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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
slide1

Empirical Orthogonal Function (EOF)

Analysis on the O2 A-band

Vijay Natraj, Run-Lie Shia, Xun Jiang and Yuk Yung

slide2

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
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
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
EOF 1

% Variance Captured: 93.51

eof 2
EOF 2

% Variance Captured: 5.80

slide8

EOF 3

% Variance Captured: 0.53

statistics
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
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!