Abstract

The radiance of clouds is calculated at nine wavelengths in the ir. The single scattering function is obtained by Mie theory from the measured values of the complex index of refraction and with two different drop size distributions. Multiple scattering is taken into account by a Monte Carlo technique which computes the exact three-dimensional paths of the photons. The upward and downward radiance is obtained as a function of optical thickness, angle of observation, drop size distribution, and incident solar angle. The mean optical path of the photon, the cloud albedo, and the flux at the lower and upper boundaries are also given.

© 1969 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. M. Gates, M. J. Harrop, Appl. Opt. 2, 887 (1963).
    [Crossref]
  2. R. P. Espinola, H. H. Blau, J. Geophys. Res. 70, 626 (1965).
    [Crossref]
  3. H. H. Blau, R. P. Espinola, Appl. Opt. 5, 555 (1966).
    [Crossref] [PubMed]
  4. W. A. Hovis, M. Tobin, Appl. Opt. 6, 1399 (1967).
    [Crossref] [PubMed]
  5. F. F. Hall, Appl. Opt. 7, 891 (1968).
    [Crossref] [PubMed]
  6. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
    [Crossref] [PubMed]
  7. W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
    [Crossref]
  8. G. W. Kattawar, G. N. Plass, Appl. Opt. 6, 1377 (1967).
    [Crossref] [PubMed]
  9. D. Deirmendjian, Appl. Opt. 3, 187 (1964).
    [Crossref]
  10. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 361 (1968).
    [Crossref] [PubMed]
  11. G. W. Kattawar, G. N. Plass, Appl. Opt. 7, 869 (1968).
    [Crossref] [PubMed]

1968 (5)

1967 (2)

1966 (1)

1965 (1)

R. P. Espinola, H. H. Blau, J. Geophys. Res. 70, 626 (1965).
[Crossref]

1964 (1)

1963 (1)

Blau, H. H.

H. H. Blau, R. P. Espinola, Appl. Opt. 5, 555 (1966).
[Crossref] [PubMed]

R. P. Espinola, H. H. Blau, J. Geophys. Res. 70, 626 (1965).
[Crossref]

Deirmendjian, D.

Espinola, R. P.

H. H. Blau, R. P. Espinola, Appl. Opt. 5, 555 (1966).
[Crossref] [PubMed]

R. P. Espinola, H. H. Blau, J. Geophys. Res. 70, 626 (1965).
[Crossref]

Gates, D. M.

Hall, F. F.

Harrop, M. J.

Hovis, W. A.

Irvine, W. M.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
[Crossref]

Kattawar, G. W.

Plass, G. N.

Pollack, J. B.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
[Crossref]

Tobin, M.

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 (22)

Fig. 1
Fig. 1

Scattering function at 1.7 μ, 2.96 μ, 3.5 μ, 6.05 μ, 11 μ, 15 μ, and 20 μ for nimbostratus model and at 2.96 μ, 3.5 μ, and 15 μ for haze C model. The inset shows the behavior from 0° to 15° scattering angle.

Fig. 2
Fig. 2

Downward radiance as a function of the cosine (μ) of the zenith angle for surface albedo A = 0 and 0.8 and for wavelengths λ = 1.7 μ, 2.1 μ, 2.5 μ, 2.75 μ, 2.8 μ, 3.1 μ, and 6.05 μ. An optical thickness τ = 0.1, cosine of solar zenith angle μ0 =− 1, and the nimbostratus model are assumed. The incident flux is normalized to unity.

Fig. 3
Fig. 3

Upward radiance for A = 0, 0.2, and 0.8, τ = 0.1, μ0 = − 1, and nimbostratus model.

Fig. 4
Fig. 4

Downward radiance for A = 0 and 0.8, λ = 2.96 μ and 3.5 μ, τ = 0.1, μ0= −1, and both nimbostratus and haze C models.

Fig. 5
Fig. 5

Upward radiance for A = 0, 0.2, and 0.8, λ = 2.96 μ and 3.5 μ, τ = 0.1, μ0 = − 1, and both nimbostratus and haze C models.

Fig. 6
Fig. 6

Downward radiance for A = 0 and 0.8, τ = 1, μ0 = −1, λ = 1.7 μ, 2.1 μ, 2.5 μ, 2.75 μ, 2.8 μ, 3.1 μ, 6.05 μ, and nimbostratus model.

Fig. 7
Fig. 7

Upward radiance. See caption to Fig. 6.

Fig. 8
Fig. 8

Downward radiance for A = 0 and 0.8, τ = 1, μ0 = − 1, λ = 2.96 μ and 3.5 μ, and both nimbostratus and haze C models.

Fig. 9
Fig. 9

Upward radiance. See caption to Fig. 8.

Fig. 10
Fig. 10

Downward radiance for A = 0 and 0.8, τ = 10, μ0 = −1, λ = 1.7 μ, 2.1 μ, 2.5 μ, 2.75 μ, 2.8 μ, 3.1 μ, 6.05 μ, and nimbostratus model.

Fig. 11
Fig. 11

Upward radiance. See caption to Fig. 10.

Fig. 12
Fig. 12

Downward radiance for A = 0, and 0.8, τ = 10, μ0 =−1, λ = 2.96 μ and 3.5 μ, and both nimbostratus and haze C models.

Fig. 13
Fig. 13

Upward radiance. See caption to Fig. 12.

Fig. 14
Fig. 14

Downward radiance for A = 0, τ = 1, μ0 = −0.15 λ = 1.7 μ, 2.5 μ, 2.8 μ, 3.1 μ, and nimbostratus model. The radiance values averaged from 0° to 45° and from 135° to 180° azimuth on either side of the principal plane which contains the incident beam are indicated by the symbols without surrounding circles. Similarly the symbols with surrounding circles are the values averaged from 45° to 90° and from 90° to 135° in azimuth. The solar horizon is on he left-hand side and the antisolar horizon is on the right-hand side of all figures for μ0 = −0.15.

Fig. 15
Fig. 15

Upward radiance for A = 0. See caption to Fig. 14.

Fig. 16
Fig. 16

Upward radiance for A = 0.8. Other parameters are as given in caption to Fig. 14.

Fig. 17
Fig. 17

Downward radiance for A = 0, τ = 1, μ0 = 0.15, λ = 2.96 μ and 3.5 μ, and both nimbostratus and haze C models. See caption to Fig. 14.

Fig. 18
Fig. 18

Upward radiance. See caption to Fig. 16.

Fig. 19
Fig. 19

Downward radiance for A = 0, τ = 10, μ0 = 0.15, λ = 1.7 μ, 2.5 μ, 2.8 μ, 3.1 μ, and nimbostratus model.

Fig. 20
Fig. 20

Upward radiance. See caption to Fig. 19.

Fig. 21
Fig. 21

Downward radiance for A = 0, τ = 10, μ0 = −0.15, λ = 2.96 μ and 3.5 μ, haze C models.

Fig. 22
Fig. 22

Upward radiance. See caption to Fig. 21.

Tables (2)

Tables Icon

Table I Complex Index of Refraction of Water

Tables Icon

Table II Mean Optical Path, Flux, and Cloud Albedo

Equations (1)

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

n ( r ) = 0.00108 r 6 exp ( 0.5 r ) .

Metrics