1. Application of Geostatistical Inverse Modeling for Data-driven Atmospheric Trace Gas Flux Estimation Anna M. Michalak UCAR VSP Visiting Scientist NOAA Climate Monitoring and Diagnostics Laboratory Anna M. Michalak Environmental and Water Resources Engineering Department of Civil and Environmental Engineering The University of Michigan

2. NOAA-CMDL Air Sampling Network

3. Bayesian Inference Applied to Inverse Modeling for Contaminant Source Identification Posterior probability density function of unknown parameter Prior distribution of unknown parameter p(y) probability of data Likelihood of unknown parameter given data y : what you know (n × 1) s : what you want to know (m×1)

4. Bayesian Inference Applied to Inverse Modeling for Trace Gas Surface Flux Estimation Posterior probability of surface flux distribution Prior information about fluxes p(y) probability of measurements Likelihood of fluxes given atmospheric distribution y : available observations (n×1) s : surface flux distribution (m×1)

5. Bayesian vs. Geostatistical Inverse Modeling Classical Bayesian inverse modeling objective function:  Q and R are diagonal  s p is prior flux estimate in each region Geostatistical inverse modeling objective function:  R is diagonal; Q is full covariance matrix  X and  define the model of the mean

6. Geostatistical Approach to Inverse Modeling Prior flux estimates are not required Key components:  Model of the mean  Prior covariance matrix Prior based on spatial and/or temporal correlation  Derived from available data Covariance parameter optimization (RML)  Model-data mismatch and prior covariance Method yields physically reasonable estimates (and uncertainties) at any resolution Conditional realizations can be generated

7. Recovery of Annually Averaged Fluxes Pseudodata study examining effect of:  Altering model-data mismatch  Considering land and ocean fluxes as correlated / independent  Specifying vs. estimating fossil fuel sources Observations at 39 NOAA-CMDL sites over 12 months ( n = 433 ) Source flux recovered on 3.75 o x 5.0 o grid ( m = 3456 ) Basis functions obtained using adjoint of TM3 model Michalak, Bruhwiler & Tans (J. Geophys. Res. 2004, in press)

8. “Actual” Fluxes

9. Low Model-Data Mismatch Best estimateStandard Deviation

10. Low Model-Data Mismatch Best estimate“Actual” fluxes

11. Higher Model-Data Mismatch Best estimateStandard Deviation

12. Best estimate“Actual” fluxes Higher Model-Data Mismatch

13. Low Model-Data Mismatch Best estimate“Actual” fluxes

14. Conclusions from Pseudodata Study Geostatistical approach to inverse modeling shows promise in application to atmospheric inversions Geostatistical inversions can be performed at fine scale and for strongly underdetermined problems Separate land and ocean correlation structures can be identified from atmospheric data Current atmospheric network can be used to obtain physically reasonable flux estimates without the use of prior estimates

15. Recovery of Monthly Fluxes (1997-2001) Atmospheric data study examining flux information that can be recovered from subset of NOAA-CMDL Cooperative Air Sampling Network Observations at 39 NOAA-CMDL sites ( n ~ 451 / year ) Source flux recovered on 7.5 o x 10 o grid ( m = 10368 / year ) Basis functions obtained using adjoint of TM3 model

16. Monthly Estimates for 2000 – Take 1

17. Monthly Estimates for 2000 – Take 2

18. TransCom 3 Regions

19. Fluxes for 2000 Aggregated by Region

20. Conclusions from Atmospheric Data Study Geostatistical approach is successful at identifying monthly fluxes using subset of NOAA-CMDL network Geostatistical inverse modeling:  Avoids biases associated with using prior estimates and aggregating fluxes to large regions  Offers strongly data-driven flux estimates Examined network sufficient to constrain certain regions, whereas other regions are not sufficiently sampled

21. Future work Incorporating and parameterizing both spatial and temporal covariance Fixed-lag Kalman smoother Influence of auxiliary variables Gridscale flux estimates  Global inversions  Regional inversions Operational flux estimation Geostatistical inversion software