Abstract

A Monte Carlo method that accurately allows for the numerous small angle scattering events is used to calculate the reflected and transmitted radiance and flux of visible radiation that has interacted with cumulus clouds. The variation of these quantities with solar zenith angle, optical thickness of the cloud, and surface albedo is studied. When the surface albedo is zero, the reflected radiance has a relative maximum at the horizon (except for very thick clouds and incident beam near zenith). When the incident beam is near the horizon, there is a strong maximum in the reflected radiance on the solar horizon and a pronounced minimum near the zenith. There is a relative maximum in the transmitted radiance around the direction of the incident beam until the cloud becomes thick in that direction. In most instances, the variations are greatly decreased when the surface albedo is unity.

© 1968 Optical Society of America

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References

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  1. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
    [CrossRef] [PubMed]
  2. S. Fritz, J. Meteorol. 11, 291 (1954).
    [CrossRef]
  3. S. Fritz, J. Opt. Soc. Amer. 10, 820 (1955).
  4. S. Twomey, H. Jacobowitz, H. B. Howell, J. Atmos. Sci. 24, 70 (1967).
    [CrossRef]
  5. 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.

1968 (1)

1967 (1)

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

1955 (1)

S. Fritz, J. Opt. Soc. Amer. 10, 820 (1955).

1954 (1)

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.

Fritz, S.

S. Fritz, J. Opt. Soc. Amer. 10, 820 (1955).

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

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. (1)

J. Atmos. Sci. (1)

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

J. Meteorol. (1)

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

J. Opt. Soc. Amer. (1)

S. Fritz, J. Opt. Soc. Amer. 10, 820 (1955).

Other (1)

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

The reflected radiance is shown 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 is τ. The sunlight is incident vertically, μ0 (cosine of incident zenith angle) = −1.0. The incident flux on a surface perpendicular to the incident beam is normalized to unity.

Fig. 2
Fig. 2

Transmitted radiance for μ0 = −1.0 and A = 0 and 1. The transmitted radiance does not include the incident photon until it has been scattered the first time. See caption for Fig. 1.

Fig. 3
Fig. 3

Reflected radiance for μ0 = −0.5 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 direction 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 the solar horizon to the zenith and back to the antisolar horizon averaged over the indicated azimuthal angles.

Fig. 4
Fig. 4

Reflected radiance for μ0 = −0.5 and A = 1. See caption for Fig. 3.

Fig. 5
Fig. 5

Transmitted radiance for μ0 = −0.5 and A = 0. See caption for Fig. 3.

Fig. 6
Fig. 6

Transmitted radiance for μ0 = −0.5 and A = 1. See caption for Fig. 3.

Fig. 7
Fig. 7

Reflected radiance for μ0 = −0.1 and A = 0. See caption for Fig. 3.

Fig. 8
Fig. 8

Reflected radiance for μ0 = −0.1 and A = 1. See caption for Fig. 3.

Fig. 9
Fig. 9

Transmitted radiance for μ0 = −0.1 and A = 0. See caption for Fig. 3.

Fig. 10
Fig. 10

Transmitted radiance for μ0 = −0.1 and A = 1. See. caption for Fig. 3.

Fig. 11
Fig. 11

Reflected radiance for μ0 = −0.02 and A = 0. See caption for Fig. 3.

Fig. 12
Fig. 12

Transmitted radiance for μ0 = −0.02 and A = 0. See caption for Fig. 3.

Fig. 13
Fig. 13

Downward diffuse flux at lower boundary of cloud as a function of optical thickness of cloud for μ0 = −1.0, −0.5, −0.1 and for A = 0. The flux on a surface perpendicular to the incident beam is normalized to unity in each case.

Fig. 14
Fig. 14

Downward diffuse flux plus remaining flux from incident beam at lower boundary of cloud as a function of optical thickness of cloud for μ0 = −1.0, −0.5, −0.1, −0.02 and for A = 1. The flux on a surface perpendicular to the incident beam is normalized to unity in each case.

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