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

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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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Presentation Transcript

Empirical Orthogonal Function (EOF)

Analysis on the O2 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
• 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

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
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
EOF 1

% Variance Captured: 93.51

EOF 2

% Variance Captured: 5.80

EOF 3

% Variance Captured: 0.53

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
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!