Abstract

Intercomparison of atmospheric measurements is often a difficult task because of the different spatial response functions of the experiments considered. We propose a new method for comparison of two atmospheric profiles characterized by averaging kernels with different vertical resolutions. The method minimizes the smoothing error induced by the differences in the averaging kernels by exploiting an optimal interpolation rule to map one profile into the retrieval grid of the other. Compared with the techniques published so far, this method permits one to retain the vertical resolution of the less-resolved profile involved in the intercomparison.

© 2006 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).
    [CrossRef]
  2. C. D. Rodgers and B. J. Connor, J. Geophys. Res. 108, 4116 (2003).
    [CrossRef]
  3. S. Ceccherini, B. Carli, E. Pascale, M. Prosperi, and B. M. Dinelli, Appl. Opt. 42, 6465 (2003).
    [CrossRef] [PubMed]
  4. W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannerly, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, 1992).
    [PubMed]
  5. European Space Agency, 'ENVISAT-MIPAS: An instrument for atmospheric chemistry and climate research,' doc. ESA SP-1229 (European Space Agency, 2000).
  6. H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

2003 (2)

Carli, B.

Ceccherini, S.

Connor, B. J.

C. D. Rodgers and B. J. Connor, J. Geophys. Res. 108, 4116 (2003).
[CrossRef]

Dinelli, B. M.

Fergg, F.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Fischer, H.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Flannerly, B. P.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannerly, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, 1992).
[PubMed]

Friedl-Vallon, F.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Fritzsche, C.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Oelhaf, H.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Pascale, E.

Piesch, C.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannerly, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, 1992).
[PubMed]

Prosperi, M.

Rabus, D.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Rodgers, C. D.

C. D. Rodgers and B. J. Connor, J. Geophys. Res. 108, 4116 (2003).
[CrossRef]

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

Seefeldner, M.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannerly, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, 1992).
[PubMed]

Volker, W.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

von Clarmann, T.

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

Wetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannerly, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, 1992).
[PubMed]

Appl. Opt. (1)

J. Geophys. Res. (1)

C. D. Rodgers and B. J. Connor, J. Geophys. Res. 108, 4116 (2003).
[CrossRef]

Other (4)

W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannerly, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, 1992).
[PubMed]

European Space Agency, 'ENVISAT-MIPAS: An instrument for atmospheric chemistry and climate research,' doc. ESA SP-1229 (European Space Agency, 2000).

H. Oelhaf, T. von Clarmann, F. Fergg, H. Fischer, F. Friedl-Vallon, C. Fritzsche, C. Piesch, D. Rabus, M. Seefeldner, and W. Volker, in Proceedings of the Tenth ESA Symposium on European Rocket and Balloon Progammes and Related Research, doc. ESA-SP-317 (European Space Agency, 1991), pp. 207-213.

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

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Figures (2)

Fig. 1
Fig. 1

Comparison of measurement errors σ i (solid curves) and smoothing errors δ i (dotted curves). (a) Linear interpolation, (b) optimal interpolation from Eq. (8).

Fig. 2
Fig. 2

Averaging kernels at 18 km altitude; optimal interpolation: A 1 (solid curve), BA 2 (filled squares), A 2 (dashed curve).

Equations (8)

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x ̂ 1 = x ̂ 0 + A 1 ( x v x 0 ) + ϵ 1 ,
x ̂ 2 = x ̂ 0 + A 2 ( x v x 0 ) + ϵ 2 ,
Δ = x ̂ 1 B x ̂ 2 .
Δ = x ̂ 0 B x ̂ 0 + ( A 1 B A 2 ) ( x v x 0 ) + ϵ 1 B ϵ 2 ,
Δ = x ̂ 0 B x ̂ 0 + ( A 1 B A 2 ) ( x v x 0 ) + ϵ 1 B ϵ 2 ,
S Δ = ( A 1 B A 2 ) S v ( A 1 B A 2 ) T + S R 1 + B S R 2 B T ,
Trace [ ( A 1 B A 2 ) S v ( A 1 B A 2 ) T ] + Trace [ S R 1 + B S R 2 B T ] .
B = A 1 S v A 2 T ( A 2 S v A 2 T + S R 2 ) 1 .

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