1. Empirical Orthogonal Function (EOF) Analysis on the O 2 A-band Vijay Natraj, Run-Lie Shia, Xun Jiang and Yuk Yung

2. Welcome-2 Rationale Multiple Scattering RT calculations time-consuming Need a speed improvement of about 1000! Solution: make use of redundancies in spectra –Correlated-k (Lacis and Wang, Lacis and Oinas, Goody et al, Fu and Liou) –Optical depth binning (Ramaswamy and Friedenreich) Problem: assume that atmospheric optical properties spectrally correlated at all points along optical path

3. Welcome-3 Rationale (contd …) Spectral Mapping (Crisp and West, Meadows and Crisp) –No assumption about spectral correlation –Combine only spectral regions that remain in agreement at ALL points along optical path –Binning parameters: optical depth, single scattering albedo, asymmetry parameter, surface albedo Problems –Inadequate speed improvement for OCO precision constraints –Glitches in partial differentials

4. Welcome-4 EOF Technique Data Set –Optical properties in M atmospheric layers at N wavelengths EOF –Eigenvectors of covariance matrix of detrended (removed mean) data set –New basis to represent original data –No loss of information PC –Projection of original data set onto EOFs

5. Welcome-5 Optical Depth and Single Scattering Albedo Profiles

6. Welcome-6 EOF 1 % Variance Captured: 93.51

7. Welcome-7 EOF 2 % Variance Captured: 5.80

8. Welcome-8 EOF 3 % Variance Captured: 0.53

9. Welcome-9 A-band Recovery from EOF Analysis

10. Welcome-10 Residues

11. Welcome-11 Percentage Residues

12. Welcome-12 Statistics Total Pixels: 7971 Total EOF Cases: 131 4 RT calls (and 4 calls to a twostream routine) per case Speed improvement of at least 10 (conservative estimate) Precision of better than 0.5% except in highly saturated regions Tunable

13. Welcome-13 What Next? Need to analyse more scenes Full retrieval using EOF analysis: what is the error? Partial derivatives with respect to EOFs, rather than the individual state vector parameters Captures all the information content available in the spectrum Looks promising!