# Presentation: 065151

## Error bar estimates

## Derivation of the uncertainties on nLw

- Statistical errors between satellite observations and in-situ measurements
- Statistical errors of the semi-analytical model

- used as inputs of the GSM retrieval procedure

## Derivation of the uncertainties on nLw

- The sensor observations nLw (l) are compared to values extracted from
- the NOMAD in-situ database

- Two sources of uncertainties:
**Statistical errors between satellite observations and in-situ measurements**
- Statistical errors of the semi-analytical model

- used as inputs of the GSM retrieval procedure

## Derivation of the uncertainties on nLw

- 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...).

- Two sources of uncertainties:
- Statistical errors between satellite observations and in-situ measurements
**Statistical errors of the semi-analytical model**

- used as inputs of the GSM retrieval procedure

## Error bars used as inputs in GlobColour

- 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.

## 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.

- 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).

- Assessment of the quality of the error budget in GlobColour v1.1

## Cost function 

**Cost function**** **
- Full covariance matrix of errors **C**tot=**C**noise+**C**mod
- 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 :
- i,j correspond to the square root of the diagonal terms of C,tot

## 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

## With and without uncertainties

**With and without uncertainties**
- Impact on the retrieved quantity

- GlobColour/GSM

- GSM - no error on nLw

## With and without uncertainties

**With and without uncertainties**
- Impact on the retrieved quantity

- GlobColour/GSM – with red bands

- GSM - no error on nLw

## With and without uncertainties

**With and without uncertainties**
- Impact on the retrieved quantity

- GlobColour/GSM – with red bands

- GSM - no error on nLw

## Analysis of the retrieval quality

- Chi-2

- GlobColour/GSM – with red bands

- GlobColour/GSM – with red bands

## Analysis of the retrieval quality

- Residual on the nLw after inversion

**Orange dots are the**
** ****a priori uncertainties (inputs of GSM) – no bias**

- GlobColour/GSM – with red bands
- SeaWiFS residuals

## 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

## Analysis of the retrieval uncertainties

- ¿What is the quality of final error bars?

**Final uncertainties (outputs of GSM)**

**Actual difference (absolute) between observed and retrieved**

- GlobColour/GSM – with red bands
- Chla uncertainty estimates

## Analysis of the retrieval uncertainties

- ¿What is the quality of final error bars?

**Final uncertainties (outputs of GSM)**

**Actual difference (absolute) between observed and retrieved**

- GlobColour/GSM – with red bands
- CDM uncertainty estimates

## Analysis of the retrieval uncertainties

- ¿What is the quality of final error bars?

**Final uncertainties (outputs of GSM)**

**Actual difference (absolute) between observed and retrieved**

- GlobColour/GSM – with red bands
- Bbp uncertainty estimates

**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 (+/-1)

## Analysis of the retrieval uncertainties

- ¿What is the quality of final error bars?

- Transition from (X,) couple to reduced variable X/
- If everything went well and there is no bias, the X/s distribution should follow a
- standard normal distribution (centered).

## Analysis of the retrieval uncertainties

- ¿What is the quality of final error bars?

- GlobColour/GSM – with red bands
- Normalised error distribution (Chla, CDM, bbp)

- Excellent behaviour of Chla AND bbp error estimates
- Suspect behaviour for CDM error estimates

- These error bars are available in GlobColour daily products

## Example of products uncertainties - daily

## Example of products uncertainties