Abstract

Single and multiple scattering contributions to the circumsolar radiation along the almucantar and sun vertical have been computed by a Gauss-Seidel solution to the radiative transfer equation. In the near forward direction, the multiple scattering contributions are significant for optical depths of the order of 0.4. However, the shape of the angular distribution of almucantar radiance up to 10° appears less sensitive to multiple scattering. The results have been compared against an existing radiative transfer code.

© 1978 Optical Society of America

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References

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  1. A. E. S. Green, A. Deepak, B. J. Lipofsky, Appl. Opt. 10, 1263 (1971).
    [CrossRef] [PubMed]
  2. R. D. McPeters, A. E. S. Green, Appl. Opt. 15, 2457 (1972).
    [CrossRef]
  3. J. T. Twitty, J. J. Parent, J. A. Weinman, E. L. Eloranta, Appl. Opt. 15, 980 (1976).
    [CrossRef] [PubMed]
  4. A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), pp. 297–323.
  5. J. V. Dave, “Development of Programs for Computing Characteristics of U.V. Radiation,” NASA contract 5-21680 (1972).
  6. O. P. Bahethi, R. S. Fraser, “Effect of Molecular Anisotropy on the Intensity and Degree of Polarization of Light Scattered from Model Atmospheres,” Goddard Space Flight Center, Greenbelt, Md., X-910-75-52.
  7. J. G. Kuriyan, “Particulate Sizes from Polarization Measurements,” The UCLA International Conference on Radiation and Remote Probing of the Atmosphere, August1973, J. G. Kuriyan, Ed.
  8. J. G. Kuriyan, D. H. Phillips, R. C. Willson, J. R. Meteorol. Soc. 100, 665 (1974).
    [CrossRef]
  9. J. V. Dave, P. H. Furukawa, “Scattered Radiation in the Ozone Absorption Bands at Selected Levels of a Terrestrial Rayleigh Atmosphere,” Meteorological Monographs, Vol. 7, No. 29 (American Meteorological Society, Boston, 1966).
  10. K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere” (U. California, Berkeley, 1960).
  11. B. M. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
    [CrossRef]
  12. A. Deepak, G. P. Box, “Analytical Modeling of Atmospheric Aerosol Size Distributions,” IFAORS-106-78 (in preparation).

1976 (1)

1974 (1)

J. G. Kuriyan, D. H. Phillips, R. C. Willson, J. R. Meteorol. Soc. 100, 665 (1974).
[CrossRef]

1972 (1)

1971 (1)

1965 (1)

B. M. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

Bahethi, O. P.

O. P. Bahethi, R. S. Fraser, “Effect of Molecular Anisotropy on the Intensity and Degree of Polarization of Light Scattered from Model Atmospheres,” Goddard Space Flight Center, Greenbelt, Md., X-910-75-52.

Box, G. P.

A. Deepak, G. P. Box, “Analytical Modeling of Atmospheric Aerosol Size Distributions,” IFAORS-106-78 (in preparation).

Browning, S. R.

B. M. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

Coulson, K. L.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere” (U. California, Berkeley, 1960).

Dave, J. V.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere” (U. California, Berkeley, 1960).

J. V. Dave, “Development of Programs for Computing Characteristics of U.V. Radiation,” NASA contract 5-21680 (1972).

J. V. Dave, P. H. Furukawa, “Scattered Radiation in the Ozone Absorption Bands at Selected Levels of a Terrestrial Rayleigh Atmosphere,” Meteorological Monographs, Vol. 7, No. 29 (American Meteorological Society, Boston, 1966).

Deepak, A.

A. E. S. Green, A. Deepak, B. J. Lipofsky, Appl. Opt. 10, 1263 (1971).
[CrossRef] [PubMed]

A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), pp. 297–323.

A. Deepak, G. P. Box, “Analytical Modeling of Atmospheric Aerosol Size Distributions,” IFAORS-106-78 (in preparation).

Eloranta, E. L.

Fraser, R. S.

O. P. Bahethi, R. S. Fraser, “Effect of Molecular Anisotropy on the Intensity and Degree of Polarization of Light Scattered from Model Atmospheres,” Goddard Space Flight Center, Greenbelt, Md., X-910-75-52.

Furukawa, P. H.

J. V. Dave, P. H. Furukawa, “Scattered Radiation in the Ozone Absorption Bands at Selected Levels of a Terrestrial Rayleigh Atmosphere,” Meteorological Monographs, Vol. 7, No. 29 (American Meteorological Society, Boston, 1966).

Green, A. E. S.

Herman, B. M.

B. M. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

Kuriyan, J. G.

J. G. Kuriyan, D. H. Phillips, R. C. Willson, J. R. Meteorol. Soc. 100, 665 (1974).
[CrossRef]

J. G. Kuriyan, “Particulate Sizes from Polarization Measurements,” The UCLA International Conference on Radiation and Remote Probing of the Atmosphere, August1973, J. G. Kuriyan, Ed.

Lipofsky, B. J.

McPeters, R. D.

Parent, J. J.

Phillips, D. H.

J. G. Kuriyan, D. H. Phillips, R. C. Willson, J. R. Meteorol. Soc. 100, 665 (1974).
[CrossRef]

Sekera, Z.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere” (U. California, Berkeley, 1960).

Twitty, J. T.

Weinman, J. A.

Willson, R. C.

J. G. Kuriyan, D. H. Phillips, R. C. Willson, J. R. Meteorol. Soc. 100, 665 (1974).
[CrossRef]

Appl. Opt. (3)

J. Atmos. Sci. (1)

B. M. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

J. R. Meteorol. Soc. (1)

J. G. Kuriyan, D. H. Phillips, R. C. Willson, J. R. Meteorol. Soc. 100, 665 (1974).
[CrossRef]

Other (7)

J. V. Dave, P. H. Furukawa, “Scattered Radiation in the Ozone Absorption Bands at Selected Levels of a Terrestrial Rayleigh Atmosphere,” Meteorological Monographs, Vol. 7, No. 29 (American Meteorological Society, Boston, 1966).

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere” (U. California, Berkeley, 1960).

A. Deepak, G. P. Box, “Analytical Modeling of Atmospheric Aerosol Size Distributions,” IFAORS-106-78 (in preparation).

A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), pp. 297–323.

J. V. Dave, “Development of Programs for Computing Characteristics of U.V. Radiation,” NASA contract 5-21680 (1972).

O. P. Bahethi, R. S. Fraser, “Effect of Molecular Anisotropy on the Intensity and Degree of Polarization of Light Scattered from Model Atmospheres,” Goddard Space Flight Center, Greenbelt, Md., X-910-75-52.

J. G. Kuriyan, “Particulate Sizes from Polarization Measurements,” The UCLA International Conference on Radiation and Remote Probing of the Atmosphere, August1973, J. G. Kuriyan, Ed.

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Figures (2)

Fig. 1
Fig. 1

Almucantar radiance vs azimuth angle (0–180°) for ISS, IRT (Dave), and IRT (Our).

Fig. 2
Fig. 2

Schematic illustration of atmospheric layers, transmitted and source matrix contribution to sky radiance.

Tables (4)

Tables Icon

Table II Almucantar Radiances ISS, IRT (Dave), and IRS (Our) Obtained by SS Theory and Dave’s and Our Codes, Respectively

Tables Icon

Table III Sun-Vertical Radiances ISS, IRT (Dave), and IRT (Our) Obtained by SS Theory and Dave’s and Our RT Codes, Respectively

Tables Icon

Table IV Normalized Almucantar Radiance Values I SS N and I RT N and for Different θsun, τR, and τPS

Equations (4)

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I SS ( ψ ) = F sec θ exp ( τ sec θ ) [ τ R R ( ψ ) + τ PS P ( ψ ) ] / 4 π ,
n ( r ) = a r 2 exp ( b r ) , 0.03 r 2.0 μ m , b = 10.0 μ m 1 ,
I N I ( ψ ) / I ( 0 ) .
cos ψ = cos 2 θ sun + sin 2 θ sun cos ϕ

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