Abstract

Calculations have been made of high-resolution transmission in the CO2 absorption bands between 12 μ and 18 μ by direct integration across the bands, for both homogeneous and atmospheric slant paths. Mixed Doppler-Lorentz broadening has been used at pressures lower than 100 mb. A method to eliminate the Curtis-Godson approximation has been developed and applied to the slant-path calculations. Comparisons have been made with previous theoretical and experimental data, and reasons for the discrepancies are discussed.

© 1966 Optical Society of America

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References

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  1. W. Hitschfeld, J. T. Houghton, Quart. J. Royal Meteorol. Soc. 87, 562 (1961).
    [CrossRef]
  2. D. M. Gates, R. F. Calfee, D. W. Hansen, Appl. Opt. 2, 117 (1963).
    [CrossRef]
  3. D. M. Gates, R. F. Calfee, D. W. Hansen, W. S. Benedict, NBS Monograph 71(1964).
  4. J. H. Shaw, J. T. Houghton, Appl. Opt. 3, 773 (1964).
    [CrossRef]
  5. R. M. Goody, Atmospheric Radiation I: Theoretical Basis (Oxford Univ. Press, Oxford, 1964).
  6. B. H. Winters, S. Silverman, W. S. Benedict, J. Quant. Spectry. Radiative Transfer 4, 527 (1964).
    [CrossRef]
  7. L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
    [CrossRef]
  8. R. F. Madden, J. Chem. Phys. 35, 2083 (1961).
    [CrossRef]
  9. A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge Univ. Press, Cambridge, 1934).
  10. C. Young, J. Quant. Spectry. Radiative Transfer 5, 549 (1965).
    [CrossRef]
  11. G. N. Plass, D. I. Fivel, Astrophys. J. 117, 225 (1953).
    [CrossRef]
  12. G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).
    [CrossRef]
  13. P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
    [CrossRef]
  14. A. R. Curtis, Quart. J. Royal Meteorol. Soc. 78, 638 (1952).
    [CrossRef]
  15. W. L. Godson, Quart. J. Royal Meteorol. Soc. 79, 367 (1953).
    [CrossRef]
  16. L. D. Kaplan, in The Atmosphere and Sea in Motion, Rossby Memorial Volume (Rockefeller Inst. Press, New York, 1959), p. 170.
  17. U.S. Standard Atmosphere, 1962(U.S. Govt. Printing Office, Washington, D.C., 1962).
  18. B. Bolin, C. D. Keeling, J. Geophys. Res. 68, 3899 (1963).
    [CrossRef]
  19. S. R. Drayson, NASA Technical Note TN D-2744, April1965.
  20. D. E. Burch, D. A. Gryvnak, D. Williams, Appl. Opt. 1, 759 (1962).
    [CrossRef]
  21. G. Yamamoto, T. Sasamori, Sci. Repts. Tohoku Univ., 5th Series (Geophysics) 10, 37 (1958).

1965 (1)

C. Young, J. Quant. Spectry. Radiative Transfer 5, 549 (1965).
[CrossRef]

1964 (3)

D. M. Gates, R. F. Calfee, D. W. Hansen, W. S. Benedict, NBS Monograph 71(1964).

B. H. Winters, S. Silverman, W. S. Benedict, J. Quant. Spectry. Radiative Transfer 4, 527 (1964).
[CrossRef]

J. H. Shaw, J. T. Houghton, Appl. Opt. 3, 773 (1964).
[CrossRef]

1963 (2)

B. Bolin, C. D. Keeling, J. Geophys. Res. 68, 3899 (1963).
[CrossRef]

D. M. Gates, R. F. Calfee, D. W. Hansen, Appl. Opt. 2, 117 (1963).
[CrossRef]

1962 (2)

1961 (2)

W. Hitschfeld, J. T. Houghton, Quart. J. Royal Meteorol. Soc. 87, 562 (1961).
[CrossRef]

R. F. Madden, J. Chem. Phys. 35, 2083 (1961).
[CrossRef]

1958 (2)

G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).
[CrossRef]

G. Yamamoto, T. Sasamori, Sci. Repts. Tohoku Univ., 5th Series (Geophysics) 10, 37 (1958).

1956 (1)

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

1953 (2)

W. L. Godson, Quart. J. Royal Meteorol. Soc. 79, 367 (1953).
[CrossRef]

G. N. Plass, D. I. Fivel, Astrophys. J. 117, 225 (1953).
[CrossRef]

1952 (1)

A. R. Curtis, Quart. J. Royal Meteorol. Soc. 78, 638 (1952).
[CrossRef]

Benedict, W. S.

B. H. Winters, S. Silverman, W. S. Benedict, J. Quant. Spectry. Radiative Transfer 4, 527 (1964).
[CrossRef]

D. M. Gates, R. F. Calfee, D. W. Hansen, W. S. Benedict, NBS Monograph 71(1964).

Bolin, B.

B. Bolin, C. D. Keeling, J. Geophys. Res. 68, 3899 (1963).
[CrossRef]

Burch, D. E.

Calfee, R. F.

D. M. Gates, R. F. Calfee, D. W. Hansen, W. S. Benedict, NBS Monograph 71(1964).

D. M. Gates, R. F. Calfee, D. W. Hansen, Appl. Opt. 2, 117 (1963).
[CrossRef]

Curtis, A. R.

A. R. Curtis, Quart. J. Royal Meteorol. Soc. 78, 638 (1952).
[CrossRef]

Drayson, S. R.

S. R. Drayson, NASA Technical Note TN D-2744, April1965.

Eggers, D. F.

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

Fivel, D. I.

G. N. Plass, D. I. Fivel, Astrophys. J. 117, 225 (1953).
[CrossRef]

Gates, D. M.

D. M. Gates, R. F. Calfee, D. W. Hansen, W. S. Benedict, NBS Monograph 71(1964).

D. M. Gates, R. F. Calfee, D. W. Hansen, Appl. Opt. 2, 117 (1963).
[CrossRef]

Godson, W. L.

W. L. Godson, Quart. J. Royal Meteorol. Soc. 79, 367 (1953).
[CrossRef]

Goody, R. M.

R. M. Goody, Atmospheric Radiation I: Theoretical Basis (Oxford Univ. Press, Oxford, 1964).

Gryvnak, D. A.

Hansen, D. W.

D. M. Gates, R. F. Calfee, D. W. Hansen, W. S. Benedict, NBS Monograph 71(1964).

D. M. Gates, R. F. Calfee, D. W. Hansen, Appl. Opt. 2, 117 (1963).
[CrossRef]

Hitschfeld, W.

W. Hitschfeld, J. T. Houghton, Quart. J. Royal Meteorol. Soc. 87, 562 (1961).
[CrossRef]

Houghton, J. T.

J. H. Shaw, J. T. Houghton, Appl. Opt. 3, 773 (1964).
[CrossRef]

W. Hitschfeld, J. T. Houghton, Quart. J. Royal Meteorol. Soc. 87, 562 (1961).
[CrossRef]

Kaplan, L. D.

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

L. D. Kaplan, in The Atmosphere and Sea in Motion, Rossby Memorial Volume (Rockefeller Inst. Press, New York, 1959), p. 170.

Keeling, C. D.

B. Bolin, C. D. Keeling, J. Geophys. Res. 68, 3899 (1963).
[CrossRef]

Madden, R. F.

R. F. Madden, J. Chem. Phys. 35, 2083 (1961).
[CrossRef]

Mitchell, A. C. G.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge Univ. Press, Cambridge, 1934).

Plass, G. N.

Sasamori, T.

G. Yamamoto, T. Sasamori, Sci. Repts. Tohoku Univ., 5th Series (Geophysics) 10, 37 (1958).

Shaw, J. H.

Silverman, S.

B. H. Winters, S. Silverman, W. S. Benedict, J. Quant. Spectry. Radiative Transfer 4, 527 (1964).
[CrossRef]

Stull, V. R.

Williams, D.

Winters, B. H.

B. H. Winters, S. Silverman, W. S. Benedict, J. Quant. Spectry. Radiative Transfer 4, 527 (1964).
[CrossRef]

Wyatt, P. J.

Yamamoto, G.

G. Yamamoto, T. Sasamori, Sci. Repts. Tohoku Univ., 5th Series (Geophysics) 10, 37 (1958).

Young, C.

C. Young, J. Quant. Spectry. Radiative Transfer 5, 549 (1965).
[CrossRef]

Zemansky, M. W.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge Univ. Press, Cambridge, 1934).

Appl. Opt. (3)

Astrophys. J. (1)

G. N. Plass, D. I. Fivel, Astrophys. J. 117, 225 (1953).
[CrossRef]

J. Chem. Phys. (2)

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

R. F. Madden, J. Chem. Phys. 35, 2083 (1961).
[CrossRef]

J. Geophys. Res. (1)

B. Bolin, C. D. Keeling, J. Geophys. Res. 68, 3899 (1963).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Quant. Spectry. Radiative Transfer (2)

B. H. Winters, S. Silverman, W. S. Benedict, J. Quant. Spectry. Radiative Transfer 4, 527 (1964).
[CrossRef]

C. Young, J. Quant. Spectry. Radiative Transfer 5, 549 (1965).
[CrossRef]

NBS Monograph (1)

D. M. Gates, R. F. Calfee, D. W. Hansen, W. S. Benedict, NBS Monograph 71(1964).

Quart. J. Royal Meteorol. Soc. (3)

A. R. Curtis, Quart. J. Royal Meteorol. Soc. 78, 638 (1952).
[CrossRef]

W. L. Godson, Quart. J. Royal Meteorol. Soc. 79, 367 (1953).
[CrossRef]

W. Hitschfeld, J. T. Houghton, Quart. J. Royal Meteorol. Soc. 87, 562 (1961).
[CrossRef]

Sci. Repts. Tohoku Univ. (1)

G. Yamamoto, T. Sasamori, Sci. Repts. Tohoku Univ., 5th Series (Geophysics) 10, 37 (1958).

Other (5)

S. R. Drayson, NASA Technical Note TN D-2744, April1965.

L. D. Kaplan, in The Atmosphere and Sea in Motion, Rossby Memorial Volume (Rockefeller Inst. Press, New York, 1959), p. 170.

U.S. Standard Atmosphere, 1962(U.S. Govt. Printing Office, Washington, D.C., 1962).

R. M. Goody, Atmospheric Radiation I: Theoretical Basis (Oxford Univ. Press, Oxford, 1964).

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge Univ. Press, Cambridge, 1934).

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Figures (9)

Fig. 1
Fig. 1

Equivalent widths for homogeneous paths at 0.5 mb pressure, 250°K, and frequency 700 cm−1, using pure Lorentz and mixed Doppler-Lorentz-broadening.

Fig. 2
Fig. 2

Maximum error in equivalent widths using Lorentz-broadening at low pressures.

Fig. 3
Fig. 3

Error in Curtis-Godson approximation for paths between 10 mb and 100 mb.

Fig. 4
Fig. 4

Maximum error in using Curtis-Godson approximation for paths between p and 1000 mb.

Fig. 5
Fig. 5

Regions of validity of line-shape integration methods.

Fig. 6
Fig. 6

Transmissivity averaged over 5-cm−1 intervals; vertical path starting outside the earth’s atmosphere to the indicated pressure levels.

Fig. 7
Fig. 7

Transmissivity for a vertical path starting outside the earth’s atmosphere down to given pressure levels. SIRS response function.

Fig. 8
Fig. 8

Comparison of SIRS transmission with corresponding transmission averaged over 5-cm−1 intervals, for a vertical path starting outside the earth’s atmosphere to the indicated pressure levels.

Fig. 9
Fig. 9

Integrated absorption between 495 cm−1 and 875 cm−1, at 0.2 atm and 300°K.

Equations (22)

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k ν = S π α L ( ν - ν 0 ) 2 + α L 2 ,
α L = α 0 ( p / p 0 ) ( T 0 / T ) ½ ,
k ν = k 0 y π - e - t 2 y 2 + ( x - t ) 2 d t ,
k 0 = S α D ( ln 2 π ) ½ , y = α L α D ( ln 2 ) ½ , x = ( ν - ν 0 ) α D ( ln 2 ) ½ .
α D = 3.58 × 10 - 7 ( T / M ) ½ ν 0 ,
k ν = k 0 exp ( - x 2 ) .
A = 0 [ 1 - exp ( - k ν u ) ] d ν .
γ ν = exp ( - k ν u ) .
k ν = i S i π α L ( ν - ν i ) 2 + α L 2 ,
S i π α L ( ν - ν i ) 2 + α L by S i π α L ( ν - ν i ) 2 ,
k = i S i π α L ( ν - ν i ) 2
γ ν = exp [ - p 1 p 2 k ν d u ] , p 2 > p 1 ,
d u = c d p ,
γ ν = exp - [ c p 1 p 2 k ν d p ] .
γ ν = exp { - c i S i 2 π α 0 ln [ α 0 2 p 2 2 + ( ν - ν i ) 2 α 0 2 p 1 2 + ( ν - ν i ) 2 ] }
γ ν = exp [ - c i S i α 0 2 π p 2 2 - p 1 2 ( ν - ν i ) 2 + α 0 2 4 ( p 1 + p 2 ) 2 ] .
τ ν = c p 1 p 2 k ν d p = p 1 p 2 k 0 y c π - e - t 2 y 2 + ( x - t ) 2 d t d p .
τ ν = - p 1 p 2 k 0 y c π e - t 2 d p y 2 + ( x - t ) 2 d t .
τ ν = k 0 c 2 π y 0 - e - t 2 ln [ y 0 2 p 2 2 + ( x - t ) 2 y 0 2 p 1 2 + ( x - t ) 2 ] d t .
γ ν = exp [ - i = 1 n p i - 1 p i k ν d u ] ,
γ ¯ = ν γ ν ϕ ( ν ) d ν ν ϕ ( ν ) d ν .
A = 495 875 A ν d ν

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