Abstract

Scattering matrix characteristics of polydisperse, randomly oriented, small ice crystals modeled by finite circular cylinders with various ratios of the length to diameter (L/D) ratio are calculated by use of the exact T-matrix approach, with emphasis on the thermal infrared spectral region that extends from the atmospheric short-wave IR window to the far-IR wavelengths to as large as 30 µm. The observed ice crystal size distribution and the well-known power-law distribution are considered. The results of the extensive calculations show that the characteristics of scattering matrix elements of small ice circular cylinders depend strongly on wavelengths and refractive indices, particle size distributions, and the L/D ratios. The applicability of the power-law distribution and particle shapes for light scattering calculations for small ice crystals is discussed. The effects of the effective variance of size distribution on light scattering characteristics are addressed. It seems from the behavior of scattering matrix elements of small ice crystals that the combination of 25 and 3.979 µm has some advantages and potential applications for remote sensing of cirrus and other ice clouds.

© 2002 Optical Society of America

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  4. P. Yang, K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 173–221.
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  12. L. Xu, G. Zhang, J. Ding, H. Chen, “Light scattering by polydispersions of randomly oriented hexagonal ice crystals in cirrus clouds: phase function analyses,” Int. J. Light Electron. Opt. 106, 103–114 (1997).
  13. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 3–27.
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    [CrossRef]
  23. M. S. Quinby-Hunt, P. G. Hull, A. J. Hunt, “Polarized light scattering in the marine environment,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 525–554.
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  29. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  30. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
    [CrossRef] [PubMed]
  31. A. J. Heymsfield, L. J. Donner, “A scheme for parameterizing ice-cloud water content in general circulation models,” J. Atmos. Sci. 47, 1865–1877 (1990).
    [CrossRef]
  32. A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
    [CrossRef] [PubMed]

1998 (2)

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current fortran implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

K. F. Evans, S. J. Walter, A. J. Heymsfield, M. N. Deeter, “Modeling of submillimeter passive remote sensing of cirrus clouds,” J. Appl. Meteorol. 37, 184–205 (1998).
[CrossRef]

1997 (2)

K. Sassen, “Contrail-cirrus and their potential for regional climate change,” Bull. Am. Meteorol. Soc. 78, 1885–1903 (1997).
[CrossRef]

L. Xu, G. Zhang, J. Ding, H. Chen, “Light scattering by polydispersions of randomly oriented hexagonal ice crystals in cirrus clouds: phase function analyses,” Int. J. Light Electron. Opt. 106, 103–114 (1997).

1996 (6)

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical Pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (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. Transfer 55, 535–575 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

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]

1995 (1)

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

1994 (1)

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

1993 (1)

1991 (1)

1990 (1)

A. J. Heymsfield, L. J. Donner, “A scheme for parameterizing ice-cloud water content in general circulation models,” J. Atmos. Sci. 47, 1865–1877 (1990).
[CrossRef]

1987 (1)

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

1983 (1)

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

1974 (1)

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

Ackerman, S. A.

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

Antonelli, P.

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

Baum, B. A.

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

Bohren, C. F.

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

Bosma, P. B.

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Bretherton, F. P.

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

Cairns, B.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Carlson, B.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Chen, H.

L. Xu, G. Zhang, J. Ding, H. Chen, “Light scattering by polydispersions of randomly oriented hexagonal ice crystals in cirrus clouds: phase function analyses,” Int. J. Light Electron. Opt. 106, 103–114 (1997).

Choe, N.

K. D. Hutchison, N. Choe, “Quantitative assessment on the value of 1.38 µm imagery for the automated analysis of optically thin cirrus in daytime imagery,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere, D. K. Lynch, E. P. Shettle, eds., Proc. SPIE2578, 53–60 (1995).
[CrossRef]

de Haan, J. F.

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Deeter, M. N.

K. F. Evans, S. J. Walter, A. J. Heymsfield, M. N. Deeter, “Modeling of submillimeter passive remote sensing of cirrus clouds,” J. Appl. Meteorol. 37, 184–205 (1998).
[CrossRef]

Del Genio, A.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Ding, J.

L. Xu, G. Zhang, J. Ding, H. Chen, “Light scattering by polydispersions of randomly oriented hexagonal ice crystals in cirrus clouds: phase function analyses,” Int. J. Light Electron. Opt. 106, 103–114 (1997).

J. Ding, L. Xu, “Light scattering characteristics by small ice circular cylinders in visible, 1.38 µm, and some infrared wavelengths,” Opt. Eng. (to be published).

L. Xu, J. Ding, “Light scattering characteristics by small ice particles with different size distributions and aspect ratios in visible and 1.38 µm wavelengths,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 311–319 (2002).
[CrossRef]

Donner, L. J.

A. J. Heymsfield, L. J. Donner, “A scheme for parameterizing ice-cloud water content in general circulation models,” J. Atmos. Sci. 47, 1865–1877 (1990).
[CrossRef]

Evans, K. F.

K. F. Evans, S. J. Walter, A. J. Heymsfield, M. N. Deeter, “Modeling of submillimeter passive remote sensing of cirrus clouds,” J. Appl. Meteorol. 37, 184–205 (1998).
[CrossRef]

Fung, I.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

J. Hansen, W. Rossow, I. Fung, “Long-term monitoring of global climate forcings and feedbacks,” NASA Conf. Publ. 3234 (NASA Goddard Space Flight Center, Greenbelt, Md., 1993).

Hansen, J.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

J. Hansen, W. Rossow, I. Fung, “Long-term monitoring of global climate forcings and feedbacks,” NASA Conf. Publ. 3234 (NASA Goddard Space Flight Center, Greenbelt, Md., 1993).

Hansen, J. E.

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

Heymsfield, A. J.

K. F. Evans, S. J. Walter, A. J. Heymsfield, M. N. Deeter, “Modeling of submillimeter passive remote sensing of cirrus clouds,” J. Appl. Meteorol. 37, 184–205 (1998).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical Pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
[CrossRef]

A. J. Heymsfield, L. J. Donner, “A scheme for parameterizing ice-cloud water content in general circulation models,” J. Atmos. Sci. 47, 1865–1877 (1990).
[CrossRef]

Hovenier, J. W.

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 3–27.
[CrossRef]

Huang, A.

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

Huffman, D. R.

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

Hull, P. G.

M. S. Quinby-Hunt, P. G. Hull, A. J. Hunt, “Polarized light scattering in the marine environment,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 525–554.
[CrossRef]

Hunt, A. J.

M. S. Quinby-Hunt, P. G. Hull, A. J. Hunt, “Polarized light scattering in the marine environment,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 525–554.
[CrossRef]

Hutchison, K. D.

K. D. Hutchison, N. Choe, “Quantitative assessment on the value of 1.38 µm imagery for the automated analysis of optically thin cirrus in daytime imagery,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere, D. K. Lynch, E. P. Shettle, eds., Proc. SPIE2578, 53–60 (1995).
[CrossRef]

Lacis, A.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Liou, K. N.

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]

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Preprints of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, L. D. Travis, J. W. Hovenier, eds. (American Meteorological Society, Boston, 1998), pp. 28–31.

P. Yang, K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 173–221.
[CrossRef]

Macke, A.

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 147–172.

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. Transfer 55, 535–575 (1996).
[CrossRef]

McFarquhar, G. M.

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical Pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
[CrossRef]

G. M. McFarquhar, University of Illinois at Urbana-Champaign, Urbana, Ill. 61801-3070 (personal communication, 2001).

Menzel, W. P.

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

Mishchenko, M.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current fortran implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

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

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

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, 4652–4666 (1993).
[CrossRef] [PubMed]

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

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 3–27.
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 147–172.

Quinby-Hunt, M. S.

M. S. Quinby-Hunt, P. G. Hull, A. J. Hunt, “Polarized light scattering in the marine environment,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 525–554.
[CrossRef]

Rossow, W.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

J. Hansen, W. Rossow, I. Fung, “Long-term monitoring of global climate forcings and feedbacks,” NASA Conf. Publ. 3234 (NASA Goddard Space Flight Center, Greenbelt, Md., 1993).

Sassen, K.

K. Sassen, “Contrail-cirrus and their potential for regional climate change,” Bull. Am. Meteorol. Soc. 78, 1885–1903 (1997).
[CrossRef]

Sato, M.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Smith, W. L.

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

Takano, Y.

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Preprints of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, L. D. Travis, J. W. Hovenier, eds. (American Meteorological Society, Boston, 1998), pp. 28–31.

Travis, L.

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current fortran implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

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

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

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

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 147–172.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 3–27.
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

van der Mee, C. V. M.

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Walter, S. J.

K. F. Evans, S. J. Walter, A. J. Heymsfield, M. N. Deeter, “Modeling of submillimeter passive remote sensing of cirrus clouds,” J. Appl. Meteorol. 37, 184–205 (1998).
[CrossRef]

Xu, L.

L. Xu, G. Zhang, J. Ding, H. Chen, “Light scattering by polydispersions of randomly oriented hexagonal ice crystals in cirrus clouds: phase function analyses,” Int. J. Light Electron. Opt. 106, 103–114 (1997).

J. Ding, L. Xu, “Light scattering characteristics by small ice circular cylinders in visible, 1.38 µm, and some infrared wavelengths,” Opt. Eng. (to be published).

L. Xu, J. Ding, “Light scattering characteristics by small ice particles with different size distributions and aspect ratios in visible and 1.38 µm wavelengths,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 311–319 (2002).
[CrossRef]

Yang, P.

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]

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Preprints of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, L. D. Travis, J. W. Hovenier, eds. (American Meteorological Society, Boston, 1998), pp. 28–31.

P. Yang, K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 173–221.
[CrossRef]

Zhang, G.

L. Xu, G. Zhang, J. Ding, H. Chen, “Light scattering by polydispersions of randomly oriented hexagonal ice crystals in cirrus clouds: phase function analyses,” Int. J. Light Electron. Opt. 106, 103–114 (1997).

Appl. Opt. (3)

Astron. Astrophys. (2)

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Bull. Am. Meteorol. Soc. (1)

K. Sassen, “Contrail-cirrus and their potential for regional climate change,” Bull. Am. Meteorol. Soc. 78, 1885–1903 (1997).
[CrossRef]

Climatic Change (1)

J. Hansen, W. Rossow, B. Carlson, A. Lacis, L. Travis, A. Del Genio, I. Fung, B. Cairns, M. Mishchenko, M. Sato, “Low-cost long-term monitoring of global climate forcings and feedbacks,” Climatic Change 31, 247–271 (1995).
[CrossRef]

Int. J. Light Electron. Opt. (1)

L. Xu, G. Zhang, J. Ding, H. Chen, “Light scattering by polydispersions of randomly oriented hexagonal ice crystals in cirrus clouds: phase function analyses,” Int. J. Light Electron. Opt. 106, 103–114 (1997).

J. Appl. Meteorol. (1)

K. F. Evans, S. J. Walter, A. J. Heymsfield, M. N. Deeter, “Modeling of submillimeter passive remote sensing of cirrus clouds,” J. Appl. Meteorol. 37, 184–205 (1998).
[CrossRef]

J. Atmos. Sci. (3)

A. J. Heymsfield, L. J. Donner, “A scheme for parameterizing ice-cloud water content in general circulation models,” J. Atmos. Sci. 47, 1865–1877 (1990).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical Pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current fortran implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[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. Transfer 55, 535–575 (1996).
[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 (14)

G. M. McFarquhar, University of Illinois at Urbana-Champaign, Urbana, Ill. 61801-3070 (personal communication, 2001).

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 3–27.
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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

P. Yang, K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 173–221.
[CrossRef]

K. D. Hutchison, N. Choe, “Quantitative assessment on the value of 1.38 µm imagery for the automated analysis of optically thin cirrus in daytime imagery,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere, D. K. Lynch, E. P. Shettle, eds., Proc. SPIE2578, 53–60 (1995).
[CrossRef]

M. S. Quinby-Hunt, P. G. Hull, A. J. Hunt, “Polarized light scattering in the marine environment,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 525–554.
[CrossRef]

L. Xu, J. Ding, “Light scattering characteristics by small ice particles with different size distributions and aspect ratios in visible and 1.38 µm wavelengths,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 311–319 (2002).
[CrossRef]

J. Ding, L. Xu, “Light scattering characteristics by small ice circular cylinders in visible, 1.38 µm, and some infrared wavelengths,” Opt. Eng. (to be published).

E. R. Washwell, ed., GOES-8 and Beyond, Proc. SPIE2812 (1996).

P. Antonelli, W. P. Menzel, F. P. Bretherton, S. A. Ackerman, A. Huang, B. A. Baum, W. L. Smith, “Retrieval of particle size, cloud top pressure, and effective emissivity from aircraft high spectral resolution infrared measurements,” in Remote Sensing of Clouds and Atmosphere VI, K. Schaefer, O. Lado-Bordowsky, A. Comeron, M. R. Carleer, J. S. Fender, eds., Proc. SPIE4539, 41–42 (2002).

J. Hansen, W. Rossow, I. Fung, “Long-term monitoring of global climate forcings and feedbacks,” NASA Conf. Publ. 3234 (NASA Goddard Space Flight Center, Greenbelt, Md., 1993).

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Preprints of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, L. D. Travis, J. W. Hovenier, eds. (American Meteorological Society, Boston, 1998), pp. 28–31.

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 147–172.

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Figures (14)

Fig. 1
Fig. 1

Average size distribution of ice crystals measured on 4 April 1993 during the CEPEX.

Fig. 2
Fig. 2

Angular distribution of the scattering matrix elements for randomly oriented ice prolate cylinders with different L/D ratios for the observed size distribution shown in Fig. 1 and Eq. (11) with r e ranging from 1.5747 µm (x = 2.4866, L/D ratio of 2) to 1.5859 µm (x = 2.5043, L/D ratio of 1) and the corresponding v e ranging from 0.0462 to 0.0442 at λ = 3.979 µm.

Fig. 3
Fig. 3

Same as Fig. 2 except for ice oblate cylinders with r e ranging from 1.5766 µm (x = 2.4896, L/D ratio of 0.2) to 1.5859 µm (x = 2.5043, L/D ratio of 1) and the corresponding v e ranging from 0.0459 to 0.0442.

Fig. 4
Fig. 4

Angular distribution of the scattering matrix elements for randomly oriented ice prolate cylinders with different L/D ratios for the modeled size distributions shown in Eq. (5) with r e = 3 µm (x = 4.737) and v e = 0.105 at λ = 3.979 µm.

Fig. 5
Fig. 5

Same as Fig. 4 except for r e = 10.17 µm (x = 16.059) and v e = 0.105 (F 11 is omitted).

Fig. 6
Fig. 6

Same as Figs. 2 and 3 except only for elements of F 22/F 11 and F 34/F 11 for (a), (b) prolate cylinders with x ranging from 0.9894 to 0.9965 and for (c), (d) oblate cylinders with x ranging from 0.9906 to 0.9965 at λ = 10 µm.

Fig. 7
Fig. 7

Same as Fig. 6 except for λ = 11.02 µm and x ranging from 0.8978 to 0.9042 for (a), (b) prolate cylinders and from 0.8989 to 0.9042 for (c), (d) oblate cylinders.

Fig. 8
Fig. 8

Same as Fig. 4 except for both prolate and oblate cylinders with r e = 10.17 µm (x = 6.39) and v e = 0.105 at λ = 10 µm.

Fig. 9
Fig. 9

Same as Fig. 4 except for prolate cylinders with r e = 10.17 µm (x = 5.809) and v e = 0.105 at λ = 11.02 µm (F 11 is omitted).

Fig. 10
Fig. 10

Same as Figs. 2 and 3 except only for elements of F 22/F 11, -F 12/F 11, and F 34/F 11 for prolate cylinders with x ranging from 0.3958 to 0.3986 (r e = 1.5747–1.5859 µm) and for oblate cylinders with x ranging from 0.3962 to 0.3986 (r e = 1.5766–1.5859 µm).

Fig. 11
Fig. 11

Same as Fig. 4 except for r e = 10.17 µm (x = 2.556) and v e = 0.105 at λ = 25 µm (F 11 is omitted).

Fig. 12
Fig. 12

Same as Fig. 4 except for r e = 30.11 µm (x = 7.567) and v e = 0.057 at λ = 25 µm (F 11 is omitted).

Fig. 13
Fig. 13

Same as Fig. 12 except for r e = 30.34 µm (x = 7.625) and v e = 0.405.

Fig. 14
Fig. 14

Same as Fig. 2 except for the PLD.

Tables (2)

Tables Icon

Table 1 Influence of Sizes and the L/D Ratios on Extinction Coefficients and Single Scattering Albedo of Ice Cylinders at 10-µm Wavelength

Tables Icon

Table 2 Refractive Indices of Ice at Some IR Wavelengths

Equations (12)

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

I=I, Q, U, VT=IQUV.
Fθ=F11θF12θ00F12θF22θ0000F33θF34θ00-F34θF44θ,
14π4πdΩF11θ=1.
Isca=Cscan0dv4πR2 FθIinc,
nr=Cforrr1Cr1r3forr1rr20forr>r2,
C=2r2r12r22-r12
re=r2-r1lnr2/r1,
ve=r2+r12r2-r1lnr2/r1-1,
re=1G0dr rπr2nr,
ve=1G re20dr r-re2 πr2nr,
G=0dr πr2nr,
Nl=clα exp-α/γ l/βγ+0.3 l-1.5,

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