1. Estimation of Carbon Fluxes for the South Asian Region using Maximum Likelihood Ensemble Filter(MLEF) Some Basic Results
K. M. P. Perera
Department of Statistics
University of Sri Jayewardenepura
Sri Lanka
5th International Conference on “Earth Science & Climate Change”
July 25-27, 2016 Bangkok, Thailand

2. Overview Background Methods used to assimilate carbon data Objectives
Pseudodata experiment
Results
Ongoing and Future works
References
Acknowledgements

3. Background Climate change is a critical environmental issue closely
linked with the increase of greenhouse gases in the
atmosphere.
CO2 plays the main role in greenhouse effect.

4. Figure 1: Atmospheric CO2 at Mauna Loa Observatory(

5. During the past two decades,
greenhouse gas emissions from Asian countries have been increased rapidly mainly due to industrialization
population growth
It is more important to estimate the CO2 fluxes with
high precision for the Asian region.
CONTRAIL (Comprehensive Observation Network for Trace gases by Airliner) aircraft measurements are now available – covers the South Asian region.
Data Assimilation method is going to be used to estimate CO2 fluxes.

6. Methods used to assimilate Carbon Data
Batch mode inversion
Variational data assimilation
Ensemble method
New ensemble method - MLEF

7. Objective
To estimate carbon fluxes more precisely using MLEF for the globe with newly available South Asian measurements.
Modified the MLEF algorithm to assimilate CONTRAIL (Comprehensive Observation Network for Trace gases by Airliner) aircraft data other than the existing flasks and continuous measurements.
Carried out a pesudodata experiment on the global domain to test the performance of MLEF on assimilating CONTRAIL and exiting data.

8. Method: MLEF (Zupanski M., 2005)
we optimize (minimize) cost function using MLEF
Assimilation scheme
Where
y = vector of observations
H = observation operator (PCTM)
β = vector of unknowns (state vector)
βb = prior (background) estimate
R = observation error covariance matrix
Pf = prior (forecast) error covariance matrix

9. Log of the posterior distribution
MLEF (contd..)
In statistical point of view, we optimize (maximize) posteriori distribution
= - log P(β)
Log of the prior
distribution
= - log P(y│β)
Log of the likelihood
= - log P(β│y)
Log of the posterior distribution
Optimal solution : Mode of the posterior distribution

10. CO2 fluxes on the Earth’s surface CO2 concentrations in the atmosphere
Transport Model
Transport model
CO2 fluxes on the Earth’s surface
CO2 concentrations in the atmosphere
Observation operator : PCTM
(Parametrerized Chemistry Transport Model)
(Kawa et al., 2004)

11. Estimate the gridded surface carbon fluxes
Ensemble based data assimilation system:
MLEF (The inversion procedure developed) +
PCTM (Parameterized Cemistry Transport Model)
(Lokupitiya et al., 2008)
Estimate the gridded surface carbon fluxes
CO2 observations
(Flasks,in-situ continuous data and CONTRAIL aircraft data)
Background information

12. Observation Network Figure 2: Flask and continuous stations
Open circles - continuous measurement sites
Crosses flask-sampling locations
(NOAA-ESRL network)

13. Figure 3: CME flight tracks for year 2006

14. Pesudodata Experiment

15. Fluxes are in 2.50 (lon) × 20(lat)
Ocean fluxes (monthly) Takahashi monthly values interpolated to model time
Fossil fuel emissions interpolated to the year
SiB3 model
land fluxes (hourly)
Mathematical representation of the
Variations of the surface fluxes
where NEE = Net Ecosystem Exchange RESP = Ecosystem respiration GPP = Gross Primary Production Ocean = Air-sea gas exchange of CO FF = Emissions due to fossil fuel combustion x, y = Spatial coordinates and t = time ’s = Multiplicative biases of the grid-scale component fluxes
Solve for biases
in 100 (lon) × 60(lat)
resolution

16. First assimilation cycle (“cold start”) –
Artificially generated CO2 observations (pseudo observations) were sampled at observation locations by running the PCTM forward for a year after three year spin-up ( ).
(ii) Simulated CO2 at the observation sites
using data assimilation with a 4 week moving window
First assimilation cycle (“cold start”) –
first guess (unbiased case was assumed) Priors:
β = 0 (unbiased case),
σNEE = 0.2, σOcean = 0.1
perturbed background vectors (ensemble members)
Compute the hourly CO2 fluxes and run through the transport
model for 4- weeks to get simulated CO2 at the observation sites

17. (iv) End of the cycle, 3-D CO2 field was saved (used to start
(III) The optimized biases were obtained
by minimizing the distance between the simulated and observed CO2 concentrations using the method of MLEF
(iv) End of the cycle, 3-D CO2 field was saved (used to start
the next cycle) by running the transport model with
optimized biases
(v) This process was followed for the remaining cycles
In each cycle, minimize the cost function by maximum likelihood method.
Minimization is done in a reduced space (preconditioned space).

18. Assimilation Scheme . . . 1st Cycle 13th Cycle 4 Weeks 2nd Cycle
13th Cycle
4 Weeks
2nd Cycle
4 Weeks
3rd Cycle
4 Weeks
30 Ensemble members
Results are given for 13 cycles

19. Results
Figure 4: Map of the monthly means of true land fluxes for year 2006
KgC/m2/Sec (Units are in 10-8 )

20. % uncertainty reduction
Figure 5. Mean annual percentage uncertainty reduction for recovered
biases using continuous and flask measurements

21. % uncertainty reduction
Figure 6. Mean annual percentage uncertainty reduction for recovered
biases using continuous, flask and CONTRAIL measurements

22. Ongoing and future work:
(I) Test the model performance for the pseudodata
experiment by increasing the ensemble size.
(II) Run the experiment with real data.

23. References
Baker, I. T., Denning, A. S., Hanan, N., Prihodko, L., Vidale, P. –L., Davis, K., and Bakwin, P Simulated and observed fluxes of sensible and latent heat and CO2 at the WLEF-TV Tower using SiB2.5.Global Change Biol. 9,
CONTRAIL, Comprehensive Observation Network for Trace Gases by Airliner. (Available online at: [Accessed: 10th December 2013].
Jiang, F., Wang, H. W., Chen, J. M., Zhou, L. X., Ju, W. M., Ding, A. J., Liu, L. X., and Peters, W Nested atmospheric inversion for the terrestrial carbon sources and sinks in China. Biogeosciences, 10, 5311–5324.   Kawa, S. R., Erickson III, D. J., Pawson, S., and Zhu, Z Global CO2 transport simulations using meteorological data from the NASA data assimilation system. J. Geophys. Res. 109(D18), doi: /2004JD

24. Lokupitiya, R. S. , Zupanski, D. , Denning, A. S. , Kawa, S. R
Lokupitiya, R. S., Zupanski, D., Denning, A. S., Kawa, S. R., Gurney, K. R., and Zupanski, M Estimation of global CO2 fluxes at regional scale using the maximum likelihood ensemble filter. J. Geophys. Res. 113, D20110, doi: /2007JD Niwa, Y., Machida, T., Sawa, Y., Matsueda, H., Schuck, T. J., Brenninkmeijer, C. A. M., Imasu, R., and Satoh, M Imposing strong constraints on tropical terrestrial CO2 fluxes using passenger aircraft based measurements. J. Geophys. Res. 117, D11303, doi: /2012JD Patra, P. K., Niwa, Y., Schuck, T. J., Brenninkmeijer, C. A. M., Machida, T., Matsueda, H., and Sawa, Y Carbon balance of South Asia constrained by passenger aircraft CO2 measurements. Atmos. Chem. Phys, 11,   Patra, P. K., Canadell, J. G., Houghton, R. A., Piao, S. L., Oh, N. –H., Ciais, P., Manjunath, K. R., Chhabra, A., Wang, T., Bhattacharya, T., Bousquet, P., Hartman, J., Ito, A., Mayorga, E., Niwa, Y., Raymond, P. A., Sarma, V. V. S. S., and Lasco, R The carbon budget of South Asia.Biogeosciences, 10,

25. Peters, W. , Miller, J. B. , Whitaker, J. , Denning, A. S. , Hirsch, A
Peters, W., Miller, J. B., Whitaker, J., Denning, A. S., Hirsch, A., Krol, M. C., Zupanski, D., Bruhwiler, L., and Tans, P. P An ensemble data assimilation system to estimate CO2 surface fluxes from atmospheric trace gas observations. J. Geophys. Res. 110(D24), doi: /2005JD Zupanski, D., Denning, A. S., Uliasz, M., Zupanski, M., Schuh, A. E., Rayner, P. J., and Peters, W Carbon flux bias estimation employing Maximum Likelihood Ensemble Filter (MLEF). J. Geophys. Res. 112, D17107, doi: /2006JD   Zupanski, M Maximum likelihood ensemble filter: Theoretical aspects. Mon. Wea. Rev.133,  

26. Acknowledgements: This research is supported by the grants from
National Research Council, Sri Lanka
I would also like to thank Dr. Prabir Patra for providing CONTRAIL aircraft information.

27. My supervisor (P.I.): Co-investigators:
Dr. R.S. lokupitiya (P.I.), University of Sri Jayawardenepura,
Sri Lanka
Co-investigators:
Dr. E. Y. K. Lokupitiya, University of colombo, Sri Lanka
Prof. R. G. N. Meegama, University of Sri Jayawardenepura, Sri Lanka
Dr. Prabir Kumar Patra, Research Institute for Global Change, Japan
Prof. A. Scott Denning, Colorado State University, USA

28. Thank You