month and transported for another 24 months. Pattern within each region derived from that used in TransCom experiments (Gurney et al.,2002, 2003). 14

15. Bayesian Synthesis Inversion Method 15

16. Tracer Transport Model • PCTM from NASA Goddard (Kawa et al., 2004) as implemented at CSU • 2.5 longitude by 2.0 latitude horizontal resolution, 25 hybrid vertical layers • 6-hourly GEOS-4 meteorology • 15 minute time step • Model has participated in TransCom experiments in two different spatial resolutions. • Carbon dioxide is transported as a passive tracer. • Sampling at past, present and possible future observation sites (nearest grid cell) • Hourly model surface pressure and vertical columns of CO2 and temperature saved, with CO2 resolved to site elevation after transport model run. • Selection of hours that match the observations for use in the inversion (co-sampling) 16

17. Bayesian Synthesis Inversion Method 17

18. CO2 Observation Time Series • Real observations (not smoothed data products) • Sources • NOAA ESRL GMD (continuous and discrete) • WDCGG (continuous and discrete) • Principal Investigators at 5 flux towers (continuous) • Calculation of monthly means and uncertainties • Monthly values are averages of daily means of selected hours with uncertainty set to the standard deviation of these daily means (range 0.50 to >10.0 ppm) • Data quality and gap filling • Minimal rejection of data • No more than 12 missing months within 2000-2004 • Gap filling strategy • GlobalView with increased standard deviation • Climatologic difference from GlobalView Marine Boundary Layer 18

19. Bayesian Synthesis Inversion Method 19

20. Prior Fluxes and Uncertainties • Priors are specified as no adjustment to the monthly background flux. • Base level uncertainties for each region/month are the 3-month background exchange for the month, centered on the month. • Total global uncertainty for the base level priors: 5.4 Pg C/yr. This compares to the most recent TransCom global uncertainty of 2.9 Pg C/yr. Background Flux for Example Region 20

21. Bayesian Synthesis Inversion Method 21

22. The Analytical Solution The solution involves finding the fluxes x that minimize the cost function: This method also yields an estimate of the uncertainty: where x0 are the prior flux estimates, cobs - cfwd are the mismatches between the observations and the model samples from the forward runs of the background fluxes, H is the matrix of transport fields, P0 contains the uncertainties in the prior flux estimates, and R contains the uncertainties in cobs – cfwd (and the transport). Baker et al. (2006) 22

23. Errors, Assumptions and Simplifications • What should be in the data uncertainty? • Data variability • Observation error • Instrument precision • Calibration across observing agencies • Transport model contributions • Transport error • Model resolution error • Other issues: • Representativeness of the observations • Large regions & assumed underlying patterns • Have we violated too many assumptions? • Kaminski et al. (2001) and Engelen et al. (2002) 23

24. The Bayesian Synthesis Inversion Method 47 regions x 12 months x 5 years 6 bg fluxes x 5 years > 200 time series evaluated < 100 used 5 years of 6-hourly met data 11 versions 30 networks > 50 variations > 800 sites sampled 24

25. Results for the 2000-2004 Networks • Estimated carbon source/sink solutions from three inversion variations • Base network solution using 54 observation sites • Enhanced network solution using 86 observation sites • Continental Extension network solution using 91 observation sites • What to look for: • Global Results • Focus on North America • Has adding the 5 flux tower sites in the continental extension network improved the uncertainty of the results? • Has adding flux tower sites changed estimated fluxes? • Are the results sensitive to experimental design choices? • How do these results compare to a reference inversion (CarbonTracker, release 2008, available at //www.esrl.noaa.gov/gmd/ccgg/carbontracker/)? 25

26. The 2000-2004 Observation Networks Base Network 54 sites Enhanced Network 86 sites Continental Extension Network 91 sites 26

27. Global results: annual mean 2001-2003 North American flux estimates in PgC/yr for different networks (prior specification is 0.00 ± 1.77 Pg C/yr): Base -0.99 ± 0.48 Enhanced -1.09 ± 0.46 Continental Extension -1.33 ± 0.38 CarbonTracker -0.54 ± 0.65 Fluxes include biomass burning emissions, but not fossil fuel emissions. Positive values are sources to the atmosphere. 27

28. Posterior Annual Covariance Posterior covariance matrix for 2002 for the 22 large regions for the Continental Extension network Boreal and Temperate North America have some significant covariances with each other and with other regions. The largest covariances are between regions in South America and Africa. Ocean regions are independent of each other, but not necessarily of the bordering land regions. 28

29. Uncertainty Reduction in the Americas Average annual uncertainty reduction for 2001-2003. Uncertainty reduction (in percent) is Uncertainty reduction is greatest in regions where sites are added in the CE network. Flux solutions for North America (2001-2003 mean annual in PgC/yr): Boreal Temperate B network: 0.23 ± 0.39 -1.22 ± 0.55 E network: 0.14 ± 0.38 -1.22 ± 0.51 CE network: 0.00 ± 0.32 -1.34 ± 0.40 29

30. Adding Local Observations to Northeast Region -0.68 ± 0.48 -0.59 ± 0.28 -0.60 ± 0.33 -0.72 ± 0.24 Numbers are the 2001-2003 mean annual flux and uncertainty for the Northeast region in PgC/yr for inversion variations with 4 different networks. 30

31. Sensitivity to Prior Flux Uncertainty One test for the inversion is to see how bound the solution is by the prior uncertainty specifications. These examples are for two of the Temperate North America regions for inversion variations using the 91-site Continental Extension network. The Northeast region, with 2 observation sites, is resistant to changes in the magnitude of the prior uncertainty. The Pacific Northwest, with no observation sites, is more vulnerable, showing the role of the prior specifications in confining the solution in biogeochemical reality. 31

32. Sensitivity to Choice of Background Fluxes The SiB3 and CASA background fluxes (on the left) differ in timing of the timing and amplitude of the seasonal cycle. The impact on the flux solution is shown on the right. The difference in the SiB and CASA inversion solution in the Northeast (magenta) is well within the posterior uncertainty. The difference is greater is the under-represented Pacific Northwest. The inversion solution difference for the seasonal and annual fossil (cyan) is less than 0.01 Pg C/yr in any month for these regions. 32

33. Regional Annual Posterior Covariance 33

34. Taylor Plot of Data Residuals Taylor plots in general: Angular distance above the horizontal is a measure of correlation (1-r). Radial distance from the origin is a normalized standard deviation. The “sweet spot” is at (0.0, 1.0 NSD) Pre-inversion values (hollow symbols) compare composite background flux responses to the observation time series. Post-inversion values (solid symbols) compare predicted observation to observation time series. North American sites are in blue. NOAA ESRL observatories are in red. 34

35. What If We Could Use a “Current” Network? • More North American research sites are now instrumented for measurement of CO2 calibrated to global standards. • Only 2000-2004 meteorological driver data were available when the forward model runs were done. • Simulated observations for the new sites for 2000-2004 to fit into the analysis period of this inversion experiment. • Intent: examine inversion results for further uncertainty reduction opportunities in North American inversion results. 35

36. Future/Current Observation Network F1 network: Continental Extension network plus 24 sites operating in 2009 F2 network: F1 network plus 8 more planned or possible sites Added sites are all continuous sampling sites (a mix of flux towers, tall towers, and sites in complex terrain) 36

37. How to Make a Synthetic Observation 1 Make an hourly time series at each location using a composite of background fluxes sampled from the forward transport. 2 Calculate monthly mean and standard deviation using a default sampling strategy (mid-day hours every day). 3 Determine a 6 parameter fit (linear trend + harmonics) to the monthly time series.. 4 Determine a similar fit for GLOBALVIEW MBL time series interpolated to the latitude of the site location. 5 Substitute the MBL offset and trend in the 6 parameter fit. 6 Use a multiplier to adjust the amplitude of the harmonic part of the fit based on nearby real observing sites. 37

38. Potential Future Uncertainty Reductions Average annual uncertainty reduction for 2001-2003. Uncertainty reduction (in percent) is Significant uncertainty improvements may be possible in regions not well-represented in the Continental Extension network. “Loading up” on sites may not help that much. Uncertainty Improvements for North America: Prior Uncertainty: 1.77 PgC/yr Posterior Uncertainty by Network: CE: 0.38 Pg C/yr F1: 0.29 Pg C/yr F2: 0.27 Pg C/yr 38

39. Improvement in Posterior Covariance within North America 39

40. Revisiting the Method • “It is generally not very easy to check the correctness of the assumptions.” (Tarantola, 2005) • At least do these: • Examination of residuals (both data and fluxes) • Examination of the posterior covariance matrix • Sensitivity studies • The major drawbacks are a lack of robustness (strong sensitivity to outliers) and an overly-optimistic estimate of posterior uncertainty. If we know that our individual errors and fluctuations follow the magic bell-shaped curve exactly, then the resulting estimates are known to have almost all the nice properties that people have been able to think of. John W. Tukey (1965) 40

41. Assumptions and Simplifications • The problem is linear, making a least-squares solution appropriate. • The errors in the data, forward model, and priors are Gaussian, enabling an analytical solution. • The errors in the data, forward model, and priors are not correlated, allowing the use of diagonal prior covariance matrices. • The underlying pattern for each region is correct, so that the solution is a multiplier that applies to the whole region. • It’s OK to use one year of meteorological data over and over, especially when solving for mean annual or mean seasonal solution. • Using the Globalview data product gives a smooth, gap-free time series, adjusted for differences in inter-agency network calibrations. • Fossil fuel emissions are assumed to be known, even though the spatial distributions are not current and the emissions are often assumed to have no seasonal structure. X X X 41

42. And There is More… • Testing of the sub-selection of hours for continental sites • Virtual Tall Tower simulation at flux tower sites • Inclusion/exclusion of classes of observation sites • Aircraft sampling • Mountaintop sites in Europe • Outlier effect of one site? (still a puzzle) • Giving back to the research community: • North American Carbon Program, Interim Synthesis • TransCom comparison of contemporary inversions 42

43. Conclusions • Yes, we can use continental surface sites with carbon dioxide measurements calibrated to global standards in the observation networks for global atmospheric inversions. • Yes, including these sites contributes to uncertainty improvement in the source/sink estimates for North America, without any serious impact to the source/sink estimates. • Yes, we can use real observations and not a smoothed data product. • Sub-sample observations at continental sites for the hours that best represent well-mixed conditions and match the boundary layer characterization of the transport model. • Co-sample the model atmosphere for the same hours as the observations. • A priority for network design is to add continental sites in under-represented regions as the uncertainty improvement is local. 43

44. Future Work • Extend the analysis time period • Detection of long-term trends • Comparison to other inversions • New sites in the network • Incorporate more observation types • Column CO2 from satellites and TCCON • Aircraft profiles • Use updated background fluxes • Keep this method in the inversion toolbox 44

45. Acknowledgements • People • Committee (Ken Davis, Ray Najjar, Sukyoung Lee, Klaus Keller and Scott Denning) • Davis Group at Penn State • Denning Group at CSU • Randy Kawa at NASA GSFC • Everyone, everywhere in the CO2 measurement network • Faculty, family and friends • Funding Agencies • NASA GSRP • NOAA, DOE, NSF • PSU, College of EMS Chelius Fellowship and Centennial Graduate Research Award Thank you! 45

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47. The ESP Puzzle – Sensitivity to an Outlier?

48. Analysis of Data Residuals

49. Analysis of Data Residuals

50. Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise. John W. Tukey (1962)