Abstract

The scalar optical properties (extinction coefficient, mass extinction coefficient, single-scattering albedo, and asymmetry parameter) of a distribution of randomly oriented ice aggregates are simulated generally to well within 4% accuracy by use of a size-shape distribution of randomly oriented circular ice cylinders at wavelengths in the terrestrial window region. The single-scattering properties of the ice aggregates are calculated over the whole size distribution function by the finite-difference time-domain and improved geometric optics methods. The single-scattering properties of the size-shape distribution of circular ice cylinders are calculated by the T-matrix method supplemented by scattering solutions obtained from complex-angular-momentum theory. Moreover, radiative-transfer studies demonstrate that the maximum error in brightness temperature space when the size-shape distribution of circular ice cylinders is used to represent scattering from ice aggregates is only ∼0.4 K. The methodology presented should find wide applicability in remote sensing of ice cloud and parameterization of cirrus cloud scalar optical properties in climate models.

© 2003 Optical Society of America

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  26. P. D. Watts, C. T. Mutlow, A. J. Baran, A. M. Zavody, “Study on cloud properties derived from Meteosat Second Generation Observations,” document EUMETSAT ITT 97/181 (European Organization for the Exploitation of Meteorological Satellites, Darmstadt, Germany, 1998).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  44. P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, M. I. Mishchenko, D. M. Winker, S. L. Nasiri, “Asymptotic solutions of optical properties of large particles with strong absorption,” Appl. Opt. 40, 1532–1547 (2001).
    [CrossRef]
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    [CrossRef]
  46. A. J. Baran, S. J. Brown, J. S. Foot, D. L. Mitchell, “Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 11.0 μm,” J. Atmos. Sci. 56, 92–110 (1999).
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2003 (1)

P. R. Field, A. J. Heymsfield, “Aggregation and scaling of ice crystal size distributions,” J. Atmos. Sci. 60, 544–560 (2003).
[CrossRef]

2002 (3)

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]

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. L. Mitchell, “Effective diameter in radiation transfer: general definition, applications, and limitations,” J. Atmos. Sci. 59, 2330–2346 (2002).
[CrossRef]

2001 (7)

A. J. Baran, P. N. Francis, L. C. Labonnote, M. Doutriaux-Boucher, “A scattering phase function for ice cloud: tests of applicability using aircraft and satellite multi-angle multi-wavelength radiance measurements of cirrus,” Q. J. R. Meteorol. Soc. 127, 2395–2416 (2001).

L. Liu, M. I. Mishchenko, “Constraints on PSC particle microphysics derived from lidar observations,” J. Quant. Spectrosc. Radiat. Transfer 70, 817–831 (2001).
[CrossRef]

N. T. Zakharova, M. I. Mishchenko, “Scattering by randomly oriented thin ice disks with moderate equivalent-sphere size parameters,” J. Quant. Spectrosc. Radiat. Transfer 70, 465–471 (2001).
[CrossRef]

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

A. V. Korolev, G. A. Isaac, P. Mazin, H. W. Barker, “Microphysical properties of continental clouds from in situ measurements,” Q. J. R. Meteorol. Soc. 127, 2117–2151 (2001).

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, M. I. Mishchenko, 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)

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, K. N. Liou, K. Wyser, D. L. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (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]

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[CrossRef]

J. E. Kristjánsson, J. M. Edwards, D. L. Mitchell, “The impact of a new scheme for the optical properties of ice crystals on the climate of two GCMs,” J. Geophys. Res. 105, 10063–10079 (2000).
[CrossRef]

1999 (2)

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]

A. J. Baran, S. J. Brown, J. S. Foot, D. L. Mitchell, “Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 11.0 μm,” J. Atmos. Sci. 56, 92–110 (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]

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 EBCM for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

T. Rother, “Generalization of the separation of variables method for nonspherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “The definition and significance of an effective radius for ice clouds,” J. Atmos. Sci. 55, 2039–2052 (1998).
[CrossRef]

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

1997 (1)

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

1996 (4)

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

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]

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]

1994 (1)

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, “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]

1993 (2)

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]

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]

1991 (1)

1989 (1)

O. B. Toon, C. P. McKay, T. P. Ackerman, “Rapid calculations of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres,” J. Geophys. Res. 94, 16287–16301 (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]

W. J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2. Means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1988).
[CrossRef] [PubMed]

1986 (1)

1984 (2)

1980 (1)

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1970 (1)

A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

1969 (1)

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

Ackerman, S. A.

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[CrossRef]

Ackerman, T. P.

O. B. Toon, C. P. McKay, T. P. Ackerman, “Rapid calculations of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres,” J. Geophys. Res. 94, 16287–16301 (1989).
[CrossRef]

Auer, A. H.

A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Baran, A. J.

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. N. Francis, L. C. Labonnote, M. Doutriaux-Boucher, “A scattering phase function for ice cloud: tests of applicability using aircraft and satellite multi-angle multi-wavelength radiance measurements of cirrus,” Q. J. R. Meteorol. Soc. 127, 2395–2416 (2001).

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, S. J. Brown, J. S. Foot, D. L. Mitchell, “Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 11.0 μm,” J. Atmos. Sci. 56, 92–110 (1999).
[CrossRef]

S. Havemann, A. J. Baran, J. M. Edwards, “Implementation of the T-matrix method on a massively parallel machine: a comparison of hexagonal ice cylinder single-scattering properties using the T-matrix and improved geometric optics methods,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

P. D. Watts, C. T. Mutlow, A. J. Baran, A. M. Zavody, “Study on cloud properties derived from Meteosat Second Generation Observations,” document EUMETSAT ITT 97/181 (European Organization for the Exploitation of Meteorological Satellites, Darmstadt, Germany, 1998).

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 Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurement, and Applications, B. Gustafson, L. Kolokolova, G. Videen, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2002), pp. 25–28.

Barber, P. W.

Barker, H. W.

A. V. Korolev, G. A. Isaac, P. Mazin, H. W. Barker, “Microphysical properties of continental clouds from in situ measurements,” Q. J. R. Meteorol. Soc. 127, 2117–2151 (2001).

Baum, B. A.

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

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[CrossRef]

Brown, S. J.

A. J. Baran, S. J. Brown, J. S. Foot, D. L. Mitchell, “Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 11.0 μm,” J. Atmos. Sci. 56, 92–110 (1999).
[CrossRef]

Bryant, F. D.

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

Doicu, A.

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

Donner, L.

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

Doutriaux-Boucher, M.

A. J. Baran, P. N. Francis, L. C. Labonnote, M. Doutriaux-Boucher, “A scattering phase function for ice cloud: tests of applicability using aircraft and satellite multi-angle multi-wavelength radiance measurements of cirrus,” Q. J. R. Meteorol. Soc. 127, 2395–2416 (2001).

Edwards, J. M.

J. E. Kristjánsson, J. M. Edwards, D. L. Mitchell, “The impact of a new scheme for the optical properties of ice crystals on the climate of two GCMs,” J. Geophys. Res. 105, 10063–10079 (2000).
[CrossRef]

S. Havemann, A. J. Baran, J. M. Edwards, “Implementation of the T-matrix method on a massively parallel machine: a comparison of hexagonal ice cylinder single-scattering properties using the T-matrix and improved geometric optics methods,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

Field, P. R.

P. R. Field, A. J. Heymsfield, “Aggregation and scaling of ice crystal size distributions,” J. Atmos. Sci. 60, 544–560 (2003).
[CrossRef]

Foot, J. S.

A. J. Baran, S. J. Brown, J. S. Foot, D. L. Mitchell, “Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 11.0 μm,” J. Atmos. Sci. 56, 92–110 (1999).
[CrossRef]

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

Francis, P. N.

A. J. Baran, P. N. Francis, L. C. Labonnote, M. Doutriaux-Boucher, “A scattering phase function for ice cloud: tests of applicability using aircraft and satellite multi-angle multi-wavelength radiance measurements of cirrus,” Q. J. R. Meteorol. Soc. 127, 2395–2416 (2001).

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, “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]

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 Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurement, and Applications, B. Gustafson, L. Kolokolova, G. Videen, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2002), pp. 25–28.

Fu, Q.

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

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

Gao, B. C.

Gao, B.-C.

Havemann, S.

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, 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]

S. Havemann, A. J. Baran, J. M. Edwards, “Implementation of the T-matrix method on a massively parallel machine: a comparison of hexagonal ice cylinder single-scattering properties using the T-matrix and improved geometric optics methods,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

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 Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurement, and Applications, B. Gustafson, L. Kolokolova, G. Videen, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2002), pp. 25–28.

Hemler, R. S.

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

Heymsfield, A. J.

P. R. Field, A. J. Heymsfield, “Aggregation and scaling of ice crystal size distributions,” J. Atmos. Sci. 60, 544–560 (2003).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “The definition and significance of an effective radius for ice clouds,” J. Atmos. Sci. 55, 2039–2052 (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]

Hill, A. C.

Hill, S. C.

Hu, Y. X.

Isaac, G. A.

A. V. Korolev, G. A. Isaac, P. Mazin, H. W. Barker, “Microphysical properties of continental clouds from in situ measurements,” Q. J. R. Meteorol. Soc. 127, 2117–2151 (2001).

Jones, A.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, “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]

Kahnert, F. M.

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).

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

King, M. D.

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[CrossRef]

Korolev, A. V.

A. V. Korolev, G. A. Isaac, P. Mazin, H. W. Barker, “Microphysical properties of continental clouds from in situ measurements,” Q. J. R. Meteorol. Soc. 127, 2117–2151 (2001).

Kristjánsson, J. E.

J. E. Kristjánsson, J. M. Edwards, D. L. Mitchell, “The impact of a new scheme for the optical properties of ice crystals on the climate of two GCMs,” J. Geophys. Res. 105, 10063–10079 (2000).
[CrossRef]

Labonnote, L. C.

A. J. Baran, P. N. Francis, L. C. Labonnote, M. Doutriaux-Boucher, “A scattering phase function for ice cloud: tests of applicability using aircraft and satellite multi-angle multi-wavelength radiance measurements of cirrus,” Q. J. R. Meteorol. Soc. 127, 2395–2416 (2001).

Latimer, P.

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

Liou, K. N.

P. Yang, K. N. Liou, K. Wyser, D. L. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (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]

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

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[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]

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]

K. N. Liou, An Introduction to Atmospheric Radiation (Academic, New York, 1980), p. 192.

Liu, L.

L. Liu, M. I. Mishchenko, “Constraints on PSC particle microphysics derived from lidar observations,” J. Quant. Spectrosc. Radiat. Transfer 70, 817–831 (2001).
[CrossRef]

Mackowski, D. W.

Mazin, P.

A. V. Korolev, G. A. Isaac, P. Mazin, H. W. Barker, “Microphysical properties of continental clouds from in situ measurements,” Q. J. R. Meteorol. Soc. 127, 2117–2151 (2001).

McFarquhar, G. M.

G. M. McFarquhar, A. J. Heymsfield, “The definition and significance of an effective radius for ice clouds,” J. Atmos. Sci. 55, 2039–2052 (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]

McKay, C. P.

O. B. Toon, C. P. McKay, T. P. Ackerman, “Rapid calculations of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres,” J. Geophys. Res. 94, 16287–16301 (1989).
[CrossRef]

Menzel, W. P.

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[CrossRef]

Mishchenko, M. I.

L. Liu, M. I. Mishchenko, “Constraints on PSC particle microphysics derived from lidar observations,” J. Quant. Spectrosc. Radiat. Transfer 70, 817–831 (2001).
[CrossRef]

N. T. Zakharova, M. I. Mishchenko, “Scattering by randomly oriented thin ice disks with moderate equivalent-sphere size parameters,” J. Quant. Spectrosc. Radiat. Transfer 70, 465–471 (2001).
[CrossRef]

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, M. I. Mishchenko, 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, 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]

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, “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]

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]

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

Mitchell, D. L.

D. L. Mitchell, “Effective diameter in radiation transfer: general definition, applications, and limitations,” J. Atmos. Sci. 59, 2330–2346 (2002).
[CrossRef]

P. Yang, K. N. Liou, K. Wyser, D. L. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

J. E. Kristjánsson, J. M. Edwards, D. L. Mitchell, “The impact of a new scheme for the optical properties of ice crystals on the climate of two GCMs,” J. Geophys. Res. 105, 10063–10079 (2000).
[CrossRef]

A. J. Baran, S. J. Brown, J. S. Foot, D. L. Mitchell, “Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 11.0 μm,” J. Atmos. Sci. 56, 92–110 (1999).
[CrossRef]

Mugnai, A.

Mutlow, C. T.

P. D. Watts, C. T. Mutlow, A. J. Baran, A. M. Zavody, “Study on cloud properties derived from Meteosat Second Generation Observations,” document EUMETSAT ITT 97/181 (European Organization for the Exploitation of Meteorological Satellites, Darmstadt, Germany, 1998).

Nasiri, S. L.

Nussenzveig, H. M.

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
[CrossRef]

Rother, T.

T. Rother, “Generalization of the separation of variables method for nonspherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

Saunders, R. W.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, “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]

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]

Seman, C. J.

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

Shine, K. P.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, “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, “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]

Soden, B. J.

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

Soulen, P. F.

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[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).

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

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).

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

Strabala, K. I.

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[CrossRef]

Strom, J.

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

Sun, W. B.

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

Toon, O. B.

O. B. Toon, C. P. McKay, T. P. Ackerman, “Rapid calculations of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres,” J. Geophys. Res. 94, 16287–16301 (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]

Veal, D. L.

A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Warren, J. C.

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

Warren, S.

S. Warren, “Optical constants of ice from the ultraviolet to the microwave,” App. Opt. 23, 1206–1224 (1984).
[CrossRef]

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Watts, P. D.

P. D. Watts, C. T. Mutlow, A. J. Baran, A. M. Zavody, “Study on cloud properties derived from Meteosat Second Generation Observations,” document EUMETSAT ITT 97/181 (European Organization for the Exploitation of Meteorological Satellites, Darmstadt, Germany, 1998).

Winker, D. M.

Wiscombe, W. J.

Wriedt, T.

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

Wyser, K.

P. Yang, K. N. Liou, K. Wyser, D. L. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

Yang, P.

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, M. I. Mishchenko, 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, K. N. Liou, K. Wyser, D. L. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (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]

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[CrossRef]

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

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

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]

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 Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurement, and Applications, B. Gustafson, L. Kolokolova, G. Videen, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2002), pp. 25–28.

Zakharova, N. T.

N. T. Zakharova, M. I. Mishchenko, “Scattering by randomly oriented thin ice disks with moderate equivalent-sphere size parameters,” J. Quant. Spectrosc. Radiat. Transfer 70, 465–471 (2001).
[CrossRef]

Zavody, A. M.

P. D. Watts, C. T. Mutlow, A. J. Baran, A. M. Zavody, “Study on cloud properties derived from Meteosat Second Generation Observations,” document EUMETSAT ITT 97/181 (European Organization for the Exploitation of Meteorological Satellites, Darmstadt, Germany, 1998).

App. Opt. (1)

S. Warren, “Optical constants of ice from the ultraviolet to the microwave,” App. Opt. 23, 1206–1224 (1984).
[CrossRef]

Appl. Opt. (11)

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to homogeneous particles with paint-group symmetries,” Appl. Opt. 40, 3110–3123 (2001).
[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, 623–625 (1993).
[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]

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]

S. C. Hill, A. C. Hill, P. W. Barber, “Light-scattering by size shape distributions of soil particles and spheroids,” Appl. Opt. 23, 1025–1031 (1984).
[CrossRef]

A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles. 1. Cross-sections, single-scattering albedo, asymmetry factor, and backscattered fraction,” Appl. Opt. 25, 1235–1244 (1986).
[CrossRef]

W. J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2. Means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1988).
[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]

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

P. Yang, B.-C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, M. I. Mishchenko, D. M. Winker, S. L. Nasiri, “Asymptotic solutions of optical properties of large particles with strong absorption,” Appl. Opt. 40, 1532–1547 (2001).
[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. (6)

G. M. McFarquhar, A. J. Heymsfield, “The definition and significance of an effective radius for ice clouds,” J. Atmos. Sci. 55, 2039–2052 (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. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

A. J. Baran, S. J. Brown, J. S. Foot, D. L. Mitchell, “Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 11.0 μm,” J. Atmos. Sci. 56, 92–110 (1999).
[CrossRef]

P. R. Field, A. J. Heymsfield, “Aggregation and scaling of ice crystal size distributions,” J. Atmos. Sci. 60, 544–560 (2003).
[CrossRef]

D. L. Mitchell, “Effective diameter in radiation transfer: general definition, applications, and limitations,” J. Atmos. Sci. 59, 2330–2346 (2002).
[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 solar radiative properties of cirrus clouds for climate models,” J. Clim. 11, 2223–2237 (1998).
[CrossRef]

J. Colloid Interface Sci. (1)

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

J. Geophys. Res. (6)

P. Yang, K. N. Liou, K. Wyser, D. L. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

L. Donner, C. J. Seman, B. J. Soden, R. S. Hemler, J. C. Warren, J. Strom, K. N. Liou, “Large-scale ice clouds in the GFDL SKYHI general circulation model,” J. Geophys. Res. 102, 21745–21768 (1997).
[CrossRef]

J. E. Kristjánsson, J. M. Edwards, D. L. Mitchell, “The impact of a new scheme for the optical properties of ice crystals on the climate of two GCMs,” J. Geophys. Res. 105, 10063–10079 (2000).
[CrossRef]

B. A. Baum, P. F. Soulen, K. I. Strabala, M. D. King, S. A. Ackerman, W. P. Menzel, P. Yang, “Remote sensing of cloud properties using MODIS airborne simulator imagery during SUCCESS 2. Cloud thermodynamic phase,” J. Geophys. Res. 105, 11781–11792 (2000).
[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]

O. B. Toon, C. P. McKay, T. P. Ackerman, “Rapid calculations of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres,” J. Geophys. Res. 94, 16287–16301 (1989).
[CrossRef]

J. Mod. Opt. (1)

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

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

J. Quant. Spectrosc. Radiat. Transfer (6)

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]

T. Rother, “Generalization of the separation of variables method for nonspherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

L. Liu, M. I. Mishchenko, “Constraints on PSC particle microphysics derived from lidar observations,” J. Quant. Spectrosc. Radiat. Transfer 70, 817–831 (2001).
[CrossRef]

N. T. Zakharova, M. I. Mishchenko, “Scattering by randomly oriented thin ice disks with moderate equivalent-sphere size parameters,” J. Quant. Spectrosc. Radiat. Transfer 70, 465–471 (2001).
[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).

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Figures (7)

Fig. 1
Fig. 1

(a) Effective distance δ e plotted against crystal maximum dimension D m for the ice aggregate (solid curve), the solid hexagonal column (dashed curve), and the circular ice cylinder at wavelengths of 4.9 μm (asterisks), 8.0 μm (triangles), and 16 μm (dashed-dotted curve). (b) Circular cylinder aspect ratio R plotted as a function of maximum dimension D m at wavelengths of 4.9 μm (asterisks), 8.0 μm (triangles), and 16 μm (dashed-dotted line).

Fig. 2
Fig. 2

(a) Circular ice cylinder extinction cross section plotted against maximum dimension D m at a wavelength of 8.5 μm, assuming that N = 1.29 + 0.039i. The T-matrix and CAM solutions are shown as squares and asterisks, respectively. (b) As in (a) but for the single-scattering albedo ω0. (c) As in (b) but for asymmetry parameter g.

Fig. 3
Fig. 3

(a) Mass extinction coefficient K ext plotted against effective diameter D e at a wavelength of 8.5 μm, assuming that N = 1.29 + 0.039i, showing solutions for the FDTD-IGO (squares) and T-matrix-CAM (asterisks) methods. (b) Same as (a) but for the 11-μm wavelength and assuming that N = 1.09 + 0.25i.

Fig. 4
Fig. 4

(a) Single-scattering albedo ω0 plotted against effective diameter D e at a wavelength of 8.5 μm, assuming that N = 1.29 + 0.039i, showing solutions for the FDTD-IGO (squares) and T-matrix-CAM (asterisks) methods. (b) Same as (a) but for the 11-μm wavelength and assuming that N = 1.09 + 0.24i.

Fig. 5
Fig. 5

(a) Asymmetry parameter g plotted against effective diameter D e at a wavelength of 8.5 μm, assuming that N = 1.29 + 0.039i, showing solutions for the FDTD-IGO (squares) and T-matrix-CAM (asterisks) methods. (b) Same as (a) but for the 11-μm wavelength and assuming that N = 1.09 + 0.25i.

Fig. 6
Fig. 6

(a) Relative percentage error in C ext plotted against effective diameter D e , assuming use of the T-matrix-CAM method at wavelengths of 8.5 μm (triangles), 11.0 μm (asterisks), and 12.0 μm (squares). (b) Relative percentage error in ω0 plotted against effective diameter D e , assuming use of the T-matrix-CAM method at wavelengths of 8.5 μm (triangles), 11.0 μm (asterisks), and 12.0 μm (squares). (c) Relative percentage error in g plotted against effective diameter D e , assuming use of the T-matrix-CAM method at wavelengths of 8.5 μm (triangles), 11.0 μm (asterisks), and 12.0 μm (squares).

Fig. 7
Fig. 7

Difference in brightness temperature between the FDTD-IGO and T-matrix-CAM methods plotted against optical thickness, assuming a crystal effective diameter of 5 μm for nadir (solid curve) and off-nadir (dashed-dotted curve) geometries. The temperature of the cirrus cloud was assumed to be 220 K, and the surface temperature was assumed to be 300K.

Equations (10)

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Cextsca= QextscaPDnDdD,
Qextsca=σextsca/PD.
Kext=Cext/IWC,
ω0=Csca/Cext,
g= CscagDnDdD CscaPDnDdD.
De=3/2  VDnDdD/PDnDdD,
e=Erig-Eapp/Erig,
rv=3V/4π1/3.
re=3/4δe.
τ=CextΔz,

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