Abstract

We calculated the scattering and absorption properties of randomly oriented hexagonal ice columns using T-matrix theory, employing analytic orientation averaging, and the finite-difference time-domain method, which uses a numerical procedure to simulate random orientation. The total optical properties calculated are the extinction efficiency, absorption efficiency, single-scattering albedo, and the asymmetry parameter. The optical properties are calculated at the wavelengths of 0.66, 8.5, and 12 µm, up to a size parameter of 20 at 0.66 µm and 15 at the two other wavelengths. The phase-matrix elements P11, P12, and P22 are also calculated and compared, up to a size parameter of 20 at 0.66 µm and 15 at 12.0 µm. The scattering and absorption solutions obtained from the two independent electromagnetic methods are compared and contrasted, as well as the central processing unit time and memory load for each size parameter. It is found that the total optical properties calculated by the two methods are well within 3% of each other for all three wavelengths and size parameters. In terms of the phase-matrix elements it is found that there are some differences between the T-matrix and the finite-difference time-domain methods appearing in all three elements. Differences between the two methods for the P11 element are seen particularly at scattering angles from approximately 120° to 180°; and at the scattering angle of 180°, relative differences are less than 16%. At scattering angles less than 100°, agreement is generally within a few percent. Similar results are also found for the P12 and P22 elements of the phase matrix. The validity of approximating randomly oriented hexagonal ice columns by randomly oriented equal surface area circular cylinders is also investigated in terms of the linear depolarization ratio.

© 2001 Optical Society of America

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2001 (1)

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]

2000 (5)

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

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

J. E. Kristjánsson, 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, 10063–10079 (2000).
[CrossRef]

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

B. A. Baum, D. P. 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]

1999 (3)

1998 (5)

M. I. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
[CrossRef]

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

M. Wiegner, P. Seifert, P. Schluessel, “Radiative effects of cirrus clouds in Meteosat Second Generation Spinning Enhanced Visible and Infrared Imager channels,” J. Geophys. Res. 103, 23217–23230 (1998).
[CrossRef]

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)

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)

1995 (1)

1994 (3)

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]

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

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

1992 (3)

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

D. L. Hartmann, M. E. Ockert-Bell, M. L. Michelsen, “The effect of cloud type on earth’s energy balance: global analysis,” J. Clim. 5, 1281–1304 (1992).
[CrossRef]

M. D. King, Y. J. Kaufman, W. P. Menzel, D. Tanre, “Remote sensing of cloud, aerosol, and water vapour properties from the Moderate Resolution Imaging Spectrometer (MODIS),” IEEE Trans. Geosci. Remote Sens. 30, 2–27 (1992).
[CrossRef]

1991 (3)

1989 (1)

J. N. Mitchell, C. A. Senior, W. J. Ingram, “CO2 and climate: a missing feedback?” Nature (London) 341, 132–134 (1989).
[CrossRef]

1986 (1)

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

1984 (1)

1972 (1)

A. J. Heymsfield, R. G. Knollenberg, “Properties of cirrus generating cells,” J. Atmos. Sci. 29, 1358–1366 (1972).
[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 dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

1966 (1)

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

1948 (1)

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

1908 (1)

G. Mie, “Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Auer, A. H.

A. H. Auer, D. L. Veal, “The dimension 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]

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

A. J. Baran, P. D. Watts, P. N. Francis, “Testing the coherence of microphysical and bulk properties retrieved from dual-viewing multispectral satellite radiance measurements,” J. Geophys. Res. 104, 31673–31683 (1999).
[CrossRef]

S. Havemann, A. J. Baran, “Extension of T-matrix to scattering of electromagnetic plane waves by general 3D dielectric particles: application to hexagonal ice columns and plates,” in Problems in Atmospheric Radiation, W. L. Smith, Y. Timofeyev, eds. (Deepak, Hampton, Va., 2000).

Baum, B. A.

B. A. Baum, D. P. 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]

Berenger, B. J.

B. J. Berenger, “Three-dimensional perfect matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

Brogniez, G.

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

Buriez, J.-C.

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

Carlson, B. E.

Chen, Z.

Comberg, U.

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

Doicu, A.

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]

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.

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

Draine, B. T.

Edwards, J. M.

J. E. Kristjánsson, 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, 10063–10079 (2000).
[CrossRef]

Flatau, P. J.

Francis, P. N.

A. J. Baran, P. D. Watts, P. N. Francis, “Testing the coherence of microphysical and bulk properties retrieved from dual-viewing multispectral satellite radiance measurements,” J. Geophys. Res. 104, 31673–31683 (1999).
[CrossRef]

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]

Fu, Q.

Gao, B. C.

Hartmann, D. L.

D. L. Hartmann, M. E. Ockert-Bell, M. L. Michelsen, “The effect of cloud type on earth’s energy balance: global analysis,” J. Clim. 5, 1281–1304 (1992).
[CrossRef]

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]

S. Havemann, A. J. Baran, “Extension of T-matrix to scattering of electromagnetic plane waves by general 3D dielectric particles: application to hexagonal ice columns and plates,” in Problems in Atmospheric Radiation, W. L. Smith, Y. Timofeyev, eds. (Deepak, Hampton, Va., 2000).

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.

A. J. Heymsfield, R. G. Knollenberg, “Properties of cirrus generating cells,” J. Atmos. Sci. 29, 1358–1366 (1972).
[CrossRef]

Hu, Y. X.

B. A. Baum, D. P. 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]

Ingram, W. J.

J. N. Mitchell, C. A. Senior, W. J. Ingram, “CO2 and climate: a missing feedback?” Nature (London) 341, 132–134 (1989).
[CrossRef]

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]

Kaufman, Y. J.

M. D. King, Y. J. Kaufman, W. P. Menzel, D. Tanre, “Remote sensing of cloud, aerosol, and water vapour properties from the Moderate Resolution Imaging Spectrometer (MODIS),” IEEE Trans. Geosci. Remote Sens. 30, 2–27 (1992).
[CrossRef]

Khlebtsov, N. G.

King, M. D.

M. D. King, Y. J. Kaufman, W. P. Menzel, D. Tanre, “Remote sensing of cloud, aerosol, and water vapour properties from the Moderate Resolution Imaging Spectrometer (MODIS),” IEEE Trans. Geosci. Remote Sens. 30, 2–27 (1992).
[CrossRef]

Knollenberg, R. G.

A. J. Heymsfield, R. G. Knollenberg, “Properties of cirrus generating cells,” J. Atmos. Sci. 29, 1358–1366 (1972).
[CrossRef]

Kratz, D. P.

B. A. Baum, D. P. 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]

Kristjánsson, J. E.

J. E. Kristjánsson, 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, 10063–10079 (2000).
[CrossRef]

Labonnote, L.

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

Laitinen, H.

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

Liou, K. N.

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]

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

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

Lumme, K.

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

Macke, A.

Mackowski, D. W.

Mano, Y.

Menzel, W. P.

M. D. King, Y. J. Kaufman, W. P. Menzel, D. Tanre, “Remote sensing of cloud, aerosol, and water vapour properties from the Moderate Resolution Imaging Spectrometer (MODIS),” IEEE Trans. Geosci. Remote Sens. 30, 2–27 (1992).
[CrossRef]

Michelsen, M. L.

D. L. Hartmann, M. E. Ockert-Bell, M. L. Michelsen, “The effect of cloud type on earth’s energy balance: global analysis,” J. Clim. 5, 1281–1304 (1992).
[CrossRef]

Mie, G.

G. Mie, “Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Mishchenko, M. I.

Mitchell, D. L.

J. E. Kristjánsson, 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, 10063–10079 (2000).
[CrossRef]

Mitchell, J. N.

J. N. Mitchell, C. A. Senior, W. J. Ingram, “CO2 and climate: a missing feedback?” Nature (London) 341, 132–134 (1989).
[CrossRef]

Muinonen, K.

Ockert-Bell, M. E.

D. L. Hartmann, M. E. Ockert-Bell, M. L. Michelsen, “The effect of cloud type on earth’s energy balance: global analysis,” J. Clim. 5, 1281–1304 (1992).
[CrossRef]

Ou, S. C.

B. A. Baum, D. P. 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]

Sassen, K.

M. I. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (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]

Schluessel, P.

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[CrossRef]

M. Wiegner, P. Seifert, P. Schluessel, “Radiative effects of cirrus clouds in Meteosat Second Generation Spinning Enhanced Visible and Infrared Imager channels,” J. Geophys. Res. 103, 23217–23230 (1998).
[CrossRef]

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Opt. Lett. (1)

Phys. Rev D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev D 3, 825–839 (1971).
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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).
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Other (1)

S. Havemann, A. J. Baran, “Extension of T-matrix to scattering of electromagnetic plane waves by general 3D dielectric particles: application to hexagonal ice columns and plates,” in Problems in Atmospheric Radiation, W. L. Smith, Y. Timofeyev, eds. (Deepak, Hampton, Va., 2000).

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Figures (6)

Fig. 1
Fig. 1

P11 element from the phase matrix of the randomly oriented hexagonal ice column of an aspect ratio of unity calculated at the wavelength of 0.66 µm by use of the T-matrix method (dashed–dotted curve) and the FDTD method (solid curve) for (a) KL = 5, (b) KL = 10, (c) KL = 15, (d) KL = 20.

Fig. 2
Fig. 2

P12/P11 element from the phase matrix of the randomly oriented hexagonal ice column of an aspect ratio of unity calculated at the wavelength of 0.66 µm by use of the T-matrix method (dashed–dotted curve) and the FDTD method (solid curve) for (a) KL = 5, (b) KL = 10, (c) KL = 15, (d) KL = 20.

Fig. 3
Fig. 3

P22/P11 element from the phase matrix of the randomly oriented hexagonal ice column of an aspect ratio of unity calculated at the wavelength of 0.66 µm with the T-matrix method (dashed–dotted curve) and the FDTD method (solid curve) for (a) KL = 5, (b) KL = 10, (c) KL = 15, (d) KL = 20.

Fig. 4
Fig. 4

P11 element from the phase matrix of the randomly oriented hexagonal ice column of an aspect ratio of unity calculated at the wavelength of 12 µm with the T-matrix method (dashed–dotted curve) and the FDTD method (solid curve) for (a) KL = 5, (b) KL = 10, (c) KL = 15.

Fig. 5
Fig. 5

P12/P11 element from the phase matrix of the randomly oriented hexagonal ice column of aspect ratio unity calculated at the wavelength of 12 µm with the T-matrix method (dashed–dotted curve) and the FDTD method (solid curve) for (a) KL = 5, (b) KL = 10, (c) KL = 15.

Fig. 6
Fig. 6

P22/P11 element from the phase matrix of the randomly oriented hexagonal ice column of aspect ratio unity calculated at the wavelength of 12 µm with the T-matrix method (dashed–dotted curve) and the FDTD method (solid curve) for (a) KL = 5, (b) KL = 10, (c) KL = 15.

Tables (7)

Tables Icon

Table 1 Wavelengths and Complex Refractive Indices37 used to Compare the T-Matrix and FDTD Methods

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Table 2 Dimensions of the Randomly Oriented Hexagonal Ice Column and Size Parameter used to Compare the T-Matrix and FDTD Methods

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Table 3 Q ext and Q abs of the Randomly Oriented Hexagonal Ice Column Calculated with the T-Matrix and FDTD Methods

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Table 4 ω0 and g of the Randomly Oriented Hexagonal Ice Column Calculated with the T-Matrix and FDTD Methods

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Table 5 Relative Percentage Differences ∊ between the T-Matrix and the FDTD Methods for Solutions of the Single-Scattering Quantities given in Tables 3 and 4

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Table 6 CPU Time (s) and Memory Load (Mbytes) Utilized by the T-Matrix and FDTD Methods to Calculate the Scattering and Absorption Properties of the Randomly Oriented Hexagonal Ice Column for Each Size Parameter (KL) a

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Table 7 Linear Depolarization Ratio δ as a Function of Size Parameter (KL), Calculated with the T-Matrix Method Applied to Randomly Oriented Hexagonal Ice Columns and Circular Ice Cylinders and with the FDTD Method Applied to Hexagonal Ice Columns

Equations (3)

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=T-FT100.
Qext=CextP,
Qabs=CabsP,

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