Abstract

Rayleigh-scattering cross sections and volume-scattering coefficients are computed for standard air; they incorporate the variation of the depolarization factor with wavelength. Rayleigh optical depths are then calculated for the 1962 U.S. Standard Atmosphere and for five supplementary models. Analytic formulas are derived for each of the parameters listed. The new optical depths can be 1.3% lower to 3% higher at midvisible wavelengths and up to 10% higher in the UV region compared with previous calculations, in which a constant or incorrect depolarization factor was used. The dispersion of the depolarization factor is also shown to affect the Rayleigh phase function slightly, by approximately 1% in the forward, backscattered, and 90° scattering-angle directions.

© 1995 Optical Society of America

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References

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  1. E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles, 1st ed. (Wiley, New York, 1976), Chap. 4, pp. 176–215.
  2. R. Penndorf, “Tables of the refractive index for standard air and the Rayleigh scattering coefficient for the spectral region between 0.2 and 20.0 μ and their application to atmospheric optics,” J. Opt. Soc. Am. 47, 176–182 (1957).
    [CrossRef]
  3. P. M. Teillet, “Rayleigh optical depth comparisons from various sources,” Appl. Opt. 29, 1897–1900 (1990).
    [CrossRef] [PubMed]
  4. A. T. Young, “Rayleigh scattering,” Appl. Opt. 20, 533–535 (1981).
    [CrossRef] [PubMed]
  5. B. Edlen, “Dispersion of standard air,” J. Opt. Soc. Am. 43, 339–344 (1953).
    [CrossRef]
  6. L. Elterman, “Atmospheric attenuation model, in the ultraviolet, the visible, and the infrared windows for altitudes to 50 km,” Environ. Res. Paper 46 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1964).
  7. L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km, 1968,” AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1968).
  8. U.S. Standard Atmosphere, 1962 (U.S. Government Printing Office, Washington, D.C., 1962).
  9. F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.
  10. F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).
  11. F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).
  12. W. A. Margraf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–476 (1969).
    [CrossRef]
  13. D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432–436 (1977).
    [CrossRef]
  14. U.S. Standard Atmosphere Supplement 1966 (U.S. Government Printing Office, Washington, D.C., 1966).
  15. C. Fröhlich, G. E. Shaw, “New determination of Rayleigh scattering in the terrestrial atmosphere,” Appl. Opt. 19, 1773–1775 (1980).
    [CrossRef] [PubMed]
  16. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, J. S. Garing, F. E. Volz, “Optical properties of the atmosphere,” AFCRL Environ. Res. Paper 331 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1975).
  17. B. Edlen, “The refractive index of air,” Meteorology 2, 71–80 (1966).
  18. E. R. Peck, K. Reeder, “Dispersion of air,” J. Opt. Soc. Am. 62, 958–962 (1972).
    [CrossRef]
  19. A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980).
    [CrossRef] [PubMed]
  20. A. T. Young, “On the Rayleigh-scattering optical depth of the atmosphere,” J. Appl. Meteorol. 20, 328–330 (1981).
    [CrossRef]
  21. A. T. Young, “Rayleigh scattering,” Phys. Today 35, (1), 42–48 (1982).
    [CrossRef]
  22. D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
    [CrossRef]
  23. M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
    [CrossRef]
  24. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL-72-0497, AD 753 075 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1972), pp. 2–8.
  25. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), Chap. 1, p. 49.

1990 (1)

1984 (2)

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[CrossRef]

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[CrossRef]

1982 (1)

A. T. Young, “Rayleigh scattering,” Phys. Today 35, (1), 42–48 (1982).
[CrossRef]

1981 (2)

A. T. Young, “Rayleigh scattering,” Appl. Opt. 20, 533–535 (1981).
[CrossRef] [PubMed]

A. T. Young, “On the Rayleigh-scattering optical depth of the atmosphere,” J. Appl. Meteorol. 20, 328–330 (1981).
[CrossRef]

1980 (2)

1977 (1)

D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432–436 (1977).
[CrossRef]

1972 (1)

1969 (1)

W. A. Margraf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–476 (1969).
[CrossRef]

1966 (1)

B. Edlen, “The refractive index of air,” Meteorology 2, 71–80 (1966).

1957 (1)

1953 (1)

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

Anderson, G. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

Bates, D. R.

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), Chap. 1, p. 49.

Chetwynd, J. H.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

Clough, S. A.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

Edlen, B.

B. Edlen, “The refractive index of air,” Meteorology 2, 71–80 (1966).

B. Edlen, “Dispersion of standard air,” J. Opt. Soc. Am. 43, 339–344 (1953).
[CrossRef]

Elterman, L.

L. Elterman, “Atmospheric attenuation model, in the ultraviolet, the visible, and the infrared windows for altitudes to 50 km,” Environ. Res. Paper 46 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1964).

L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km, 1968,” AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1968).

Fenn, R. W.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL-72-0497, AD 753 075 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1972), pp. 2–8.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, J. S. Garing, F. E. Volz, “Optical properties of the atmosphere,” AFCRL Environ. Res. Paper 331 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1975).

Fröhlich, C.

Gallery, W. O.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, J. S. Garing, F. E. Volz, “Optical properties of the atmosphere,” AFCRL Environ. Res. Paper 331 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1975).

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL-72-0497, AD 753 075 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1972), pp. 2–8.

Griggs, M.

W. A. Margraf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–476 (1969).
[CrossRef]

Hoyt, D. V.

D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432–436 (1977).
[CrossRef]

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

Margraf, W. A.

W. A. Margraf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–476 (1969).
[CrossRef]

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles, 1st ed. (Wiley, New York, 1976), Chap. 4, pp. 176–215.

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL-72-0497, AD 753 075 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1972), pp. 2–8.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, J. S. Garing, F. E. Volz, “Optical properties of the atmosphere,” AFCRL Environ. Res. Paper 331 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1975).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

Nicolet, M.

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[CrossRef]

Peck, E. R.

Penndorf, R.

Reeder, K.

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, J. S. Garing, F. E. Volz, “Optical properties of the atmosphere,” AFCRL Environ. Res. Paper 331 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1975).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL-72-0497, AD 753 075 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1972), pp. 2–8.

Shaw, G. E.

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

Teillet, P. M.

Volz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL-72-0497, AD 753 075 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1972), pp. 2–8.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, J. S. Garing, F. E. Volz, “Optical properties of the atmosphere,” AFCRL Environ. Res. Paper 331 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1975).

Young, A. T.

A. T. Young, “Rayleigh scattering,” Phys. Today 35, (1), 42–48 (1982).
[CrossRef]

A. T. Young, “Rayleigh scattering,” Appl. Opt. 20, 533–535 (1981).
[CrossRef] [PubMed]

A. T. Young, “On the Rayleigh-scattering optical depth of the atmosphere,” J. Appl. Meteorol. 20, 328–330 (1981).
[CrossRef]

A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980).
[CrossRef] [PubMed]

Appl. Opt. (4)

J. Appl. Meteorol. (2)

A. T. Young, “On the Rayleigh-scattering optical depth of the atmosphere,” J. Appl. Meteorol. 20, 328–330 (1981).
[CrossRef]

D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432–436 (1977).
[CrossRef]

J. Atmos. Sci. (1)

W. A. Margraf, M. Griggs, “Aircraft measurements and calculations of the total downward flux of solar radiation as a function of altitude,” J. Atmos. Sci. 26, 469–476 (1969).
[CrossRef]

J. Opt. Soc. Am. (3)

Meteorology (1)

B. Edlen, “The refractive index of air,” Meteorology 2, 71–80 (1966).

Phys. Today (1)

A. T. Young, “Rayleigh scattering,” Phys. Today 35, (1), 42–48 (1982).
[CrossRef]

Planet. Space Sci. (2)

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[CrossRef]

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[CrossRef]

Other (11)

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL-72-0497, AD 753 075 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1972), pp. 2–8.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), Chap. 1, p. 49.

U.S. Standard Atmosphere Supplement 1966 (U.S. Government Printing Office, Washington, D.C., 1966).

E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles, 1st ed. (Wiley, New York, 1976), Chap. 4, pp. 176–215.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, J. S. Garing, F. E. Volz, “Optical properties of the atmosphere,” AFCRL Environ. Res. Paper 331 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1975).

L. Elterman, “Atmospheric attenuation model, in the ultraviolet, the visible, and the infrared windows for altitudes to 50 km,” Environ. Res. Paper 46 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1964).

L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km, 1968,” AFCRL-68-0153 (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1968).

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

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, R. W. Fenn, R. A. McClatchey, “Atmospheric transmittance/radiance: computer code lowtran 5,” AFGL-TR-80-0067 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1980), p. 56.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users Guide to lowtran 7,” AFGL-TR-88-0177 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1988).

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Figures (4)

Fig. 1
Fig. 1

Dispersion of the depolarization factor with wavelength (adapted from Bates22).

Fig. 2
Fig. 2

Comparison of the total Rayleigh-scattering cross section as computed in this paper (see Table 2) with those calculated by Penndorf,2 Bates,22 and Nicolet.23 The percent difference is defined as 100[x B (λ) − x i (λ)]/x B (λ), where x B is the cross section computed here at wavelength λ and x i is the cross section at λ of Penndorf,2 Bates,22 or Nicolet.23

Fig. 3
Fig. 3

Comparison of the Rayleigh phase function at 0.5 μm computed with and without taking into account the effect of molecular anisotropy. The percent difference is defined as in Fig. 2, where x B now represents the phase function computed with molecular anisotropy included and x i represents the phase function computed without molecular anisotropy taken into account.

Fig. 4
Fig. 4

Comparison of the Rayleigh optical depth at 0-km altitude for the 1962 U.S. Standard Atmosphere8 as computed in this paper (see Table 4) with those optical depths calculated by Eltermann,7 Fröhlich and Shaw,15 along with Fröhlich and Shaw’s value15 multiplied by a 1.031 correction factor. The percent difference is defined as in Fig. 2, where x now represents optical depth.

Tables (5)

Tables Icon

Table 1 King Correction Factor F k , Depolarization Factor ρ n , and γ, a Term Used in the Rayleigh Phase Function (Ref. 22)

Tables Icon

Table 2 Total Rayleigh-Scattering Cross Section σ and Total Rayleigh Volume-Scattering Coefficient β s for Standard Air (P S = 1013.25 mbars, T S = 288.15 K)

Tables Icon

Table 3 Constants Used in Analytic Formulas for the Total Rayleigh-Scattering Cross Section and Total Rayleigh Volume-Scattering Coefficient (for Standard Air): σ or β = Aλ−( B + C λ+ D /λ)

Tables Icon

Table 4 Rayleigh Optical Depths at 0-km Altitude for Six Different Atmosphere Models

Tables Icon

Table 5 Constants Used in the Analytic Formula for the Optical Depth Along with the Surface Pressure and Temperature of Each Model Atmosphere Used in Table 4 a

Equations (17)

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σ ( λ ) = 24 π 3 ( n s 2 - 1 ) 2 λ 4 N s 2 ( n s 2 + 2 ) 2 ( 6 + 3 ρ n 6 - 7 ρ n ) ,
β ( λ , z ) = N ( z ) σ ( λ )
τ ( λ , z 0 ) = z 0 β ( λ , z ) d z .
( n s - 1 ) × 10 8 = 5 , 791 , 817 238.0185 - ( 1 / λ ) 2 + 167 , 909 57.362 - ( 1 / λ ) 2 ,
( n s - 1 ) × 10 8 = 8060.51 + 2 , 480 , 990 132.274 - ( 1 - λ ) 2 + 17 , 455.7 39.32957 - ( 1 / λ ) 2 .
F k = ( 6 + 3 ρ n 6 - 7 ρ n ) .
Percent Difference = 100 [ x B ( λ ) - x i ( λ ) x B ( λ ) ] ,
σ = A λ - ( B + C λ + D / λ ) ,
β s ( λ ) = N s σ ( λ ) ( 10 5 cm / km ) .
β = β s N N s = β s P P s T s T ,
P ray ( θ ) = ¾ ( 1 + cos 2 θ ) ,
P ray ( θ ) = 3 4 ( 1 + 2 γ ) [ ( 1 + 3 γ ) + ( 1 - γ ) cos 2 θ ] ,
γ = ρ n 2 - ρ n
β ( θ , λ , z ) = β ( λ , z ) 4 π P ray ( θ , λ ) ,
τ ( λ , z 0 ) = z 0 β s ( λ ) P ( z ) P s T s T ( z ) d z .
τ ( λ , z 0 ) = σ ( λ ) N col , z 0 ,
τ ( λ , z ) = τ ( λ , z 0 ) N col , z N col , z 0 τ ( λ , z 0 ) P ( z ) P ( z 0 ) .

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