Abstract

The dependence of the reflected and transmitted light from clouds on the single scattering albedo ω0 is studied. The multiple scattered path of the photon in the cloud is accurately simulated by Monte Carlo techniques. When the cloud is optically thin and the surface albedo A = 0, the reflected and transmitted radiances vary nearly as ω0 for fixed angles of incidence and observation and they depend strongly on the value of A. As ω0 becomes small and for optically thick clouds, the reflected radiance approaches more closely the value calculated from the single scattering function. As the absorption increases, the transmitted radiance at the zenith becomes larger relative to the value near the horizon. Also, as the optical thickness increases, the maximum of the transmitted radiance moves from the incident direction toward the zenith. The variations in the flux, cloud albedo, and the mean optical path are also discussed.

© 1968 Optical Society of America

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References

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  1. G. N. Plass, G. W. Kattawar, Appl. Opt. 7,March (1968).
    [PubMed]
  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. Atmospheric Sci. 24, 70 (1967).
    [CrossRef]
  5. J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods (John Wiley and 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. D. Deirmendjian, Appl. Opt. 3, 187 (1964).
    [CrossRef]

1968

G. N. Plass, G. W. Kattawar, Appl. Opt. 7,March (1968).
[PubMed]

1967

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

1964

1955

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

1954

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

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.

Deirmendjian, D.

Fritz, S.

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

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

Hammersley, J. M.

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

Handscomb, D. C.

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

Howell, H. B.

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

Jacobowitz, H.

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

Kattawar, G. W.

G. N. Plass, G. W. Kattawar, Appl. Opt. 7,March (1968).
[PubMed]

Plass, G. N.

G. N. Plass, G. W. Kattawar, Appl. Opt. 7,March (1968).
[PubMed]

Twomey, S.

S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmospheric 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.

G. N. Plass, G. W. Kattawar, Appl. Opt. 7,March (1968).
[PubMed]

D. Deirmendjian, Appl. Opt. 3, 187 (1964).
[CrossRef]

J. Atmospheric Sci.

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

J. Meteorol.

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

J. Opt. Soc. Am.

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

Other

J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods (John Wiley and 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.

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Figures (14)

Fig. 1
Fig. 1

Reflected radiance as a function of μ, the cosine of the zenith angle. The curves on the left and right portion of the figure are for A (surface albedo) = 0 and 1, respectively. The optical depth of the cloud τ = 0.1. The sunlight is incident vertically, μ0 (cosine of incident zenith angle) = −1.0. The single scattering albedo is ω0. The incident intensity is normalized to unity.

Fig. 2
Fig. 2

Reflected radiance for μ0 = −0.5, τ = 0.1, and A = 0 as a function of μ, the cosine of the zenith angle. The left hand portion of the graph refers to values averaged over the azimuthal angle for 90° on both sides of the original beam. The values on the right portion of the graph are for values averaged over the remaining azimuthal angles. Thus, one intensity curve from left to right shows the variation from one horizon to the zenith and back to the other horizon averaged over the indicated azimuthal angles.

Fig. 3
Fig. 3

Reflected radiance for μ0 = −0.1, τ = 0.1, and A = 0 as a function of μ. See caption for Fig. 2.

Fig. 4
Fig. 4

Reflected radiance for μ0 = −1.0, τ = 1.0, and A = 0 and 1 as a function of μ. See caption for Fig. 1.

Fig. 5
Fig. 5

Reflection radiance for μ0 = −1.0, τ = 10, and A = 0 and 1 as a function of μ. See caption for Fig. 1.

Fig. 6
Fig. 6

Reflected radiance for μ0 = −0.5, τ = 10, and A = 0 as a function of μ. See caption for Fig. 2.

Fig. 7
Fig. 7

Reflected radiance for μ0 = −0.1, τ = 10, and A = 0 as a function of μ. See caption for Fig. 2.

Fig. 8
Fig. 8

Transmitted radiance for μ0 = −0.1, τ = 0.1, and A = 0 and 1 as a function of μ. The radiance from the unscattered photons of the original beam is not included. See caption for Fig. 1.

Fig. 9
Fig. 9

Transmitted radiance for μ0 = −0.5, τ = 0.1, and A = 0 as a function of μ. See caption for Fig. 2.

Fig. 10
Fig. 10

Transmitted radiance for μ0 = −0.1, τ = 0.1, and A = 0 as a function of μ. See caption for Fig. 2.

Fig. 11
Fig. 11

Transmitted radiance for μ0 = −1.0, τ = 1, and A = 0 and 1 as a function of μ. See caption for Fig. 1.

Fig. 12
Fig. 12

Transmitted radiance for μ0 = −1.0, τ = 10, and A = 0 and 1 as a function of μ. See caption for Fig. 1.

Fig. 13
Fig. 13

Transmitted radiance for μ0 = −0.5, τ = 10, and A = 0 as a function of μ. See caption for Fig. 2.

Fig. 14
Fig. 14

Transmitted radiance for μ0 = −0.1, τ = 10, and A = 0 as a function of μ. See caption for Fig. 2.

Tables (1)

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Table I Mean Optical Path, Flux at Lower Boundary for A = 0, and Cloud Albedo

Equations (1)

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

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