Abstract

An iterative solution is developed for the temperature and absorbing gas profiles of an atmosphere from spectral and angular measurements of atmospheric radiance. This iterative solution is novel in that there is no limiting assumption made about the analytical form of the profile imposed by the number of radiance observations available. The solution is demonstrated through the determination of temperature and water vapor profiles of the earth’s atmosphere from Nimbus III and Nimbus IV Satellite InfraRed Spectrometer (SIRS) observations. The solutions are compared with conventional rawinsonde and rocketsonde observations. The results indicate that this solution can be used effectively to specify the general meteorological characteristics of an atmosphere from satellite or ground-based radiometric observations.

© 1970 Optical Society of America

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References

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  1. J. I. F. King, Scientific Uses of Earth Satellites, Ed. J. A. Van Allen (Univ. Mich., Ann Arbor, 1958), p. 133.
  2. J. I. F. King, J. Atmos. Sci. 20, 245 (1963).
    [CrossRef]
  3. J. I. F. King, J. Atmos. Sci. 21, 324 (1964).
    [CrossRef]
  4. L. D. Kaplan, J. Opt. Soc. Amer. 49, 1004 (1959).
    [CrossRef]
  5. L. D. Kaplan, J. Quant. Spectrosc. Radiative Transfer 1, 89 (1961).
    [CrossRef]
  6. D. Q. Wark, D. T. Hilleary, Science 165, 1256 (1969).
    [CrossRef] [PubMed]
  7. R. A. Hanel, B. Conrath, Science 165, 1258 (1969).
    [CrossRef] [PubMed]
  8. W. L. Smith, H. M. Woolf, W. J. Jacob, Monthly Weather Rev. 98, 582 (1970).
    [CrossRef]
  9. D. Q. Wark, H. E. Fleming, Monthly Weather Rev. 94, 351 (1966).
    [CrossRef]
  10. C. D. Rodgers, “Satellite Infrared Radiometer; A Discussion of Inversion Methods,” Univ. Oxford Clarendon Lab. Mem. No. 66.13, Oxford, 1966.
  11. E. R. Westwater, O. N. Strand, ESSA Tech. Rep. IER 37-ITSA 37, U.S. Dept. Commerce, Washington, D.C., 1967.
  12. W. L. Smith, Monthly Weather Rev. 95, 363 (1967).
    [CrossRef]
  13. W. L. Smith, Monthly Weather Rev. 96, 387 (1968).
    [CrossRef]
  14. M. T. Chahine, J. Opt. Soc. Amer. 58, 1634 (1968).
    [CrossRef]
  15. B. Conrath, J. Geophys. Res. 74, 3347 (1969).
    [CrossRef]
  16. Nimbus Project, The Nimbus III User’s Guide (Goddard Space Flight Ctr., NASA, 1969).
  17. Nimbus Project, The Nimbus IV User’s Guide (Goddard Space Flight Ctr., NASA, 1970).

1970 (1)

W. L. Smith, H. M. Woolf, W. J. Jacob, Monthly Weather Rev. 98, 582 (1970).
[CrossRef]

1969 (3)

D. Q. Wark, D. T. Hilleary, Science 165, 1256 (1969).
[CrossRef] [PubMed]

R. A. Hanel, B. Conrath, Science 165, 1258 (1969).
[CrossRef] [PubMed]

B. Conrath, J. Geophys. Res. 74, 3347 (1969).
[CrossRef]

1968 (2)

W. L. Smith, Monthly Weather Rev. 96, 387 (1968).
[CrossRef]

M. T. Chahine, J. Opt. Soc. Amer. 58, 1634 (1968).
[CrossRef]

1967 (1)

W. L. Smith, Monthly Weather Rev. 95, 363 (1967).
[CrossRef]

1966 (1)

D. Q. Wark, H. E. Fleming, Monthly Weather Rev. 94, 351 (1966).
[CrossRef]

1964 (1)

J. I. F. King, J. Atmos. Sci. 21, 324 (1964).
[CrossRef]

1963 (1)

J. I. F. King, J. Atmos. Sci. 20, 245 (1963).
[CrossRef]

1961 (1)

L. D. Kaplan, J. Quant. Spectrosc. Radiative Transfer 1, 89 (1961).
[CrossRef]

1959 (1)

L. D. Kaplan, J. Opt. Soc. Amer. 49, 1004 (1959).
[CrossRef]

Chahine, M. T.

M. T. Chahine, J. Opt. Soc. Amer. 58, 1634 (1968).
[CrossRef]

Conrath, B.

B. Conrath, J. Geophys. Res. 74, 3347 (1969).
[CrossRef]

R. A. Hanel, B. Conrath, Science 165, 1258 (1969).
[CrossRef] [PubMed]

Fleming, H. E.

D. Q. Wark, H. E. Fleming, Monthly Weather Rev. 94, 351 (1966).
[CrossRef]

Hanel, R. A.

R. A. Hanel, B. Conrath, Science 165, 1258 (1969).
[CrossRef] [PubMed]

Hilleary, D. T.

D. Q. Wark, D. T. Hilleary, Science 165, 1256 (1969).
[CrossRef] [PubMed]

Jacob, W. J.

W. L. Smith, H. M. Woolf, W. J. Jacob, Monthly Weather Rev. 98, 582 (1970).
[CrossRef]

Kaplan, L. D.

L. D. Kaplan, J. Quant. Spectrosc. Radiative Transfer 1, 89 (1961).
[CrossRef]

L. D. Kaplan, J. Opt. Soc. Amer. 49, 1004 (1959).
[CrossRef]

King, J. I. F.

J. I. F. King, J. Atmos. Sci. 21, 324 (1964).
[CrossRef]

J. I. F. King, J. Atmos. Sci. 20, 245 (1963).
[CrossRef]

J. I. F. King, Scientific Uses of Earth Satellites, Ed. J. A. Van Allen (Univ. Mich., Ann Arbor, 1958), p. 133.

Rodgers, C. D.

C. D. Rodgers, “Satellite Infrared Radiometer; A Discussion of Inversion Methods,” Univ. Oxford Clarendon Lab. Mem. No. 66.13, Oxford, 1966.

Smith, W. L.

W. L. Smith, H. M. Woolf, W. J. Jacob, Monthly Weather Rev. 98, 582 (1970).
[CrossRef]

W. L. Smith, Monthly Weather Rev. 96, 387 (1968).
[CrossRef]

W. L. Smith, Monthly Weather Rev. 95, 363 (1967).
[CrossRef]

Strand, O. N.

E. R. Westwater, O. N. Strand, ESSA Tech. Rep. IER 37-ITSA 37, U.S. Dept. Commerce, Washington, D.C., 1967.

Wark, D. Q.

D. Q. Wark, D. T. Hilleary, Science 165, 1256 (1969).
[CrossRef] [PubMed]

D. Q. Wark, H. E. Fleming, Monthly Weather Rev. 94, 351 (1966).
[CrossRef]

Westwater, E. R.

E. R. Westwater, O. N. Strand, ESSA Tech. Rep. IER 37-ITSA 37, U.S. Dept. Commerce, Washington, D.C., 1967.

Woolf, H. M.

W. L. Smith, H. M. Woolf, W. J. Jacob, Monthly Weather Rev. 98, 582 (1970).
[CrossRef]

J. Atmos. Sci. (2)

J. I. F. King, J. Atmos. Sci. 20, 245 (1963).
[CrossRef]

J. I. F. King, J. Atmos. Sci. 21, 324 (1964).
[CrossRef]

J. Geophys. Res. (1)

B. Conrath, J. Geophys. Res. 74, 3347 (1969).
[CrossRef]

J. Opt. Soc. Amer. (2)

M. T. Chahine, J. Opt. Soc. Amer. 58, 1634 (1968).
[CrossRef]

L. D. Kaplan, J. Opt. Soc. Amer. 49, 1004 (1959).
[CrossRef]

J. Quant. Spectrosc. Radiative Transfer (1)

L. D. Kaplan, J. Quant. Spectrosc. Radiative Transfer 1, 89 (1961).
[CrossRef]

Monthly Weather Rev. (4)

W. L. Smith, H. M. Woolf, W. J. Jacob, Monthly Weather Rev. 98, 582 (1970).
[CrossRef]

D. Q. Wark, H. E. Fleming, Monthly Weather Rev. 94, 351 (1966).
[CrossRef]

W. L. Smith, Monthly Weather Rev. 95, 363 (1967).
[CrossRef]

W. L. Smith, Monthly Weather Rev. 96, 387 (1968).
[CrossRef]

Science (2)

D. Q. Wark, D. T. Hilleary, Science 165, 1256 (1969).
[CrossRef] [PubMed]

R. A. Hanel, B. Conrath, Science 165, 1258 (1969).
[CrossRef] [PubMed]

Other (5)

C. D. Rodgers, “Satellite Infrared Radiometer; A Discussion of Inversion Methods,” Univ. Oxford Clarendon Lab. Mem. No. 66.13, Oxford, 1966.

E. R. Westwater, O. N. Strand, ESSA Tech. Rep. IER 37-ITSA 37, U.S. Dept. Commerce, Washington, D.C., 1967.

J. I. F. King, Scientific Uses of Earth Satellites, Ed. J. A. Van Allen (Univ. Mich., Ann Arbor, 1958), p. 133.

Nimbus Project, The Nimbus III User’s Guide (Goddard Space Flight Ctr., NASA, 1969).

Nimbus Project, The Nimbus IV User’s Guide (Goddard Space Flight Ctr., NASA, 1970).

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Figures (10)

Fig. 1
Fig. 1

The derivative of transmittance with respect to the logarithm of pressure. These functions approximately describe the relative sensitivity of the eight SIRS radiance observations to temperature variations in various altitude layers of the atmosphere.

Fig. 2
Fig. 2

The derivative of transmittance with respect to the logarithm of pressure. These functions approximately describe the relative sensitivity of the six SIRS radiance observations to water vapor variations in various altitude layers of the atmosphere.

Fig. 3
Fig. 3

Global mean temperature profile.

Fig. 4
Fig. 4

Comparison between a temperature profile at 75°N and that calculated from satellite radiance observations simulated for the 669 cm−1, 692 cm−1, 714 cm−1, 750 cm−1, and 899 cm−1 spectral channels of SIRS-A.

Fig. 5
Fig. 5

Comparison between a temperature profile at 60°N and that calculated from the five simulated SIRS-A radiances with and without random error.

Fig. 6
Fig. 6

Comparison between SIRS-A calculated and radiosonde, rocketsonde temperature profiles for August 1969.

Fig. 7
Fig. 7

Comparison between SIRS-A calculated and radiosonde, rocketsonde temperature profiles for March 1970.

Fig. 8
Fig. 8

Comparison between SIRS-B calculated and a radiosonde-observed temperature profile.

Fig. 9
Fig. 9

Comparison between SIRS-B calculated and a radiosonde-observed water vapor profile.

Fig. 10
Fig. 10

Comparison between SIRS-B calculated and a radiosonde-observed water vapor profile.

Tables (1)

Tables Icon

Table I Spectral Positions of SIRS Channels (cm−1)

Equations (21)

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N ( ν , ϕ ) = B [ ν , T ( p s ) ] τ ( ν , ϕ , p s ) 1 τ ( ν , ϕ , p s ) B [ ν , T ( p ) ] d τ ( ν , ϕ , p ) ,
B [ ν , T ( p ) ] = C 1 ν 3 { exp [ C 2 ν / T ( p ) ] 1 } 1 .
N ( x i ) = B ( x i , p s ) τ ( x i , p s ) 1 τ ( x i , P s ) B ( x i , p ) d τ ( x i , p ) ,
N ( x i ) N j ( x i ) = [ B j + 1 ( x i , p s ) B j ( x i , p s ) ] τ ( x i , p s ) 1 τ ( ν , p s ) [ B j + 1 ( x i , p ) B j ( x i , p ) ] d τ ( x i , p ) ,
B j + 1 ( x i , p ) = B j ( x i , p ) + [ N ( x i ) N j ( x i ) ] .
T j + 1 ( x i , p ) = C 2 ν i / ln [ C 1 ν i 3 + B j + 1 ( x i , p ) B j + 1 ( x i , p ) ] .
T j + 1 ( p ) = i = 1 n T j + 1 ( x i , p ) W ( x i , p ) / i = 1 n W ( x i , p ) ,
W ( x i , p ) = d τ ( x i , p ) , p < p s ,
W ( x i , p s ) = τ ( x i , p s ) .
| N j + 1 ( x i ) N j ( x i ) | / N ( x i ) Criterion = 0.0001 i = 1,2 , , n .
N ( x ) = B ( x , p t ) + B ( x , p t ) B ( x , p s ) τ ( x , p ) d B ( x , p ) ,
N ( x i ) N j ( x i ) = B ( x i , p t ) B ( x i , p s ) [ τ j + 1 ( x i , p ) τ j ( x i , p ) ] d B ( x i , p ) .
τ j + 1 ( x i , p ) τ j ( x i , p ) = [ U j + 1 ( x i , p ) U j ( p ) ] [ τ ( x i , p ) U ( p ) ] j .
N ( x i ) N j ( x i ) = B ( x i , p t ) B ( x i , p s ) [ U j + 1 ( x i , p ) U j ( p ) ] × [ τ ( x i , p ) U ( p ) ] j d B ( x i , p ) .
N ( x i ) N j ( x i ) = U j + 1 ( x i , p ) U j ( p ) U j ( p ) × B ( x i , p t ) B ( x i , p s ) U j ( p ) [ τ ( x i , p ) U ( p ) ] j d B ( x i , p ) .
U j + 1 ( x i , p ) = U j ( p ) { 1 + [ N ( x i ) N j ( x i ) ] / S j } ,
S j = B ( x i , p t ) B ( x i , p s ) U j ( p ) [ τ ( x i , p ) U ( p ) ] j d B ( x i , p ) .
U j ( p ) = 1 / g 0 p q j ( p ) d p and q j ( p ) = g U j ( p ) p .
q j + 1 ( x i , p ) = q j ( p ) { 1 + [ N ( x i ) N j ( x i ) ] / S j } .
q j + 1 ( p ) = i = 1 m q j + 1 ( x i , p ) W j + 1 ( x i , p ) / i = 1 m W j + 1 ( x i , p ) ,
W j + 1 ( x i , p ) = [ τ ( x i , p ) U j ( p ) ] d B ( x i , p ) .

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