1. Hartmut Bösch and Sarah Dance
Estimating Terrestrial CO2 Fluxes from XCO2 Data using an EnKF: Sensitivity to Glint-view Measurements & Spatial Resolution of Control Variables
Liang Feng, Paul Palmer
Hartmut Bösch and Sarah Dance

2. Observing System Simulation Experiments
Overall Aim: Determine the potential of space-borne XCO2 data to improve 8-day surface CO2 flux estimates over tropical continental regions of size ~12º×15º.
How sensitive are these estimates to changes in alternative measurement and model configurations?

3. XCO2 Data Model XCO2 Posteriori + error Prior + error 8-day
Flux Forecasts
(climatology)
Model XCO2
Ensemble
8-day forecasts
(3-D CO2, T & H2O etc)
Surface CO2
GEOS-Chem
Obs operator
GEOS-Chem
8-day forecast
(3-D CO2, T & H2O etc)
Prior + error
Posteriori + error
I have added noises to the prior surface fluxes. But no noise is added to observed Xco2 data. As we are interested in reduction ratios, the noises do not really matter.
The noise is added randomly according to the uncertainties (i.e., the PDF) in prior surface flux estimates.
Obs operator
8-day
OCO XCO2
ETKF
(Living and Dance, 2008)

4. XCO2 Data Model XCO2 Posteriori + error Prior + error 8-day
Flux Forecasts
(climatology)
(+Perturbations)
Surface CO2
Ensemble
GEOS-Chem
GEOS-Chem
8-day forecast
(3-D CO2, T & H2O etc)
8-day forecasts
(3-D CO2, T & H2O etc)
Prior + error
Posteriori + error
I have added noises to the prior surface fluxes. But no noise is added to observed Xco2 data. As we are interested in reduction ratios, the noises do not really matter.
The noise is added randomly according to the uncertainties (i.e., the PDF) in prior surface flux estimates.
Obs operator
Obs operator
8-day
OCO XCO2
ETKF
(Living and Dance, 2008)
Model XCO2
Ensemble

5. XCO2 Data Model XCO2 Posteriori + error Prior + error 8-day
Flux Forecasts
(climatology)
Surface CO2
Ensemble
GEOS-Chem
GEOS-Chem
8-day forecast
(3-D CO2, T & H2O etc)
8-day forecasts
(3-D CO2, T & H2O etc)
Prior + error
Posteriori + error
I have added noises to the prior surface fluxes. But no noise is added to observed Xco2 data. As we are interested in reduction ratios, the noises do not really matter.
The noise is added randomly according to the uncertainties (i.e., the PDF) in prior surface flux estimates.
Obs operator
Obs operator
8-day
OCO XCO2
ETKF
(Living and Dance, 2008)
Model XCO2
Ensemble

6. Realistic XCO2 observation operator
1) Sampled along Aqua orbits
GEOS-Chem transport model (4x5 degree resolution): Biosphere (CASA), Biomass (GFED), Fossil fuel (NDIAC), Ocean (Takahashi)
1-day
2) Scenes with cloud or AOD > 0.3 removed
3) Averaging kernels applied
1.)  orbit_aqua.png  ===>  Aqua footprints in one day   2.)  cld_coverage.png ===>  the ratio of the cloud contaminated data to all OCO data at each grid box of 4x5 during January.   3.) opd_coverage.png  ===> the same as cld_coverage.png, but for aerosol-contamination.   4.) residual_err.png  ===>  the ratio for 'left departures in inversions' defined as    abs(Posterior Flux -True)/abs(prior Flux-True)
Glint mode
Pressure [hPa]
Jan
Averaging kernels

7. Ensemble Kalman Filter Approach
Based on Kalman Filter:
Forecast:
Analysis:
K=PfHT(HPfHT+R)-1 is the Kalman gain matrix
H is the Jacobian (adjoint) matrix.
EnKF samples the forecast error covariance of the forecast using an ensemble of forecasts.
Advantages: no adjoint; provides error characterization; can sample non-Gaussian PDF (e.g., CO2-CO-CH4 inversion).
Disadvantages: the size of the ensemble can be large (12x144+1).

8. Regional flux definitions based on TransCom 3 regions
Control calculation: 9×11 land regions, 4×11 ocean regions and 1 snow region (cf T3: 11 land and 11 ocean regions)
Uncertainties based on TransCom 3
We assume NO correlation in prior estimates
Assume model error of 2.5 (1.5) ppm over land (ocean)

9. Mean Error Reduction from 2-Month Control Inversion of 8-Day Surface Fluxes
Large
Small
Jan - Feb
Hi Paul, Now the South American Tropical has been divided into 9 regions, and from different regions, the error reductions are not the same.
Example: South American Tropical:
A priori err ~ 3.2 Gt C/y;
A posteriori err ~ Gt C/y ;
Error reduction~

10. Error reductions are obviously sensitive to number of clean (aerosol and cloud free) observations

11. Because of large assumed model error results are insensitive to observation error of single OCO retrieval 

12. [Results for 8-day mean flux estimates during May to June]
Glint observations over ocean are more effective at constraining continental fluxes than nadir measurements
[Results for 8-day mean flux estimates during May to June] 

13. South American Tropical Region
Sensitivity to the spatial resolution of control variables: from TransCom3 to Model Grid
South American Tropical Region 1
Avg Error Reduction
0.3
4x1/4 Transcom3
9x1/9 Transcom3
4x5 degree model grid
Transcom3
Correlations between neighbouring regions get progressively larger using regions smaller than 1000x1000 km2.

14. Sensitivity to the spatial resolution of control variables: from TransCom3 to Model Grid
Inversions at high spatial resolutions are under-determined, and usually show strong negative spatial correlation in the resulting error covariances:

15. Concluding Remarks
We have an EnKF assimilation tool for interpreting XCO2 data
Realistic XCO2 distributions and associated errors will significantly reduce the uncertainty of continental CO2 fluxes on 8-day timescales BUT some consideration must be given to the lag window (not shown)
Perturbing random and systematic components of measurement error lead to results consistent with 4DVAR studies (not shown)
Results are sensitive to assumed model error
The number of clean observations impacts the quality of the flux estimates
Glint observations offer the most leverage to reduce uncertainty in estimated continental CO2 fluxes – implications for duty cycle?
The spatial resolution of independently estimated CO2 fluxes from realistic XCO2 distributions is close to 1000x1000 km2