Post on 04-Jan-2016
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.