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Empirical Orthogonal Function (EOF) Analysis on the O 2 A-band

Empirical Orthogonal Function (EOF) Analysis on the O 2 A-band Vijay Natraj, Run-Lie Shia, Xun Jiang and Yuk Yung. Rationale. Multiple Scattering RT calculations time-consuming Need a speed improvement of about 1000! Solution: make use of redundancies in spectra

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Empirical Orthogonal Function (EOF) Analysis on the O 2 A-band

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  1. Empirical Orthogonal Function (EOF) Analysis on the O2 A-band Vijay Natraj, Run-Lie Shia, Xun Jiang and Yuk Yung

  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. 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. 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. Optical Depth and Single Scattering Albedo Profiles

  6. EOF 1 % Variance Captured: 93.51

  7. EOF 2 % Variance Captured: 5.80

  8. EOF 3 % Variance Captured: 0.53

  9. A-band Recovery from EOF Analysis

  10. Residues

  11. Percentage Residues

  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. 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!

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