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 MPICSIRO 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 Priors Biome correlation No IAV prior Distance correlation Casa prior No corelation Fluxes Monthly mean Conc. 74 sites Flask data 74 sites Montly mean Conc. 64 sites Pixel inversion Monthly fluxes Pixel inversion Weekly fluxes 116 regions Monthly 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. : 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) Average across sites  Compute an Obs correlation matrix using “average” structure

Results…. GtC / year  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 F anom = G # F posterior P anom = G # P # G T

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 site Mod Obs Hainich 1) Compare model NEE to observed Eddy flux data Principle :

36 in situ FLUXNET sites between 1994 and ,500 daily-mean fluxes PDF of the model-minus-observations departures + 2 standard distributions Study of Chevallier et al ….. Std error = 2 gC/m2/day

36 in situ FLUXNET sites between 1994 and ,500 daily-mean fluxes Study of Chevallier et al ….. 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

Deciduous Broadleaf forest Mediteranean forest Grassland

Mediteranean forest Model Obs  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 CO 2 fluxes 2001 surface networkFuture surface network % of error reduction Carouge, phd, 2006.