Abstract

The scattering of visible light by clouds is calculated from an efficient Monte Carlo code which follows the multiple scattered path of the photon. The single scattering function is obtained from the Mie theory by integration over a particle size distribution appropriate for cumulus clouds at 0.7-μ wavelength. The photons are followed through a sufficient number of collisions and reflections from the lower surface (which may have any desired albedo) until they make a negligible contribution to the intensity. Various variance reduction techniques are used to improve the statistics. The cloud albedo and the mean optical path of the transmitted and reflected photons are given as a function of the solar zenith angle, optical thickness, and surface albedo. The numerous small angle scatterings of the photon in the direction of the incident beam are followed accurately and produce a greater penetration into the cloud than is obtained with a more isotropic and less realistic phase function.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Chandrasekhar, Radiative Transfer (Dover Publications, New York, 1960).
  2. S. Fritz, J. Meteorol. 11, 291 (1954).
    [CrossRef]
  3. S. Fritz, J. Opt. Soc. Am. 10, 820 (1955).
    [CrossRef]
  4. S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmos. Sci. 24, 70 (1967).
    [CrossRef]
  5. J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods (John Wiley & Sons, Inc., New York, 1964).
    [CrossRef]
  6. D. G. Collins, M. B. Wells, Monte Carlo Codes for the Study of Light Transport in the Atmosphere (Radiation Research Associates, Inc., Fort Worth, Texas, 1965), Vols. I and II.
  7. S. W. Churchill, C. M. Chu, J. A. Leacock, J. Chen, The Effect of Anisotropic Scattering on Radiative Transfer (The University of Michigan Research Institute, Ann Arbor, 1966).
  8. K. L. Coulson, G. M. Bouricius, E. L. Grany, J. Geophys. Res. 70, 4601 (1965).
    [CrossRef]
  9. D. Deirmendjian, Appl. Opt. 3, 187 (1964).
    [CrossRef]
  10. G. W. Kattawar, G. N. Plass, Appl. Opt. 6, 1377 (1967).
    [CrossRef] [PubMed]

1967 (2)

S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmos. Sci. 24, 70 (1967).
[CrossRef]

G. W. Kattawar, G. N. Plass, Appl. Opt. 6, 1377 (1967).
[CrossRef] [PubMed]

1965 (1)

K. L. Coulson, G. M. Bouricius, E. L. Grany, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

1964 (1)

1955 (1)

S. Fritz, J. Opt. Soc. Am. 10, 820 (1955).
[CrossRef]

1954 (1)

S. Fritz, J. Meteorol. 11, 291 (1954).
[CrossRef]

Bouricius, G. M.

K. L. Coulson, G. M. Bouricius, E. L. Grany, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover Publications, New York, 1960).

Chen, J.

S. W. Churchill, C. M. Chu, J. A. Leacock, J. Chen, The Effect of Anisotropic Scattering on Radiative Transfer (The University of Michigan Research Institute, Ann Arbor, 1966).

Chu, C. M.

S. W. Churchill, C. M. Chu, J. A. Leacock, J. Chen, The Effect of Anisotropic Scattering on Radiative Transfer (The University of Michigan Research Institute, Ann Arbor, 1966).

Churchill, S. W.

S. W. Churchill, C. M. Chu, J. A. Leacock, J. Chen, The Effect of Anisotropic Scattering on Radiative Transfer (The University of Michigan Research Institute, Ann Arbor, 1966).

Collins, D. G.

D. G. Collins, M. B. Wells, Monte Carlo Codes for the Study of Light Transport in the Atmosphere (Radiation Research Associates, Inc., Fort Worth, Texas, 1965), Vols. I and II.

Coulson, K. L.

K. L. Coulson, G. M. Bouricius, E. L. Grany, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

Deirmendjian, D.

Fritz, S.

S. Fritz, J. Opt. Soc. Am. 10, 820 (1955).
[CrossRef]

S. Fritz, J. Meteorol. 11, 291 (1954).
[CrossRef]

Grany, E. L.

K. L. Coulson, G. M. Bouricius, E. L. Grany, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

Hammersley, J. M.

J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods (John Wiley & Sons, Inc., New York, 1964).
[CrossRef]

Handscomb, D. C.

J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods (John Wiley & Sons, Inc., New York, 1964).
[CrossRef]

Howell, H. B.

S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmos. Sci. 24, 70 (1967).
[CrossRef]

Jacobowitz, H.

S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmos. Sci. 24, 70 (1967).
[CrossRef]

Kattawar, G. W.

Leacock, J. A.

S. W. Churchill, C. M. Chu, J. A. Leacock, J. Chen, The Effect of Anisotropic Scattering on Radiative Transfer (The University of Michigan Research Institute, Ann Arbor, 1966).

Plass, G. N.

Twomey, S.

S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmos. Sci. 24, 70 (1967).
[CrossRef]

Wells, M. B.

D. G. Collins, M. B. Wells, Monte Carlo Codes for the Study of Light Transport in the Atmosphere (Radiation Research Associates, Inc., Fort Worth, Texas, 1965), Vols. I and II.

Appl. Opt. (2)

J. Atmos. Sci. (1)

S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmos. Sci. 24, 70 (1967).
[CrossRef]

J. Geophys. Res. (1)

K. L. Coulson, G. M. Bouricius, E. L. Grany, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

J. Meteorol. (1)

S. Fritz, J. Meteorol. 11, 291 (1954).
[CrossRef]

J. Opt. Soc. Am. (1)

S. Fritz, J. Opt. Soc. Am. 10, 820 (1955).
[CrossRef]

Other (4)

S. Chandrasekhar, Radiative Transfer (Dover Publications, New York, 1960).

J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods (John Wiley & Sons, Inc., New York, 1964).
[CrossRef]

D. G. Collins, M. B. Wells, Monte Carlo Codes for the Study of Light Transport in the Atmosphere (Radiation Research Associates, Inc., Fort Worth, Texas, 1965), Vols. I and II.

S. W. Churchill, C. M. Chu, J. A. Leacock, J. Chen, The Effect of Anisotropic Scattering on Radiative Transfer (The University of Michigan Research Institute, Ann Arbor, 1966).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Reflected radiance from a semiinfinite atmosphere with isotropic scattering and μ0 (cosine of incident zenith angle) = −0.2 and ω0 (single scattering albedo) = 0.2. The results are given as a function of μ (cosine of zenith angle). The continuous curve is calculated from Chandrasekhar.1 The Monte Carlo results are for 20,000 histories. The incident flux on a surface perpendicular to the incident beam is normalized to unity in all calculations reported here.

Fig. 2
Fig. 2

Reflected and transmitted radiance for a Rayleigh scattering function for an atmosphere with τ (optical depth) = 1. The upper curves are for A (surface albedo) = 0.8 and the lower curves are for A = 0. The continuous curve was calculated by a program written by C. N. Adams. The Monte Carlo results are for 30,000 histories.

Fig. 3
Fig. 3

Angular scattering function for Mie scattering as a function of the cosine of scattering angle μ averaged over the size distribution given by Eq. (1) and over the two directions of polarization. The inset in upper left shows the curve near μ = 1. It is assumed that the wavelength of the incident light is 0.7 μ and that the index of refraction of the water drops is 1.33.

Fig. 4
Fig. 4

Cloud albedo as a function of optical thickness for μ0 = −1.0 and surface albedo A = 0, 0.2, 0.4, 0.6, 0.8.

Fig. 5
Fig. 5

Cloud albedo as a function of optical thickness for μ0 = −0.5 and A = 0, 0.2, 0.4, 0.6, 0.8.

Fig. 6
Fig. 6

Cloud albedo as a function of optical thickness for μ0 = −0.1 and A = 0, 0.2, 0.4, 0.6, 0.8.

Fig. 7
Fig. 7

Cloud albedo as a function of optical thickness for μ0 = −0.02 and A = 0, 0.2, 0.4, 0.6, 0.8.

Fig. 8
Fig. 8

Mean optical path of reflected photon as a function of optical thickness of cloud for μ0 = −0.02, −0.1, −0.5, −1.0.

Fig. 9
Fig. 9

Mean optical path of transmitted photon as a function of optical thickness of cloud for μ0 = −0.02, −0.1, −0.5, −1.0.

Tables (1)

Tables Icon

Table I Cloud Albedo

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

n ( r ) = 2.373 r 6 exp ( - 1.5 r ) ,

Metrics