Abstract

We investigate the errors associated with the use of circular cylinders as surrogates for hexagonal columns in computing the optical properties of pristine ice crystals at infrared (8–12-μm) wavelengths. The equivalent circular cylinders are specified in terms of volume (V), projected area (A), and volume-to-area ratio that are equal to those of the hexagonal columns. We use the T-matrix method to compute the optical properties of the equivalent circular cylinders. We apply the finite-difference time-domain method to compute the optical properties of hexagonal ice columns smaller than 40 μm. For hexagonal columns larger than 40 μm we employ an improved geometric optics method and a stretched scattering potential technique developed in previous studies to calculate the phase function and the extinction (or absorption) efficiency, respectively. The differences between the results for circular cylinders and hexagonal columns are of the order of a few percent. Thus it is quite reasonable to use a circular cylinder geometry as a surrogate for pristine hexagonal ice columns for scattering calculations at infrared (8–12-μm) wavelengths. Although the pristine ice crystals can be approximated as circular cylinders in scattering calculations at infrared wavelengths, it is shown that optical properties of individual aggregates cannot be well approximated by those of individual finite columns or cylinders.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  61. D. L. Mitchell, W. P. Arnott, “A model prediction the evolution of ice particle size spectra and radiative properties of cirrus cloud. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
    [CrossRef]
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2002 (7)

A. J. Heymsfield, S. Lewis, A. Bansemer, J. Iaquinta, L. M. Miloshevich, M. Kajikawa, C. Twohy, M. R. Poellot, “A general approach for deriving the properties of cirrus and stratiform ice cloud particles,” J. Atmos. Sci. 59, 3–29 (2002).
[CrossRef]

G. M. McFarquhar, P. Yang, A. Macke, A. J. Baran, “A new parameterization of single-scattering solar radiative properties for tropical anvils using observed ice crystal size and shape distributions,” J. Atmos. Sci. 59, 2458–2478 (2002).
[CrossRef]

M.-D. Chou, K.-T. Lee, P. Yang, “Parameterization of shortwave cloud optical properties for a mixture of ice particle habits for use in atmospheric models,” J. Geophys. Res. 107, doi: 10.109/2002JD002061 (2002).
[CrossRef]

J. R. Key, P. Yang, B. A. Baum, S. L. Nasiri, “Parameterization of shortwave ice cloud optical properties for various particle habits,” J. Geophys. Res. 107, 10.1029/2001JD000742 (2002).

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Can simple particle shapes be used to model scalar optical properties of an ensemble of wavelength-sized particles with complex shapes?” J. Quant. Spectrosc. Radiat. Transfer 19, 521–531 (2002).

D. W. Mackowski, “Discrete dipole moment method for calculation of the T matrix for nonspherical particles,” J. Opt. Soc. Am. A 19, 881–893 (2002).
[CrossRef]

L. Xu, J. Ding, A. Cheng, “Scattering matrix of infrared radiation by ice finite circular cylinders,” Appl. Opt. 41, 2333–2348 (2002).
[CrossRef] [PubMed]

2001 (5)

S. Havemann, A. J. Baran, “Extension of T-matrix to scattering of electromagnetic plane waves by non-axisymmetric dielectric particles: application to hexagonal ice cylinders,” J. Quant. Spectrosc. Radiat. Transfer 70, 139–158 (2001).
[CrossRef]

P. Yang, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, S. L. Nasiri, “Radiative properties of cirrus clouds in the infrared (8–13 μm) spectral region,” J. Quant. Spectrosc. Radiat. Transfer 70, 473–504 (2001).
[CrossRef]

A. J. Baran, P. Yang, S. Havemann, “Calculation of the single-scattering properties of randomly oriented hexagonal ice columns: a comparison of the T-matrix and the finite-difference time-domain methods,” App. Opt. 40, 4376–4386 (2001).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, W. Wiscombe, Y. Hu, S. Nasiri, P. Soulen, A. Heymsfield, G. McFarquhar, L. Miloshevich, “Sensitivity of cirrus bidirectional reflectance to vertical inhomogeneity of ice crystal habits and size distributions for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands,” J. Geophys. Res. 106, 17267–17291 (2001).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. Wiscombe, M. I. Mischenko, D. M. Winker, S. L. Nasiri, “Asymptotic solutions of optical properties of large particles with strong absorption,” Appl. Opt. 40, 1532–1547 (2001).
[CrossRef]

2000 (5)

B. A. Baum, D. Kratz, P. Yang, S. C. Ou, Y. X. Hu, P. F. Soulen, S. C. Tsay, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS. 1. Data and models,” J. Geophys. Res. 105, 11767–11780 (2000).
[CrossRef]

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

J. E. Kristjansson, J. M. Edwards, D. L. Mitchell, “The impact of a new scheme for optical properties of ice crystals on the climate of two GCMs,” J. Geophys. Res. 105, 10,063–10,079 (2000).
[CrossRef]

A. J. Heymsfield, J. Iaquinta, “Cirrus crystal terminal velocities,” J. Atmos. Sci. 57, 916–938 (2000).
[CrossRef]

A. J. Baran, S. Havemann, “Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns,” Appl. Opt. 39, 5560–5568 (2000).
[CrossRef]

1999 (3)

W.-B. Sun, Q. Fu, Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141–3151 (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]

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by cirrus nonspherical ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

1998 (6)

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]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Clim. 11, 2223–2237 (1998).
[CrossRef]

K. Wyser, P. Yang, “Average crystal size and bulk shortwave single scattering properties in ice clouds,” Atmos. Res. 49, 315–335 (1998).
[CrossRef]

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

T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

1997 (1)

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo of ice crystals in laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

1996 (5)

1995 (2)

1994 (7)

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

D. L. Mitchell, W. P. Arnott, “A model prediction the evolution of ice particle size spectra and radiative properties of cirrus cloud. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poellot, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

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

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

P. Chylek, G. Videen, “Longwave radiative properties of polydispersed hexagonal ice crystal,” J. Atmos. Sci. 51, 175–190 (1994).
[CrossRef]

1993 (1)

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, 623–625 (1993).
[CrossRef]

1992 (1)

E. E. Ebert, J. A. Curry, “A parameterization of ice cloud optical properties for climate models,” J. Geophys. Res. 97, 3831–3836 (1992).
[CrossRef]

1991 (1)

1990 (1)

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 climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

1989 (2)

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

1988 (2)

J. S. Foot, “Some observations of the optical properties of clouds. II. Cirrus,” Q. J. R. Meteorol. Soc. 114, 145–164 (1988).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1986 (2)

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

W. J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2. Means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1986).
[CrossRef]

1984 (1)

1973 (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Arnott, W. P.

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo of ice crystals in laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, “Extinction efficiency in the infrared (2–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
[CrossRef] [PubMed]

D. L. Mitchell, W. P. Arnott, “A model prediction the evolution of ice particle size spectra and radiative properties of cirrus cloud. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poellot, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Bansemer, A.

A. J. Heymsfield, S. Lewis, A. Bansemer, J. Iaquinta, L. M. Miloshevich, M. Kajikawa, C. Twohy, M. R. Poellot, “A general approach for deriving the properties of cirrus and stratiform ice cloud particles,” J. Atmos. Sci. 59, 3–29 (2002).
[CrossRef]

Baran, A. J.

G. M. McFarquhar, P. Yang, A. Macke, A. J. Baran, “A new parameterization of single-scattering solar radiative properties for tropical anvils using observed ice crystal size and shape distributions,” J. Atmos. Sci. 59, 2458–2478 (2002).
[CrossRef]

S. Havemann, A. J. Baran, “Extension of T-matrix to scattering of electromagnetic plane waves by non-axisymmetric dielectric particles: application to hexagonal ice cylinders,” J. Quant. Spectrosc. Radiat. Transfer 70, 139–158 (2001).
[CrossRef]

A. J. Baran, P. Yang, S. Havemann, “Calculation of the single-scattering properties of randomly oriented hexagonal ice columns: a comparison of the T-matrix and the finite-difference time-domain methods,” App. Opt. 40, 4376–4386 (2001).
[CrossRef]

A. J. Baran, S. Havemann, “Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns,” Appl. Opt. 39, 5560–5568 (2000).
[CrossRef]

A. J. Baran, P. Francis, P. Yang, “A process study of the dependence of ice crystal absorption on particle geometry: application to aircraft radiometric measurements of cirrus clouds in the terrestrial window region,” J. Atmos. Sci. (to be published).

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A. J. Heymsfield, S. Lewis, A. Bansemer, J. Iaquinta, L. M. Miloshevich, M. Kajikawa, C. Twohy, M. R. Poellot, “A general approach for deriving the properties of cirrus and stratiform ice cloud particles,” J. Atmos. Sci. 59, 3–29 (2002).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poellot, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Saunders, R. W.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Shine, K. P.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Slingo, A.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Soulen, P.

P. Yang, B.-C. Gao, B. A. Baum, W. Wiscombe, Y. Hu, S. Nasiri, P. Soulen, A. Heymsfield, G. McFarquhar, L. Miloshevich, “Sensitivity of cirrus bidirectional reflectance to vertical inhomogeneity of ice crystal habits and size distributions for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands,” J. Geophys. Res. 106, 17267–17291 (2001).
[CrossRef]

Soulen, P. F.

B. A. Baum, D. Kratz, P. Yang, S. C. Ou, Y. X. Hu, P. F. Soulen, S. C. Tsay, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS. 1. Data and models,” J. Geophys. Res. 105, 11767–11780 (2000).
[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 climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Stamnes, J. J.

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Can simple particle shapes be used to model scalar optical properties of an ensemble of wavelength-sized particles with complex shapes?” J. Quant. Spectrosc. Radiat. Transfer 19, 521–531 (2002).

Stamnes, K.

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Can simple particle shapes be used to model scalar optical properties of an ensemble of wavelength-sized particles with complex shapes?” J. Quant. Spectrosc. Radiat. Transfer 19, 521–531 (2002).

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 climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Sun, W. B.

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by cirrus nonspherical ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Clim. 11, 2223–2237 (1998).
[CrossRef]

Sun, W.-B.

Sun, Z.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).

Takano, Y.

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

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[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, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, San Diego, Calif., 2000).

Tsay, S. C.

P. Yang, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, S. L. Nasiri, “Radiative properties of cirrus clouds in the infrared (8–13 μm) spectral region,” J. Quant. Spectrosc. Radiat. Transfer 70, 473–504 (2001).
[CrossRef]

B. A. Baum, D. Kratz, P. Yang, S. C. Ou, Y. X. Hu, P. F. Soulen, S. C. Tsay, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS. 1. Data and models,” J. Geophys. Res. 105, 11767–11780 (2000).
[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 climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Twohy, C.

A. J. Heymsfield, S. Lewis, A. Bansemer, J. Iaquinta, L. M. Miloshevich, M. Kajikawa, C. Twohy, M. R. Poellot, “A general approach for deriving the properties of cirrus and stratiform ice cloud particles,” J. Atmos. Sci. 59, 3–29 (2002).
[CrossRef]

Videen, G.

P. Chylek, G. Videen, “Longwave radiative properties of polydispersed hexagonal ice crystal,” J. Atmos. Sci. 51, 175–190 (1994).
[CrossRef]

G. Videen, Army Research Laboratory AMSRL-CI-EE, 2800 Powder Mill Road, Adelphi, Md. 20783-1197 (personal communication, 2002).

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]

S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

Waterman, P. C.

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Winker, D. M.

P. Yang, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, S. L. Nasiri, “Radiative properties of cirrus clouds in the infrared (8–13 μm) spectral region,” J. Quant. Spectrosc. Radiat. Transfer 70, 473–504 (2001).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. Wiscombe, M. I. Mischenko, D. M. Winker, S. L. Nasiri, “Asymptotic solutions of optical properties of large particles with strong absorption,” Appl. Opt. 40, 1532–1547 (2001).
[CrossRef]

P. Yang, B. A. Baum, H.-L. Huang, S. Platnick, Y. X. Hu, D. M. Winker, A. J. Baran, P. N. Francis, “Single and multiple scattering/absorption properties of pristine ice crystals and polycrystals in the terrestrial window region,” in Proceedings of the Sixth Conference on Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (Army Research Laboratory, Adelphi, Md., 2002), pp. 369–372.

Wiscombe, W.

P. Yang, B.-C. Gao, B. A. Baum, W. Wiscombe, Y. Hu, S. Nasiri, P. Soulen, A. Heymsfield, G. McFarquhar, L. Miloshevich, “Sensitivity of cirrus bidirectional reflectance to vertical inhomogeneity of ice crystal habits and size distributions for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands,” J. Geophys. Res. 106, 17267–17291 (2001).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. Wiscombe, M. I. Mischenko, D. M. Winker, S. L. Nasiri, “Asymptotic solutions of optical properties of large particles with strong absorption,” Appl. Opt. 40, 1532–1547 (2001).
[CrossRef]

Wiscombe, W. J.

P. Yang, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, S. L. Nasiri, “Radiative properties of cirrus clouds in the infrared (8–13 μm) spectral region,” J. Quant. Spectrosc. Radiat. Transfer 70, 473–504 (2001).
[CrossRef]

W. J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2. Means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1986).
[CrossRef]

Wriedt, T.

T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

Wyser, K.

K. Wyser, P. Yang, “Average crystal size and bulk shortwave single scattering properties in ice clouds,” Atmos. Res. 49, 315–335 (1998).
[CrossRef]

Xu, L.

Yang, P.

J. R. Key, P. Yang, B. A. Baum, S. L. Nasiri, “Parameterization of shortwave ice cloud optical properties for various particle habits,” J. Geophys. Res. 107, 10.1029/2001JD000742 (2002).

M.-D. Chou, K.-T. Lee, P. Yang, “Parameterization of shortwave cloud optical properties for a mixture of ice particle habits for use in atmospheric models,” J. Geophys. Res. 107, doi: 10.109/2002JD002061 (2002).
[CrossRef]

G. M. McFarquhar, P. Yang, A. Macke, A. J. Baran, “A new parameterization of single-scattering solar radiative properties for tropical anvils using observed ice crystal size and shape distributions,” J. Atmos. Sci. 59, 2458–2478 (2002).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, W. Wiscombe, Y. Hu, S. Nasiri, P. Soulen, A. Heymsfield, G. McFarquhar, L. Miloshevich, “Sensitivity of cirrus bidirectional reflectance to vertical inhomogeneity of ice crystal habits and size distributions for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands,” J. Geophys. Res. 106, 17267–17291 (2001).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. Wiscombe, M. I. Mischenko, D. M. Winker, S. L. Nasiri, “Asymptotic solutions of optical properties of large particles with strong absorption,” Appl. Opt. 40, 1532–1547 (2001).
[CrossRef]

P. Yang, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, S. L. Nasiri, “Radiative properties of cirrus clouds in the infrared (8–13 μm) spectral region,” J. Quant. Spectrosc. Radiat. Transfer 70, 473–504 (2001).
[CrossRef]

A. J. Baran, P. Yang, S. Havemann, “Calculation of the single-scattering properties of randomly oriented hexagonal ice columns: a comparison of the T-matrix and the finite-difference time-domain methods,” App. Opt. 40, 4376–4386 (2001).
[CrossRef]

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

B. A. Baum, D. Kratz, P. Yang, S. C. Ou, Y. X. Hu, P. F. Soulen, S. C. Tsay, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS. 1. Data and models,” J. Geophys. Res. 105, 11767–11780 (2000).
[CrossRef]

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by cirrus nonspherical ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Clim. 11, 2223–2237 (1998).
[CrossRef]

K. Wyser, P. Yang, “Average crystal size and bulk shortwave single scattering properties in ice clouds,” Atmos. Res. 49, 315–335 (1998).
[CrossRef]

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

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo of ice crystals in laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

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]

P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics methods,” J. Opt. Soc. Am. A 12, 162–176 (1995).
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A. J. Baran, P. N. Francis, P. Yang, S. Havemann, “Simulation of scattering from ice aggregates using size/shape distributions of circular ice cylinders: an application of T-matrix,” in Proceedings of the Sixth Conference on Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (Army Research Laboratory, Adelphi, Md., 2002), pp. 25–28.

P. Yang, B. A. Baum, H.-L. Huang, S. Platnick, Y. X. Hu, D. M. Winker, A. J. Baran, P. N. Francis, “Single and multiple scattering/absorption properties of pristine ice crystals and polycrystals in the terrestrial window region,” in Proceedings of the Sixth Conference on Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (Army Research Laboratory, Adelphi, Md., 2002), pp. 369–372.

A. J. Baran, P. Francis, P. Yang, “A process study of the dependence of ice crystal absorption on particle geometry: application to aircraft radiometric measurements of cirrus clouds in the terrestrial window region,” J. Atmos. Sci. (to be published).

App. Opt. (1)

A. J. Baran, P. Yang, S. Havemann, “Calculation of the single-scattering properties of randomly oriented hexagonal ice columns: a comparison of the T-matrix and the finite-difference time-domain methods,” App. Opt. 40, 4376–4386 (2001).
[CrossRef]

Appl. Opt. (10)

L. Xu, J. Ding, A. Cheng, “Scattering matrix of infrared radiation by ice finite circular cylinders,” Appl. Opt. 41, 2333–2348 (2002).
[CrossRef] [PubMed]

W. P. Arnott, Y. Y. Dong, J. Hallett, “Extinction efficiency in the infrared (2–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
[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, 623–625 (1993).
[CrossRef]

W. J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2. Means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1986).
[CrossRef]

S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

A. J. Baran, S. Havemann, “Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns,” Appl. Opt. 39, 5560–5568 (2000).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. Wiscombe, M. I. Mischenko, D. M. Winker, S. L. Nasiri, “Asymptotic solutions of optical properties of large particles with strong absorption,” Appl. Opt. 40, 1532–1547 (2001).
[CrossRef]

W.-B. Sun, Q. Fu, Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141–3151 (1999).
[CrossRef]

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

Astrophys. J. (2)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Atmos. Res. (2)

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

K. Wyser, P. Yang, “Average crystal size and bulk shortwave single scattering properties in ice clouds,” Atmos. Res. 49, 315–335 (1998).
[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).

J. Atmos. Sci. (10)

D. L. Mitchell, W. P. Arnott, “A model prediction the evolution of ice particle size spectra and radiative properties of cirrus cloud. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

G. M. McFarquhar, P. Yang, A. Macke, A. J. Baran, “A new parameterization of single-scattering solar radiative properties for tropical anvils using observed ice crystal size and shape distributions,” J. Atmos. Sci. 59, 2458–2478 (2002).
[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 climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

A. J. Heymsfield, J. Iaquinta, “Cirrus crystal terminal velocities,” J. Atmos. Sci. 57, 916–938 (2000).
[CrossRef]

A. J. Heymsfield, S. Lewis, A. Bansemer, J. Iaquinta, L. M. Miloshevich, M. Kajikawa, C. Twohy, M. R. Poellot, “A general approach for deriving the properties of cirrus and stratiform ice cloud particles,” J. Atmos. Sci. 59, 3–29 (2002).
[CrossRef]

D. L. Mitchell, A. Macke, Y. Liu, “Modeling cirrus clouds. II. Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

P. Chylek, G. Videen, “Longwave radiative properties of polydispersed hexagonal ice crystal,” J. Atmos. Sci. 51, 175–190 (1994).
[CrossRef]

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by cirrus nonspherical ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

J. Clim. (2)

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Clim. 9, 2058–2082 (1996).
[CrossRef]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Clim. 11, 2223–2237 (1998).
[CrossRef]

J. Geophys. Res. (9)

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]

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo of ice crystals in laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

B. A. Baum, D. Kratz, P. Yang, S. C. Ou, Y. X. Hu, P. F. Soulen, S. C. Tsay, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS. 1. Data and models,” J. Geophys. Res. 105, 11767–11780 (2000).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, W. Wiscombe, Y. Hu, S. Nasiri, P. Soulen, A. Heymsfield, G. McFarquhar, L. Miloshevich, “Sensitivity of cirrus bidirectional reflectance to vertical inhomogeneity of ice crystal habits and size distributions for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands,” J. Geophys. Res. 106, 17267–17291 (2001).
[CrossRef]

M.-D. Chou, K.-T. Lee, P. Yang, “Parameterization of shortwave cloud optical properties for a mixture of ice particle habits for use in atmospheric models,” J. Geophys. Res. 107, doi: 10.109/2002JD002061 (2002).
[CrossRef]

J. R. Key, P. Yang, B. A. Baum, S. L. Nasiri, “Parameterization of shortwave ice cloud optical properties for various particle habits,” J. Geophys. Res. 107, 10.1029/2001JD000742 (2002).

E. E. Ebert, J. A. Curry, “A parameterization of ice cloud optical properties for climate models,” J. Geophys. Res. 97, 3831–3836 (1992).
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W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poellot, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

J. E. Kristjansson, J. M. Edwards, D. L. Mitchell, “The impact of a new scheme for optical properties of ice crystals on the climate of two GCMs,” J. Geophys. Res. 105, 10,063–10,079 (2000).
[CrossRef]

J. Mod. Opt. (1)

T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Quant. Spectrosc. Radiat. Transfer (5)

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]

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Can simple particle shapes be used to model scalar optical properties of an ensemble of wavelength-sized particles with complex shapes?” J. Quant. Spectrosc. Radiat. Transfer 19, 521–531 (2002).

P. Yang, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, S. L. Nasiri, “Radiative properties of cirrus clouds in the infrared (8–13 μm) spectral region,” J. Quant. Spectrosc. Radiat. Transfer 70, 473–504 (2001).
[CrossRef]

S. Havemann, A. J. Baran, “Extension of T-matrix to scattering of electromagnetic plane waves by non-axisymmetric dielectric particles: application to hexagonal ice cylinders,” J. Quant. Spectrosc. Radiat. Transfer 70, 139–158 (2001).
[CrossRef]

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
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K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Opt. Commun. (1)

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

Proc. IEEE (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
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Q. J. R. Meteorol. Soc. (2)

J. S. Foot, “Some observations of the optical properties of clouds. II. Cirrus,” Q. J. R. Meteorol. Soc. 114, 145–164 (1988).
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P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Other (8)

A. J. Baran, P. Francis, P. Yang, “A process study of the dependence of ice crystal absorption on particle geometry: application to aircraft radiometric measurements of cirrus clouds in the terrestrial window region,” J. Atmos. Sci. (to be published).

P. Yang, B. A. Baum, H.-L. Huang, S. Platnick, Y. X. Hu, D. M. Winker, A. J. Baran, P. N. Francis, “Single and multiple scattering/absorption properties of pristine ice crystals and polycrystals in the terrestrial window region,” in Proceedings of the Sixth Conference on Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (Army Research Laboratory, Adelphi, Md., 2002), pp. 369–372.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

G. Videen, Army Research Laboratory AMSRL-CI-EE, 2800 Powder Mill Road, Adelphi, Md. 20783-1197 (personal communication, 2002).

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A. J. Baran, P. N. Francis, P. Yang, S. Havemann, “Simulation of scattering from ice aggregates using size/shape distributions of circular ice cylinders: an application of T-matrix,” in Proceedings of the Sixth Conference on Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (Army Research Laboratory, Adelphi, Md., 2002), pp. 25–28.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).

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Figures (9)

Fig. 1
Fig. 1

Radii and lengths of circular cylinders defined as having the same volume, surface area, or ratio of volume to surface area as hexagonal columns when the same length or aspect ratio is applied to the two geometries. Left, same lengths of circular cylinders and hexagonal columns; Middle and right, aspect ratio kept constant in defining the equivalence.

Fig. 2
Fig. 2

Comparison of phase functions of circular cylinders and hexagonal columns. The circular cylinders are defined to have the same volume and length as the hexagonal columns. The results for circular cylinders are computed by Mishchenko’s T-matrix code.38 For hexagonal columns the FDTD method is used for small particles (L = 10, 20, 40 μm), whereas an improved geometric optics method is used for L = 140 μm.

Fig. 3
Fig. 3

Comparison of extinction efficiencies at a wavelength of 8.5 μm for hexagonal columns and various equivalent circular cylinders. The results for hexagonal particles are taken from Yang et al.50

Fig. 4
Fig. 4

Absorption efficiencies that correspond to the extinction efficiencies shown in Fig. 3.

Fig. 5
Fig. 5

Asymmetry factors that correspond to the efficiencies shown in Figs. 3 and 4.

Fig. 6
Fig. 6

Same as Fig. 3, except that the calculations are performed at a wavelength of 11 μm.

Fig. 7
Fig. 7

Same as Fig. 4, except that the calculations are performed at a wavelength of 11 μm.

Fig. 8
Fig. 8

Same as Fig. 5, except that the calculations are performed at a wavelength of 11 μm.

Fig. 9
Fig. 9

Comparison of absorption efficiencies of pristine hexagonal ice columns and aggregate ice crystals. The procedure for computing the optical properties of aggregates was explained by Yang et al.59

Tables (1)

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Table 1 Minimum and Maximum Relative Errors of the Approximation of Hexagonal Column by a Circular Cylinder by Use of a T Matrix Compared with Reference Results Given by Yang et al.a

Equations (14)

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2a/L=1L40 μmexp-0.017835L-4040 μm<L50 μm,5.916/L1/2L>50 μm
Rv=332π a,
Ra=L2+63a2+12aL/π1/2-L2.
Rv/a=32 a.
Rv*=332π1/3a,
Ra*=33a+6L2πa+L1/2a,
Rv/a*=3a+L3a+2L a.
Hv*=332π1/3L,
Ha*=33a+6L2πa+L1/2L,
Hv/a*=3a+L3a+2L L.
PH-Gθ=1-g21+g2-2g cos θ3/2=l=0N2l+1glPlcos θ,
g=½0π Pθcosθsinθdθ,
ε=Resultcirc cyl-Resulthexag colResulthexag col×100%.
Re=34VA,

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