Development of an EnKF to estimate CO 2 fluxes from realistic distributions of X CO2 Liang Feng, Paul Palmer

Gurney et al, 2002 Current quantitative understanding of continental fluxes has not progressed significantly since late 20 th century Region Source (Gt C /yr)

274 ground stations in the world. The observing data from these stations is distributed from WDCGG of WMO The number of stations is limited, and they exists unevenly in the world. ・ Over 100,000 points per 3days ・ Global and frequent observations Ground Stations (current) From Space (GOSAT and OCO) From January 2009, the GHG community will suddenly become data-rich

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

8-day OCO X CO2 ETKF (Living and Dance, 2008) 8-day Flux Forecasts (climatology) Obs operator 8-day forecast ( 3-D CO2, T & H2O etc ) GEOS-Chem Model X CO2 Ensemble 8-day forecasts ( 3-D CO2, T & H2O etc ) Surface CO2 Ensemble GEOS-Chem Obs operator Prior + error Posteriori + error X CO2 DataModel X CO2 (enlarged by 80%)

We use the GEOS-Chem transport model Global 3-d model driven by assimilated meteorology from the NASA GEOS model Experiment run at 2x2.5 degree horizontal resolution during 2003 Emissions: Monthly mean fossil and bio- fuel scaled to day Global Fire Emission Database for 2003 Daily net biosphere fluxes from CASA Monthly mean ocean fluxes from Takahashi

We sample data along Aqua orbits 1-day

Realistic OCO X CO2 observations Cloudy scenes removedScenes with AOD > 0.3 removed Jan MODIS MODIS/MISR Bösch et al, 2008

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)

OCO averaging kernels over 5 different surfaces. OCO observation errors as a function of SZAs. We use realistic averaging kernels and errors associated with OCO nadir and glint modes Bösch et al, 2008

NadirGlint Resulting distribution of clean observations (2x2.5 resolution), Jan 17--Feb 2.

8-day OCO X CO2 ETKF (Living and Dance, 2008) 8-day Flux Forecasts (climatology) Obs operator 8-day forecast ( 3-D CO2, T & H2O etc ) GEOS-Chem Model X CO2 Ensemble 8-day forecasts ( 3-D CO2, T & H2O etc ) Surface CO2 Ensemble GEOS-Chem Obs operator Prior + error Posteriori + error X CO2 DataModel X CO2 (enlarged by 80%)

8-day OCO X CO2 ETKF (Living and Dance, 2008) 8-day Flux Forecasts (climatology) Obs operator 8-day forecast ( 3-D CO2, T & H2O etc ) GEOS-Chem Model X CO2 Ensemble 8-day forecasts ( 3-D CO2, T & H2O etc ) Surface CO2 Ensemble GEOS-Chem Obs operator Prior + error Posteriori + error X CO2 DataModel X CO2 (enlarged by 80%)

In a Kalman filter, the analysis is given by Ensemble Kalman Filter Approach AnalysisForecastKalman gainObservations Observation operator Forecast error covariance Analysis error covariance Observation error covariance Jacobian of H

The projection of this forecast and its ensemble to observation space generates 1) the model observation and 2) the deviations as the result of perturbations represented by the forecast ensemble: To simplify calculation of the Jacobian H, we represent P f using an ensemble of forecasts where

Using the ensemble approach the analysis equation is given by: The resulting analysis error covariance can also be represented by the ensemble using a transform T K e and T can be further simplified using SVD (not shown)

We use a fixed-lag window, recognizing that observations at time t will provide information on CO 2 surface fluxes at previous times. We use a lag of ~3 months (8x12 days). At assimilation cycle i we estimate regional 8-day surface fluxes (day d to d+8) for a 96-day period from day d-(11×8) to day d+8. We use a sequential approach to reduce computational burden

From the previous assimilation cycles New forecasts for d to d+8 Diagonal – simple ensemble perturbation Previous cycles are progressively smaller as a function of time away from present

Current mechanics of our XCO 2 EnKF t0t0 Mean state (MS) Time = 0x8 days: x f = 144 regions + 1 MS t 0 +8 d Time = 1x8 days: x f = 2x144 regions + 1 MS t d Time = 2x8 days: x f = 3x144 regions + 1 MS … t d Time = 12x8 days: x f = 12x144 regions + 1 MS X X X X

Experiments 1) Control experiment: -16-day nadir/16-day glint -assume no bias 2) Sensitivity to bias and unbiased error 3) Sensitivity to observation coverage 4) Sensitivity to duty cycle 5) Sensitivity to spatial resolution of estimates fluxes

Mean Error Reduction from 2-Month Control Inversion of 8-Day Surface Fluxes Large Small 

We find that flux estimates usually converge using less than a month of data  Days since t=0 Nadir Glint

Variable sensitivity of estimated fluxes to bias and unbiased error prior

Including observation correlations has a similar effect to reducing the number of available observations 

Glint observations over ocean are more effective at constraining tropical terrestrial fluxes than nadir measurements  Error reduction in the control run, averaged over 32 days from Jan 17 to Feb 17.

Would we get better science from OCO if they devoted their duty cycle to glint measurements? 

Sensitivity to the spatial resolution of control variables: from TransCom3 to Model Grid Avg Error Reduction South American Tropical Region Transcom3 4x1/4 Transcom3 9x1/9 Transcom3 4x5 degree model grid Correlations between neighbouring regions get progressively larger using regions smaller than 1000x1000 km 2.

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

Concluding Remarks We have an EnKF assimilation tool for interpreting X CO2 data Realistic X CO2 distributions and associated errors will significantly reduce the uncertainty of continental CO 2 fluxes on 8-day timescales Perturbing random and systematic components of measurement error lead to results consistent with previous 4DVAR studies Results are sensitive to assumed model error (not shown) Introducing observation correlations has a similar effect to reducing the number of clean observations Glint observations offer the most leverage to reduce uncertainty in estimated continental CO 2 fluxes – implications for duty cycle? The spatial resolution of independently estimated CO 2 fluxes from realistic X CO2 distributions is close to 1000x1000 km 2

SPARE SLIDES

SVD is used to simplify calculation of the gain and transfer matrices

Magnitudes of the diverse ensemble state vectors for the newest forecasts (left plot) and other 11×144 ones (right plot) which have experienced previous 1-11 assimilation cycles. The resulting maximum deviations from the mean ‘current’ observation values for the diverse ensemble state vectors.