Empirical Orthogonal Function (EOF)

Analysis on the O2 A-bandVijay Natraj, Run-Lie Shia, Xun Jiang and Yuk

Yung

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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

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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

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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

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Optical Depth and Single Scattering Albedo Profiles

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EOF 1

% Variance Captured: 93.51

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EOF 2

% Variance Captured: 5.80

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EOF 3

% Variance Captured: 0.53

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A-band Recovery from EOF Analysis

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Residues

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Percentage Residues

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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

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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!