1. Carbon Flux Bias Estimation at Regional Scale using Coupled MLEF-PCTM model Ravindra Lokupitiya Department of Atmospheric Science Colorado State University Collaborators: Dusanka Zupanski,Scott Denning, Kevin Gurney, Randy Kawa, and Milija Zupanski

2. known SiB hourly Fluxes known Taka02 midmonth values interpolated to model time

3. State Vector known SiB hourly Fluxes known Taka02 midmonth values interpolated to model time unknown slow varying

4. Method Maximum Likelihood Ensemble Filter (MLEF)  = state vector y = observation vector H = observation operator (PCTM)  b = background (prior) vector R = observation error covariance matrix P f = forecast (prior) error covariance matrix Minimize Cost Function:

5. MLEF (contd..) Minimize cost function numerically (maximum likelihood estimation)-estimated by mode instead of by mean step-length Kalman gain matrix is estimated by using ensemble members “Kalman Gain”

6. MLEF (contd..) Hessian Preconditioning-minimization is done in a preconditioned space State Space  Ensemble Space with preconditioning without preconditioning

7. MLEF (contd..) Forecast Step ( move to next cycle…) for the state vector for the covariance matrix Inflate the covariance matrix to avoid filter divergence

8. To reduce number of degrees of freedom (unknowns) Covariance smoothing (only at 1st cycle) Localization based on sigma ratio where  2 = variance, d ij = distance b/w i th and j th locations L = de-correlation length Select upper tail values of sigma-ratio distribution, which shows high influence areas from observations

9. Covariance Structure other methods Error covariance in many methods is assumed to be exponential with distance MLEF In the MLEF, we solve for the covariance structure dynamically

10. Pseudo Data Experiment Truth: Create global maps (10 0 x6 0 ) of biases by generating random numbers [  GPP,  Res  N(1,0.3 2 );  Ocn  N(1,0.2 2 )]-then smoothing Prior: –  GPP =  Res =  Ocn =1.0 (unbiased) –  GPP =  Res =0.05 and  Ocn =0.02 –Smoothing: de-correlation length scales 800 km over land and 1600 km over ocean –Localization: select 60% land & 10% ocean Each cycle consists of 8 weeks-non overlapping windows 200 ensemble members

11. Observation Network + : flask  : aircraft profiles O : continuous Observation error: flask/aircraft = 1 ppm continuous –2 ppm daytime –~40 ppm nighttime Pseudo observations are sampled at obs locations by running transport forward, after 3 year spin-up

12. Results -  GPP after 6 eight-week cycles TruthRecovered % difference % uncertainty reduction Note: “Yellow Color” indicates the Prior

13. Results -  RESP after 6 eight-week cycles TruthRecovered % difference% uncertainty reduction

14. Results -  Ocean after 6 eight-week cycles TruthRecovered % difference% uncertainty reduction

15. Flux Estimation Mean over a region Corresponding variance whereIndicates monthly mean fluxes

16. Prior covariance over Temperate North America region GPP RESPCross-cov (GPP & RESP) units=10 -4 1 2 34 5 678 9 10 11 12131415 1617 18

17. Posterior covariance over Temperate North America region (after 6 cycles) GPP RESPCross-cov (GPP & RESP) units=10 -4 1 2 34 5 678 9 10 11 12131415 1617 18

18. Flux Estimation for TC Regions Boreal North America Temperate North America Europe Boreal Asia Black = Prior Red = Recovered Blue = Truth

19. Flux Estimation for TC Regions (contd…) Temperate Asia South Africa Southern OceanSouth Indian Ocean

20. Summary We have introduced an ensemble based assimilation method to flux bias estimation, which utilizes a dynamic localization scheme. Method is suitable for assimilating large observation vectors, hence suitable for satellite inversions-no sequential assimilation required. It is capable of incorporating nonlinear observation operators and dynamic models.

21. Method satisfactorily recovered well- represented land regions. However, oceanic regions are poorly recovered by the atmospheric observations. Assimilation of real data is in progress…