Abstract

Vertical mixing-ratio profiles of atmospheric gases can be retrieved from solar occultation spectra. The influence of systematic errors in the parameters of the models required in the analysis has been investigated. It is concluded that, because of smearing effects and other uncertainties, it may be preferable to calibrate the spectra internally by measuring absorption lines of gases such as CO2 or N2 whose vertical distributions can be assumed, rather than to rely on externally supplied information.

© 1984 Optical Society of America

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References

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  1. C. B. Farmer, “Atmospheric Trace Molecule Spectroscopy (ATMOS),” NASA Upper Atmosphere Research Program Summaries (1982).
  2. C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
    [CrossRef]
  3. W. A. Shaffer, Ph.D. thesis, Ohio State Univ., Columbus (1983); W. A. Shaffer, J. H. Shaw, “Resolution of Vertical Mixing-Ratio Profiles of Atmospheric Constituents Retrieved from Solar Spectra,” Appl. Opt. 22, 2977 (1983).
    [CrossRef] [PubMed]
  4. “The Stratosphere 1981 Theory and Measurements,” WMO Global Ozone Research and Monitoring Project Report 11 (1982).
  5. D. E. Snider, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” J. Atmos. Sci. 32, 2178 (1975).
    [CrossRef]
  6. D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1790, Ball. Res. Lab., Aberdeen Proving Ground, Md. (1975).
  7. U.S. Standard Atmosphere 1976 (U.S. GPO, Washington, D.C., 1976).
  8. A. J. Kantor, “Variability of Atmospheric Density in the Middle Atmosphere,” AFGL-TR-83-0079, AFGL, Hanscom AFB, Mass. (1983).
  9. O. K. Garriott, “Visual Observations From Space,” J. Opt. Soc. Am. 69, 1064 (1972).
    [CrossRef]
  10. J. M. Russell, “Satellite Solar Occultation Sounding of the Middle Atmosphere,” Pure Appl. Geophys. 118, 616 (1980).
    [CrossRef]
  11. J. H. Park, “Effect of Interferogram Smearing on Atmospheric Limb Sounding by Fourier Transform Spectroscopy,” Appl. Opt. 21, 1356 (1982).
    [CrossRef] [PubMed]
  12. D. A. Roewe, J. C. Gille, P. L. Bailey, “Infrared Limb Smearing in the Presence of Horizontal Temperature Gradients: An Operational Approach,” Appl. Opt. 21, 3775 (1982).
    [CrossRef] [PubMed]
  13. K. Mauersberger, R. Finstead, “Carbon Dioxide Measurements in the Stratosphere,” Geophys. Res. Lett. 7, 873 (1980).
    [CrossRef]
  14. R. A. Toth, “Temperature Sounding From the Absorption Spectrum of CO2 at 4.3 μm,” Appl. Opt. 16, 2661 (1977).
    [CrossRef] [PubMed]
  15. C. P. Rinsland et al., “Stratospheric Temperature Profile from Balloon-Borne Measurements of the 10.4 μm Band of CO2,” J. Quant. Spectrosc. Radiat. Transfer 30, 237 (1983).
    [CrossRef]
  16. Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, “Determination of Abundances of Gases from Solar Spectra,” J. Quant. Spectrosc. Radiat. Transfer 19, 599 (1978).
    [CrossRef]
  17. E. Niple, J. H. Shaw, “Information in Spectra of Collision-broadened Absorption Lines,” Appl. Spectrosc. 33, 569 (1979).
    [CrossRef]

1983

C. P. Rinsland et al., “Stratospheric Temperature Profile from Balloon-Borne Measurements of the 10.4 μm Band of CO2,” J. Quant. Spectrosc. Radiat. Transfer 30, 237 (1983).
[CrossRef]

1982

1980

K. Mauersberger, R. Finstead, “Carbon Dioxide Measurements in the Stratosphere,” Geophys. Res. Lett. 7, 873 (1980).
[CrossRef]

C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

J. M. Russell, “Satellite Solar Occultation Sounding of the Middle Atmosphere,” Pure Appl. Geophys. 118, 616 (1980).
[CrossRef]

1979

1978

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, “Determination of Abundances of Gases from Solar Spectra,” J. Quant. Spectrosc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

1977

1975

D. E. Snider, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” J. Atmos. Sci. 32, 2178 (1975).
[CrossRef]

1972

Bailey, P. L.

Calvert, J. G.

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, “Determination of Abundances of Gases from Solar Spectra,” J. Quant. Spectrosc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Chang, Y. S.

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, “Determination of Abundances of Gases from Solar Spectra,” J. Quant. Spectrosc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Farmer, C. B.

C. B. Farmer, “Atmospheric Trace Molecule Spectroscopy (ATMOS),” NASA Upper Atmosphere Research Program Summaries (1982).

C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Finstead, R.

K. Mauersberger, R. Finstead, “Carbon Dioxide Measurements in the Stratosphere,” Geophys. Res. Lett. 7, 873 (1980).
[CrossRef]

Garriott, O. K.

Gille, J. C.

Goldman, A.

D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1790, Ball. Res. Lab., Aberdeen Proving Ground, Md. (1975).

Kantor, A. J.

A. J. Kantor, “Variability of Atmospheric Density in the Middle Atmosphere,” AFGL-TR-83-0079, AFGL, Hanscom AFB, Mass. (1983).

Mauersberger, K.

K. Mauersberger, R. Finstead, “Carbon Dioxide Measurements in the Stratosphere,” Geophys. Res. Lett. 7, 873 (1980).
[CrossRef]

Muller, C.

C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Niple, E.

Park, J. H.

Raper, D. F.

C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Rinsland, C. P.

C. P. Rinsland et al., “Stratospheric Temperature Profile from Balloon-Borne Measurements of the 10.4 μm Band of CO2,” J. Quant. Spectrosc. Radiat. Transfer 30, 237 (1983).
[CrossRef]

Robbins, B. D.

C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Roewe, D. A.

Russell, J. M.

J. M. Russell, “Satellite Solar Occultation Sounding of the Middle Atmosphere,” Pure Appl. Geophys. 118, 616 (1980).
[CrossRef]

Shaffer, W. A.

W. A. Shaffer, Ph.D. thesis, Ohio State Univ., Columbus (1983); W. A. Shaffer, J. H. Shaw, “Resolution of Vertical Mixing-Ratio Profiles of Atmospheric Constituents Retrieved from Solar Spectra,” Appl. Opt. 22, 2977 (1983).
[CrossRef] [PubMed]

Shaw, J. H.

E. Niple, J. H. Shaw, “Information in Spectra of Collision-broadened Absorption Lines,” Appl. Spectrosc. 33, 569 (1979).
[CrossRef]

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, “Determination of Abundances of Gases from Solar Spectra,” J. Quant. Spectrosc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Snider, D. E.

D. E. Snider, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” J. Atmos. Sci. 32, 2178 (1975).
[CrossRef]

D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1790, Ball. Res. Lab., Aberdeen Proving Ground, Md. (1975).

Toth, R. A.

C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

R. A. Toth, “Temperature Sounding From the Absorption Spectrum of CO2 at 4.3 μm,” Appl. Opt. 16, 2661 (1977).
[CrossRef] [PubMed]

Uselman, W. M.

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, “Determination of Abundances of Gases from Solar Spectra,” J. Quant. Spectrosc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Appl. Opt.

Appl. Spectrosc.

Geophys. Res. Lett.

K. Mauersberger, R. Finstead, “Carbon Dioxide Measurements in the Stratosphere,” Geophys. Res. Lett. 7, 873 (1980).
[CrossRef]

J. Atmos. Sci.

D. E. Snider, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” J. Atmos. Sci. 32, 2178 (1975).
[CrossRef]

J. Geophys. Res.

C. B. Farmer, D. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl and HF at Northern and Southern Mid-Latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

C. P. Rinsland et al., “Stratospheric Temperature Profile from Balloon-Borne Measurements of the 10.4 μm Band of CO2,” J. Quant. Spectrosc. Radiat. Transfer 30, 237 (1983).
[CrossRef]

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, “Determination of Abundances of Gases from Solar Spectra,” J. Quant. Spectrosc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

NASA Upper Atmosphere Research Program Summaries

C. B. Farmer, “Atmospheric Trace Molecule Spectroscopy (ATMOS),” NASA Upper Atmosphere Research Program Summaries (1982).

Pure Appl. Geophys.

J. M. Russell, “Satellite Solar Occultation Sounding of the Middle Atmosphere,” Pure Appl. Geophys. 118, 616 (1980).
[CrossRef]

Other

W. A. Shaffer, Ph.D. thesis, Ohio State Univ., Columbus (1983); W. A. Shaffer, J. H. Shaw, “Resolution of Vertical Mixing-Ratio Profiles of Atmospheric Constituents Retrieved from Solar Spectra,” Appl. Opt. 22, 2977 (1983).
[CrossRef] [PubMed]

“The Stratosphere 1981 Theory and Measurements,” WMO Global Ozone Research and Monitoring Project Report 11 (1982).

D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1790, Ball. Res. Lab., Aberdeen Proving Ground, Md. (1975).

U.S. Standard Atmosphere 1976 (U.S. GPO, Washington, D.C., 1976).

A. J. Kantor, “Variability of Atmospheric Density in the Middle Atmosphere,” AFGL-TR-83-0079, AFGL, Hanscom AFB, Mass. (1983).

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Figures (9)

Fig. 1
Fig. 1

Occultation geometry. For a mean earth radius R = 6360 km and a satellite height a = 500 km, the distance L is ~2500 km, the angle θ is ~21°, and the zenith angle z is ~111°.

Fig. 2
Fig. 2

Dependence of the air mass traversed by rays with tangent heights of ~3, 12, and 48 km on the thickness of the atmospheric layers used in the calculation. The fractional change in air mass with respect to that calculated for 25-m thick layers is shown.

Fig. 3
Fig. 3

Dependence of the fractional air mass error along the rays due to the neglect of atmospheric refraction on the tangent height of the rays for the case of an observer at 500 km.

Fig. 4
Fig. 4

Height dependence of the fractional errors in the mixing-ratio profile caused by the neglect of atmospheric refraction in the retrieval.

Fig. 5
Fig. 5

Height dependence of the fractional errors in the mixing-ratio profile caused by 5% errors in sea level pressure.

Fig. 6
Fig. 6

Height dependence of the fractional errors in the retrieved mixing-ratio profile caused by assuming ±5 K changes at all heights in the U.S. Standard Atmosphere temperature profile.

Fig. 7
Fig. 7

Height dependence of the fractional errors in the retrieved mixing-ratio profile caused by errors of ±1 km in the satellite height.

Fig. 8
Fig. 8

Height dependence of the fractional errors in the retrieved mixing-ratio profile caused by errors of ±0.01° in the angles of the incoming rays.

Fig. 9
Fig. 9

Fractional rate of change of air mass (sec−1) for an observer at 500 km: (a) atmosphere with a temperature gradient of 1 K/km; (b) U.S. Standard Atmosphere. The tangent heights of the rays decrease from 90 to 0 km.

Tables (3)

Tables Icon

Table I Quantities Affecting the Equivalent Widths of Weak Lines in Solar Spectra

Tables Icon

Table II Sources of Error and Their Effects on Retrieved Mixing Ratio Profiles

Tables Icon

Table III Dependence of the Errors in the Tangent Heights of Rays Made by Using Internal Calibration Methods on Systematic Errors in the Assumed Parameters Values

Equations (23)

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W ( z i ) = j S j ρ j d j δ l i j ,
d W ( z i ) = j S j ρ j d j δ l i j ( 1 S j g S j s g Δ s g + 1 ρ j p ρ j t p Δ t p + 1 d j q d j x q Δ x q + 1 δ l i j r δ l i j y r Δ y r ) .
a ( z i ) = W ( z i ) / S ,
Δ a ( z i ) = j ρ j d j δ l i j ( 1 ρ j p ρ j t p Δ t p + 1 d j q d j x q Δ x q + 1 δ l i j r δ l i j y r Δ y r ) ,
j ( 1 ρ j ρ j x 1 Δ x 1 + 1 d j d j x 1 Δ x 1 ) = 0.
j ( ρ j ρ j + Δ d j d j ) = 0.
similarly             Δ ρ j ρ j + Δ d j d j = 0 ; Δ ρ j ρ j + Δ δ i j δ i j = 0. }
Δ d / d = Δ P 0 / P 0 ,
Δ ρ / ρ = - Δ P 0 / P 0 .
P ( h ) = P 0 exp ( - h / H ) ,
d ( h ) = d 0 exp ( - h / H ) ,
H = R T / M g ,
Δ h / H = Δ P 0 P 0 ,
Δ P = M g h P Δ T / R T 2 ,
Δ d = M Δ P / R T - M P Δ T / R T 2 ,
Δ d / d = ( h - H ) Δ T / H T .
Δ h = ( H - h ) Δ T / T .
z = 90 + θ ,             Δ z = Δ θ .
cos θ = ( R + b ) / ( R + a ) , Δ b = L Δ z , - sin θ Δ θ = - ( R + b ) Δ a / ( R + a ) 2 + ( a - b ) Δ R / ( R + a ) 2 + Δ b / ( R + a ) .
a 0 = W 0 / S 0 ,
a 1 = W 1 / S 1 .
A = W 0 / S 0 ρ 0 ,
ρ 1 = a 1 / A .

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