Abstract

The single-scattering phase function of cirrus particles in the free atmosphere has been determined between angles of 15 and 90° in the forward direction and at 180° in the back direction. The technique involved measuring the solar radiation intensity scattered by thin cirrus with a lidar receiver and also determining the cirrus optical depth simultaneously from a lidar backscatter return. The solar scattered radiance appeared as a background signal on the lidar echo. The phase function at 180° was determined from the integrated cloud backscatter using standard techniques. Data were obtained during two experimental phases covering summer and winter periods. The values of the measured scattering functions fell within the range of various laboratory measurements. The results showed evidence for the 22° halo associated with scattering from hexagonal crystals.

© 1984 Optical Society of America

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References

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  1. G. L. Stephens, P. J. Webster, J. Atmos. Sci. 38, 235 (1981).
    [CrossRef]
  2. J. E. Hansen, J. Atmos. Sci. 26, 478 (1969).
    [CrossRef]
  3. K. N. Liou, J. Geophys. Res. 78, 1409 (1973).
    [CrossRef]
  4. C. Magono, C. W. Lee, J. Fac. Sci. Hokkaido Univ. Ser. 4 3, No. 4 (1966).
  5. M. Kumai, J. Appl. Meteorol. 21, 579 (1982).
    [CrossRef]
  6. B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, Atmos. Environ. 16, 1193 (1982).
    [CrossRef]
  7. G. W. Paltridge, C. M. R. Platt, J. R. Meteorol. Soc. 107, 367 (1981).
    [CrossRef]
  8. C. M. R. Platt, D. W. Reynolds, N. L. Abshire, Mon. Weather Rev. 108, 195 (1980).
    [CrossRef]
  9. P. J. Huffman, W. R. Thursby, J. Atmos. Sci. 27, 1207 (1969).
    [CrossRef]
  10. V. P. Dugin, O. A. Volkovitskiy, S. O. Mirumyants, N. K. Nikiforova, Akad. Nauk SSSR Fiz. Atmos. Okeana 13, 22 (1977).
  11. K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 852 (1979).
    [CrossRef]
  12. P. Wendling, R. Wendling, H. K. Weickman, Appl. Opt. 18, 2663 (1979).
    [CrossRef] [PubMed]
  13. C. M. R. Platt, J. Appl. Meteorol. 18, 1130 (1979).
    [CrossRef]
  14. C. M. R. Platt, A. C. Dilley, J. Atmos. Sci. 38, 1069 (1981).
    [CrossRef]
  15. N. Braslau, J. V. Dave, J. Appl. Meteorol. 12, 601 (1973).
    [CrossRef]
  16. C. M. R. Platt, J. Atmos. Sci. 38, 156 (1981).
    [CrossRef]
  17. H. K. Weickmann, The Ice Phase in the ATmosphere (Ministry of Supply, London, 1947), 154 pp.
  18. A. J. Heymsfield, J. Atmos. Sci. 32, 799 (1975).
    [CrossRef]

1982 (2)

M. Kumai, J. Appl. Meteorol. 21, 579 (1982).
[CrossRef]

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, Atmos. Environ. 16, 1193 (1982).
[CrossRef]

1981 (4)

G. W. Paltridge, C. M. R. Platt, J. R. Meteorol. Soc. 107, 367 (1981).
[CrossRef]

G. L. Stephens, P. J. Webster, J. Atmos. Sci. 38, 235 (1981).
[CrossRef]

C. M. R. Platt, A. C. Dilley, J. Atmos. Sci. 38, 1069 (1981).
[CrossRef]

C. M. R. Platt, J. Atmos. Sci. 38, 156 (1981).
[CrossRef]

1980 (1)

C. M. R. Platt, D. W. Reynolds, N. L. Abshire, Mon. Weather Rev. 108, 195 (1980).
[CrossRef]

1979 (3)

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 852 (1979).
[CrossRef]

P. Wendling, R. Wendling, H. K. Weickman, Appl. Opt. 18, 2663 (1979).
[CrossRef] [PubMed]

C. M. R. Platt, J. Appl. Meteorol. 18, 1130 (1979).
[CrossRef]

1977 (1)

V. P. Dugin, O. A. Volkovitskiy, S. O. Mirumyants, N. K. Nikiforova, Akad. Nauk SSSR Fiz. Atmos. Okeana 13, 22 (1977).

1975 (1)

A. J. Heymsfield, J. Atmos. Sci. 32, 799 (1975).
[CrossRef]

1973 (2)

N. Braslau, J. V. Dave, J. Appl. Meteorol. 12, 601 (1973).
[CrossRef]

K. N. Liou, J. Geophys. Res. 78, 1409 (1973).
[CrossRef]

1969 (2)

J. E. Hansen, J. Atmos. Sci. 26, 478 (1969).
[CrossRef]

P. J. Huffman, W. R. Thursby, J. Atmos. Sci. 27, 1207 (1969).
[CrossRef]

1966 (1)

C. Magono, C. W. Lee, J. Fac. Sci. Hokkaido Univ. Ser. 4 3, No. 4 (1966).

Abshire, N. L.

C. M. R. Platt, D. W. Reynolds, N. L. Abshire, Mon. Weather Rev. 108, 195 (1980).
[CrossRef]

Bentley, A. N.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, Atmos. Environ. 16, 1193 (1982).
[CrossRef]

Braslau, N.

N. Braslau, J. V. Dave, J. Appl. Meteorol. 12, 601 (1973).
[CrossRef]

Caughey, S. J.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, Atmos. Environ. 16, 1193 (1982).
[CrossRef]

Conway, B. J.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, Atmos. Environ. 16, 1193 (1982).
[CrossRef]

Dave, J. V.

N. Braslau, J. V. Dave, J. Appl. Meteorol. 12, 601 (1973).
[CrossRef]

Dilley, A. C.

C. M. R. Platt, A. C. Dilley, J. Atmos. Sci. 38, 1069 (1981).
[CrossRef]

Dugin, V. P.

V. P. Dugin, O. A. Volkovitskiy, S. O. Mirumyants, N. K. Nikiforova, Akad. Nauk SSSR Fiz. Atmos. Okeana 13, 22 (1977).

Hansen, J. E.

J. E. Hansen, J. Atmos. Sci. 26, 478 (1969).
[CrossRef]

Heymsfield, A. J.

A. J. Heymsfield, J. Atmos. Sci. 32, 799 (1975).
[CrossRef]

Huffman, P. J.

P. J. Huffman, W. R. Thursby, J. Atmos. Sci. 27, 1207 (1969).
[CrossRef]

Kumai, M.

M. Kumai, J. Appl. Meteorol. 21, 579 (1982).
[CrossRef]

Lee, C. W.

C. Magono, C. W. Lee, J. Fac. Sci. Hokkaido Univ. Ser. 4 3, No. 4 (1966).

Liou, K. N.

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 852 (1979).
[CrossRef]

K. N. Liou, J. Geophys. Res. 78, 1409 (1973).
[CrossRef]

Magono, C.

C. Magono, C. W. Lee, J. Fac. Sci. Hokkaido Univ. Ser. 4 3, No. 4 (1966).

Mirumyants, S. O.

V. P. Dugin, O. A. Volkovitskiy, S. O. Mirumyants, N. K. Nikiforova, Akad. Nauk SSSR Fiz. Atmos. Okeana 13, 22 (1977).

Nikiforova, N. K.

V. P. Dugin, O. A. Volkovitskiy, S. O. Mirumyants, N. K. Nikiforova, Akad. Nauk SSSR Fiz. Atmos. Okeana 13, 22 (1977).

Paltridge, G. W.

G. W. Paltridge, C. M. R. Platt, J. R. Meteorol. Soc. 107, 367 (1981).
[CrossRef]

Platt, C. M. R.

G. W. Paltridge, C. M. R. Platt, J. R. Meteorol. Soc. 107, 367 (1981).
[CrossRef]

C. M. R. Platt, A. C. Dilley, J. Atmos. Sci. 38, 1069 (1981).
[CrossRef]

C. M. R. Platt, J. Atmos. Sci. 38, 156 (1981).
[CrossRef]

C. M. R. Platt, D. W. Reynolds, N. L. Abshire, Mon. Weather Rev. 108, 195 (1980).
[CrossRef]

C. M. R. Platt, J. Appl. Meteorol. 18, 1130 (1979).
[CrossRef]

Reynolds, D. W.

C. M. R. Platt, D. W. Reynolds, N. L. Abshire, Mon. Weather Rev. 108, 195 (1980).
[CrossRef]

Sassen, K.

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 852 (1979).
[CrossRef]

Stephens, G. L.

G. L. Stephens, P. J. Webster, J. Atmos. Sci. 38, 235 (1981).
[CrossRef]

Thursby, W. R.

P. J. Huffman, W. R. Thursby, J. Atmos. Sci. 27, 1207 (1969).
[CrossRef]

Turton, J. D.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, Atmos. Environ. 16, 1193 (1982).
[CrossRef]

Volkovitskiy, O. A.

V. P. Dugin, O. A. Volkovitskiy, S. O. Mirumyants, N. K. Nikiforova, Akad. Nauk SSSR Fiz. Atmos. Okeana 13, 22 (1977).

Webster, P. J.

G. L. Stephens, P. J. Webster, J. Atmos. Sci. 38, 235 (1981).
[CrossRef]

Weickman, H. K.

Weickmann, H. K.

H. K. Weickmann, The Ice Phase in the ATmosphere (Ministry of Supply, London, 1947), 154 pp.

Wendling, P.

Wendling, R.

Akad. Nauk SSSR Fiz. Atmos. Okeana (1)

V. P. Dugin, O. A. Volkovitskiy, S. O. Mirumyants, N. K. Nikiforova, Akad. Nauk SSSR Fiz. Atmos. Okeana 13, 22 (1977).

Appl. Opt. (1)

Atmos. Environ. (1)

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, Atmos. Environ. 16, 1193 (1982).
[CrossRef]

J. Appl. Meteorol. (3)

M. Kumai, J. Appl. Meteorol. 21, 579 (1982).
[CrossRef]

C. M. R. Platt, J. Appl. Meteorol. 18, 1130 (1979).
[CrossRef]

N. Braslau, J. V. Dave, J. Appl. Meteorol. 12, 601 (1973).
[CrossRef]

J. Atmos. Sci. (7)

C. M. R. Platt, J. Atmos. Sci. 38, 156 (1981).
[CrossRef]

C. M. R. Platt, A. C. Dilley, J. Atmos. Sci. 38, 1069 (1981).
[CrossRef]

P. J. Huffman, W. R. Thursby, J. Atmos. Sci. 27, 1207 (1969).
[CrossRef]

A. J. Heymsfield, J. Atmos. Sci. 32, 799 (1975).
[CrossRef]

G. L. Stephens, P. J. Webster, J. Atmos. Sci. 38, 235 (1981).
[CrossRef]

J. E. Hansen, J. Atmos. Sci. 26, 478 (1969).
[CrossRef]

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 852 (1979).
[CrossRef]

J. Fac. Sci. Hokkaido Univ. Ser. 4 (1)

C. Magono, C. W. Lee, J. Fac. Sci. Hokkaido Univ. Ser. 4 3, No. 4 (1966).

J. Geophys. Res. (1)

K. N. Liou, J. Geophys. Res. 78, 1409 (1973).
[CrossRef]

J. R. Meteorol. Soc. (1)

G. W. Paltridge, C. M. R. Platt, J. R. Meteorol. Soc. 107, 367 (1981).
[CrossRef]

Mon. Weather Rev. (1)

C. M. R. Platt, D. W. Reynolds, N. L. Abshire, Mon. Weather Rev. 108, 195 (1980).
[CrossRef]

Other (1)

H. K. Weickmann, The Ice Phase in the ATmosphere (Ministry of Supply, London, 1947), 154 pp.

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Figures (5)

Fig. 1
Fig. 1

Geometry of the single scattering of solar rays by a cloud.

Fig. 2
Fig. 2

Lidar returns from (A) a cloudless sky; (B) thin cirrus. Various features of the curves are illustrated.

Fig. 3
Fig. 3

Scattered irradiance ETλdλ plotted against cloud optical depth δc (θ = 25 · 6°). Observations on 2 Dec. 1980 at 1406-h LT.

Fig. 4
Fig. 4

Observed normalized scattering phase functions P(θ) normalized by 4π at various scattering angles compared to a theoretical curve for hexagonal crystals (Wendling et al.12).

Fig. 5
Fig. 5

Observed normalized scattering phase functions normalized by 4π compared to laboratory data: 1, Dugin et al.,10 columns 30 × 50 to 40 × 40 μm, 30–40-μm plates; 2, Dugin et al.,10 20–40-μm columns, 20–40-μm plates; 3, Sassen and Liou,11 1 · 5-μm plates, 5-μm columns; 4, Huffman and Thursby,9 5–50-μm plates, 5–50-μm columns, 5–15-μm irregular crystals. Other captions as in Fig. 4.

Tables (3)

Tables Icon

Table I Variation of the backscatter to extinction ratio k and the multiple-scattering factor η

Tables Icon

Table II Values of Quantities used In the Calculation of P(θ)/4π

Tables Icon

Table III Dependence of the Ratio ESλ/EDλ on Angle θ

Equations (32)

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E T λ d λ = ( E D λ + E S λ + E a R λ ) d λ ,
d L λ / d δ = - E 0 λ exp ( - δ / μ 0 ) [ P ( θ ) / 4 π ] ,
L λ d λ = E 0 λ [ P ( θ ) / 4 π ] μ 0 [ 1 - exp ( - δ c / μ 0 ) ] d λ ,
E D λ d λ = E 0 λ [ P ( θ ) / 4 π ] μ 0 [ 1 - exp ( - δ c / μ 0 ) ] τ a R d ω d λ ,
E D λ d λ = ξ λ [ 1 - exp ( - δ c / μ 0 ) ] ,
P ( θ ) / 4 π = ξ λ / E 0 λ μ 0 τ a R λ d ω d λ = ξ λ / B ( say ) } .
E 0 S λ d λ = E 0 λ τ A ( 1 - α c ) cos θ d λ ,
L c λ d λ = τ A E 0 S λ α g { 2 π π π / 2 ( P ( θ ) / 4 π ) ( 1 - exp ( - δ c sec θ ) ) × sin θ cos θ d θ } d λ ,
E S λ d λ = τ A 2 E 0 S λ α g α c ¯ d ω d λ ,
α c ¯ = 0 · 0293 ( 1 - exp ( - 2 · 06 δ c ) )
α c = [ ( 4 · 32 × 10 - 10 ) θ 4 · 72 + 0 · 03 ] ( δ c / 0 · 38 ) ,
E S λ d λ = E 0 λ τ A 3 cos θ α c ¯ α g ( 1 - α c ) d ω d λ .
γ ( π ) = Z b Z T B ( π , z ) d z ,
δ c = γ ( π ) / k .
γ ( π ) [ = Z b Z T B ( π , z ) d z ]
E T λ d λ = ξ λ [ 1 - exp ( - δ c sec θ ) ] + E S λ d λ + E a R λ d λ .
E T λ d λ = ξ λ [ 1 - exp ( - δ c sec θ ) ] + E a R λ d λ ,
E S λ = ( ξ λ - ξ λ ) [ 1 - exp ( - δ c sec θ ) ] ,
E S λ / E D λ ( = ξ λ - ξ λ ξ λ )
P ( θ ) / 4 π = ξ λ / B ,
P ( θ ) = P ( θ ) / ( 1 + E S λ / E D λ ) .
P ( θ ) P 0 ( θ ) = P ( θ 1 ) P 0 ( θ 1 )             ( 90 ° < θ < 180 ° ) ,
P ( θ ) = P ( θ ) / [ 1 + P ( θ 1 ) P 0 ( θ 1 ) E S λ E D λ ] .
E ( z ) = W c B ( π , z ) 8 π z 2 τ ( z ) 2 ,
V = ζ E ( z )
B ( π , z ) = B R ( π , z R ) V V R τ ( z R ) 2 τ ( z ) 2 W R W z 2 z R 2
= V z 2 W τ ( z ) 2 S ,
S = [ V R z R 2 τ ( z R ) 2 W R B R ( π , z R ) ]
V T = ζ E T λ d λ ,
E T λ d λ = ( V T ) / ζ .
ζ = 8 π Z R 2 V R W R c B R ( π , z R ) τ ( Z R ) 2 = 8 π S c .
E T λ d λ = V T c 8 π S

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