Abstract

The infrared transmittance of water vapor has been calculated over a wide range of path lengths, pressures, and temperatures. All contributing lines whose relative intensity is greater than 10−8 times that of the strongest line in any particular band have been included in the calculation. In addition, the contributions from the four major isotopic species have been included. Although the vibrational analysis has been done exactly, the rotational contributions for some of the weaker lines have been calculated from the symmetric rotator approximation. This approximation was not used for the frequencies and intensities of the stronger lines below 3400 cm−1 which are correctly included in the calculations. The final transmittance tables have been generated using the quasi-random model of molecular band absorption.

© 1964 Optical Society of America

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References

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  1. “The Infrared Absorption of Water Vapor”, Report SSD-TDR-62-127, Volume II, Space Systems Division, Air Force Systems Command, Los Angeles, California (1962).
  2. “The Infrared Absorption of Carbon Dioxide”, Report SSD-TDR-62-127, Volume III, Space Systems Division, Air Force Systems Command, Los Angeles, California (1963). Volumes II and III of this report contain improvements and correct computational errors of an earlier version, Aeronutronic reports U-1504 and U-1505, which should be discarded.
  3. S. S. Ballard, L. Larmore, S. Passman, “Fundamentals of Infrared for Military Application”, The Rand Corporation, R-297C (1956) Conf.
  4. V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).
  5. P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
    [CrossRef]
  6. D. E. Burch, E. B. Singleton, W. L. France, D. Williams, “Infrared Absorption by Carbon Dioxide, Water Vapor, and Minor Atmospheric Constituents”, AF 19(604)-2633, The Ohio State University, December1960.
  7. G. Herzberg, Infrared and Raman Spectra (Van Nostrand, Princeton, N.J., 1945).
  8. B. T. Darling, D. M. Dennison, Phys. Rev. 57, 128 (1940).
    [CrossRef]
  9. W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
    [CrossRef]
  10. V. R. Stull, P. J. Wyatt, G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
    [CrossRef]
  11. P. C. Cross, R. M. Hainer, G. W. King, J. Chem. Phys. 11, 27 (1943); J. Chem. Phys. 12, 210 (1944).
    [CrossRef]
  12. S. S. Penner, A. Thomson, Tech. Rept. No. 25, Contract No. Nonr 220(03) NR 015401, Guggenheim Jet Propulsion Center, California Institute of Technology.
  13. W. S. Benedict, Bull. Am. Phys. Soc. 23, 54 (1948).
  14. W. S. Benedict, Phys. Rev. 74, 1246 (1948).
  15. W. S. Benedict, H. H. Claassen, J. H. Shaw, J. Research Natl. Bur. Standards 49, 91 (1951).
    [CrossRef]
  16. E. F. Barker, W. W. Sleator, J. Chem. Phys. 3, 660 (1935).
    [CrossRef]
  17. H. H. Nielsen, Phys. Rev. 59, 565 (1941).
    [CrossRef]
  18. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949).
  19. H. Mayer, “Methods of Opacity Calculations,” Los Alamos Scientific Laboratory Report No. LA647 (1947).
  20. R. M. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
    [CrossRef]
  21. G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958); J. Opt. Soc. Am. 50, 868 (1960).
    [CrossRef]
  22. R. Ladenberg, F. Reiche, Ann. Physik 42, 181 (1913).
    [CrossRef]
  23. W. S. Benedict, private communication.

1962

P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[CrossRef]

1961

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

1958

1956

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

1952

R. M. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
[CrossRef]

1951

W. S. Benedict, H. H. Claassen, J. H. Shaw, J. Research Natl. Bur. Standards 49, 91 (1951).
[CrossRef]

1948

W. S. Benedict, Bull. Am. Phys. Soc. 23, 54 (1948).

W. S. Benedict, Phys. Rev. 74, 1246 (1948).

1943

P. C. Cross, R. M. Hainer, G. W. King, J. Chem. Phys. 11, 27 (1943); J. Chem. Phys. 12, 210 (1944).
[CrossRef]

1941

H. H. Nielsen, Phys. Rev. 59, 565 (1941).
[CrossRef]

1940

B. T. Darling, D. M. Dennison, Phys. Rev. 57, 128 (1940).
[CrossRef]

1935

E. F. Barker, W. W. Sleator, J. Chem. Phys. 3, 660 (1935).
[CrossRef]

1913

R. Ladenberg, F. Reiche, Ann. Physik 42, 181 (1913).
[CrossRef]

Ballard, S. S.

S. S. Ballard, L. Larmore, S. Passman, “Fundamentals of Infrared for Military Application”, The Rand Corporation, R-297C (1956) Conf.

Barker, E. F.

E. F. Barker, W. W. Sleator, J. Chem. Phys. 3, 660 (1935).
[CrossRef]

Benedict, W. S.

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

W. S. Benedict, H. H. Claassen, J. H. Shaw, J. Research Natl. Bur. Standards 49, 91 (1951).
[CrossRef]

W. S. Benedict, Bull. Am. Phys. Soc. 23, 54 (1948).

W. S. Benedict, Phys. Rev. 74, 1246 (1948).

W. S. Benedict, private communication.

Burch, D. E.

D. E. Burch, E. B. Singleton, W. L. France, D. Williams, “Infrared Absorption by Carbon Dioxide, Water Vapor, and Minor Atmospheric Constituents”, AF 19(604)-2633, The Ohio State University, December1960.

Claassen, H. H.

W. S. Benedict, H. H. Claassen, J. H. Shaw, J. Research Natl. Bur. Standards 49, 91 (1951).
[CrossRef]

Cross, P. C.

P. C. Cross, R. M. Hainer, G. W. King, J. Chem. Phys. 11, 27 (1943); J. Chem. Phys. 12, 210 (1944).
[CrossRef]

Darling, B. T.

B. T. Darling, D. M. Dennison, Phys. Rev. 57, 128 (1940).
[CrossRef]

Dennison, D. M.

B. T. Darling, D. M. Dennison, Phys. Rev. 57, 128 (1940).
[CrossRef]

France, W. L.

D. E. Burch, E. B. Singleton, W. L. France, D. Williams, “Infrared Absorption by Carbon Dioxide, Water Vapor, and Minor Atmospheric Constituents”, AF 19(604)-2633, The Ohio State University, December1960.

Gailar, N.

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

Goody, R. M.

R. M. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
[CrossRef]

Hainer, R. M.

P. C. Cross, R. M. Hainer, G. W. King, J. Chem. Phys. 11, 27 (1943); J. Chem. Phys. 12, 210 (1944).
[CrossRef]

Herzberg, G.

G. Herzberg, Infrared and Raman Spectra (Van Nostrand, Princeton, N.J., 1945).

King, G. W.

P. C. Cross, R. M. Hainer, G. W. King, J. Chem. Phys. 11, 27 (1943); J. Chem. Phys. 12, 210 (1944).
[CrossRef]

Ladenberg, R.

R. Ladenberg, F. Reiche, Ann. Physik 42, 181 (1913).
[CrossRef]

Larmore, L.

S. S. Ballard, L. Larmore, S. Passman, “Fundamentals of Infrared for Military Application”, The Rand Corporation, R-297C (1956) Conf.

Mayer, H.

H. Mayer, “Methods of Opacity Calculations,” Los Alamos Scientific Laboratory Report No. LA647 (1947).

Nielsen, H. H.

H. H. Nielsen, Phys. Rev. 59, 565 (1941).
[CrossRef]

Passman, S.

S. S. Ballard, L. Larmore, S. Passman, “Fundamentals of Infrared for Military Application”, The Rand Corporation, R-297C (1956) Conf.

Penner, S. S.

S. S. Penner, A. Thomson, Tech. Rept. No. 25, Contract No. Nonr 220(03) NR 015401, Guggenheim Jet Propulsion Center, California Institute of Technology.

Plass, G. N.

V. R. Stull, P. J. Wyatt, G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[CrossRef]

P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958); J. Opt. Soc. Am. 50, 868 (1960).
[CrossRef]

Plyler, E. K.

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

Reiche, F.

R. Ladenberg, F. Reiche, Ann. Physik 42, 181 (1913).
[CrossRef]

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949).

Shaw, J. H.

W. S. Benedict, H. H. Claassen, J. H. Shaw, J. Research Natl. Bur. Standards 49, 91 (1951).
[CrossRef]

Singleton, E. B.

D. E. Burch, E. B. Singleton, W. L. France, D. Williams, “Infrared Absorption by Carbon Dioxide, Water Vapor, and Minor Atmospheric Constituents”, AF 19(604)-2633, The Ohio State University, December1960.

Sleator, W. W.

E. F. Barker, W. W. Sleator, J. Chem. Phys. 3, 660 (1935).
[CrossRef]

Stull, V. R.

V. R. Stull, P. J. Wyatt, G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[CrossRef]

P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

Thomson, A.

S. S. Penner, A. Thomson, Tech. Rept. No. 25, Contract No. Nonr 220(03) NR 015401, Guggenheim Jet Propulsion Center, California Institute of Technology.

Williams, D.

D. E. Burch, E. B. Singleton, W. L. France, D. Williams, “Infrared Absorption by Carbon Dioxide, Water Vapor, and Minor Atmospheric Constituents”, AF 19(604)-2633, The Ohio State University, December1960.

Wyatt, P. J.

V. R. Stull, P. J. Wyatt, G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[CrossRef]

P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

Ann. Physik

R. Ladenberg, F. Reiche, Ann. Physik 42, 181 (1913).
[CrossRef]

Bull. Am. Phys. Soc.

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

W. S. Benedict, Bull. Am. Phys. Soc. 23, 54 (1948).

J. Chem. Phys.

E. F. Barker, W. W. Sleator, J. Chem. Phys. 3, 660 (1935).
[CrossRef]

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[CrossRef]

P. C. Cross, R. M. Hainer, G. W. King, J. Chem. Phys. 11, 27 (1943); J. Chem. Phys. 12, 210 (1944).
[CrossRef]

J. Opt. Soc. Am.

J. Research Natl. Bur. Standards

W. S. Benedict, H. H. Claassen, J. H. Shaw, J. Research Natl. Bur. Standards 49, 91 (1951).
[CrossRef]

Phys. Rev.

B. T. Darling, D. M. Dennison, Phys. Rev. 57, 128 (1940).
[CrossRef]

H. H. Nielsen, Phys. Rev. 59, 565 (1941).
[CrossRef]

W. S. Benedict, Phys. Rev. 74, 1246 (1948).

Quart. J. Roy. Meteorol. Soc.

R. M. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
[CrossRef]

Other

W. S. Benedict, private communication.

“The Infrared Absorption of Water Vapor”, Report SSD-TDR-62-127, Volume II, Space Systems Division, Air Force Systems Command, Los Angeles, California (1962).

“The Infrared Absorption of Carbon Dioxide”, Report SSD-TDR-62-127, Volume III, Space Systems Division, Air Force Systems Command, Los Angeles, California (1963). Volumes II and III of this report contain improvements and correct computational errors of an earlier version, Aeronutronic reports U-1504 and U-1505, which should be discarded.

S. S. Ballard, L. Larmore, S. Passman, “Fundamentals of Infrared for Military Application”, The Rand Corporation, R-297C (1956) Conf.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949).

H. Mayer, “Methods of Opacity Calculations,” Los Alamos Scientific Laboratory Report No. LA647 (1947).

D. E. Burch, E. B. Singleton, W. L. France, D. Williams, “Infrared Absorption by Carbon Dioxide, Water Vapor, and Minor Atmospheric Constituents”, AF 19(604)-2633, The Ohio State University, December1960.

G. Herzberg, Infrared and Raman Spectra (Van Nostrand, Princeton, N.J., 1945).

S. S. Penner, A. Thomson, Tech. Rept. No. 25, Contract No. Nonr 220(03) NR 015401, Guggenheim Jet Propulsion Center, California Institute of Technology.

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Figures (3)

Fig. 1
Fig. 1

Comparison of the theoretical calculations of the transmittance of the 1.87-μ band with the experimental measurements of Burch et al.6 The theoretical values have been averaged over a 20 cm−1 interval.

Fig. 2
Fig. 2

Comparison of the theoretical calculations of the transmittance of the 6.3-μ band with the experimental measurements of Burch et al.6 The theoretical values have been averaged over a 20 cm−1 interval.

Fig. 3
Fig. 3

Comparison of the theoretical calculations of the transmittance of the 6.3-μ band with the experimental measurements of Burch et al.6 The theoretical values have been averaged over a 20 cm−1 interval.

Tables (5)

Tables Icon

Table I The Vibrational Constants for Water Vapor

Tables Icon

Table II Rotational Constants of Water Vapor

Tables Icon

Table III Vibrational Transitions and Their Corresponding Relative Intensities

Tables Icon

Table IV Water Vapor Normalization Constants

Tables Icon

Table V Infrared Transmittance of Water Vapor at 1-Atm Pressure, 300°K, and Averaged Over 100 cm−1 Intervals

Equations (21)

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G 0 ( υ 1 , υ 2 , υ 3 ) = i = 1 3 ω i ( υ i + 1 2 ) + i = 1 3 j > i x i j ( υ i + 1 2 ) ( y j + 1 2 ) ,
ω 3 2 = 1 4 π 2 c 2 ( 1 m ( H ) + 2 sin 2 α m ( O ) ) 8.520 × 10 5 ,
ω 1 2 + ω 2 2 = 1 4 π 2 c 2 ( 14.690 × 10 5 6.140 × 10 5 sin α m ( H ) + 21.232 × 10 5 cos 2 α m ( O ) ) ,
ω 1 2 ω 2 2 = 1 16 π 4 c 4 ( 2 m ( H ) + m ( O ) [ m ( H ) ] 2 m ( O ) 33.824 × 10 5 cos 2 α ) ,
x i j ( isotope ) = x i j ω i ( isotope ) ω j ( isotope ) ω i ω j .
W υ 1 2 , υ 2 , υ 3 + 2 υ 1 , υ 2 , υ 3 = 1 2 γ [ υ 1 ( υ 1 1 ) ( υ 3 + 1 ) ( υ 3 + 2 ) ] 1 / 2 ,
W υ 1 + 1 , υ 2 2 , υ 3 υ 1 , υ 2 , υ 3 = 1 2 γ [ ( υ 1 + 1 ) υ 2 ( υ 2 1 ) ] 1 / 2 ,
F υ ( J , K ) = B ¯ υ 2 J ( J + 1 ) + ( B υ 1 B ¯ υ 2 ) K 2 ,
B ¯ υ 2 = 1 2 ( B υ 2 + B υ 3 ) ,
B υ n = B e n m = 1 3 α n m ( υ m + 1 2 ) ,
B e n ( isotope ) = B e n ( m = 1 3 ρ m ) 2 / 3
α n m ( isotope ) = α n m ( ρ n ) 3 ,
S = 8 π 3 3 h c ω N Q p exp [ E υ R k T ] | M | 2 [ 1 exp ( h ω k T ) ] ,
S K J υ K J = C υ υ ω υ K J υ K J ω υ υ exp [ h c F υ ( J , K ) k T ] S ( J , K ) ,
S ( J , K ) = { ( J + 2 ± K ) ( J + 1 ± K ) 2 ( J + 1 ) Δ J = + 1 ( J + 1 ± K ) ( J K ) ( 2 J + 1 ) 2 J ( J + 1 ) Δ J = 0 ( J 1 K ) ( J K ) 2 J Δ J = 1
S ( J , K ) = { ( J + 1 + K ) ( J + 1 K ) J + 1 Δ J = + 1 ( 2 J + 1 ) K 2 J ( J + 1 ) Δ J = 0 ( J + K ) ( J K ) J Δ J = 1
C υ υ = 8 π 3 3 h c ω υ υ N Q p exp [ h c G ( υ ) k T ] | R υ υ | 2 ,
C υ υ ( T ) = | R υ υ | 2 | R υ * υ * | 2 C υ * υ * ( T 0 ) N ( T ) Q ( T 0 ) N ( T 0 ) Q ( T ) × exp [ + G ( υ * ) h c k T 0 G ( υ ) h c k T ] .
Q ( T ) = 1 = i 3 { 1 exp [ h c ω i 0 k T ] } 1 exp ( B e 2 1 / 2 B e 3 1 / 2 4 ( k T / h c ) ) × [ π ( k T / h c ) 3 B e 1 B e 2 B e 3 ] 1 2 [ 1 + 1 12 ( 1 B e 2 1 / 2 B e 3 1 / 2 B e 1 ) B e 2 1 / 2 B e 3 1 / 2 ( k T / h c ) ] × exp [ h c G ( 0 ) k T ] .
b ( ν , ν i ) = ( α / π ) [ ( ν ν i ) 2 + α 2 ] 1 ,
ξ o k = S k p 0 / π α 0 ,

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