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

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

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

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

Welcome-5 Optical Depth and Single Scattering Albedo Profiles

Welcome-6 EOF 1 % Variance Captured: 93.51

Welcome-7 EOF 2 % Variance Captured: 5.80

Welcome-8 EOF 3 % Variance Captured: 0.53

Welcome-9 A-band Recovery from EOF Analysis

Welcome-10 Residues

Welcome-11 Percentage Residues

Welcome-12 Statistics Total Pixels: 7971 Total EOF Cases: 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

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!