1. Improving Understanding of Global and Regional Carbon Dioxide Flux Variability through Assimilation of in Situ and Remote Sensing Data in a Geostatistical Framework Kim Mueller 1 Sharon Gourdji 1 Anna M. Michalak 1,2 1 Department of Civil and Environmental Engineering 2 Department of Atmospheric, Oceanic and Space Sciences The University of Michigan

2. Synthesis Bayesian Inversion Meteorological Fields Transport Model Sensitivity of observations to fluxes (H) Residual covariance structure (Q, R) Prior flux estimates (s p ) CO 2 Observations (y) Inversion Flux estimates and covariance ŝ, V ŝ Biospheric Model Auxiliary Variables Slide from Anna Michalak

3. Key Questions  Is there another inversion approach available to estimate: Spatial and temporal autocorrelation structure of fluxes and/or flux residuals? Sources and sinks of CO 2 without relying on prior estimates? Significance of available auxiliary data? Relationship between auxiliary data and flux distribution? Realistic grid-scale flux variability

4. Geostatistical Approach to Inverse Modeling  Geostatistical inverse modeling objective function: H = transport information, s = unknown fluxes, y = CO 2 measurements X and  define the model of the trend R = model data mismatch covariance Q = spatio-temporal covariance matrix for the flux deviations from the trend Deterministic componentStochastic component

5. Global Gridscale CO 2 Flux Estimation  Estimate monthly CO 2 fluxes (ŝ) and their uncertainty on 3.75° x 5° global grid from 1997 to 2001 in a geostatistical inverse modeling framework using: CO 2 flask data from NOAA-ESRL network (y) TM3 (atmospheric transport model) (H) Assume spatial correlation but no temporal correlation a priori (Q )  Three models of trend flux (X β) considered: Simple monthly land and ocean constants Terrestrial latitudinal flux gradient and ocean constants Terrestrial gradient, ocean constants and auxiliary variables

6. Inversion Results –

7. Transcom Regions TransCom, Gurney et al. 2003

8. Regional comparison of seasonal cycle GtC/yr

9. Regional comparison of inter annual variability GtC/yr

10. Key Questions  Is there another inversion approach available to estimate: Spatial and temporal autocorrelation structure of fluxes and/or flux residuals? Sources and sinks of CO 2 without relying on prior estimates? Significance of available auxiliary data? Relationship between auxiliary data and flux distribution? Realistic grid-scale flux variability …. Sharon

11. Key Questions  Is there another inversion approach available to estimate: Spatial and temporal autocorrelation structure of fluxes and/or flux residuals? Sources and sinks of CO 2 without relying on prior estimates? Significance of available auxiliary data? Relationship between auxiliary data and flux distribution? Realistic grid-scale flux variability

12. Sample Auxiliary Data Gourdji et al. (in prep.)

13. Variance-Ratio Test uses atmospheric data to assess significant improvement in fit of more complex trend Physical understanding combined with results of VRT to choose final set of auxiliary variables: % AgLAISST % ForestfPARdSSt/dt % ShrubNDVIPalmer Drought Index % GrassPrecipitationGDP Density Land Air Temp.Population Density Variance-Ratio Test uses atmospheric data to assess significant improvement in fit of more complex trend Physical understanding combined with results of VRT to choose final set of auxiliary variables: % AgLAISST % ForestfPARdSSt/dt % ShrubNDVIPalmer Drought Index % GrassPrecipitationGDP Density Land Air Temp.Population Density Variance-Ratio Test and Auxiliary Variables  Three models of trend flux (X β) considered: Monthly land and ocean constants (simple) Terrestrial latitudinal flux gradient and ocean constants (modified) Latitudinal gradient, ocean constants and auxiliary variables (variable) ˆ

14. Deterministic component Stochastic component Building up the best estimate in January 2000 Gourdji et al. (in prep.) ˆ

15. Uncertainty Reduction from Simple to Variable Trend Gourdji et al. (in prep.) %

16. Regional comparison of seasonal cycle Gourdji et al. (in prep.)

17. Comparison of annual average non-fossil fuel flux Gourdji et al. (in prep.)

18. Conclusions  Atmospheric data information and geostatistical approach can: Quantify model-data mismatch and flux covariance structure Identify significant auxiliary environmental variables and estimate their relationship with flux Constrain continental-scale fluxes independently of biospheric model and oceanic exchange estimates  Uncertainties at grid scale are high, but uncertainties of continental and global estimates are comparable to synthesis Bayesian studies  Upscaling fluxes a posteriori minimizes the risk of aggregation errors associated with inversions that estimate fluxes directly at large scale  Auxiliary data inform grid-scale flux variability; seasonal cycle at larger scales is consistent across models  Use of auxiliary variables within a geostatistical framework can be used to derive process-based understanding directly from an inverse model

19. North American CO 2 Flux Estimation  Estimate North American CO 2 fluxes at 1°x1° resolution & daily/weekly/monthly timescales using: CO 2 concentrations from 3 tall towers in Wisconsin (Park Falls), Maine (Argyle) and Texas (Moody) STILT – Lagrangian atmospheric transport model Auxiliary remote- sensing and in situ environmental data Pseudodata and recovered fluxes (Source: Adam Hirsch, NOAA-ESRL)

20. Acknowledgements  Collaborators: Advisor: Anna Michalak Research group: Alanood Alkhaled, Abhishek Chatterjee, Sharon Gourdji, Charles Humphriss, Meng Ying Li, Miranda Malkin, Kim Mueller, Shahar Shlomi, and Yuntao Zhou  Data providers: NOAA-ESRL cooperative air sampling network Christian Rödenbeck, MPIB Kevin Schaefer, NSIDC  Funding sources:

21. QUESTIONS? kimlm@umich.edu & sgourdji@umich.edu

22. Drift Coefficients (β) Aux. Variable  CV X (GtC/yr)  GDP  LAI  fPAR  % Shrub  L. Temp GDP0.090.2472.410.01-0.190.240.10 LAI-0.670.094-44.6---1-0.930.03-0.05 fPAR0.600.09449.3--- 1-0.15 % Shrub-0.110.175-4.4--- 10.02 LandTemp0.060.4851.7--- 1 Land Constants --- 0.9--- Ocean Constants --- -2.6--- Complete trend --- 2.7--- Gourdji et al. (in prep.) ˆ Inversion estimates drift coefficients (β) for variable trend: ˆ ˆ ˆ

23. 4 3 2 1 Variogram Model  Used to describe spatial correlation