Source: Kim Mueller, UM

1. All models are wrong … we make tentative assumptions about the real world which we know are false but which we believe may be useful … the statistician knows, for example, that in nature there never was a normal distribution, there never was a straight line, yet with normal and linear assumptions, known to be false, he can often derive results which match, to a useful approximation, those found in the real world.(Box, 1976) Source: Kim Mueller, UM

2. Determining Regional Emissions Patterns of Greenhouse Gases Anna M. Michalak1, Sharon M. Gourdji1, Kim Mueller1, Deborah Huntzinger1, Vineet Yadav1, Adam Hirsch2,3, Arlyn E. Andrews2, Thomas Nehrkorn4 1 The University of Michigan 2 NOAA Earth Systems Research Laboratory 3 University of Colorado 4 Atmospheric and Environmental Research, Inc.

3. North American Carbon Program • Science questions: • Diagnosis – What is the carbon balance of NA? • Attribution – What processes control sources and sinks? • Prediction – How will the carbon balance evolve? • Decision support – How can we manage the carbon cycle?

4. GPP Ra Disturbance Fossil fuels Rh Bottom-up CO2 Sink CO2 Source Measurement location Total CO2 flux Top-down Source: Kim Mueller, UM

5. Synthesis Bayesian Inversion Prior flux estimates (sp) BiosphericModel CO2Observations (y) AuxiliaryVariables Inversion Flux estimates and covarianceŝ, Vŝ ? TransportModel Sensitivity of observations to fluxes (H) Meteorological Fields Residual covariancestructure (Q, R) ?

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

7. Bottom-Up Estimates Deciduous Broad-Leaf Forests Grasslands Deborah Huntzinger, U. Michigan

8. Synthesis Bayesian Inversion Prior flux estimates (sp) Biosphericmodel CO2observations (y) Auxiliaryvariables Inversion Flux estimates and covarianceŝ, Vŝ Transportmodel Sensitivity of observations to fluxes (H) Meteorological fields Residualcovariancestructure (Q, R)

9. Geostatistical Inversion 1 2 3 4 select significant variables Auxiliaryvariables (X) Variable selection CO2observations (y) Flux estimates and covariance ŝ, Vŝ Inversion Transportmodel Sensitivity of observations to fluxes (H) Trend estimate and covariance β, Vβ Meteorological fields Residual covariancestructure (Q, R) Covarianceoptimization optimize covariance parameters

10. Geostatistical Approach to Inverse Modeling • Geostatistical inverse modeling objective function: • H = transport information, s = unknown fluxes, y = CO2 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

11. Features of GIM • Minimizes a priori assumptions: • Does not require prior estimates of fluxes • Provides strongly data driven estimates • Does not assume fixed “patterns” within regions or biomes • Uses available auxiliary information • Minimizes aggregation errors • Provides independent estimates • Can be applied directly at multiple spatial and temporal scales • Can be used to infer scale-specific process-based understanding • Provides path to ecosystem model improvement

12. Global Gridscale CO2 Flux Estimation Estimate global monthly CO2 fluxes (ŝ) at 3.75°x5°for 1997 to 2001 in a GIM framework using: CO2 flask data from NOAA-ESRL network (y) TM3 (atmospheric transport model) (H) Auxiliary environmental data (X)

13. Global Gridscale CO2 Flux Estimation S. Gourdji January 2000 Gourdji et al. (JGR 2008)

14. Annual Average Biospheric Flux Mueller et al. (JGR, 2008)

15. Global/ bottom-up comparison Background

16. North American CO2 Flux Estimation Estimate North American monthly/ weekly/ daily CO2 fluxes (ŝ) at 1°x1° for 2004 to 2007 in a GIM framework using: CO2 continuous measurements (y) STILT Lagrangian atmospheric transport model (H) Auxiliary environmental data (X) Sample influence function, June 2004 WRF domains and locations of continuous measurements LAI June 2004 T. Nehrkorn

17. Recovered fluxes (F8d/C3hr-aft) Source: Sharon Gourdji (UM) and Adam Hirsch (NOAA ESRL)

18. Auxiliary variable selection Objective 3: N.A. CO2 fluxes for 2004

19. Scalability

20. 3.75o x 5.0o ―: est. flux ―: CASA ―: X km2 --: NEE --: X 1o x 1o -. : CASA/SiB

21. Key Differences for Non-CO2 Inversions • Larger variety of types of sources • Point vs. areal sources • Chemistry • Cannot “pre-subtract” fossil fuel emissions • Multi-species inversions • Available data: • Types (flask, continuous, aircraft, flux, remote sensing) • Quantity of available atmospheric information • Inventories and auxiliary data • Availability of prior information

22. GOT MET? T. Nehrkorn A. Hirsch T. Nehrkorn

23. Conclusions Geostatistical approach Yields strongly atmospheric data driven estimates of flux variability Can be used to estimate fluxes at fine resolutions, without the use of prior flux estimates Allows benefit of auxiliary data to be evaluated Allows fluxes and the influence of auxiliary data to be estimated concurrently (w/ uncertainties) Geostatistical approach offers an opportunity to examine processes across spatial and temporal scales Use of auxiliary variables within a geostatistical framework can be used to derive process-based understanding directly from an inverse model

24. Acknowledgments Research group: Alanood Alkhaled, Abhishek Chatterjee, Sharon Gourdji, Deborah Huntzinger, Kim Mueller, Shahar Shlomi, Vineet Yadav, and Yuntao Zhou Kevin Gurney (Purdue U.) Peter Curtis (Ohio State U.) Christian Rödenbeck (MPIB) Kevin Schaefer (NSIDC) Data providers: Marc Fischer (LBL), Sherri Heck (NCAR), Andy Jacobson (NOAA), Natasha Miles (Penn State), Wouter Peters (NOAA), Scott Richardson (Penn State), Britt Stephens (NCAR), Margaret Torn (LBL), Tris West (ORNL), Steve Wofsy (Harvard), Doug Worthy (MSC), Jeff Morisette (NASA), ISLSCP II, LEDAPS, MOD14, GEIA, MODIS, GOES, TERRASTAT, GPCP, NSIDC, TOPS, NLDAS, NOAA-ESRL cooperative air sampling network Funding sources: