Abstract

The single-scattering phase functions of polyhedral-shaped ice particles are calculated by means of geometric optics and the diffraction theory. Particle orientation is assumed to be random in space. Particle shapes are taken both from ice-crystal classifications and from in situ measurements. The effects of particle concavity on the scattering signature are discussed in detail. A common feature is the pronounced forward-scattering peak, as well as different halo peaks that are due to a minimum deviation at corresponding ice prisms. An unusual halo phenomena, which results from a minimum deviation in a double-prism configuration, is found and verified. The comparison of different particle types shows that backscattering is a sensitive indicator for the identification of types of ice-crystal. Aggregate particles, like bullet rosettes, basically show the scattering characteristics of their individual components.

© 1993 Optical Society of America

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References

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1991

1990

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Feature on the First ISCCP Regional Experiment (FIRE), Mon. Weather Rev. 118, (x), (1990).

E. Raschke, J. Schmetz, J. Heintzenberg, R. Kandel, R. Saunders, “The international cirrus experiment (ICE)—a joint European effort,” Eur. Space Agency J. 14, 193–199 (1990).

A. J. Heymsfield, K. M. Miller, J. D. Spinhirne, “The 27–28 October 1986 FIRE IFO cirrus case study: cloud microstructure,” Mon. Weather Rev. 118, 2313–2328 (1990).
[CrossRef]

1989

1986

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Am. Meteorol. Soc. 114, 1167–1199 (1986).

1984

1981

R. F. Coleman, K. N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos, Sci. 38, 1260–1271 (1981).
[CrossRef]

1966

C. Magono, C. Lee, “Meteorological classification of natural snow crystals,” J. Fac Sci. Hokkaido Univ. Ser. 7 2, 321–335 (1966).

Bohren, C. F.

C. F. Bohren, D. R. Hoffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.4.5.

Bottlinger, M.

Coleman, R. F.

R. F. Coleman, K. N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos, Sci. 38, 1260–1271 (1981).
[CrossRef]

Flatau, P. J.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Heintzenberg, J.

E. Raschke, J. Schmetz, J. Heintzenberg, R. Kandel, R. Saunders, “The international cirrus experiment (ICE)—a joint European effort,” Eur. Space Agency J. 14, 193–199 (1990).

Heymsfield, A. J.

A. J. Heymsfield, K. M. Miller, J. D. Spinhirne, “The 27–28 October 1986 FIRE IFO cirrus case study: cloud microstructure,” Mon. Weather Rev. 118, 2313–2328 (1990).
[CrossRef]

Hoffman, D. R.

C. F. Bohren, D. R. Hoffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.4.5.

Hovenac, E. A.

Irvine, W. M.

Kandel, R.

E. Raschke, J. Schmetz, J. Heintzenberg, R. Kandel, R. Saunders, “The international cirrus experiment (ICE)—a joint European effort,” Eur. Space Agency J. 14, 193–199 (1990).

Krupp, C.

C. Krupp, “Holographische Messungen an Eiskristallen in Cirruswolken während ICE,” M. S. thesis (Institute for Physics, University of Cologne, Cologne, Germany, 1991).

Lee, C.

C. Magono, C. Lee, “Meteorological classification of natural snow crystals,” J. Fac Sci. Hokkaido Univ. Ser. 7 2, 321–335 (1966).

Liou, K. N.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds, part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–18 (1989).
[CrossRef]

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Am. Meteorol. Soc. 114, 1167–1199 (1986).

R. F. Coleman, K. N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos, Sci. 38, 1260–1271 (1981).
[CrossRef]

Lumme, K.

Magono, C.

C. Magono, C. Lee, “Meteorological classification of natural snow crystals,” J. Fac Sci. Hokkaido Univ. Ser. 7 2, 321–335 (1966).

McLaurin, G. E.

Miller, K. M.

A. J. Heymsfield, K. M. Miller, J. D. Spinhirne, “The 27–28 October 1986 FIRE IFO cirrus case study: cloud microstructure,” Mon. Weather Rev. 118, 2313–2328 (1990).
[CrossRef]

Muinonen, K.

Pattloch, F.

Peltoniemi, J. I.

Raschke, E.

E. Raschke, J. Schmetz, J. Heintzenberg, R. Kandel, R. Saunders, “The international cirrus experiment (ICE)—a joint European effort,” Eur. Space Agency J. 14, 193–199 (1990).

Rockwitz, K.-D.

Saunders, R.

E. Raschke, J. Schmetz, J. Heintzenberg, R. Kandel, R. Saunders, “The international cirrus experiment (ICE)—a joint European effort,” Eur. Space Agency J. 14, 193–199 (1990).

Schmetz, J.

E. Raschke, J. Schmetz, J. Heintzenberg, R. Kandel, R. Saunders, “The international cirrus experiment (ICE)—a joint European effort,” Eur. Space Agency J. 14, 193–199 (1990).

Spinhirne, J. D.

A. J. Heymsfield, K. M. Miller, J. D. Spinhirne, “The 27–28 October 1986 FIRE IFO cirrus case study: cloud microstructure,” Mon. Weather Rev. 118, 2313–2328 (1990).
[CrossRef]

Stackhouse, P. W.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Stephens, G. L.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Takano, Y.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds, part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–18 (1989).
[CrossRef]

Tränkle, E.

Tsay, S.-C.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Umhauer, H.

Whalley, E.

Am. Meteorol. Soc.

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Am. Meteorol. Soc. 114, 1167–1199 (1986).

Appl. Opt.

Eur. Space Agency J.

E. Raschke, J. Schmetz, J. Heintzenberg, R. Kandel, R. Saunders, “The international cirrus experiment (ICE)—a joint European effort,” Eur. Space Agency J. 14, 193–199 (1990).

Feature on the First ISCCP Regional Experiment (FIRE), Mon. Weather Rev.

Feature on the First ISCCP Regional Experiment (FIRE), Mon. Weather Rev. 118, (x), (1990).

J. Atmos, Sci.

R. F. Coleman, K. N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos, Sci. 38, 1260–1271 (1981).
[CrossRef]

J. Atmos. Sci.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds, part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–18 (1989).
[CrossRef]

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

J. Fac Sci. Hokkaido Univ. Ser. 7

C. Magono, C. Lee, “Meteorological classification of natural snow crystals,” J. Fac Sci. Hokkaido Univ. Ser. 7 2, 321–335 (1966).

J. Opt. Soc. Am. A

Mon. Weather Rev.

A. J. Heymsfield, K. M. Miller, J. D. Spinhirne, “The 27–28 October 1986 FIRE IFO cirrus case study: cloud microstructure,” Mon. Weather Rev. 118, 2313–2328 (1990).
[CrossRef]

Other

C. Krupp, “Holographische Messungen an Eiskristallen in Cirruswolken während ICE,” M. S. thesis (Institute for Physics, University of Cologne, Cologne, Germany, 1991).

C. F. Bohren, D. R. Hoffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.4.5.

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Figures (8)

Fig. 1
Fig. 1

Typical ice particle sizes and shapes observed during the intensive field operations program, ICE IFO '89. The data were taken from an airborne holographic measurement system operated by the Metereological Office Research Flight, UK.

Fig. 2
Fig. 2

Geometric shapes of all particles presented in this paper.

Fig. 3
Fig. 3

Scattering phase function of a hexagonal column for different numbers p of considered internal reflections compared with the results of Takano and Liou.6 An enhancement of the forward-scattering region is also included in the diagram.

Fig. 4
Fig. 4

Scattering phase function of (a) the pyramid, (b) the solid bullet, (c) the cube (dotted curve) and the asymmetric double bullet.

Fig. 5
Fig. 5

(a) Successive transmissions, (b) successive external reflections at a concave particle.

Fig. 6
Fig. 6

Minimum deviation for successive transmission through two prisms: deviation angle θs as a function of the first incoming angle θ1 [see also Fig. 5(a)] for the test crystal, the hollow bullet, and the cup.

Fig. 7
Fig. 7

Scattering phase function of (a) the test crystal, (b) the hollow bullet, (c) the hollow (dotted curve) and solid columns.

Fig. 8
Fig. 8

Scattering phase function for (a) the capped column (dotted curve, measured), (b) the cup, (c) the bullet rosettes.

Tables (2)

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Table 1 Surface Area and Averaged Geometric Cross Section for All Particles under Consideration

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Table 2 Sizes of All Hexagonal Symmetric Particles under Consideration

Equations (3)

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P dif ( θ ) = k 2 r 2 ( 1 + cos θ ) 2 [ J 1 ( kr sin θ ) kr sin θ ] 2 ,
P ( θ ) = P ref ( θ ) + P dif ( θ ) 2 ,
θ s = θ 1 + θ 2 γ 1 + θ 3 + θ 4 γ 3 ,

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