1. Channel selection for IASI in clear-sky conditions Florence Rabier and Nadia Fourrié Météo-France ITSC-XII February 2002

2. Rationale and objectives  Advanced IR sounders –large volume of data, prohibitive in operational NWP  Selection of individual channels –Which channel selection method leads to the best analysis accuracy? –In practice, how can this method be applied robustly to a large set of atmospheric conditions?  IASI  IASI = Infrared Atmospheric Sounding Interferometer developed by CNES-EUMETSAT

3. Linear estimation theory  Retrieval  Retrievalx a = x b + K(y-Hx b )  Covariance matrix  Covariance matrix A -1 =B -1 +H T R -1 H  Gain matrix  Gain matrix K= A H T R -1  Data Resolution Matrix  Data Resolution Matrix DRM=HK  Model Resolution Matrix  Model Resolution Matrix MRM=KH  Metric based Jacobian matrix  Metric based Jacobian matrix H’=R -1/2 HB 1/2  Degree of freedom for signal  Degree of freedom for signal DFS = Tr (I-AB -1 )  Shannon entropy reduction  Shannon entropy reductionER = -1/2 log 2 |AB -1 |

4. Linear estimation theory  Resolution matrices x a- x b = K(y-Hx b ) =KH (x- x b ) = MRM (x- x b ) y a- y b = H (x a- x b )=HK (y- y b ) = DRM (y- y b ) –Link the analysis and the signal from the data  Diagnostics of retrieval accuracy Standard-deviations of analysis errors  a (i) Vertical resolution (Purser and Huang) Resol(i) = dz (i) /MRM(i,i)

5. Channel selection methods  Methods based on the DRM  Methods based on the DRM (Menke, Prunet) –Equation y a- y b = DRM (y- y b ) –Select the most useful data in the analysis  Method based on Jacobians  Method based on Jacobians (Goldberg, Aires) –Characteristics of H’=R -1/2 HB 1/2 –For each parameter to be retrieved, select the most useful channel  Iterative method  Iterative method (Rodgers) –Measures of improvement ER or DFS (AB -1 ) –Iteratively, pick up the most useful channel to improve on the current analysis. Update the analysis errors.

6. Methods based on the DRM (Menke) Data resolution matrix: DRM=HK From y a -y b =DRM (y-y b ), the diagonal elements of DRM indicate how much weight a datum has in its own analysis These diagonal elements measure the « importance » of the various channels The method needs the computation of A

7. Methods based on the DRM (Prunet) SVD of H, with metrics B and R G= R -1/2 HB 1/2 =UΛV T Truncation in Λ 2 such that eigenvalues of G T G= B 1/2 H T R -1 HB 1/2, equivalent to σ b 2 / σ o 2 represent 10% of contribution of the observations to the analysis G= R -1/2 HB 1/2 =>U p Λ p V p T DRM = V p V p T. Its diagonal elements are used as channel « importance »

8. Method based on the Jacobians (Goldberg, Aires) Is it based on the shape of the weighting functions Normalisation of H: R -1/2 HB 1/2 For each retrieved parameter, at each level in the vertical, one selects channels Among those peaking next to the level With the largest ratio: Amplitude of the peak/Width of the weighting function

9. Iterative Method (Rodgers) This method is a step by step selection scheme. At each step, B i =A i-1 is updated by using the most informative channel among those which have been previously selected. After normalisation of the Jacobian by R A i -1 =B i -1 +h T h Where B 0 =B and h is a line of H The selection criterion is either DFS or ER DFS(h) i =Tr(I-AB i -1 )=h T B i h/(1+ h T B i h ) ER (h) i =-1/2 log 2 det(AB i -1 )=1/2 log 2 (1+ h T B i h )

10. Experimental context  500 atmospheric situations –Profiles (T,Q), various sites and dates  IASI data simulated with RTIASI (Matricardi and Saunders) –8461 radiances (645 cm -1 – 2760 cm -1 )  B  B based on a 60-level ECMWF matrix  O F  O from CNES, F=0.2K  Removal of bands sensitive to trace gases –(700-720, 1000-1080, 1267-1312, 2092-2355 cm -1 )

11. Results on mid-lat profiles  24 atmospheric situations –Profiles (T,Q), one site at various dates  4 channel selection methods tested –For each profile, optimal selection performed –Results averaged over all profiles Profile i Selection i Retrieval i = Profile i + Selection i

12. Results on mid-lat profiles

13. First Channels for T Iterative method

15. Non-optimal set of channels Iterative method  For a set of profiles  For a set of profiles, optimal selection performed  « Constant » selection  « Constant » selection obtained by averaging the ranks of the channels Cst selection =Ave (Selection i)  Non-optimal retrievals pre-compute  Would allow to pre-compute a constant selection off-line, and to apply it to new profiles in real time Profile i Selection i Retrieval j = Profile j + Cst Selection Profile j

16. « Constant » selection (300 channels) Iterative method (492 profiles)

17. Results for analysis errors Iterative and Jacobian methods (300 channels, 492 profiles)

18. Results for analysis vert resolution Iterative and Jacobian methods (300 channels, 492 profiles)

19. Influence of number of channels Results for analysis errors Iterative method (24 profiles)

20. Influence of number of channels Results for analysis vert resolution Iterative method (24 profiles)

21. Conclusions  Iterative method –Among 4 channel selection methods tested, the iterative method is giving the best results  Main strength –Update the error covariance matrix each time a channel is selected  Constant selection gives promising results –Pre-selection based on a set of profiles, then applied to all profiles –Robustness: selection performed for 62 profiles out of 492 gave 84% of channels in common with the one computed on all 492 profiles

22. Perspectives  Method can be applied to other sounders –Thépaut and Fourrié  Study to be extended –Inclusion of different scan angles, surface types, cloud conditions  Possible operational channel selection –Pre-selection based on monitoring statistics –Use several sets of channels for various configurations of scan angles, surface types, cloud conditions and also air-mass