Abstract

The reflection of light pulses from clouds is calculated by a Monte Carlo technique for all orders of multiple scattering. The photons are emitted within a narrow cone, scattered by water droplets and ice crystals in clouds as well as by Rayleigh scattering centers and aerosols, and finally detected at the source position. The returned flux is determined as a function of the photon path length for: (1) three different size distributions for the cloud particles (haze C, nimbostratus, ice crystal); (2) two different variations of the number density with height of the scattering centers within the cloud; (3) six different zenith angles of the source. The influence of detector half-width and of the atmosphere on the returned flux is studied. The returned flux as a function of the photon path length depends on both the size distribution of the particles within the cloud and on the density of scattering centers as a function of height.

© 1971 Optical Society of America

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References

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  1. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 361 (1968).
    [CrossRef] [PubMed]
  2. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
    [CrossRef] [PubMed]
  3. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 699 (1968).
    [CrossRef] [PubMed]
  4. G. W. Kattawar, G. N. Plass, Appl. Opt. 7, 869 (1968).
    [CrossRef] [PubMed]
  5. G. N. Plass, G. W. Kattawar, Appl. Opt. 8, 2489 (1969).
    [CrossRef] [PubMed]
  6. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  7. D. Deirmendjian, Appl. Opt. 3, 187 (1964).
    [CrossRef]
  8. A. C. Holland, G. Gagne, Appl. Opt. 9, 1113 (1970).
    [CrossRef] [PubMed]
  9. G. N. Plass, G. W. KattawarAppl. Opt. 10, 1172 (1971).
    [CrossRef]
  10. G. W. Kattawar, G. N. Plass, Appl. Opt. 6, 1377, 1549 (1967).
    [CrossRef] [PubMed]
  11. G. N. Plass, G. W. Kattawar, Appl. Opt. 10, 738 (1971).
    [CrossRef] [PubMed]
  12. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 1129 (1968).
    [CrossRef] [PubMed]
  13. G. N. Plass, G. W. Kattawar, Appl. Opt. 9, 1122 (1970).
    [CrossRef] [PubMed]
  14. L. Elterman, in Handbook of Geophysics and Space Environments, S. L. Valley, Ed. (McGraw-Hill, New York, 1965).
  15. F. Singleton, D. J. Smith, Quart. J. Roy. Meteorol. Soc. 86, 454 (1960); also see Chap. 5, Ref. 14.
    [CrossRef]

1971

1970

1969

1968

1967

G. W. Kattawar, G. N. Plass, Appl. Opt. 6, 1377, 1549 (1967).
[CrossRef] [PubMed]

1964

1960

F. Singleton, D. J. Smith, Quart. J. Roy. Meteorol. Soc. 86, 454 (1960); also see Chap. 5, Ref. 14.
[CrossRef]

Deirmendjian, D.

Elterman, L.

L. Elterman, in Handbook of Geophysics and Space Environments, S. L. Valley, Ed. (McGraw-Hill, New York, 1965).

Gagne, G.

Holland, A. C.

Kattawar, G. W.

Plass, G. N.

Singleton, F.

F. Singleton, D. J. Smith, Quart. J. Roy. Meteorol. Soc. 86, 454 (1960); also see Chap. 5, Ref. 14.
[CrossRef]

Smith, D. J.

F. Singleton, D. J. Smith, Quart. J. Roy. Meteorol. Soc. 86, 454 (1960); also see Chap. 5, Ref. 14.
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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Figures (11)

Fig. 1
Fig. 1

Returned flux (as fraction of emitted flux) as a function of photon path length in km. Curves are given for the nimbostratus, ice crystal, and haze C cloud models when the density of scattering centers varies linearly from the cloud base to the cloud top. The result is also given for the nimbostratus model for a homogeneous spatial distribution of scattering centers (use right-hand scale). The lower surface of the cloud is at 1 km and the upper surface at 2 km with an optical thickness τ = 1. The angular half-width of the detector is 0.005 rad. The laser is pointed at the zenith (cosine of zenith angle μ0 = 1). The solid curves include all orders of multiple scattering. The dashed curves are the corresponding results for single scattered photons only.

Fig. 2
Fig. 2

Returned flux as a function of photon path length for the haze C, nimbostratus, and ice crystal models. The lower surface of the cloud is at 1 km and the upper surface at 2 km with τ = 10. See legend to Fig. 1.

Fig. 3
Fig. 3

Returned flux as a function of photon path length for the haze C, nimbostratus, and ice crystal models. The lower surface of the cloud is at 1 km and the upper surface at 2 km with τ = 10. An additional curve is shown for the nimbostratus model with the lower cloud surface at 1 km, the upper surface at 10 km, and with τ = 10. (Use upper scale.) See legend to Fig. 1.

Fig. 4
Fig. 4

Returned flux as a function of photon path length for the haze C model, τ = 1, and μ0 = 1. The distribution of scattering centers varies linearly from the cloud base to the cloud top. Curves are given for the angular half-width of the detector of 0.005 rad, 0.02 rad, 0.2 rad, and 0.5 rad.

Fig. 5
Fig. 5

Returned flux as a function of photon path length for the haze C model, τ = 10, and μ0 = 1. The distribution of scattering centers varies linearly from the cloud base to the cloud top. Curves are given for the angular half-width of the detector of 0.005 rad, 0.02 rad, 0.2 rad, and 0.5 rad.

Fig. 6
Fig. 6

Returned flux as a function of photon path length for the nimbostratus model, linear distribution with height, τ = 1 and 10, and μ0 = 1. The lower cloud surface is at 1 km and the upper surface at 2 km. Scattering within the atmosphere from both Rayleigh and aerosol scattering centers is taken into account both above and below the cloud. The scale on the right should be used for the cloud with τ = 10.

Fig. 7
Fig. 7

Returned flux as a function of photon path length for the nimbostratus model with both a linear and homogenous distribution of scattering centers with height, τ = 1 and 10, and μ0 = 0.83333. The lower cloud surface is at 1 km, and the upper cloud surface is at 2 km.

Fig. 8
Fig. 8

Same as Fig. 7, except μ0 = 0.64516.

Fig. 9
Fig. 9

Same as Fig. 7, except μ0 = 0.454545.

Fig. 10
Fig. 10

Same as Fig. 7, except μ0 = 0.25.

Fig. 11
Fig. 11

Same as Fig. 7, except μ0 = 0.15038. An additional curve is shown with the lower cloud surface at 1 km, the upper surface at 10 km, and τ = 10. (Use upper scale.)

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