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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
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
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 ?
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 ?