Development of an EnKF to estimate CO2 fluxes

from realistic distributions of XCO2

Liang Feng, Paul Palmerhttp://www.geos.ed.ac.uk/eochem

Gurney et al, 2002

Current quantitative understanding of continental fluxes has not progressed significantly since late 20th century

Region

Sou

rce (

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

XCO2 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?

8-dayOCO XCO2

ETKF(Living and Dance, 2008)

8-day Flux Forecasts

(climatology)

Obs operator

8-day forecast(3-D CO2, T & H2O etc)

GEOS-Chem

Model XCO2

Ensemble

8-day forecasts(3-D CO2, T & H2O etc)

Surface CO2 Ensemble GEOS-Chem

Obs operator

Pri

or

+ e

rror P

oste

riori +

erro

r

XCO2 Data Model XCO2

(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 2003

•8-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 XCO2 observations

Cloudy scenes removed Scenes with AOD > 0.3 removedJan 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

Nadir Glint

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

8-dayOCO XCO2

ETKF(Living and Dance, 2008)

8-day Flux Forecasts

(climatology)

Obs operator

8-day forecast(3-D CO2, T & H2O etc)

GEOS-Chem

Model XCO2

Ensemble

8-day forecasts(3-D CO2, T & H2O etc)

Surface CO2 Ensemble GEOS-Chem

Obs operator

Pri

or

+ e

rror P

oste

riori +

erro

r

XCO2 Data Model XCO2

(enlarged by 80%)

8-dayOCO XCO2

ETKF(Living and Dance, 2008)

8-day Flux Forecasts

(climatology)

Obs operator

8-day forecast(3-D CO2, T & H2O etc)

GEOS-Chem

Model XCO2

Ensemble

8-day forecasts(3-D CO2, T & H2O etc)

Surface CO2 Ensemble GEOS-Chem

Obs operator

Pri

or

+ e

rror P

oste

riori +

erro

r

XCO2 Data Model XCO2

(enlarged by 80%)

In a Kalman filter, the analysis is given by

)]([ fobs

fa H xyKxx

Ensemble Kalman Filter Approach

Analysis Forecast Kalman gain

Observations

Observation operator

1][ RHPHHPK fTTf

fa PKHP )1(

Forecast error covariance

Analysis error covariance

Observation error covariance

Jacobian of H

] ...,,[ 21 nf xxx ,X

Tfff ) X(XP

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:

1][ RY)Y(Y)(XK TTfe

To simplify calculation of the Jacobian H, we represent P f using an ensemble of forecasts

fff x-XX where

)()( ff HH x-Xy-YY

)yyxx obsfa (K e

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

Y)(RY)Y(Y)(-ITT 1 ][ TTT

TXX fa Tffa )( TXTXP

Ke 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 CO2 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

)14412(

...

)114411(

)14411(

...

)1(

x

x

x

x

fx

From the previous assimilation cycles

New forecasts for d to d+8

14412 to114411

14411 to1

0

0

P

PP f

Diagonal – simple ensemble perturbation

Previous cycles are progressively smaller as a function of time away from present

Current mechanics of our XCO2 EnKF

t0

Mean state (MS)

Time = 0x8 days: xf = 144 regions + 1 MS

t0+8 d

Time = 1x8 days: xf = 2x144 regions + 1 MS

t0+16 d

Time = 2x8 days: xf = 3x144 regions + 1 MS …

t0+24 d

Time = 12x8 days: xf = 12x144 regions + 1 MS

X XX 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

f

a

1

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 E

rror

Red

uct

ion South American Tropical

Region1

0.3

Transcom3

4x1/4 Transcom

3

9x1/9 Transcom

3

4x5 degree model grid

Correlations between neighbouring regions get progressively larger using regions smaller than 1000x1000 km2.

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 XCO2 data

• Realistic XCO2 distributions and associated errors will significantly reduce the uncertainty of continental CO2 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 CO2 fluxes – implications for 16-16 duty cycle?

• The spatial resolution of independently estimated CO2 fluxes from realistic XCO2 distributions is close to 1000x1000 km2

SPARE SLIDES

TTR VUΣY 2/1

2/11 RV]ΣΣ[IUΣXK TTfe

TT UΣΣIUT 2/1][

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.