Abstract

We compute the scalar optical properties of size–shape distributions of wavelength-sized randomly oriented homogeneous particles with different nonaxially symmetric geometries and investigate how well they can be modeled with a simple spherical, spheroidal, or cylindrical particle model. We find that a spherical particle model can be used to determine the extinction and scattering cross sections, the single-scattering albedo, and the asymmetry parameter with an error of less than 2%, whereas the extinction-to-backscatter ratio Reb is reproduced only with an error of 9%. The cylindrical and spheroidal particle models yield slightly improved results for Reb that deviate from those obtained for the complex particle ensemble by 7% and 5%, respectively. Large discrepancies between results of the different models are observed for the linear depolarization ratio, thus indicating limitations of models based on simple particle shapes.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  26. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape-dependence of the optical properties in size–shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
    [CrossRef]
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  28. P. Yang, K. N. Liou, M. I. Mishchenko, B.-C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols,” Appl. Opt. 39, 3727–3737 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2001 (1)

2000 (4)

1999 (5)

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape-dependence of the optical properties in size–shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

P. N. Francis, J. S. Foot, A. J. Baran, “Aircraft measurements of the solar and infrared radiative properties of cirrus and their dependence on ice crystal shape,” J. Geophys. Res. 104, 31685–31695 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Point group symmetries in electromagnetic scattering,” J. Opt. Soc. Am. A 16, 853–865 (1999).
[CrossRef]

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

1998 (6)

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transf. 60, 411–423 (1998).
[CrossRef]

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contrib. Atmos. Phys. 71, 223–248 (1998).

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Modeling the radiative transfer properties of media containing particles of moderately and highly elongated shape,” Geophys. Res. Lett. 25, 4481–4484 (1998).
[CrossRef]

K. Lumme, J. Rahola, “Comparison of light scattering by stochastically rough spheres, best-fit spheroids and spheres,” J. Quant. Spectrosc. Radiat. Transf. 60, 439–450 (1998).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T-matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
[CrossRef]

1997 (2)

P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm,” J. Opt. Soc. Am. A 14, 2278–2289 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

1996 (5)

P. Yang, K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

P. Yang, K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16973–16985 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55, 535–575 (1996).
[CrossRef]

1995 (2)

1994 (3)

1993 (2)

1992 (1)

1991 (1)

1975 (1)

1974 (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Asano, S.

Baran, A. J.

M. Doutriaux-Boucher, J.-C. Buriez, G. Brogniez, L. C.-Labonnote, A. J. Baran, “Sensitivity of retrieved POLDER directional cloud optical thickness to various ice particle models,” Geophys. Res. Lett. 27, 109–112 (2000).
[CrossRef]

P. N. Francis, J. S. Foot, A. J. Baran, “Aircraft measurements of the solar and infrared radiative properties of cirrus and their dependence on ice crystal shape,” J. Geophys. Res. 104, 31685–31695 (1999).
[CrossRef]

Bishop, D. M.

D. M. Bishop, Group Theory and Chemistry (Dover, Mineola, N.Y., 1993).

Brogniez, G.

M. Doutriaux-Boucher, J.-C. Buriez, G. Brogniez, L. C.-Labonnote, A. J. Baran, “Sensitivity of retrieved POLDER directional cloud optical thickness to various ice particle models,” Geophys. Res. Lett. 27, 109–112 (2000).
[CrossRef]

Buriez, J.-C.

M. Doutriaux-Boucher, J.-C. Buriez, G. Brogniez, L. C.-Labonnote, A. J. Baran, “Sensitivity of retrieved POLDER directional cloud optical thickness to various ice particle models,” Geophys. Res. Lett. 27, 109–112 (2000).
[CrossRef]

C.-Labonnote, L.

M. Doutriaux-Boucher, J.-C. Buriez, G. Brogniez, L. C.-Labonnote, A. J. Baran, “Sensitivity of retrieved POLDER directional cloud optical thickness to various ice particle models,” Geophys. Res. Lett. 27, 109–112 (2000).
[CrossRef]

Chýlek, P.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 274–308.

Comberg, U.

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transf. 60, 411–423 (1998).
[CrossRef]

Dobbie, J. S.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 274–308.

Doutriaux-Boucher, M.

M. Doutriaux-Boucher, J.-C. Buriez, G. Brogniez, L. C.-Labonnote, A. J. Baran, “Sensitivity of retrieved POLDER directional cloud optical thickness to various ice particle models,” Geophys. Res. Lett. 27, 109–112 (2000).
[CrossRef]

Draine, B. T.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 131–144.

Farafonov, V. G.

N. V. Voshchinnikov, V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

Flatau, P. J.

Foot, J. S.

P. N. Francis, J. S. Foot, A. J. Baran, “Aircraft measurements of the solar and infrared radiative properties of cirrus and their dependence on ice crystal shape,” J. Geophys. Res. 104, 31685–31695 (1999).
[CrossRef]

Francis, P. N.

P. N. Francis, J. S. Foot, A. J. Baran, “Aircraft measurements of the solar and infrared radiative properties of cirrus and their dependence on ice crystal shape,” J. Geophys. Res. 104, 31685–31695 (1999).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

P. N. Francis, “Some aircraft observations of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
[CrossRef]

Fuller, K. A.

K. A. Fuller, D. W. Mackowski, “Electromagnetic scattering by compounded spherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 226–273.

Gao, B.-C.

Geldart, D. J. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 274–308.

Grenfell, T. C.

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Kahn, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

Kahnert, F. M.

Khlebtsov, N. G.

Kinne, S.

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16973–16985 (1996).
[CrossRef]

Liou, K. N.

Lumme, K.

K. Lumme, J. Rahola, “Comparison of light scattering by stochastically rough spheres, best-fit spheroids and spheres,” J. Quant. Spectrosc. Radiat. Transf. 60, 439–450 (1998).
[CrossRef]

Macke, A.

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16973–16985 (1996).
[CrossRef]

A. Macke, “Monte Carlo calculations of light scattering by large particles with multiple internal inclusions,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 309–323.

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55, 535–575 (1996).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

K. A. Fuller, D. W. Mackowski, “Electromagnetic scattering by compounded spherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 226–273.

Mano, Y.

McFarquhar, G. M.

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

Mishchenko, M. I.

P. Yang, K. N. Liou, M. I. Mishchenko, B.-C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols,” Appl. Opt. 39, 3727–3737 (2000).
[CrossRef]

N. T. Zakharova, M. I. Mishchenko, “Scattering properties of needle-like and plate-like ice spheroids with moderate size parameters,” Appl. Opt. 39, 5052–5057 (2000).
[CrossRef]

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
[CrossRef]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16973–16985 (1996).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

M. I. Mishchenko, “Light scattering by size–shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4665 (1993).
[CrossRef] [PubMed]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[CrossRef]

Mugnai, A.

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of publications,” in (NASA/Goddard Space Flight Center, Greenbelt, Md., 1986).

Muinonen, K.

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 323–354.

Rahola, J.

K. Lumme, J. Rahola, “Comparison of light scattering by stochastically rough spheres, best-fit spheroids and spheres,” J. Quant. Spectrosc. Radiat. Transf. 60, 439–450 (1998).
[CrossRef]

Rossow, W. B.

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16973–16985 (1996).
[CrossRef]

Schulz, F. M.

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape-dependence of the optical properties in size–shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Point group symmetries in electromagnetic scattering,” J. Opt. Soc. Am. A 16, 853–865 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Modeling the radiative transfer properties of media containing particles of moderately and highly elongated shape,” Geophys. Res. Lett. 25, 4481–4484 (1998).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T-matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
[CrossRef]

Stamnes, J. J.

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to homogeneous particles with point-group symmetries,” Appl. Opt. 40, 3110–3123 (2001).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Point group symmetries in electromagnetic scattering,” J. Opt. Soc. Am. A 16, 853–865 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape-dependence of the optical properties in size–shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Modeling the radiative transfer properties of media containing particles of moderately and highly elongated shape,” Geophys. Res. Lett. 25, 4481–4484 (1998).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T-matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
[CrossRef]

Stamnes, K.

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to homogeneous particles with point-group symmetries,” Appl. Opt. 40, 3110–3123 (2001).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Point group symmetries in electromagnetic scattering,” J. Opt. Soc. Am. A 16, 853–865 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape-dependence of the optical properties in size–shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Modeling the radiative transfer properties of media containing particles of moderately and highly elongated shape,” Geophys. Res. Lett. 25, 4481–4484 (1998).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T-matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
[CrossRef]

Takano, Y.

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Tso, H. C. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 274–308.

van de Hulst, H. C.

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

Videen, G.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 274–308.

Voshchinnikov, N. V.

N. V. Voshchinnikov, V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

Warren, S. G.

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

Wiscombe, W. J.

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of publications,” in (NASA/Goddard Space Flight Center, Greenbelt, Md., 1986).

Wriedt, T.

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transf. 60, 411–423 (1998).
[CrossRef]

Yamamoto, G.

Yang, P.

Zakharova, N. T.

Appl. Opt. (11)

S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
[CrossRef] [PubMed]

M. I. Mishchenko, “Light scattering by size–shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4665 (1993).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T-matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
[CrossRef]

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
[CrossRef]

P. Yang, K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

Y. Mano, “Exact solution of electromagnetic scattering by a three-dimensional hexagonal ice column obtained with the boundary-element method,” Appl. Opt. 39, 5541–5546 (2000).
[CrossRef]

P. Yang, K. N. Liou, M. I. Mishchenko, B.-C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols,” Appl. Opt. 39, 3727–3737 (2000).
[CrossRef]

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to homogeneous particles with point-group symmetries,” Appl. Opt. 40, 3110–3123 (2001).
[CrossRef]

N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992).
[CrossRef] [PubMed]

N. T. Zakharova, M. I. Mishchenko, “Scattering properties of needle-like and plate-like ice spheroids with moderate size parameters,” Appl. Opt. 39, 5052–5057 (2000).
[CrossRef]

Astrophys. Space Sci. (1)

N. V. Voshchinnikov, V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

Atmos. Res. (1)

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Contrib. Atmos. Phys. (1)

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contrib. Atmos. Phys. 71, 223–248 (1998).

Geophys. Res. Lett. (2)

M. Doutriaux-Boucher, J.-C. Buriez, G. Brogniez, L. C.-Labonnote, A. J. Baran, “Sensitivity of retrieved POLDER directional cloud optical thickness to various ice particle models,” Geophys. Res. Lett. 27, 109–112 (2000).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Modeling the radiative transfer properties of media containing particles of moderately and highly elongated shape,” Geophys. Res. Lett. 25, 4481–4484 (1998).
[CrossRef]

J. Atmos. Sci. (2)

P. N. Francis, “Some aircraft observations of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

J. Geophys. Res. (5)

P. N. Francis, J. S. Foot, A. J. Baran, “Aircraft measurements of the solar and infrared radiative properties of cirrus and their dependence on ice crystal shape,” J. Geophys. Res. 104, 31685–31695 (1999).
[CrossRef]

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16973–16985 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape-dependence of the optical properties in size–shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

J. Opt. Soc. Am. A (7)

J. Quant. Spectrosc. Radiat. Transf. (3)

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55, 535–575 (1996).
[CrossRef]

K. Lumme, J. Rahola, “Comparison of light scattering by stochastically rough spheres, best-fit spheroids and spheres,” J. Quant. Spectrosc. Radiat. Transf. 60, 439–450 (1998).
[CrossRef]

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transf. 60, 411–423 (1998).
[CrossRef]

Space Sci. Rev. (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Other (8)

B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 131–144.

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

D. M. Bishop, Group Theory and Chemistry (Dover, Mineola, N.Y., 1993).

A. Macke, “Monte Carlo calculations of light scattering by large particles with multiple internal inclusions,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 309–323.

K. A. Fuller, D. W. Mackowski, “Electromagnetic scattering by compounded spherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 226–273.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 274–308.

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 323–354.

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of publications,” in (NASA/Goddard Space Flight Center, Greenbelt, Md., 1986).

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Figures (7)

Fig. 1
Fig. 1

Phase matrix elements for an ensemble of randomly oriented hexahedral prisms computed with the EBCM (solid curves) and the DDA (circles).

Fig. 2
Fig. 2

Extinction cross section Cext as a function of the effective shape parameter ξext for an ensemble of polyhedral prisms (solid curve), spheroids (dashed curve), and finite circular cylinders (dotted–dashed curve). The corresponding value for an ensemble of spheres is marked by an arrow on the ordinate axis.

Fig. 3
Fig. 3

Same as Fig. 2, but for the scattering cross section Csca.

Fig. 4
Fig. 4

Same as Fig. 2, but for the single-scattering albedo ω.

Fig. 5
Fig. 5

Same as Fig. 2, but for the asymmetry parameter cos θ.

Fig. 6
Fig. 6

Same as Fig. 2, but for the extinction-to-backscatter ratio Reb.

Fig. 7
Fig. 7

Same as Fig. 2, but for the linear depolarization ratio δL. The corresponding value for an ensemble of spheres is zero and thus off the scale.

Tables (2)

Tables Icon

Table 1 Parameters Describing the Size–Shape Distributions of Polyhedral Prismsa

Tables Icon

Table 2 Minimum and Maximum Relative Difference Δ(OP) (in Percent) between the Optical Properties of a Multiple-Geometry Size–Shape Distribution of Randomly Oriented Polyhedral Prisms and Corresponding Results Obtained with Spherical, Spheroidal, and Cylindrical Particle Modelsa

Equations (10)

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

nsize(r)=C1,rr1,nsize(r)=C1(r1/r)3,r1rr2,nsize(r)=0,r>r2,
0dr nsize(r)=1.
reff=1G0d r rπr2nsize(r)
νeff=1reff2G0dr(r-reff)2πr2nsize(r),
G=0dr πr2nsize(r).
ξ=1-1,<1(prolate),ξ=-1,1(oblate).
nshape(ξ)=1ξ2-ξ1,ξ1ξξ20,otherwise,
ξeff=ξ1+ξ22,
μeff=|ξ1-ξ2|2.
Δ(OP)=1-OPmodel(ξeff)OPpolyhed(ξeff)×100%,

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