Abstract

A method for the retrieval of concentration profiles of atmospheric constituents from spectra, recorded by balloon-borne spectrometers with the limb-scanning technique, is presented. The method uses a nonlinear least-squares fit procedure to fit simultaneously the whole concentration profile on a limb-scanning sequence of spectra. A use in interferometric measurements of the stratospheric emission is shown and a comparison is discussed with the results obtained from the analysis of the same data set, by using the onion-peeling method in which the error propagation, over concentrations, is taken into account. With the global-fit, error bars smaller than with the onion-peeling analysis are obtained. Computational details are also discussed.

© 1988 Optical Society of America

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References

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  1. A. Goldman, D. G. Murcray, F. J. Murcray, W. J. Williams, J. N. Brooks, “Distribution of Water Vapor in the Stratosphere as Determined from Balloon Measurements of Atmospheric Emission Spectra in the 24–29-μm Region,” Appl. Opt. 12, 1045 (1973).
    [CrossRef] [PubMed]
  2. D. G. Murcray, F. J. Murcray, A. Goldman, F. H. Murcray, J. J. Kosters, “Balloon-Borne Remote Sensing of Stratospheric Constituents,” Appl. Opt. 22, 2629 (1983).
    [CrossRef] [PubMed]
  3. A. Goldman, R. S. Saunders, “Analysis of Atmospheric Infrared Spectra for Altitude Distribution of Atmospheric Trace Constituents—I: Method of Analysis,” J. Quant. Spectrosc. Radiat. Transfer 21, 155 (1979).
    [CrossRef]
  4. A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
    [CrossRef]
  5. A. Goldman, F. J. Murcray, R. D. Blatherwick, D. G. Murcray, “Quantification of HC1 from High Resolution, Ground-Based, Infrared Solar Spectra in the 3000-cm−1 Region,” J. Quant. Spectrosc. Radiat. Transfer 36, 385 (1986).
    [CrossRef]
  6. E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
    [CrossRef]
  7. C. P. Rinsland et al.“Stratospheric N2O Mixing Ratio Profile from High-Resolution Balloon-Borne Solar Absorption Spectra and Laboratory Spectra Near 1880 cm−1,” Appl. Opt. 21, 4351 (1982).
    [CrossRef] [PubMed]
  8. J. H. Park, B. Carli, “Analysis of Far-Infrared Emission Fourier Transform Spectra,” Appl. Opt. 25, 3490 (1986).
    [CrossRef] [PubMed]
  9. M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
    [CrossRef]
  10. J. H. Park, “Analysis Method for Fourier Transform Spectroscopy,” Appl. Opt. 22, 835 (1983).
    [CrossRef] [PubMed]
  11. B. Carli, F. Mencaraglia, A. Bonetti, “Submillimeter High-Resolution FT Spectrometer for Atmospheric Studies,” Appl. Opt. 23, 2594 (1984).
    [CrossRef] [PubMed]
  12. B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
    [CrossRef]
  13. D. W. Marquardt, “An Algorithm for the Least-Squares Estimation of NonLinear Parameters,” J. Soc. Appl. Math. 11, 431 (1963).
    [CrossRef]

1987 (1)

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

1986 (2)

A. Goldman, F. J. Murcray, R. D. Blatherwick, D. G. Murcray, “Quantification of HC1 from High Resolution, Ground-Based, Infrared Solar Spectra in the 3000-cm−1 Region,” J. Quant. Spectrosc. Radiat. Transfer 36, 385 (1986).
[CrossRef]

J. H. Park, B. Carli, “Analysis of Far-Infrared Emission Fourier Transform Spectra,” Appl. Opt. 25, 3490 (1986).
[CrossRef] [PubMed]

1985 (1)

B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
[CrossRef]

1984 (2)

B. Carli, F. Mencaraglia, A. Bonetti, “Submillimeter High-Resolution FT Spectrometer for Atmospheric Studies,” Appl. Opt. 23, 2594 (1984).
[CrossRef] [PubMed]

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

1983 (2)

1982 (1)

1980 (1)

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

1979 (1)

A. Goldman, R. S. Saunders, “Analysis of Atmospheric Infrared Spectra for Altitude Distribution of Atmospheric Trace Constituents—I: Method of Analysis,” J. Quant. Spectrosc. Radiat. Transfer 21, 155 (1979).
[CrossRef]

1973 (1)

1963 (1)

D. W. Marquardt, “An Algorithm for the Least-Squares Estimation of NonLinear Parameters,” J. Soc. Appl. Math. 11, 431 (1963).
[CrossRef]

Abbas, M. M.

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

Blatherwick, R. D.

A. Goldman, F. J. Murcray, R. D. Blatherwick, D. G. Murcray, “Quantification of HC1 from High Resolution, Ground-Based, Infrared Solar Spectra in the 3000-cm−1 Region,” J. Quant. Spectrosc. Radiat. Transfer 36, 385 (1986).
[CrossRef]

Bonetti, A.

Brooks, J. N.

Carli, B.

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

J. H. Park, B. Carli, “Analysis of Far-Infrared Emission Fourier Transform Spectra,” Appl. Opt. 25, 3490 (1986).
[CrossRef] [PubMed]

B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
[CrossRef]

B. Carli, F. Mencaraglia, A. Bonetti, “Submillimeter High-Resolution FT Spectrometer for Atmospheric Studies,” Appl. Opt. 23, 2594 (1984).
[CrossRef] [PubMed]

Carlotti, M.

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

Coffey, M. T.

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

Dinelli, B. M.

B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
[CrossRef]

Goldman, A.

A. Goldman, F. J. Murcray, R. D. Blatherwick, D. G. Murcray, “Quantification of HC1 from High Resolution, Ground-Based, Infrared Solar Spectra in the 3000-cm−1 Region,” J. Quant. Spectrosc. Radiat. Transfer 36, 385 (1986).
[CrossRef]

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

D. G. Murcray, F. J. Murcray, A. Goldman, F. H. Murcray, J. J. Kosters, “Balloon-Borne Remote Sensing of Stratospheric Constituents,” Appl. Opt. 22, 2629 (1983).
[CrossRef] [PubMed]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

A. Goldman, R. S. Saunders, “Analysis of Atmospheric Infrared Spectra for Altitude Distribution of Atmospheric Trace Constituents—I: Method of Analysis,” J. Quant. Spectrosc. Radiat. Transfer 21, 155 (1979).
[CrossRef]

A. Goldman, D. G. Murcray, F. J. Murcray, W. J. Williams, J. N. Brooks, “Distribution of Water Vapor in the Stratosphere as Determined from Balloon Measurements of Atmospheric Emission Spectra in the 24–29-μm Region,” Appl. Opt. 12, 1045 (1973).
[CrossRef] [PubMed]

Guo, J.

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

Kosters, J. J.

Mankin, W. G.

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Marquardt, D. W.

D. W. Marquardt, “An Algorithm for the Least-Squares Estimation of NonLinear Parameters,” J. Soc. Appl. Math. 11, 431 (1963).
[CrossRef]

Mencaraglia, F.

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
[CrossRef]

B. Carli, F. Mencaraglia, A. Bonetti, “Submillimeter High-Resolution FT Spectrometer for Atmospheric Studies,” Appl. Opt. 23, 2594 (1984).
[CrossRef] [PubMed]

Murcray, D. G.

A. Goldman, F. J. Murcray, R. D. Blatherwick, D. G. Murcray, “Quantification of HC1 from High Resolution, Ground-Based, Infrared Solar Spectra in the 3000-cm−1 Region,” J. Quant. Spectrosc. Radiat. Transfer 36, 385 (1986).
[CrossRef]

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

D. G. Murcray, F. J. Murcray, A. Goldman, F. H. Murcray, J. J. Kosters, “Balloon-Borne Remote Sensing of Stratospheric Constituents,” Appl. Opt. 22, 2629 (1983).
[CrossRef] [PubMed]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

A. Goldman, D. G. Murcray, F. J. Murcray, W. J. Williams, J. N. Brooks, “Distribution of Water Vapor in the Stratosphere as Determined from Balloon Measurements of Atmospheric Emission Spectra in the 24–29-μm Region,” Appl. Opt. 12, 1045 (1973).
[CrossRef] [PubMed]

Murcray, F. H.

Murcray, F. J.

A. Goldman, F. J. Murcray, R. D. Blatherwick, D. G. Murcray, “Quantification of HC1 from High Resolution, Ground-Based, Infrared Solar Spectra in the 3000-cm−1 Region,” J. Quant. Spectrosc. Radiat. Transfer 36, 385 (1986).
[CrossRef]

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

D. G. Murcray, F. J. Murcray, A. Goldman, F. H. Murcray, J. J. Kosters, “Balloon-Borne Remote Sensing of Stratospheric Constituents,” Appl. Opt. 22, 2629 (1983).
[CrossRef] [PubMed]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

A. Goldman, D. G. Murcray, F. J. Murcray, W. J. Williams, J. N. Brooks, “Distribution of Water Vapor in the Stratosphere as Determined from Balloon Measurements of Atmospheric Emission Spectra in the 24–29-μm Region,” Appl. Opt. 12, 1045 (1973).
[CrossRef] [PubMed]

Niple, E.

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Nolt, I. G.

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

Park, J. H.

Piccioli, S.

B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
[CrossRef]

Rinsland, C. P.

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

C. P. Rinsland et al.“Stratospheric N2O Mixing Ratio Profile from High-Resolution Balloon-Borne Solar Absorption Spectra and Laboratory Spectra Near 1880 cm−1,” Appl. Opt. 21, 4351 (1982).
[CrossRef] [PubMed]

Saunders, R. S.

A. Goldman, R. S. Saunders, “Analysis of Atmospheric Infrared Spectra for Altitude Distribution of Atmospheric Trace Constituents—I: Method of Analysis,” J. Quant. Spectrosc. Radiat. Transfer 21, 155 (1979).
[CrossRef]

Valboni, A.

B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
[CrossRef]

Williams, W. J.

Appl. Opt. (6)

Geophys. Res. Lett. (2)

M. M. Abbas, J. Guo, B. Carli, F. Mencaraglia, M. Carlotti, I. G. Nolt, “Stratospheric Distribution of HCN from Far Infrared Observations,” Geophys. Res. Lett. 14, 531 (1987).
[CrossRef]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratosphere NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

J. Atmos. Chem. (1)

A. Goldman, C. P. Rinsland, F. J. Murcray, D. G. Murcray, M. T. Coffey, W. G. Mankin, “Balloon-Borne and Aircraft Infrared Measurements of Ethane (C2H6) in the Upper Troposphere and Lower Stratosphere,” J. Atmos. Chem. 2, 211 (1984).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

A. Goldman, F. J. Murcray, R. D. Blatherwick, D. G. Murcray, “Quantification of HC1 from High Resolution, Ground-Based, Infrared Solar Spectra in the 3000-cm−1 Region,” J. Quant. Spectrosc. Radiat. Transfer 36, 385 (1986).
[CrossRef]

A. Goldman, R. S. Saunders, “Analysis of Atmospheric Infrared Spectra for Altitude Distribution of Atmospheric Trace Constituents—I: Method of Analysis,” J. Quant. Spectrosc. Radiat. Transfer 21, 155 (1979).
[CrossRef]

J. Soc. Appl. Math. (1)

D. W. Marquardt, “An Algorithm for the Least-Squares Estimation of NonLinear Parameters,” J. Soc. Appl. Math. 11, 431 (1963).
[CrossRef]

Nuovo Cimento C (1)

B. Carli, F. Mencaraglia, B. M. Dinelli, S. Piccioli, A. Valboni, “Comparison of Measured and Calculated High-Resolution Spectra of Far-Infrared Stratospheric Emission,” Nuovo Cimento C 8, 631 (1985).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Ray geometry of three limb-scanning spectra (A,B,C) recorded from float altitude Hf with zenith angles φ1,φ2,φ3. Here H1,H2,H3 are the tangent altitudes defining, together with Hf, the three layers L1,L2,L3.

Fig. 2
Fig. 2

Comparison between the observed spectra (upper curves) and the synthetic spectra (middle curves) computed using the ozone concentration profile retrieved by the global-fit analysis on the limb-scanning sequence. The lower curves are the difference between the upper and middle curves. The curves are shifted along they axis for clarity and the emissivity scales refer to the observed spectra.

Fig. 3
Fig. 3

Comparison between the ozone concentration profile retrieved by the global-fit analysis (thick line) and the onion-peeling analysis (thin line). The error bars are located at the tangent altitudes in the global-fit profile but they are shifted to the nearest whole kilometer in the onion-peeling profile. The dashed lines delimit the error band accounting for the error propagation in the onion-peeling analysis.

Tables (2)

Tables Icon

Table I Observation Details for the Spectra Analyzed

Tables Icon

Table II Computational Details of the Analysis

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

F ( p 1 , p 2 p k ) = i = 1 N [ B σ i m - B σ i c ( p 1 , p 2 p k ) ] 2 ,
F sum ( c 1 c L ) = j = 1 M F j
F ( p 1 , p 2 p k ) = J = 1 M i = 1 N [ B j m σ i - B j c σ i ( p 1 , p 2 p k ) ] 2 ,

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