Abstract

In the retrieval of vertical profiles of atmospheric constituents, regularization methods are frequently used to improve the conditioning of the solution. The regularization reduces the retrieval errors and causes the vertical resolution to deteriorate. One obtains a trade-off by tuning the strength of the regularization by way of a regularization parameter. A new analytical method for determining the regularization parameter is presented. This method is suitable for operational retrievals, for which an unattended procedure is required. The performance of the new method is compared with that of the L-curve method, and the results show that a better trade-off between retrieval errors and vertical resolution is obtained.

© 2005 Optical Society of America

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References

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  1. C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, Vol. 2 of Series on Atmospheric, Oceanic and Planetary Physics (World Scientific, 2000).
  2. A. Tikhonov, Dokl. Akad. Nauk SSSR 151, 501 (1963).
  3. P. C. Hansen, SIAM Rev. 34, 561 (1992)
    [CrossRef]
  4. B. Schimpf and F. Schreier, J. Geophys. Res. 102, 16,037. (1997)
    [CrossRef]
  5. A. Doicu, F. Schreier, and M. Hess, Comput. Phys. Commun. 148, 214 (2002).
    [CrossRef]
  6. T. Steck, Appl. Opt. 41, 1788 (2002).
    [CrossRef] [PubMed]
  7. European Space Agency, “ENVISAT-MIPAS: an instrument for atmospheric chemistry and climate research,” doc. ESA SP-1229 (European Space Agency, European Space Research and Technology Centre, 2000).

2002

A. Doicu, F. Schreier, and M. Hess, Comput. Phys. Commun. 148, 214 (2002).
[CrossRef]

T. Steck, Appl. Opt. 41, 1788 (2002).
[CrossRef] [PubMed]

1997

B. Schimpf and F. Schreier, J. Geophys. Res. 102, 16,037. (1997)
[CrossRef]

1992

P. C. Hansen, SIAM Rev. 34, 561 (1992)
[CrossRef]

1963

A. Tikhonov, Dokl. Akad. Nauk SSSR 151, 501 (1963).

Doicu, A.

A. Doicu, F. Schreier, and M. Hess, Comput. Phys. Commun. 148, 214 (2002).
[CrossRef]

Hansen, P. C.

P. C. Hansen, SIAM Rev. 34, 561 (1992)
[CrossRef]

Hess, M.

A. Doicu, F. Schreier, and M. Hess, Comput. Phys. Commun. 148, 214 (2002).
[CrossRef]

Rodgers, C. D.

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, Vol. 2 of Series on Atmospheric, Oceanic and Planetary Physics (World Scientific, 2000).

Schimpf, B.

B. Schimpf and F. Schreier, J. Geophys. Res. 102, 16,037. (1997)
[CrossRef]

Schreier, F.

A. Doicu, F. Schreier, and M. Hess, Comput. Phys. Commun. 148, 214 (2002).
[CrossRef]

B. Schimpf and F. Schreier, J. Geophys. Res. 102, 16,037. (1997)
[CrossRef]

Steck, T.

Tikhonov, A.

A. Tikhonov, Dokl. Akad. Nauk SSSR 151, 501 (1963).

Appl. Opt.

Comput. Phys. Commun.

A. Doicu, F. Schreier, and M. Hess, Comput. Phys. Commun. 148, 214 (2002).
[CrossRef]

Dokl. Akad. Nauk SSSR

A. Tikhonov, Dokl. Akad. Nauk SSSR 151, 501 (1963).

J. Geophys. Res.

B. Schimpf and F. Schreier, J. Geophys. Res. 102, 16,037. (1997)
[CrossRef]

SIAM Rev.

P. C. Hansen, SIAM Rev. 34, 561 (1992)
[CrossRef]

Other

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, Vol. 2 of Series on Atmospheric, Oceanic and Planetary Physics (World Scientific, 2000).

European Space Agency, “ENVISAT-MIPAS: an instrument for atmospheric chemistry and climate research,” doc. ESA SP-1229 (European Space Agency, European Space Research and Technology Centre, 2000).

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Figures (2)

Fig. 1
Fig. 1

L curve for the retrieval of the CH 4 VMR from simulated MIPAS measurements. Positions on the L-curve that correspond to four methods of regularization are shown: nonregularized profile ( λ = 0 ) , EC method ( λ = 83 ) , strong regularization ( λ = 5067 ) , and L-curve method ( λ = 4650 ) .

Fig. 2
Fig. 2

Results of three regularizations. (a) Retrieved profiles of the CH 4 VMR in parts in 10 6 by volume (ppmv). (b) Differences from the true profile ( λ = 0 is not shown). (c) Retrieval errors. (d) Vertical resolution. The number of degrees of freedom, which is the trace of the AKM,[6] is 27 for λ = 0 , 19.7 for λ = 83 , and 7.9 for λ = 4650 .

Equations (8)

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f ( x ) = [ y F ( x ) ] T S y 1 [ y F ( x ) ] + λ ( x x a ) T R ( x x a ) ,
x = ( S x ̂ 1 + λ R ) 1 ( S x ̂ 1 x ̂ + λ R x a ) ,
x ̂ = x ̂ 0 + ( K T S y 1 K ) 1 K T S y 1 [ y F ( x ̂ 0 ) ] ,
S x ̂ = ( K T S y 1 K ) 1 ,
A x = ( S x ̂ 1 + λ R ) 1 S x ̂ 1 ,
S x = A x S x ̂ A x T .
( x x ̂ ) T S x 1 ( x x ̂ ) = n ,
λ = [ n ( x a x ̂ ) T R S x ̂ R ( x a x ̂ ) ] 1 2 .

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