Abstract

Thermal emission measurements of the earth’s stratospheric limb from space platforms require an accurate knowledge of the observation angles for retrieval of temperature and constituent distributions. Without the use of expensive stabilizing systems, however, most observational instruments do not meet the required pointing accuracies, thus leading to large errors in the retrieval of atmospheric data. This paper describes a self-constituent method of correcting errors in pointing angles by using information contained in the observed spectrum. Numerical results based on temperature inversions of synthetic thermal emission spectra with assumed random errors in pointing angles are presented.

© 1984 Optical Society of America

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References

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  1. J. C. Gille, F. B. House, J. Atmos. Sci. 28, 1427 (1971).
    [CrossRef]
  2. M. T. Chahine, J. Atmos. Sci. 27, 960 (1970).
    [CrossRef]
  3. B. J. Conrath, Backus-Gilbert Theory and its Application to Retrieval of Ozone and Temperature Profiles, Inversion Methods in Atmospheric Remote Sounding (Academic, New York, 1977).
  4. A. Deepak, Ed., Inversion Methods in Atmospheric Remote Sounding (Academic, New York, 1977).
  5. M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
    [CrossRef]
  6. M. M. Abbas, G. L. Shapiro, J. M. Alvarez, Appl. Opt. 20, 3755 (1981).
    [CrossRef] [PubMed]
  7. V. B. Kunde, W. C. Maguire, J. Quant. Spectrosc. Radiative Transfer 14, 803 (1974).
    [CrossRef]

1981 (1)

1979 (1)

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

1974 (1)

V. B. Kunde, W. C. Maguire, J. Quant. Spectrosc. Radiative Transfer 14, 803 (1974).
[CrossRef]

1971 (1)

J. C. Gille, F. B. House, J. Atmos. Sci. 28, 1427 (1971).
[CrossRef]

1970 (1)

M. T. Chahine, J. Atmos. Sci. 27, 960 (1970).
[CrossRef]

Abbas, M. M.

M. M. Abbas, G. L. Shapiro, J. M. Alvarez, Appl. Opt. 20, 3755 (1981).
[CrossRef] [PubMed]

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Alvarez, J. M.

Buhl, D.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Chahine, M. T.

M. T. Chahine, J. Atmos. Sci. 27, 960 (1970).
[CrossRef]

Conrath, B. J.

B. J. Conrath, Backus-Gilbert Theory and its Application to Retrieval of Ozone and Temperature Profiles, Inversion Methods in Atmospheric Remote Sounding (Academic, New York, 1977).

Gille, J. C.

J. C. Gille, F. B. House, J. Atmos. Sci. 28, 1427 (1971).
[CrossRef]

House, F. B.

J. C. Gille, F. B. House, J. Atmos. Sci. 28, 1427 (1971).
[CrossRef]

Kostiuk, T.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Kunde, V. B.

V. B. Kunde, W. C. Maguire, J. Quant. Spectrosc. Radiative Transfer 14, 803 (1974).
[CrossRef]

Kunde, V. G.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Maguire, W. C.

V. B. Kunde, W. C. Maguire, J. Quant. Spectrosc. Radiative Transfer 14, 803 (1974).
[CrossRef]

Mumma, M. J.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Shapiro, G. L.

Appl. Opt. (1)

J. Atmos. Sci. (2)

J. C. Gille, F. B. House, J. Atmos. Sci. 28, 1427 (1971).
[CrossRef]

M. T. Chahine, J. Atmos. Sci. 27, 960 (1970).
[CrossRef]

J. Geophys. Res. (1)

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

J. Quant. Spectrosc. Radiative Transfer (1)

V. B. Kunde, W. C. Maguire, J. Quant. Spectrosc. Radiative Transfer 14, 803 (1974).
[CrossRef]

Other (2)

B. J. Conrath, Backus-Gilbert Theory and its Application to Retrieval of Ozone and Temperature Profiles, Inversion Methods in Atmospheric Remote Sounding (Academic, New York, 1977).

A. Deepak, Ed., Inversion Methods in Atmospheric Remote Sounding (Academic, New York, 1977).

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Figures (6)

Fig. 1
Fig. 1

Geometry of limb-scan measurements.

Fig. 2
Fig. 2

Errors in retrieved temperature profile relative to model values obtained from noise-free synthetic limb radiance data for six limb scans with zenith angles 90, 92.0, 92.9, 92.5, 94.0, and 94.50 corresponding to tangent heights at 35, 31, 27, 23, 19, and 15 km.

Fig. 3
Fig. 3

Envelope of errors based on four retrieved temperature profiles obtained from noise-free synthetic limb radiance data of Fig. 2 with random errors of ±0.3° introduced in the pointing angles. No correction of the angular errors is made.

Fig. 4
Fig. 4

Envelope of errors based on the data of Figs. 2 and 3 with the angular errors corrected by using the formulation discussed in this paper.

Fig. 5
Fig. 5

Envelope of errors based on the data of Figs. 24 with noise superimposed on the synthetic radiances with the mean standard deviation of the random noise being ±0.1 (erg sec−1 cm−2 sr−1/cm−1).

Fig. 6
Fig. 6

Envelope of errors based on the data of Figs. 25 with noise superimposed on the synthetic radiances with mean standard deviation of the random noise being ±0.5 (erg sec−1 cm−2 sr−1/cm−1).

Equations (9)

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I ν s = s B ν s = ( 1 - τ ν s ) B ν s ,
I ν w = w B ν w = ( 1 - τ ν w ) B ν w ,
r I = I ν s I ν w ,             r B = B ν s ( T s ) B ν w ( T w ) ,
τ ν w = 1 - r B r I ( 1 - τ ν s ) .
τ ν w = exp ( - k ν w d u ) = exp ( - k ¯ ν w u ) ,
u 0 = - 1 k ¯ ν w ln [ 1 - r B r I ( 1 - τ ν s ) ]
k ¯ ν w = k ν w d u d u = 1 u k ν w d u = 1 u ln ( τ ν w - 1 ) .
u 0 = u ln τ ν w ln [ 1 - r B r I ( 1 - τ ν s ) ] .
Δ θ j = Δ u j u j sec θ j tan θ j | ,

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