Abstract

Rayleigh optical depth values obtained from various computations, tabulations, and parameterizations are not always in good agreement. Important differences as large as 3 or 4% can arise depending on the choice of depolarization factor, the formula used for the refractive index of air, and the choice of standard values for columnar and molecular number densities. The fitting equations generally give rise to the largest differences. The use of different standard altitude profiles for atmospheric pressure and temperature causes a variation of 1% or less in Rayleigh optical depth.

© 1990 Optical Society of America

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References

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  1. 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 Microns and their Application to Atmospheric Optics,” J. Opt. Soc. Am. 47, 176–182 (1957).
    [CrossRef]
  2. L. Elterman, “Atmospheric Attenuation Model, in the Ultraviolet, the Visible, and the Infrared Windows for Altitudes to 50 KM,” Environmental Research Paper 46, AFCRL (1964).
  3. L. Elterman, “UV Visible, and IR Attenuation for Altitudes to 50KM, 1968,” AFCRL-68-0153 (1968), pp. 49.
  4. S. L. Valley, Ed., Handbook of Geophysics and Space Environment, (Air Force Cambridge Research Labs, 1965).
  5. V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere, (Wiley, New York, 1974).
  6. D. V. Hoyt, “A Redetermination of Rayleigh Optical Depth and Its Application to Selected Solar Radiation Problems,” J. Appl. Meteorol. 16, 432–436 (1977).
    [CrossRef]
  7. M. Iqbal, An Introduction to Solar Radiation, (Academic, New York, 1983) pp. 114–115.
  8. K. L. Coulson, Solar and Terrestrial Radiation—Methods and Measurements (Academic, New York, 1975), p. 43.
  9. C. Frohlich, G. E. Shaw, “New Determination of Rayleigh Scattering in the Terrestrial Atmosphere,” Appl. Opt. 19, 1773–1775 (1980).
    [CrossRef] [PubMed]
  10. B. Leckner, “The Spectral Distribution of Solar Radiation at the Earth’s Surface—Elements of a Model,” Sol. Energy 20, 143–150 (1978).
    [CrossRef]
  11. F. Moller, “Strahlung in der Unteren Atmosphare,” Handbuch der PhysikS. Flugge, Ed., (Springer-Verlag, New York, 1957).
    [CrossRef]
  12. J. Hill, B. Sturm, “Image-Based Atmospheric Correction of Multi-Temporal Thematic Mapper Data for Agricultural Land Cover Classification,” in Proceedings, IGARSS’88 Symposium, ESA SP-284, Edinburgh, Scotland (1988) pp. 895–899.
  13. W. A. Margraff, M. Griggs, “Aircraft Measurements and Calculations of the Total Downward Flux of Solar Radiation as a Function of Altitude,” J. Atmos. Sci., 26, 469–477 (1969).
    [CrossRef]
  14. R. T. Pinker, J. A. Ewing, “Modeling Surface Solar Radiation: Model Formulation and Validation,” J. Climate Appl. Meteorol. 24, 389–401 (1985).
    [CrossRef]
  15. F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL-TR-80-0067, Environmental Research Papers 697 (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1980).
  16. R. E. Bird, C. Riordan, “Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres,” J. Climate Appl. Meteorol. 25, 87–97 (1986).
    [CrossRef]
  17. J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
    [CrossRef]
  18. H. R. Gordon, J. W. Brown, R. H. Evans, “Exact Rayleigh Scattering Calculations for Use with the NIMBUS-7 Coastal Zone Color Scanner,” Appl. Opt. 27, 862–871 (1988).
    [CrossRef] [PubMed]
  19. A. T. Young, “Revised Depolarization Corrections for Atmospheric Extinction,” Appl. Opt. 19, 3427–3428 (1980).
    [CrossRef] [PubMed]
  20. A. T. Young, “Rayleigh Scattering,” Appl. Opt. 20, 533–535 (1981).
    [CrossRef] [PubMed]
  21. A. T. Young, “On the Rayleigh-Scattering Optical Depth of the Atmosphere,” J. Appl. Meteorol. 20, 328–330 (1981b).
    [CrossRef]
  22. E. P. Shettle, F. X. Kneizys, W. O. Gallery, “Suggested Modification to the Total Volume Molecular Scattering Coefficient in lowtran: Comment,” Appl. Opt. 19, 2873–2874 (1980).
  23. D. Tanre et al., Simulation of the Satellite Signal in the Solar Spectrum” (Laboratoire d’Optique Atmosphérique, Université des Sciences et Techniques de Lille, France, 1986).
  24. N. T. O’Neill, “A Radiative Transfer Experiment in an Urban Atmosphere,” Ph.D. Thesis, York U., Toronto (1982).
  25. B. Edlen, “The Refractive Index of Air,” Meteorol., 2, 71–80 (1966).
  26. B. Edlen, “Dispersion of Standard Air,” J. Opt. Soc. Am. 43, 339–344 (1953).
    [CrossRef]
  27. R. W. Fenn et al., Handbook of Geophysics and the Space EnvironmentA. S. Juras, Ed. (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1985), p. 18–7.
  28. E. R. Peck, K. Reeder, “Dispersion of Air,” J. Opt. Soc. Am. 62, 958–962 (1972).
    [CrossRef]
  29. F. X. Kneizys et al., “Atmospheric Transmission/Radiance: Computer Code lowtran 6,” AFGL-TR-83-0187, Environmental Research Papers 846 (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1983).
  30. P. M. Teillet, R. P. Santer, P. N. Slater, “Surface Reflectance Retrieval Methods and the Effects of Spectral Shifts on Sensor Response,” in preparation (1989).

1988 (1)

1986 (1)

R. E. Bird, C. Riordan, “Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres,” J. Climate Appl. Meteorol. 25, 87–97 (1986).
[CrossRef]

1985 (1)

R. T. Pinker, J. A. Ewing, “Modeling Surface Solar Radiation: Model Formulation and Validation,” J. Climate Appl. Meteorol. 24, 389–401 (1985).
[CrossRef]

1981 (2)

A. T. Young, “On the Rayleigh-Scattering Optical Depth of the Atmosphere,” J. Appl. Meteorol. 20, 328–330 (1981b).
[CrossRef]

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

1980 (3)

1978 (1)

B. Leckner, “The Spectral Distribution of Solar Radiation at the Earth’s Surface—Elements of a Model,” Sol. Energy 20, 143–150 (1978).
[CrossRef]

1977 (1)

D. V. Hoyt, “A Redetermination of Rayleigh Optical Depth and Its Application to Selected Solar Radiation Problems,” J. Appl. Meteorol. 16, 432–436 (1977).
[CrossRef]

1974 (1)

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

1972 (1)

1969 (1)

W. A. Margraff, M. Griggs, “Aircraft Measurements and Calculations of the Total Downward Flux of Solar Radiation as a Function of Altitude,” J. Atmos. Sci., 26, 469–477 (1969).
[CrossRef]

1968 (1)

L. Elterman, “UV Visible, and IR Attenuation for Altitudes to 50KM, 1968,” AFCRL-68-0153 (1968), pp. 49.

1966 (1)

B. Edlen, “The Refractive Index of Air,” Meteorol., 2, 71–80 (1966).

1957 (1)

1953 (1)

Bird, R. E.

R. E. Bird, C. Riordan, “Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres,” J. Climate Appl. Meteorol. 25, 87–97 (1986).
[CrossRef]

Brown, J. W.

Coulson, K. L.

K. L. Coulson, Solar and Terrestrial Radiation—Methods and Measurements (Academic, New York, 1975), p. 43.

Edlen, B.

B. Edlen, “The Refractive Index of Air,” Meteorol., 2, 71–80 (1966).

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

Elterman, L.

L. Elterman, “UV Visible, and IR Attenuation for Altitudes to 50KM, 1968,” AFCRL-68-0153 (1968), pp. 49.

L. Elterman, “Atmospheric Attenuation Model, in the Ultraviolet, the Visible, and the Infrared Windows for Altitudes to 50 KM,” Environmental Research Paper 46, AFCRL (1964).

Evans, R. H.

Ewing, J. A.

R. T. Pinker, J. A. Ewing, “Modeling Surface Solar Radiation: Model Formulation and Validation,” J. Climate Appl. Meteorol. 24, 389–401 (1985).
[CrossRef]

Fenn, R. W.

R. W. Fenn et al., Handbook of Geophysics and the Space EnvironmentA. S. Juras, Ed. (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1985), p. 18–7.

Frohlich, C.

Gallery, W. O.

Gordon, H. R.

Griggs, M.

W. A. Margraff, M. Griggs, “Aircraft Measurements and Calculations of the Total Downward Flux of Solar Radiation as a Function of Altitude,” J. Atmos. Sci., 26, 469–477 (1969).
[CrossRef]

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Hill, J.

J. Hill, B. Sturm, “Image-Based Atmospheric Correction of Multi-Temporal Thematic Mapper Data for Agricultural Land Cover Classification,” in Proceedings, IGARSS’88 Symposium, ESA SP-284, Edinburgh, Scotland (1988) pp. 895–899.

Hoyt, D. V.

D. V. Hoyt, “A Redetermination of Rayleigh Optical Depth and Its Application to Selected Solar Radiation Problems,” J. Appl. Meteorol. 16, 432–436 (1977).
[CrossRef]

Iqbal, M.

M. Iqbal, An Introduction to Solar Radiation, (Academic, New York, 1983) pp. 114–115.

Kneizys, F. X.

E. P. Shettle, F. X. Kneizys, W. O. Gallery, “Suggested Modification to the Total Volume Molecular Scattering Coefficient in lowtran: Comment,” Appl. Opt. 19, 2873–2874 (1980).

F. X. Kneizys et al., “Atmospheric Transmission/Radiance: Computer Code lowtran 6,” AFGL-TR-83-0187, Environmental Research Papers 846 (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1983).

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL-TR-80-0067, Environmental Research Papers 697 (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1980).

Leckner, B.

B. Leckner, “The Spectral Distribution of Solar Radiation at the Earth’s Surface—Elements of a Model,” Sol. Energy 20, 143–150 (1978).
[CrossRef]

Margraff, W. A.

W. A. Margraff, M. Griggs, “Aircraft Measurements and Calculations of the Total Downward Flux of Solar Radiation as a Function of Altitude,” J. Atmos. Sci., 26, 469–477 (1969).
[CrossRef]

Moller, F.

F. Moller, “Strahlung in der Unteren Atmosphare,” Handbuch der PhysikS. Flugge, Ed., (Springer-Verlag, New York, 1957).
[CrossRef]

O’Neill, N. T.

N. T. O’Neill, “A Radiative Transfer Experiment in an Urban Atmosphere,” Ph.D. Thesis, York U., Toronto (1982).

Peck, E. R.

Penndorf, R.

Pinker, R. T.

R. T. Pinker, J. A. Ewing, “Modeling Surface Solar Radiation: Model Formulation and Validation,” J. Climate Appl. Meteorol. 24, 389–401 (1985).
[CrossRef]

Reeder, K.

Riordan, C.

R. E. Bird, C. Riordan, “Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres,” J. Climate Appl. Meteorol. 25, 87–97 (1986).
[CrossRef]

Santer, R. P.

P. M. Teillet, R. P. Santer, P. N. Slater, “Surface Reflectance Retrieval Methods and the Effects of Spectral Shifts on Sensor Response,” in preparation (1989).

Shaw, G. E.

Shettle, E. P.

Slater, P. N.

P. M. Teillet, R. P. Santer, P. N. Slater, “Surface Reflectance Retrieval Methods and the Effects of Spectral Shifts on Sensor Response,” in preparation (1989).

Sturm, B.

J. Hill, B. Sturm, “Image-Based Atmospheric Correction of Multi-Temporal Thematic Mapper Data for Agricultural Land Cover Classification,” in Proceedings, IGARSS’88 Symposium, ESA SP-284, Edinburgh, Scotland (1988) pp. 895–899.

Tanre, D.

D. Tanre et al., Simulation of the Satellite Signal in the Solar Spectrum” (Laboratoire d’Optique Atmosphérique, Université des Sciences et Techniques de Lille, France, 1986).

Teillet, P. M.

P. M. Teillet, R. P. Santer, P. N. Slater, “Surface Reflectance Retrieval Methods and the Effects of Spectral Shifts on Sensor Response,” in preparation (1989).

Travis, L. D.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Young, A. T.

Zuev, V. E.

V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere, (Wiley, New York, 1974).

AFCRL-68-0153 (1)

L. Elterman, “UV Visible, and IR Attenuation for Altitudes to 50KM, 1968,” AFCRL-68-0153 (1968), pp. 49.

Appl. Opt. (5)

J. Appl. Meteorol. (2)

D. V. Hoyt, “A Redetermination of Rayleigh Optical Depth and Its Application to Selected Solar Radiation Problems,” J. Appl. Meteorol. 16, 432–436 (1977).
[CrossRef]

A. T. Young, “On the Rayleigh-Scattering Optical Depth of the Atmosphere,” J. Appl. Meteorol. 20, 328–330 (1981b).
[CrossRef]

J. Atmos. Sci. (1)

W. A. Margraff, M. Griggs, “Aircraft Measurements and Calculations of the Total Downward Flux of Solar Radiation as a Function of Altitude,” J. Atmos. Sci., 26, 469–477 (1969).
[CrossRef]

J. Climate Appl. Meteorol. (2)

R. T. Pinker, J. A. Ewing, “Modeling Surface Solar Radiation: Model Formulation and Validation,” J. Climate Appl. Meteorol. 24, 389–401 (1985).
[CrossRef]

R. E. Bird, C. Riordan, “Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres,” J. Climate Appl. Meteorol. 25, 87–97 (1986).
[CrossRef]

J. Opt. Soc. Am. (3)

Meteorol. (1)

B. Edlen, “The Refractive Index of Air,” Meteorol., 2, 71–80 (1966).

Sol. Energy (1)

B. Leckner, “The Spectral Distribution of Solar Radiation at the Earth’s Surface—Elements of a Model,” Sol. Energy 20, 143–150 (1978).
[CrossRef]

Space Sci. Rev. (1)

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Other (13)

D. Tanre et al., Simulation of the Satellite Signal in the Solar Spectrum” (Laboratoire d’Optique Atmosphérique, Université des Sciences et Techniques de Lille, France, 1986).

N. T. O’Neill, “A Radiative Transfer Experiment in an Urban Atmosphere,” Ph.D. Thesis, York U., Toronto (1982).

R. W. Fenn et al., Handbook of Geophysics and the Space EnvironmentA. S. Juras, Ed. (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1985), p. 18–7.

F. X. Kneizys et al., “Atmospheric Transmission/Radiance: Computer Code lowtran 6,” AFGL-TR-83-0187, Environmental Research Papers 846 (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1983).

P. M. Teillet, R. P. Santer, P. N. Slater, “Surface Reflectance Retrieval Methods and the Effects of Spectral Shifts on Sensor Response,” in preparation (1989).

F. Moller, “Strahlung in der Unteren Atmosphare,” Handbuch der PhysikS. Flugge, Ed., (Springer-Verlag, New York, 1957).
[CrossRef]

J. Hill, B. Sturm, “Image-Based Atmospheric Correction of Multi-Temporal Thematic Mapper Data for Agricultural Land Cover Classification,” in Proceedings, IGARSS’88 Symposium, ESA SP-284, Edinburgh, Scotland (1988) pp. 895–899.

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL-TR-80-0067, Environmental Research Papers 697 (Air Force Geophysics Laboratory, Hanscom AFB, MA, 1980).

M. Iqbal, An Introduction to Solar Radiation, (Academic, New York, 1983) pp. 114–115.

K. L. Coulson, Solar and Terrestrial Radiation—Methods and Measurements (Academic, New York, 1975), p. 43.

S. L. Valley, Ed., Handbook of Geophysics and Space Environment, (Air Force Cambridge Research Labs, 1965).

V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere, (Wiley, New York, 1974).

L. Elterman, “Atmospheric Attenuation Model, in the Ultraviolet, the Visible, and the Infrared Windows for Altitudes to 50 KM,” Environmental Research Paper 46, AFCRL (1964).

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Figures (4)

Fig. 1
Fig. 1

Percentage difference in the factor (n2 − 1)2 as a function of wavelength, where n is the refractive index of air. Factors based on formulas for n due to Edlen26 (E53), lowtran 515 (L5), and the 5S code23 (5S) are compared to the reference case from Edlen.25

Fig. 2
Fig. 2

Percentage difference in Rayleigh optical depths derived from various sources as a function of wavelength. The comparisons are with respect to values from Eq. (1). The different curves are distinguished by the label nearest to the short wavelength end of each curve, where the labels are defined as follows: C = Coulson;8 L5 = lowtran 5;15 E = Elterman;3 P = Penndorf;1 MG = Margraff and Griggs;13 M = Moller;11 HT = Hansen and Travis;17 L = Leckner;10 FS = Frohlich and Shaw;9 5S/88 = modified 5S code30 with γ = 0.0279, 5S/86 = 5S code23 with γ = 0.0139.

Fig. 3
Fig. 3

Absolute difference in Rayleigh optical depths derived from various sources as a function of wavelength. The comparisons are with respect to values from Eq. (1). The different curves are labeled as in Fig. 2.

Fig. 4
Fig. 4

Percentage difference in Rayleigh optical depths computed by the 5S code for a variety of standard altitude profiles for atmospheric pressure and temperature. The comparisons are between values from Eq. (1). Curve 7 is for a mid-latitude summer profile model and a depolarization factor of γ = 0.0139. The remaining curves are for γ = 0.0279 and the profile models are identified as follows: 1 = mid-latitude winter, 2 = sub-arctic winter, 3 = tropical, 4 = mid-latitude summer, 5 = U.S. Standard Atmosphere 1962, 6 = sub-arctic summer.

Equations (14)

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δ R = 8 π 3 ( n 2 - 1 ) 2 N c 3 λ 4 N s 2 ( 6 + 3 γ 6 - 7 γ ) ( p p o ) ( T o T ) ,
δ R = 0.008735 · λ - 4.08 .
δ R = 0.00879 · λ - 4.09 .
δ R = 0.0088 · λ ( - 4.15 + 0.2 · λ ) .
δ R = 0.00838 · λ α ,
α = - 3.916 - 0.074 · λ - 0.05 / λ .
δ R = λ - 4 · ( 115.6406 - 1.3366 · λ - 2 ) - 1 .
δ R = 0.008569 · λ - 4 ( 1 + 0.0113 · λ - 2 + 0.00013 · λ - 4 ) .
10 8 ( n - 1 ) = 8342.13 + 2406030 130 - λ - 2 + 15997 38.9 - λ - 2 ,
10 8 ( n - 1 ) = 6432.8 + 2949810 146 - λ - 2 + 25540 41 - λ - 2 .
10 6 ( n - 1 ) = 83.42 + 185.08 1 - ( 1 11.40 λ ) 2 + 4.11 1 - ( 1 6.24 λ ) 2 .
10 8 ( n - 1 ) = 5791817 238.0185 - λ - 2 + 167909 57.362 - λ - 2 .
10 6 ( n - 1 ) = ( 77.46 + 0.459 λ - 2 ) ( 1013.25 288.15 ) .
10 8 ( n - 1 ) = 6593.1 + 3010189.3 146 - λ - 2 + 26113.82 41 - λ - 2 .

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