Abstract

A highly convergent relaxation method has been developed for the inversion of the full radiative-transfer equation. The results of the iterative solution indicate that convergence can be achieved over a wide range of initial guesses, enabling the temperature profile of a relatively unknown atmosphere to be unambiguously determined. The method is illustrated by examples for the outgoing radiance in the earth’s atmosphere for the region of the 4.3-μ CO2 band, but can be similarly applied in other frequency ranges.

© 1968 Optical Society of America

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References

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  1. Lewis D. Kaplan, J. Opt. Soc. Am. 49, 1004 (1959).
    [Crossref]
  2. D. Q. Wark and H. E. Fleming, Monthly Weather Rev. 94, 351 (1966).
    [Crossref]
  3. Moustafa T. Chahine, in Methods in Computational Physics, Vol. 4, E. Alder, S. Fernbach, and M. Rotenberg, Eds. (Academic Press Inc., New York, 1965), p. 83.

1966 (1)

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

1959 (1)

Chahine, Moustafa T.

Moustafa T. Chahine, in Methods in Computational Physics, Vol. 4, E. Alder, S. Fernbach, and M. Rotenberg, Eds. (Academic Press Inc., New York, 1965), p. 83.

Fleming, H. E.

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

Kaplan, Lewis D.

Wark, D. Q.

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

J. Opt. Soc. Am. (1)

Monthly Weather Rev. (1)

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

Other (1)

Moustafa T. Chahine, in Methods in Computational Physics, Vol. 4, E. Alder, S. Fernbach, and M. Rotenberg, Eds. (Academic Press Inc., New York, 1965), p. 83.

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Figures (2)

Fig. 1
Fig. 1

Temperature profile, from ten sounding frequencies, at the fifth iteration using the U. S. Standard Atmosphere as initial guess. ●●●, iterative solution. –·–·, exact profile. — —, initial guess.

Fig. 2
Fig. 2

Temperature profile, from ten sounding frequencies, at the eighth iteration using as initial guess any one of three isothermal profiles: 280, 240, or 200 K. ●●●, iterative solution. — · — ·, exact profile. — —, initial guess.

Tables (1)

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Table I Average residuals 〈Rnav, %.

Equations (14)

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I ( ν , P ¯ ) = B [ ν , T ( P 0 ) ] τ ( ν , P 0 ) + P 0 P ¯ B [ ν , T ( P ) ] τ ( ν , P ) P d P ,
I ( ν , P ¯ ) / I 1 ( ν , P ¯ ) B [ ν , T ( P ) ] / B [ ν , T 1 ( P ) ] ,
B ( ν , T ) / a ν 3 = ( e b ν / T - 1 ) - 1
= X ( T ) β ( ν ) δ ( ν , T ) ,
C j ν ν T T [ b ν T - C 1 - C 2 ν - C 3 T ] 2 d T d ν = 0 ,             ( j = 1 , 2 , 3 ) .
C 1 = - b ln ( T / T ) T - T ν + ν 2 ,
C 2 = b ln ( T / T ) T - T ,
C 3 = b ( ν + ν ) / 2.
X ( T ) = exp [ - C 1 - ( C 3 / T ) ] .
B ( ν , T ) a ν 3 X ( T ) { [ exp ( - b ν T + C 1 + C 3 T ) ] / ( 1 - e - b ν / T ) } ,
I ( ν , P ¯ ) = X [ T ( P 0 ) ] A ( ν , P 0 ) + P 0 P ¯ X [ T ( P ) ] K ( ν , P ) d P ,
X i n = X i n - 1 ( Ĩ i / I i n - 1 ) ,
R i n = Ĩ i - I i n / Ĩ i ,
R n av = 1 i R i n .