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

2. Outline  Introduction to geostatistics  Inverse modeling approaches to estimating flux distributions  Geostatistical approach to quantifying fluxes: Global flux estimation Use of auxiliary data Regional scale synthesis

3. Spatial Correlation  Measurements in close proximity to each other generally exhibit less variability than measurements taken farther apart.  Assuming independence, spatially-correlated data may lead to: 1. Biased estimates of model parameters 2. Biased statistical testing of model parameters  Spatial correlation can be accounted for by using geostatistical techniques

4. Parameter Bias Example map of an alpine basin snow depth measurements mean of snow depth measurements (assumes spatial independence) kriging estimate of mean snow depth (assumes spatial correlation) Q: What is the mean snow depth in the watershed?

5. H 0 is TRUE 5% H 0 rejected 5% H 0 Rejected H 0 Rejected! H 0 Not Rejected

6. 4 3 2 1 Variogram Model  Used to describe spatial correlation

7. Geostatistics in Practice  Main uses: Data integration Numerical models for prediction Numerical assessment (model) of uncertainty

8. Geostatistical Inverse Modeling Actual flux historyAvailable data

9. 31 data 11 fluxes 31 data 21 fluxes 31 data 41 fluxes 31 data 101 fluxes 31 data 201 fluxes Geostatistical Inverse Modeling GeostatisticalBayesian / Independent Errors

10. Key Points  If the parameter(s) that you are modeling exhibits spatial (and/or temporal) autocorrelation, this feature must be taken into account to avoid biased solutions  Spatial (and/or temporal) autocorrelation can be used as a source of information in helping to constrain parameter distributions  The field of geostatistics provides a framework for addressing the above two issues

11. ASIDE: CO 2 Measurements from Space  Factors such as clouds, aerosols and computational limitations limit sampling for existing and upcoming satellite missions such as the Orbiting Carbon Observatory  A sampling strategy based on X CO2 spatial structure assures that the satellite gathers enough information to fill data gaps within required precision Alkhaled et al. (in prep.)

12. X CO2 Variability  Regional spatial covariance structure is used to evaluate: Regional sampling densities required for a set interpolation precision Minimum sampling requirements and optimal sampling locations x10 4 km

13. Source: NOAA-ESRL

14. Longitude Latitude Height Above Ground Level (km) 24 June 2000: Particle Trajectories -24 hours -48 hours -72 hours -96 hours -120 hours Source: Arlyn Andrews, NOAA-GMD What Surface Fluxes do Atmospheric Measurements See?

15. Need for Additional Information  Current network of atmospheric sampling sites requires additional information to constrain fluxes: Problem is ill-conditioned Problem is under-determined (at least in some areas) There are various sources of uncertainty:  Measurement error  Transport model error  Aggregation error  Representation error  One solution is to assimilate additional information through a Bayesian approach

16. 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) Bayesian Inference Applied to Inverse Modeling for Surface Flux Estimation

17. 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 ? ?

18. TransCom, Gurney et al. 2003 Large Regions Inversion

19. Transport Model Gridscale Inversions Rödenbeck et al. 2003

20. 4 3 2 1 Variogram Model  Used to describe spatial correlation

21. 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 component Stochastic component

22. 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

23. Geostatistical Inversion Meteorological Fields Transport Model Sensitivity of observations to fluxes (H) Residual covariance structure (Q, R) Auxiliary Variables CO 2 Observations (y) Variance Ratio Test Inversion RML Optimization Flux estimates and covariance ŝ, V ŝ Trend estimate and covariance β, V β select significant variables optimize covariance parameters

24. Key Questions  Can the geostatistical approach estimate: Sources and sinks of CO 2 without relying on prior estimates? Spatial and temporal autocorrelation structure of residuals? Significance of available auxiliary data? Relationship between auxiliary data and flux distribution?  If so, what do we learn about: Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error  What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?

25. Fluxes Used in Pseudodata Study Michalak, Bruhwiler & Tans (JGR, 2004)

26. Recovery of Annually Averaged Fluxes Best estimate“Actual” fluxes Michalak, Bruhwiler & Tans (JGR, 2004)

27. Recovery of Annually Averaged Fluxes Best estimateStandard Deviation Michalak, Bruhwiler & Tans (JGR, 2004)

28. Key Questions  Can the geostatistical approach estimate Sources and sinks of CO 2 without relying on prior estimates? Spatial and temporal autocorrelation structure of residuals? Significance of available auxiliary data? Relationship between auxiliary data and flux distribution?  If so, what do we learn about: Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error  What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?

29. Auxiliary Data and Carbon Flux Processes Image Source: NCAR Terrestrial Flux: Photosynthesis (FPAR, LAI, NDVI) Respiration (temperature) Oceanic Flux: Gas transfer ( sea surface temperature, air temperature) Anthropogenic Flux: Fossil fuel combustion (GDP density, population) Other: Spatial trends (sine latitude, absolute value latitude) Environmental parameters: (precipitation, %landuse, Palmer drought index)

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

31. Which Model is Best?

32. 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 component Stochastic component

33. 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) Auxiliary environmental variables correlated with CO 2 flux  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

34. Measurement Locations Gourdji et al. (in prep.) Mueller et al. (in prep.)

35. Combine physical understanding with results of VRT to choose final set of auxiliary variables: % AgLAISST % ForestfPARdSSt/dt % ShrubNDVIPalmer Drought Index % GrassPrecipitationGDP Density Land Air Temp.Population Density Combine physical understanding with results of VRT to choose final set of auxiliary variables: % AgLAISST % ForestfPARdSSt/dt % ShrubNDVIPalmer Drought Index % GrassPrecipitationGDP Density Land Air Temp.Population Density Selected Auxiliary Variables Inversion estimates 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 Gourdji et al. (in prep.)

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

37. A posteriori uncertainty for January 2000 Gourdji et al. (in prep.)

38. Transcom Regions TransCom, Gurney et al. 2003

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

40. Regional comparison of seasonal cycle #2 Gourdji et al. (in prep.)

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

42. Key Questions  Can the geostatistical approach estimate Sources and sinks of CO 2 without relying on prior estimates? Spatial and temporal autocorrelation structure of residuals? Significance of available auxiliary data? Relationship between auxiliary data and flux distribution?  If so, what do we learn about: Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error  What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?

43. Opportunities for Regional Synthesis Photo credit: B. Stephens, UND Citation crew, COBRA Continuous tall-tower data available More consistent relationship to auxiliary variables Flux tower and aircraft campaign data available for validation NACP offers opportunities for intercomparison / collaborations WLEF tall tower (447m) in Wisconsin with CO 2 mixing ratio measurements at 11, 30, 76, 122, 244 and 396 m

44. 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)

45. Analysis steps:  Compile auxiliary variables  Select significant variables to include in model of the trend  Estimate covariance parameters:  Model-data mismatch  Flux deviations from overall trend.  Perform inversion, estimating both (i) the relationship between auxiliary variables and flux , and (ii) the flux distribution s.  A posteriori covariance includes the uncertainties of fluxes, trend parameters, and all cross-covariances Assimilation of Remote Sensing and Atmospheric Data

46. Key Questions  Can the geostatistical approach estimate Sources and sinks of CO 2 without relying on prior estimates? Spatial and temporal autocorrelation structure of residuals? Significance of available auxiliary data? Relationship between auxiliary data and flux distribution?  If so, what do we learn about: Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error  What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?

47. Conclusions  Atmospheric data information content is sufficient to: Quantify model-data mismatch and flux covariance structure Identify significant auxiliary environmental variables and estimate their relationship with flux Constrain continental 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  Auxiliary data inform regional (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

48. Acknowledgements  Collaborators: Research group: Alanood Alkhaled, Abhishek Chatterjee, Sharon Gourdji, Charles Humphriss, Meng Ying Li, Miranda Malkin, Kim Mueller, Shahar Shlomi, and Yuntao Zhou NOAA-ESRL: Pieter Tans, Adam Hirsch, Lori Bruhwiler and Wouter Peters JPL: Bhaswar Sen, Charles Miller Kevin Gurney (Purdue U.), John C. Lin (U. Waterloo), Ian Enting (U. Melbourne), Peter Curtis (Ohio State U.)  Data providers: NOAA-ESRL cooperative air sampling network Seth Olsen (LANL) and Jim Randerson (UCI) Christian Rödenbeck, MPIB Kevin Schaefer, NSIDC  Funding sources:

49. QUESTIONS? Anna.Michalak@umich.edu http://www.umich.edu/~amichala/