FEW RESULTS LINKED TO

INVERSE MODELING at LSCE

- IAV comparison from 3 inversions

- Impact of Obs. error correlations

- How to define flux error correlations ?

Christian Roedenbeck

What happen in 2003 ?

Recent carbon flux anomalies from 3 inversions…

3 independent inversion… (Differences)

LSCE MPI CSIRO

Transport model

A-Priori Info

Data use

LMDz (~ 2.5 x 3.5)Observed winds

TM3 (~ 4 x 5)Observed winds

CRC-MATCH (~ 4 x 3)1yr GCM winds

ORCHIDEE & GFED PriorsBiome correlation

No IAV priorDistance correlation

Casa priorNo corelation

Fluxes

Monthly mean Conc.74 sites

Flask data74 sites

Montly mean Conc.64 sites

Pixel inversionMonthly fluxes

Pixel inversionWeekly fluxes

116 regionsMonthly fluxes

Flux anomalies

Filtered fluxes : 120 days

Results for the 3 different inversions (+ T3-mean)

Global scale

T3 mean LSCE MPI Peter-CSIRO

« Agreement »

For the

Major

Anomalies !

« still

agreement »

For the

Major

Anomalies !

Continental scale

T3 mean LSCE MPI Peter-CSIRO

European scale

« poor

agreement »

for the

different

anomalies !

T3 mean LSCE MPI Peter-CSIRO

European scale

« JJA anom. »

Jun-Jul-Aug anomaly (gC/m2/month)

LSCE (inter-annual prior) LSCE (constant prior)

JENA Ref

gC/m2/mth

Jena-extended 93

Too little attention has been paid to errors !

Posterior flux errors are still very LARGE !

(even for anomalies)

Conclusions

Emerging IAV agreement between independent inversions

Net fluxes at regional scales remain too uncertain

Robustness is scale dependant !

However :

Need for :

a comparison exercise with many inversion : T3-L4 ?

(initial idea from Sander 3 years ago)

(Carbon tracker systems appear; how to compare ? )

Observation errors correlations ?

• Initial idea :

- Over a beer at a “CarboEurope” meeting in Crete… (Peter, Philippe, Sander, Christian)

- Data Uncertainties are “usually scaled” to account for all biases and to give a Chi-2 lower than 1 !

- However : A large part of model error are biases they should be accounted for with error correlations

This could potentially increase our confidence on the flux anomalies (as error affect systematically succeeding Obs)

• How to define those error correlations ?

Experience

(run by P. Rayner; M. Logan)

Standard inversion from Rayner et al. :- 116 regions- monthly fluxes

Compute the residuals (Model – Obs) after an inversion.

Use the residuals to compute TIME-LAG error correlations

Test a new inversion With Obs error correlations based on this residuals analysis

Time-lag correlation :

Barrow

Time lag (months)Halley Bay

Time lag (months)

Time lag (months)

Average across sitesCompute an Obs correlation matrix using “average” structure

Results….G

tC /

yea

r

Errors for the European flux anomalies :

With correlations

Without correlations

Monthly anomalies 5-month triang-smoothed anomalies

20% reduction of flux error anomalies

No reduction

Fanom = G # Fposterior

Panom = G # P # GT

Summary…

• Accounting for Obs error correlations can change :

- partially the fluxes (not shown)

- significantly the posterior errors on the flux anomalies

- but small effect with smoothed error anomalies

- Results depend on the Correlation structure !

• Work that need to be continued and improved

- I am testing a little “formal case” with pseudo-data !

• USE T3 continuous experiment to compute correlations !

• Other ideas ??

• Variational inversion systems usually do not take observation error correlations into account but– Data thinning or Error inflating

• Impact studied for the case of “OCO”– Hypothesised correlations of 0.5 from one observation to the next– Error analysis computed from an ensemble of inversions (Monte Carlo) with

observations and prior consistent with the specified error statistics

Impact of error correlation in the context of satellite data..F. Chevallier (subm.)

• Small impact when properly accounted for ! But,– Computationally expensive

– Correlations difficult to estimate

• Large impact when ignored

• Thinning or error inflating removes a significant part of the observation information content

Results:

How to define flux errors

variances & covariances ?

Critical point for « pixel based » inversion !

So far correlations defined exponentially as :

cor = Exp (-distance / length)

with length = 500 to 1000 km

Need to be validated with data !

Use flux tower measurement…

together with ORCHIDEE biosphere model (our prior fluxes) (prognostic, full carbon cycle, 1/2h time step,…)

2) Statistics of the residuals : - Std deviations

- Auto-correlation in time for each site

- Spatial correlations between sites

Compute residuals (Model – Obs)for each siteMod

Obs

Hainich

1) Compare model NEE to observed Eddy flux dataPrinciple :

• 36 in situ FLUXNET sites between 1994 and 2004• 31,500 daily-mean fluxes

PDF of the model-minus-observations

departures+ 2 standard distributions

Study of Chevallier et al. 2006 …..

Std error = 2 gC/m2/day

• 36 in situ FLUXNET sites between 1994 and 2004• 31,500 daily-mean fluxes

Study of Chevallier et al. 2006 …..

Overall error temporal correlations

Error spatial Correlations = f(distance)

Significant up to 10 days

Small correlations !

No evidence of strong spatial error correlations for daily values in Chevallier et al. !

WHY ? Is it robust ?

Few ideas :

- Error of ORCHIDEE should depend on the biomes and

thus should be correlated btw pixels (i.e. too low Vcmax,…)

- Correlation should depend on the time step considered !

(separation of flux time-scales might help)

- BUT Meteorology might de-correlate the errors at short time step

(daily fluxes depend on local cloud cover,…)

Need more detailed analysis !

New analysis of ORCHIDEE Results

Only European sites !

One year of daily values !

Questions :

- Do correlations improve for specific biomes ?

- Do correlation improve with Time-averaging ?

Evergreen Needleleaf Forest

Exp (-dist/500)

Exp (-dist/1000)

Daily values “20 days” values

Crop ecosystems

Exp (-dist/500)

Exp (-dist/1000)

Daily values “20 days” values

DeciduousBroadleaf

forest

Mediteraneanforest

Grassland

Mediteraneanforest

ModelObs

Need to account for BIAS in the variance/covariance error matrix !

BUT correlations derived from residuals does not account for bias !

Period with Hydric stress

Correlated errors

Summary of errors from ORCHIDEE…

Analysis of Eddy-covariance data is very usefull

Gauss multivariate distribution should be used with care !

Temporal error correlations up to 10 days…

Spatial error correlations depend on : - biome type- time-step chosen

« exponential distance-based correlation » works at 1st order !

Need to perform the analysis with other sites (i.e. Siberia)

Problem of tower representativity compared to size of pixel !

DEPEND on the biosphere model ! Check with others ?

Reduction of error using daily data and

LMDz zoomed over Europe

(Carouge et al. in preparation)

Network design : testing current /

forthcoming network potential

(like flux networks), test sampling frequency,

quality of data ?

Error reduction on estimated COError reduction on estimated CO22 fluxesfluxes

2001 surface network Future surface network

% of error reduction

0 10 20 30 0 10 20 30

Carouge, phd, 2006.