Abstract

The applicability of various approximations for computing the absorption efficiency and single-scattering albedo of a randomly oriented hexagonal column is tested versus electromagnetic theory. To calculate the absorption efficiency and single-scattering albedo of the hexagonal column from electromagnetic theory we used a generalization to the separation-of-variables method, which enables continuous calculation of optical properties up to size parameters of 86. We found that the asymptotic absorption efficiency is independent of particle shape, and that, as the size parameter increases, the hexagonal column tends to its asymptotic absorption value more quickly than Mie theory. The asymptotic absorption limit of the hexagonal column is calculated accurately (to within 1%) and rapidly by use of the complex-angular-momentum approximation, indicating that this approximation could be used to calculate the absorption limit of nonspherical particles. The equal-volume sphere best approximates the hexagonal column single-scattering albedo at a strongly absorbing wavelength (e.g., 11.9 µm for an ice particle). However, in the resonance region (e.g., 80 µm for an ice particle) Mie theory fails to approximate the single-scattering albedo of the hexagonal column, but as the size parameter exceeds 10 the error in the sphere approximation reduces to within 2%. At 80-µm wavelength there is a characteristic ripple structure superimposed on the hexagonal column absorption efficiency solutions between size parameters from approximately 1 to 4. The ripple structure is indicative of surface-wave interference and is similar to the sphere but less pronounced on the hexagonal column. We investigated the applicability of ray tracing for calculating the single-scattering albedo at absorbing wavelengths relevant to remote sensing of ice particles in the atmosphere and found it to be within 4% for size parameters between 3 and 42 at 3.7-µm wavelength. At mid-infrared wavelengths (e.g., 8.5 and 11.9 µm) ray tracing is within 5% of electromagnetic theory for size parameters exceeding 10. We also tested the Bryant and Latimer absorption approximation to anomalous diffraction theory by using the separation-of-variables method.

© 2000 Optical Society of America

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References

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  1. M. Wiegner, P. Seifert, P. Schlussel, “Radiative effects of cirrus clouds in Meteosat Second Generation Spinning Enhanced Visible and Infrared Imager channels,” J. Geophys. Res. 103, 23217–23230 (1998).
    [CrossRef]
  2. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [CrossRef]
  3. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
    [CrossRef] [PubMed]
  4. 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]
  5. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space. Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  6. A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
    [CrossRef] [PubMed]
  7. P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
    [CrossRef]
  8. 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]
  9. 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]
  10. T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with non-circular cross-sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMV Publishing, Cambridge, Mass., 1999), pp. 79–105.
    [CrossRef]
  11. H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
    [CrossRef]
  12. A. J. Baran, S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transfer 63, 499–519 (1999).
    [CrossRef]
  13. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  14. F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
    [CrossRef]
  15. Y. Takano, K. N. Liou, “Solar radiation transfer in cirrus clouds. Part 1: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  16. S. Havemann, “Modelling of atmospheric, non-spherical scatterers and its application in radiative transfer studies,” Ph.D dissertation (University of Kiel, Kiel, Germany, 2000).
  17. W. 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]
  18. Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
    [CrossRef]
  19. Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
    [CrossRef]
  20. S. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]
  21. V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
    [CrossRef]
  22. 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]
  23. A. Kokhanovsky, A. Macke, “The dependence of the radiative characteristics of optically thick media on the shape of particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 393–407 (1999).
    [CrossRef]
  24. H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988).
    [CrossRef]
  25. D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
    [CrossRef]
  26. D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
    [CrossRef]

1999 (5)

A. J. Baran, S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transfer 63, 499–519 (1999).
[CrossRef]

W. 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]

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

A. Kokhanovsky, A. Macke, “The dependence of the radiative characteristics of optically thick media on the shape of particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 393–407 (1999).
[CrossRef]

1998 (4)

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

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

1996 (3)

1995 (2)

1994 (1)

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

1991 (1)

1989 (1)

Y. Takano, K. N. Liou, “Solar radiation transfer in cirrus clouds. Part 1: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

1988 (1)

H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988).
[CrossRef]

1984 (1)

1980 (1)

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

1974 (1)

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

1948 (1)

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

Arnott, W. P.

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

Baran, A. J.

A. J. Baran, S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transfer 63, 499–519 (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]

Carlson, B. E.

Chen, Z.

Fu, Q.

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

W. 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]

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

Grenfell, T. C.

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

Hansen, J. E.

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

Havemann, S.

A. J. Baran, S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transfer 63, 499–519 (1999).
[CrossRef]

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with non-circular cross-sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMV Publishing, Cambridge, Mass., 1999), pp. 79–105.
[CrossRef]

S. Havemann, “Modelling of atmospheric, non-spherical scatterers and its application in radiative transfer studies,” Ph.D dissertation (University of Kiel, Kiel, Germany, 2000).

Kokhanovsky, A.

A. Kokhanovsky, A. Macke, “The dependence of the radiative characteristics of optically thick media on the shape of particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 393–407 (1999).
[CrossRef]

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.

Liu, Y. G.

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

Macke, A.

A. Kokhanovsky, A. Macke, “The dependence of the radiative characteristics of optically thick media on the shape of particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 393–407 (1999).
[CrossRef]

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

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

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

Mishchenko, M. I.

Mitchell, D. L.

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

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

Muinonen, K.

Nussenzveig, H. M.

H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988).
[CrossRef]

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]

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with non-circular cross-sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMV Publishing, Cambridge, Mass., 1999), pp. 79–105.
[CrossRef]

Schlussel, P.

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

Schmidt, K.

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with non-circular cross-sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMV Publishing, Cambridge, Mass., 1999), pp. 79–105.
[CrossRef]

Seifert, P.

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

Sun, W.

Sun, W. B.

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus 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. Climate 11, 2223–2237 (1998).
[CrossRef]

Takano, Y.

Y. Takano, K. N. Liou, “Solar radiation transfer in cirrus clouds. Part 1: 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, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

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

van de Hulst, H. C.

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

Vouk, V.

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

Warren, S.

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]

Wiegner, M.

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

Wiscombe, W. J.

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

Yang, P.

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus 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. Climate 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, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
[CrossRef]

Appl. Opt. (4)

J. Atmos. Sci. (4)

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

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

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

Y. Takano, K. N. Liou, “Solar radiation transfer in cirrus clouds. Part 1: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

J. Climate (1)

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 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. (2)

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

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

J. Phys. A (1)

H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (4)

A. Kokhanovsky, A. Macke, “The dependence of the radiative characteristics of optically thick media on the shape of particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 393–407 (1999).
[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]

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]

A. J. Baran, S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transfer 63, 499–519 (1999).
[CrossRef]

Nature (London) (1)

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

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

Space. Sci. Rev. (1)

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

Other (3)

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with non-circular cross-sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMV Publishing, Cambridge, Mass., 1999), pp. 79–105.
[CrossRef]

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

S. Havemann, “Modelling of atmospheric, non-spherical scatterers and its application in radiative transfer studies,” Ph.D dissertation (University of Kiel, Kiel, Germany, 2000).

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Figures (11)

Fig. 1
Fig. 1

Absorption efficiency Q abs calculated as a function of X e by use of the methods labeled MIE, SVM, and CAMGO. The SVM calculations assume a randomly oriented hexagonal ice column and α = 6. All the calculations were taken at 11.9-µm wavelength with N = 1.259 + 0.408i.

Fig. 2
Fig. 2

Same as Fig. 1 but for 80-µm wavelength with N = 1.902 + 0.235i.

Fig. 3
Fig. 3

Q abs as a function of X e . The upper curve represents the SVM, diamonds represent IGO, and the bottom curve represents the CAMGO term. All the calculations were done at 12.99-µm wavelength with N = 1.47 + 0.389i.

Fig. 4
Fig. 4

Q abs plotted versus X e at 80-µm wavelength with N = 1.902 + 0.235i. The absorption solutions are labeled MIE, T-M (exact T-matrix theory), and SVM.

Fig. 5
Fig. 5

Calculation of Q abs as a function of the imaginary refractive index; the real refractive index is 1.0. The ADA and the SVM results are represented by squares and diamonds, respectively. The calculations assume that α = 4 and X e = 36.

Fig. 6
Fig. 6

Comparison of single-scattering albedo ω0 as a function of X e for the SVM and Mie theory. The sphere is represented in terms of (a) equivalent volume-to-area radius R vp , (b) equal-area radius R a , (c) equal-volume radius R v . The calculations were performed at 11.9-µm wavelength with N = 1.259 + 0.408i and α = 6 for the hexagonal ice column.

Fig. 7
Fig. 7

Same as Fig. 6 but for an 80-µm wavelength with N = 1.902 + 0.235i.

Fig. 8
Fig. 8

Comparison of the SVM (diamonds) and ray tracing (squares) for the calculation of ω0 as a function of the imaginary refractive index. The real refractive index is 1.263, size parameter X is 42, and α = 4 for the hexagonal column.

Fig. 9
Fig. 9

Comparison of ω0 as a function of X with the SVM (diamonds) and ray tracing (squares) for the 3.7-µm wavelength with N = 1.40 + 0.007i and α = 6.

Fig. 10
Fig. 10

Same as Fig. 9 but for the 8.5-µm wavelength with N = 1.292 + 0.039i.

Fig. 11
Fig. 11

Same as Fig. 10 but for the 11.9-µm wavelength with N = 1.259 + 0.408i.

Equations (4)

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

ω0=1-Qabs/Qext,
X=2πa/λ,
Xe=πde/λ,
=100×E-A/E,

Metrics