Abstract

In the case of a band model concept for molecular line absorption, since the absorption coefficient is a rapidly varying function of frequency, the averaged transmittance does not, in general, obey the simple exponential law with range. Mathematical expressions are obtained for the molecular line absorbers in the Lowtran 3B computer code. These expressions exhibit a variation of transmission, which is exponential with the range raised to some power the value of which is dependent on the contributor.

© 1978 Optical Society of America

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References

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  1. J. E. A. Selby, E. P. Shettle, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Supplement LOWTRAN 3B,” AFGL Environmental Research Paper 587 (Air Force Geophysics Laboratory, Hanscom AFB, Mass., 1976).
  2. J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 2,” AFCRL Environmental Research Paper 427 (AFCRL, Hanscom AFB, Mass., 1972).
  3. J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 3,” AFCRL Environmental Research Paper 513 (AFCRL, Hanscom AFB, Mass., 1975).

McClatchey, R. A.

J. E. A. Selby, E. P. Shettle, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Supplement LOWTRAN 3B,” AFGL Environmental Research Paper 587 (Air Force Geophysics Laboratory, Hanscom AFB, Mass., 1976).

J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 2,” AFCRL Environmental Research Paper 427 (AFCRL, Hanscom AFB, Mass., 1972).

J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 3,” AFCRL Environmental Research Paper 513 (AFCRL, Hanscom AFB, Mass., 1975).

Selby, J. E. A.

J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 3,” AFCRL Environmental Research Paper 513 (AFCRL, Hanscom AFB, Mass., 1975).

J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 2,” AFCRL Environmental Research Paper 427 (AFCRL, Hanscom AFB, Mass., 1972).

J. E. A. Selby, E. P. Shettle, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Supplement LOWTRAN 3B,” AFGL Environmental Research Paper 587 (Air Force Geophysics Laboratory, Hanscom AFB, Mass., 1976).

Shettle, E. P.

J. E. A. Selby, E. P. Shettle, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Supplement LOWTRAN 3B,” AFGL Environmental Research Paper 587 (Air Force Geophysics Laboratory, Hanscom AFB, Mass., 1976).

Other

J. E. A. Selby, E. P. Shettle, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Supplement LOWTRAN 3B,” AFGL Environmental Research Paper 587 (Air Force Geophysics Laboratory, Hanscom AFB, Mass., 1976).

J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 2,” AFCRL Environmental Research Paper 427 (AFCRL, Hanscom AFB, Mass., 1972).

J. E. A. Selby, R. A. McClatchey, “Atmospheric Transmittance from 0.25 to 28.5 μm: Computer Code LOWTRAN 3,” AFCRL Environmental Research Paper 513 (AFCRL, Hanscom AFB, Mass., 1975).

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Figures (2)

Fig. 1
Fig. 1

The transmission vs the scaling factors for water vapor and the uniformly mixed gases. The computer listed data (×) are compared with the mathematical expression (−).

Fig. 2
Fig. 2

The transmission vs the scaling factor for ozone. The computer listed data (×) are compared with the mathematical expression (−).

Equations (18)

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τ ¯ ( ν ¯ ) = 1 Δ ν Δ ν τ ( ν ) d ν ,
τ ¯ ( ν ¯ ) = 1 Δ ν Δ ν exp [ c ( ν ) R ] d ν exp [ c ¯ ( ν ¯ ) R ] ,
w 1 = 0.1 ρ w R ( P P 0 ) 0.9 ( T 0 T ) 0.45 ,
p 1 ( ν ¯ ) = c ¯ 1 ( ν ¯ ) + log 10 ( w 1 )
τ ¯ 1 ( ν ¯ ) = exp [ a 1 10 b 1 p 1 ( ν ¯ ) ]
log 10 [ ln τ ¯ 1 ( ν ¯ ) ] = log 10 ( a 1 ) + b 1 p 1 ( ν ¯ ) .
τ ¯ 1 ( ν ¯ ) = exp [ a 1 w 1 b 1 10 b 1 c ¯ 1 ( ν ¯ ) ] .
w 2 = R ( P P 0 ) 7 / 4 ( T 0 T ) 11 / 8 ,
p 2 ( ν ¯ ) = c ¯ 2 ( ν ¯ ) + log 10 ( w 2 ) ,
τ ¯ 2 ( ν ¯ ) = exp [ a 2 w 2 b 2 10 b 2 c ¯ 2 ( ν ¯ ) ] ,
w 3 = 46.667 ρ 0 R ( P P 0 ) 2 / 5 ( T 0 T ) 1 / 5 ,
p 3 ( ν ¯ ) = c ¯ 3 ( ν ¯ ) + log 10 ( w 3 ) ,
τ ¯ 3 ( ν ¯ ) = exp [ a 3 10 b 3 p 3 ( ν ¯ ) ]
τ ¯ 3 ( ν ¯ ) = exp [ a 4 10 b 4 p 3 ( ν ¯ ) + d 4 p 3 2 ( ν ¯ ) ]
log 10 [ ln τ ¯ 3 ( ν ¯ ) ] = log 10 ( a 3 ) + b 3 p 3 ( ν ¯ )
log 10 [ ln τ ¯ 3 ( ν ¯ ) ] = log 10 a 4 + b 4 p 3 ( ν ¯ ) + d 4 p 3 2 ( ν ¯ )
τ ¯ 3 ( ν ¯ ) = exp [ a 3 w 3 b 3 10 b 3 c ¯ 3 ( ν ¯ ) ]
τ ¯ i ( ν ¯ ) = exp [ M i 10 b i c ¯ i ( ν ¯ ) R b i ] ,

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