Abstract

A simple inversion technique in the single scattering regime has been developed to deduce cloud droplet size parameters by using the measurement of the radiance of near-forward scattered solar radiation as a function of angle. Compared with the numerical inversion technique that uses exact Mie scattering calculations, the new technique is much less time-consuming and hence should be usable in an on-line real time analysis. To test the effectiveness of the new technique, we use the results of polydispersed cloud size distribution calculated by Deirmendjian to retrieve the model size parameters. The agreement is excellent. We also generalize the theory to include the broadband source. A typical experimental example is given. Its comparison with time-consuming Mie scattering inversion technique again shows excellent agreement.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. M. Lerfald, “A Solar Aureole Photometer for use in Measuring Size Distributions of Particles in the Atmosphere,” NOAA Tech. Memo. ERL WPL-36 (1977).
  2. J. R. Hodkinson, Appl. Opt. 5, 839 (1966).
    [CrossRef] [PubMed]
  3. D. Deirmendjian, “Use of Scattering Techniques in Cloud Micro-physics Research 1. The Aureole Method,” Rand Corp. report R-590-PR (1970).
  4. A. E. S. Green, A. Deepak, B. J. Lipofsky, Appl. Opt. 10, 1263 (1971).
    [CrossRef] [PubMed]
  5. M. J. Post, J. Opt. Soc. Am. 66, 483 (1976).
    [CrossRef]
  6. A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed., NASA-CP004 (U.S. GPO, Washington, D.C., 1977), Chap. 10, pp. 265–291.
  7. E. R. Westwater, A. Cohen, Appl. Opt. 12, 1340 (1973).
    [CrossRef] [PubMed]
  8. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  9. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).
  10. M. A. Box, A. Deepak, Appl. Opt. 17, 3794 (1978).
    [CrossRef] [PubMed]

1978 (1)

1976 (1)

1973 (1)

1971 (1)

1966 (1)

Box, M. A.

Cohen, A.

Deepak, A.

M. A. Box, A. Deepak, Appl. Opt. 17, 3794 (1978).
[CrossRef] [PubMed]

A. E. S. Green, A. Deepak, B. J. Lipofsky, Appl. Opt. 10, 1263 (1971).
[CrossRef] [PubMed]

A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed., NASA-CP004 (U.S. GPO, Washington, D.C., 1977), Chap. 10, pp. 265–291.

Deirmendjian, D.

D. Deirmendjian, “Use of Scattering Techniques in Cloud Micro-physics Research 1. The Aureole Method,” Rand Corp. report R-590-PR (1970).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

Green, A. E. S.

Hodkinson, J. R.

Lerfald, G. M.

G. M. Lerfald, “A Solar Aureole Photometer for use in Measuring Size Distributions of Particles in the Atmosphere,” NOAA Tech. Memo. ERL WPL-36 (1977).

Lipofsky, B. J.

Post, M. J.

van de Hulst, H. C.

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

Westwater, E. R.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Other (5)

G. M. Lerfald, “A Solar Aureole Photometer for use in Measuring Size Distributions of Particles in the Atmosphere,” NOAA Tech. Memo. ERL WPL-36 (1977).

D. Deirmendjian, “Use of Scattering Techniques in Cloud Micro-physics Research 1. The Aureole Method,” Rand Corp. report R-590-PR (1970).

A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed., NASA-CP004 (U.S. GPO, Washington, D.C., 1977), Chap. 10, pp. 265–291.

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

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

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 (5)

Fig. 1
Fig. 1

Quantity x0f(x0) [see Eqs. (8) and (9)] as a function of x0 for a monochromatic source.

Fig. 2
Fig. 2

Angular dependence of the scattering intensity: —, diffraction theory for large particles; ---, λ = 0.45 μm, a = 3.58 μm; ·····, λ = 0.7 μm, a = 5.56 μm. All three curves are for size parameter α = 50. Agreement among curves is good for small scattering angle (<4°), whereas significant variations are noticed for large scattering angle.

Fig. 3
Fig. 3

Quantity x ¯ 0 f ( x ¯ 0 ) as a function of x ¯ 0 for broadband case and monochromatic case, where x ¯ 0 = k ¯ a ¯ θ 0; k ¯ = 2 π / λ ¯, and λ ¯ is the mean wavelength of the passband.

Fig. 4
Fig. 4

Typical example of the measured solar aureole data of an orographic wave cloud. These data were obtained using a broadband photometer filter, (0.63–1.1 μm).

Fig. 5
Fig. 5

Retrieved cloud drop size distribution of the solar aureole data shown in Fig. 4. Solid line indicates the result of a complicated numerical inversion technique based on exact Mie theory. Dashed line is a γ distribution whose first three moments satisfy the results retrieved based on the technique described in this paper. Disagreement in the small size region is known to be due to the limitations of the numerical inversion technique.

Tables (3)

Tables Icon

Table I Parameters for γ-Distributed Cloud Models

Tables Icon

Table II Retrieved Cloud Parameters of Cloud Model C.1 for Different θ0

Tables Icon

Table III Retrieved Cloud Parameters for Three Cloud Models and Two Wavelengths

Equations (20)

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

S 1 ( θ ) = S 2 ( θ ) = α J 1 ( α θ ) θ + 0 ( 1 ξ ) ,
i ( θ ) = 1 k 2 r 2 0 d a n ( a ) k 2 a 2 J 1 2 ( k a θ ) θ 2 ,
i ( 0 ) = k 2 4 r 2 0 d a n ( a ) a 4 .
I ( θ ) = i ( θ ) i ( 0 ) = 1 C 0 d a p ( a ) k 2 a 2 J 1 2 ( k a θ ) θ 2 ,
C 0 θ 0 d θ θ n I ( θ ) = k 3 n 0 × d a p ( a ) a 3 n [ 0 k a θ 0 d x x n 2 J 1 2 ( x ) ] ,
a m ¯ = c 0 θ 0 d θ θ 3 m I ( θ ) k m 0 x 0 d x x 1 m J 1 2 ( x ) .
a m ¯ = 0 θ 0 d θ θ 3 m I ( θ ) 0 θ 0 d θ θ 3 I ( θ ) 0 x 0 d x x J 1 2 ( x ) k m 0 x 0 d x x 1 m J 1 2 ( x ) .
α ( θ 0 ) θ 0 0 θ 0 d θ θ 2 I ( θ ) 0 θ 0 d θ θ 3 I ( θ ) = x 0 f ( x 0 ) ,
f ( x 0 ) 0 x 0 d x J 1 2 ( x ) d x x J 1 2 ( x ) .
a ¯ = 0 k a ¯ θ 0 d x x J 1 2 ( x ) 0 k a ¯ θ 0 d x J 1 2 ( x ) 0 d a a p ( a ) 0 d a p ( a ) 0 k a θ 0 d x J 1 2 ( x ) 0 k a θ 0 d x x J 1 2 ( x ) .
J 1 2 ( x ) 1 π x 2 ( 4 / π ) + x 3 .
0 x d x x 2 4 π + x 3 ln x ,
0 x d x x 3 4 π + x 3 x 0.95 .
a ¯ = a ¯ t + a ln ( a / a ¯ t ) ¯ ln ( k a ¯ t θ 0 ) a ¯ t [ 1 + σ a 2 a ¯ t 2 ln ( k a ¯ t θ 0 ) ] ,
n ( a ) = A a α exp ( β a γ ) ,
3.75 x 0 3.85 ; if θ 0 [ λ / ( 4 a 0 ) ] ;
θ 0 = λ / ( 4 a 0 ) ,
a m ¯ = 1 λ 2 d λ w ( λ ) k 2 0 x 0 d x x J 1 2 ( x ) λ 1 λ 2 d λ w ( λ ) k m 2 0 x 0 d x x 1 m J 1 2 ( x ) × 0 θ 0 d θ θ 3 m I ( θ ) 0 θ 0 d θ θ 3 I ( θ ) ,
α ( θ ) 0 θ 0 0 θ 0 d θ θ 2 I ( θ ) 0 θ 0 d θ θ 3 I ( θ ) = a ¯ θ 0 f ( a ¯ θ 0 ) ,
f ( a ¯ θ 0 ) λ 1 λ 2 d λ w ( λ ) k 1 0 x 0 d x J 1 2 ( x ) λ 1 λ 2 d λ w ( λ ) k 2 0 x d x x J 1 2 ( x ) .

Metrics