Error bar estimates

1. Estimates of the uncertainties on input LwN Estimates of the error model Estimates of the uncertainties on outputs Chla, bbp,cdm (Co-variance matrix between all ingredients) Error bar estimates

2. Derivation of the uncertainties on nLw used as inputs of the GSM retrieval procedure • Two sources of uncertainties: • Statistical errors between satellite observations and in-situ measurements • Statistical errors of the semi-analytical model

3. Derivation of the uncertainties on nLw used as inputs of the GSM retrieval procedure • Two sources of uncertainties: • Statistical errors between satellite observations and in-situ measurements • Statistical errors of the semi-analytical model The sensor observations nLw(l) are compared to values extracted from the NOMAD in-situ database

4. Derivation of the uncertainties on nLw used as inputs of the GSM retrieval procedure • Two sources of uncertainties: • Statistical errors between satellite observations and in-situ measurements • Statistical errors of the semi-analytical model The radiances from the NOMAD database have been used as input for the GSM model in order to get Chla, bbp and aCDM. These quantities have been used to rebuild the values of radiances nLw(l) and then compared with original radiances values. The discrepancies have been quantified in terms of statistical quantities(RMS, bias, etc…).

5. Final uncertainties are computed as the quadratic sum of the satellite vs in-situ data RMS and of the GSM model characterisation RMS. The net result has been divided by two, considering as a preliminary assumption that the error on measurements used for characterization counts for half of the final uncertainties levels. Error bars used as inputs in GlobColour

6. Weakness and limitation of current approach • A constant absolute value of the uncertainty is used instead of a varying one (relative) • The observations are implicitly considered as unbiased. Assessment of the quality of the error budget in GlobColour v1.1 • Computation of chi-2 (should be close to 1 if error budget is correct). • Computation of residuals (residual is the difference between observed LwN and modeled nLw rebuilt with GSM direct model) - rms of residuals should be comparable with error budget, assuming no bias (cf. limitation 2). • Computation of covariance matrix of retrieved parameters (diagonal of the matrix should compare well with uncertainty estimates derived from statistical analysis with in situ ; off-diagonal terms give an indication of the correlation of retrieved parameters - the lower the better).

7. Cost function Full covariance matrix of errors Ctot=Cnoise+Cmod Maximum likelihood solution: minimize • Currently we do not consider the covariance terms, neither on the model nor on the measurements, so that the cost function reduces to: where : si,j correspond to the square root of the diagonal terms of C,tot

8. Background • Full Nomad-2 is used for matchups with • SeaWiFs and/or MODIS-Aqua and/or MERIS • GSM – versions (all with red bands) • with no error on nLw – no reliable error budget • with error on nLw – reliable error budget ? • with error on nLw with a new parameters tuning (GSM08) • Taking into account the uncertainties on nLw + error model for item 2 and 3

9. With and without uncertainties Impact on the retrieved quantity GlobColour/GSM GSM - no error on nLw

10. With and without uncertainties Impact on the retrieved quantity GlobColour/GSM – with red bands GSM - no error on nLw

11. With and without uncertainties Impact on the retrieved quantity GlobColour/GSM – with red bands GSM - no error on nLw

12. Analysis of the retrieval quality Chi-2 GlobColour/GSM – with red bands GlobColour/GSM – with red bands

13. Mean of the residual +/-1 s of the residual Analysis of the retrieval quality Residual on the nLw after inversion GlobColour/GSM – with red bands SeaWiFS residuals Orange dots are the a priori uncertainties (inputs of GSM) – no bias

14. Conclusions Input uncertainties on nLw are consistent with residual However, a bias is observed for 443 and 490. As similar bias exists for MERIS and MODIS: this points towards a weakness in the reflectance model GlobColour/GSM – with red bands MERIS residuals GlobColour/GSM – with red bands MODIS residuals

15. Analysis of the retrieval uncertainties ¿What is the quality of final error bars? GlobColour/GSM – with red bands Chla uncertainty estimates Final uncertainties (outputs of GSM) Actual difference (absolute) between observed and retrieved

16. Analysis of the retrieval uncertainties ¿What is the quality of final error bars? GlobColour/GSM – with red bands CDM uncertainty estimates Final uncertainties (outputs of GSM) Actual difference (absolute) between observed and retrieved

17. Analysis of the retrieval uncertainties ¿What is the quality of final error bars? GlobColour/GSM – with red bands Bbp uncertainty estimates Final uncertainties (outputs of GSM) Actual difference (absolute) between observed and retrieved Hair-splitting plots… How to quantify the quality of the result ? If the orange dots are reliable standard deviation – there should be, statistically, about 68% of blue points below the corresponding orange points (+/-1s)

18. Analysis of the retrieval uncertainties ¿What is the quality of final error bars? Transition from (X,s) couple to reduced variable X/s If everything went well and there is no bias, the X/s distribution should follow a standard normal distribution (centered).

19. Analysis of the retrieval uncertainties ¿What is the quality of final error bars? GlobColour/GSM – with red bands Normalised error distribution (Chla, CDM, bbp) These error bars are available in GlobColour daily products Excellent behaviour of Chla AND bbp error estimates Suspect behaviour for CDM error estimates

20. GlobColour Chla-merged product – May,15 2006 GlobColour Chla-merged product relative uncertainties – May,15 2006 100 50 0 Example of products uncertainties - daily

21. GlobColour Chla-merged product – May 2006 GlobColour Chla-merged product relative uncertainties– May 2006 100 50 0 Example of products uncertainties