The single-scattering properties of ice particles in the near- through far-infrared spectral region are computed from a composite method that is based on a combination of the finite-difference time-domain technique, the T-matrix method, an improved geometrical-optics method, and Lorenz-Mie theory. Seven nonspherical ice crystal habits (aggregates, hexagonal solid and hollow columns, hexagonal plates, bullet rosettes, spheroids, and droxtals) are considered. A database of the single-scattering properties for each of these ice particles has been developed at 49 wavelengths between 3 and 100 µm and for particle sizes ranging from 2 to 10,000 µm specified in terms of the particle maximum dimension. The spectral variations of the single-scattering properties are discussed, as well as their dependence on the particle maximum dimension and effective particle size. The comparisons show that the assumption of spherical ice particles in the near-IR through far-IR region is generally not optimal for radiative transfer computation. Furthermore, a parameterization of the bulk optical properties is developed for mid-latitude cirrus clouds based on a set of 21 particle size distributions obtained from various field campaigns.

© 2005 Optical Society of America

1. K. N. Liou, Y. Takano, and P. Yang, "Light scattering and radiative transfer by ice crystal clouds: applications to climate research," in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 417-449.
2. Q. Fu, P. Yang, and W. B. Sun, "An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models," J. Clim. 25, 2223-2237 (1998). [CrossRef]
3. Q. Fu, W. B. Sun, and P. Yang, "On model of scattering and absorption by cirrus nonspherical ice particles at thermal infrared wavelength," J. Atmos. Res. 56, 2937-2947 (1999). [CrossRef]
4. H. Chepfer, P. Goloub, J. Riedi, J. De Haan, J. W. Hovenier, and P. H. Flamant, "Ice crystal shapes in cirrus clouds derived from POLDER-1/ADEOS-1," J. Geophys. Res. 106, 7955-7966 (2001). [CrossRef]
5. A. J. Baran, "Simulation of infrared scattering from ice aggregates by use of a size-shape distribution of circular ice cylinders," Appl. Opt. 42, 2811-2818 (2003).
6. P. Minnis, P. W. Heck, and D. F. Young, "Inference of cirrus cloud properties from satellite observed visible and infrared radiances. Part II: Verification of theoretical radiative properties," J. Atmos. Sci. 50, 1305-1322 (1993). [CrossRef]
7. J. Reichardt, S. Reichardt, M. Hess, and T. J. McGee, "Corrections among the optical properties of cirrus-cloud particle microphysical interpretation," J. Geophys. Res. 107, 4562, 10.1029/2002JD002589 (2002). [CrossRef]
8. M. I. Mishchenko, W. B. Rossow, A. Macke, and A. A. Lacis, "Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape," J. Geophys. Res. 101, 16973-16985 (1996). [CrossRef]
9. Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part I. Single-scattering and optical properties of hexagonal ice crystals," J. Atmos. Sci. 46, 3-19 (1989). [CrossRef]
10. Y. Takano and K. N. Liou, "Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals," J. Atmos. Sci. 52, 818-837 (1995). [CrossRef]
11. A. Macke, J. Mueller, and E. Raschke, "Single scattering properties of atmospheric ice crystal," J. Atmos. Sci. 53, 2813-2825 (1996). [CrossRef]
12. W. Sun, Q. Fu, and Z. Chen, "Finite-difference time-domain solution of light scattering by dielectric particles with perfectly matched layer absorbing boundary conditions," Appl. Opt. 38, 3141-3151 (1999).
13. A. J. Baran, S. Haveman, P. N. Francis, and P. Yang, "A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus," J. Quant. Spectrosc. Radiat. Transfer 70, 505-518 (2001). [CrossRef]
14. P. Yang and 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).
15. K. Muinonen, "Scattering of light by crystals: a modified Kirchhoff approximation," Appl. Opt. 28, 3044-3050 (1989).
16. A. Macke, "Monte Carlo calculations of light scattering by large particles with multiple internal inclusions," in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., (Academic, 2000), pp. 309-322.
17. P. Yang and K. N. Liou, "Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals," Appl. Opt. 35, 6568-6584 (1996).
18. P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, "Parameterization of scattering and absorption properties of individual ice crystals," J. Geophys. Res. 105, 4699-4718 (2000). [CrossRef]
19. P. Yang, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, and 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]
20. P. Yang, B. A. Baum, A. J. Heymsfield, Y. X. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, "Single-scattering properties of droxtals," J. Quant. Spectrosc. Radiat. Transfer 79-80, 1159-1180 (2003). [CrossRef]
21. P. Yang, M. G. Mlynczak, H. L. Wei, D. P. Kratz, B. A. Baum, Y. X. Hu, W. J. Wiscombe, A. Heidinger, and M. I. Mishchenko, "Spectral signature of ice clouds in the far-infrared region: single-scattering calculations and radiative sensitivity study," J. Geophys. Res. 108, 4569, 10.1029/2002JD2002JD003291 (2003). [CrossRef]
22. W. L. Smith, X. Ma, A. Steven, S. A. Ackerman, H. E. Revercomb, and R. O. Knuteson, "Remote sensing cloud properties from high spectral resolution infrared observations," J. Atmos. Sci. 50, 1708-1720 (1993). [CrossRef]
23. S. A. Ackerman, W. L. Smith, J. D. Spinhirne, and H. E. Revercomb, "The 27-28 October 1986 far-IRE IFO cirrus case study: spectral properties of cirrus clouds in the 8-12 µm window," Mon. Weather Rev. 118, 2377-2388 (1990). [CrossRef]
24. W. L. Smith, S. Ackerman, H. Revercomb, H. Huang, D. H. DeSlover, W. Feltz, L. Gumley, and A. Collard, "Infrared spectral absorption of nearly invisible cirrus clouds," Geophys. Res. Lett. 25, 1137-1140 (1998). [CrossRef]
25. A. H. Huang, P. Yang, H.-L. Wei, B. A. Baum, Y.-X. Hu, P. Antonelli, and S. A. Ackerman, "Retrieval of ice cloud properties from high spectral resolution infrared observations," IEEE Trans. Geosci. Remote Sens. 42, 842-853 (2004). [CrossRef]
26. H. Wei, P. Yang, J. Li, B. A. Baum, H.-L. Huang, S. Platnick, Y. X. Hu, and L. Strow, "Retrieval of semitransparent ice cloud optical thickness from Atmospheric Infrared Sounder (AIRS) measurements," IEEE Trans. Geosci. Remote Sens. 42, 2254-2267 (2004). [CrossRef]
27. S. Chung, S. Ackerman, P. F. Van Delst, and W. P. Menzel, "Model calculations and interferometer measurements of ice-cloud characteristics," J. Appl. Meteorol. 39, 634-644 (2000).
28. D. H. DeSlover, W. L. Smith, P. K. Piironen, and E. W. Eloranta, "A methodology for measuring cirrus cloud visible-to-infrared spectral optical thickness ratios," J. Atmos. Oceanic Technol. 16, 251-262 (1999). [CrossRef]
29. A. J. Heymsfield and J. Iaquinta, "Cirrus crystal terminal velocities," J. Atmos. Sci. 5, 916-938 (2000). [CrossRef]
30. K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966). [CrossRef]
31. M. I. Mishchenko and 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]
32. Z. Zhang, P. Yang, G. W. Kattawar, S.-C. Tsay, B. A. Baum, H.-L. Huang, Y. X. Hu, A. J. Heymsfield, and J. Reichardt, "Geometrical-optics solution to light scattering by droxtal ice crystals," Appl. Opt. 43, 2490-2499 (2004). [CrossRef]
33. P. Yang and K. N. Liou, "Single-scattering properties of complex ice crystals in terrestrial atmosphere," Contrib. Atmos. Phys. 71, 223-248 (1998).
34. T. C. Grenfell and S. G. Warren, "Representation of nonspherical ice particles by a collection of independent spheres for scattering and absorption of radiation," J. Geophys. Res. 104, 31697-31709 (1999). [CrossRef]
35. D. L. Mitchell, A. Macke, and Y. Liu, "Modeling cirrus clouds. Part II: Treatment of radiative properties," J. Atmos. Sci. 53, 2967-2987 (1996). [CrossRef]
36. S. G. Warren, "Optical constants of ice from the ultraviolet to the microwave," Appl. Opt. 23, 1206-1225 (1984).
37. A. J. Baran, P. N. Francis, and P. Yang, "A process study of the dependence of ice crystal absorption on particle geometry: application to aircraft radiometric measurements of cirrus cloud in the terrestrial window region," J. Atmos. Sci. 60, 417-427 (2003). [CrossRef]
38. H. M. Nussenzveig and W. J. Wiscombe, "Diffraction as tunneling," Phys. Rev. Lett. 59, 1667-1670 (1987). [CrossRef]
39. D. L. Mitchell, W. P. Arnott, C. Schmitt, A. J. Baran, S. Havemann, and Q. Fu, "Contributions of photon tunneling to extinction in laboratory grown hexagonal columns," J. Quant. Spectrosc. Radiat. Transfer 70, 761-776 (2001). [CrossRef]
40. D. L. Mitchell, "Parameterization of the Mie extinction and absorption coefficients for water clouds," J. Atmos. Sci. 57, 1311-1326 (2000). [CrossRef]
41. D. L. Mitchell, "Effective diameter in radiation transfer: general definition, applications, and limitations," J. Atmos. Sci. 59, 2330-2346 (2002). [CrossRef]
42. Y. K. Lee, P. Yang, M. I. Mishchenko, B. A. Baum, Y. Hu, H.-L. Huang, W. J. Wiscombe, and A. J. Baran, "On the use of circular cylinders as surrogates for hexagonal pristine ice crystals in scattering calculations at infrared wavelengths," Appl. Opt. 42, 2653-2664 (2003).
43. J. S. Foot, "Some observations of the optical properties of clouds: II. Cirrus," Q. J. R. Meteorol. Soc. 114, 145-164 (1988). [CrossRef]
44. P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, and 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]
45. Q. Fu, "An accurate parameterization of the solar radiative properties of cirrus clouds for climate models," J. Clim. 9, 2058-2082 (1996). [CrossRef]
46. M. D. King, S. Platnick, P. Yang, G. T. Arnold, M. A. Gray, J. C. Riedi, S. A. Ackerman, and K. N. Liou, "Remote sensing of liquid water and ice cloud optical thickness, and effective radius in the arctic: application of air-borne multispectral MAS data," J. Atmos. Oceanic Technol. 21, 857-875 (2004). [CrossRef]
47. B. A. Baum, D. P. Kratz, P. Yang, S. C. Ou, Y. Hu, P. Soulen, and S. C. Tsay, "Remote sensing of cloud properties using MODIS Airborne Simulator imagery during SUCCESS. I: Data and models," J. Geophys. Res. 105, 11767-11780 (2000). [CrossRef]

Appl. Opt.

• A. J. Baran, "Simulation of infrared scattering from ice aggregates by use of a size-shape distribution of circular ice cylinders," Appl. Opt. 42, 2811-2818 (2003).
• W. Sun, Q. Fu, and Z. Chen, "Finite-difference time-domain solution of light scattering by dielectric particles with perfectly matched layer absorbing boundary conditions," Appl. Opt. 38, 3141-3151 (1999).
• P. Yang and K. N. Liou, "Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals," Appl. Opt. 35, 6568-6584 (1996).
• K. Muinonen, "Scattering of light by crystals: a modified Kirchhoff approximation," Appl. Opt. 28, 3044-3050 (1989).
• Z. Zhang, P. Yang, G. W. Kattawar, S.-C. Tsay, B. A. Baum, H.-L. Huang, Y. X. Hu, A. J. Heymsfield, and J. Reichardt, "Geometrical-optics solution to light scattering by droxtal ice crystals," Appl. Opt. 43, 2490-2499 (2004). [CrossRef]
• S. G. Warren, "Optical constants of ice from the ultraviolet to the microwave," Appl. Opt. 23, 1206-1225 (1984).
• Y. K. Lee, P. Yang, M. I. Mishchenko, B. A. Baum, Y. Hu, H.-L. Huang, W. J. Wiscombe, and A. J. Baran, "On the use of circular cylinders as surrogates for hexagonal pristine ice crystals in scattering calculations at infrared wavelengths," Appl. Opt. 42, 2653-2664 (2003).

Contrib. Atmos. Phys.

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

Geophys. Res. Lett.

• W. L. Smith, S. Ackerman, H. Revercomb, H. Huang, D. H. DeSlover, W. Feltz, L. Gumley, and A. Collard, "Infrared spectral absorption of nearly invisible cirrus clouds," Geophys. Res. Lett. 25, 1137-1140 (1998). [CrossRef]

IEEE Trans. Antennas Propag.

• K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966). [CrossRef]

IEEE Trans. Geosci. Remote Sens.

• A. H. Huang, P. Yang, H.-L. Wei, B. A. Baum, Y.-X. Hu, P. Antonelli, and S. A. Ackerman, "Retrieval of ice cloud properties from high spectral resolution infrared observations," IEEE Trans. Geosci. Remote Sens. 42, 842-853 (2004). [CrossRef]
• H. Wei, P. Yang, J. Li, B. A. Baum, H.-L. Huang, S. Platnick, Y. X. Hu, and L. Strow, "Retrieval of semitransparent ice cloud optical thickness from Atmospheric Infrared Sounder (AIRS) measurements," IEEE Trans. Geosci. Remote Sens. 42, 2254-2267 (2004). [CrossRef]

J. Appl. Meteorol.

• S. Chung, S. Ackerman, P. F. Van Delst, and W. P. Menzel, "Model calculations and interferometer measurements of ice-cloud characteristics," J. Appl. Meteorol. 39, 634-644 (2000).

J. Atmos. Oceanic Technol.

• D. H. DeSlover, W. L. Smith, P. K. Piironen, and E. W. Eloranta, "A methodology for measuring cirrus cloud visible-to-infrared spectral optical thickness ratios," J. Atmos. Oceanic Technol. 16, 251-262 (1999). [CrossRef]
• M. D. King, S. Platnick, P. Yang, G. T. Arnold, M. A. Gray, J. C. Riedi, S. A. Ackerman, and K. N. Liou, "Remote sensing of liquid water and ice cloud optical thickness, and effective radius in the arctic: application of air-borne multispectral MAS data," J. Atmos. Oceanic Technol. 21, 857-875 (2004). [CrossRef]

J. Atmos. Res.

• Q. Fu, W. B. Sun, and P. Yang, "On model of scattering and absorption by cirrus nonspherical ice particles at thermal infrared wavelength," J. Atmos. Res. 56, 2937-2947 (1999). [CrossRef]

J. Atmos. Sci.

• P. Minnis, P. W. Heck, and D. F. Young, "Inference of cirrus cloud properties from satellite observed visible and infrared radiances. Part II: Verification of theoretical radiative properties," J. Atmos. Sci. 50, 1305-1322 (1993). [CrossRef]
• Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part I. Single-scattering and optical properties of hexagonal ice crystals," J. Atmos. Sci. 46, 3-19 (1989). [CrossRef]
• Y. Takano and K. N. Liou, "Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals," J. Atmos. Sci. 52, 818-837 (1995). [CrossRef]
• A. Macke, J. Mueller, and E. Raschke, "Single scattering properties of atmospheric ice crystal," J. Atmos. Sci. 53, 2813-2825 (1996). [CrossRef]
• A. J. Heymsfield and J. Iaquinta, "Cirrus crystal terminal velocities," J. Atmos. Sci. 5, 916-938 (2000). [CrossRef]
• W. L. Smith, X. Ma, A. Steven, S. A. Ackerman, H. E. Revercomb, and R. O. Knuteson, "Remote sensing cloud properties from high spectral resolution infrared observations," J. Atmos. Sci. 50, 1708-1720 (1993). [CrossRef]
• A. J. Baran, P. N. Francis, and P. Yang, "A process study of the dependence of ice crystal absorption on particle geometry: application to aircraft radiometric measurements of cirrus cloud in the terrestrial window region," J. Atmos. Sci. 60, 417-427 (2003). [CrossRef]
• D. L. Mitchell, A. Macke, and Y. Liu, "Modeling cirrus clouds. Part II: Treatment of radiative properties," J. Atmos. Sci. 53, 2967-2987 (1996). [CrossRef]
• D. L. Mitchell, "Parameterization of the Mie extinction and absorption coefficients for water clouds," J. Atmos. Sci. 57, 1311-1326 (2000). [CrossRef]
• D. L. Mitchell, "Effective diameter in radiation transfer: general definition, applications, and limitations," J. Atmos. Sci. 59, 2330-2346 (2002). [CrossRef]

J. Clim.

• 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, and W. B. Sun, "An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models," J. Clim. 25, 2223-2237 (1998). [CrossRef]

J. Geophys. Res.

• H. Chepfer, P. Goloub, J. Riedi, J. De Haan, J. W. Hovenier, and P. H. Flamant, "Ice crystal shapes in cirrus clouds derived from POLDER-1/ADEOS-1," J. Geophys. Res. 106, 7955-7966 (2001). [CrossRef]
• J. Reichardt, S. Reichardt, M. Hess, and T. J. McGee, "Corrections among the optical properties of cirrus-cloud particle microphysical interpretation," J. Geophys. Res. 107, 4562, 10.1029/2002JD002589 (2002). [CrossRef]
• M. I. Mishchenko, W. B. Rossow, A. Macke, and A. A. Lacis, "Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape," J. Geophys. Res. 101, 16973-16985 (1996). [CrossRef]
• P. Yang, K. N. Liou, K. Wyser, and D. Mitchell, "Parameterization of scattering and absorption properties of individual ice crystals," J. Geophys. Res. 105, 4699-4718 (2000). [CrossRef]
• T. C. Grenfell and S. G. Warren, "Representation of nonspherical ice particles by a collection of independent spheres for scattering and absorption of radiation," J. Geophys. Res. 104, 31697-31709 (1999). [CrossRef]
• P. Yang, M. G. Mlynczak, H. L. Wei, D. P. Kratz, B. A. Baum, Y. X. Hu, W. J. Wiscombe, A. Heidinger, and M. I. Mishchenko, "Spectral signature of ice clouds in the far-infrared region: single-scattering calculations and radiative sensitivity study," J. Geophys. Res. 108, 4569, 10.1029/2002JD2002JD003291 (2003). [CrossRef]
• B. A. Baum, D. P. Kratz, P. Yang, S. C. Ou, Y. Hu, P. Soulen, and S. C. Tsay, "Remote sensing of cloud properties using MODIS Airborne Simulator imagery during SUCCESS. I: Data and models," J. Geophys. Res. 105, 11767-11780 (2000). [CrossRef]

J. Opt. Soc. Am. A

• P. Yang and 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).

J. Quant. Spectrosc. Radiat. Transfer

• M. I. Mishchenko and 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, B. C. Gao, B. A. Baum, Y. X. Hu, W. J. Wiscombe, S. C. Tsay, D. M. Winker, and 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. A. Baum, A. J. Heymsfield, Y. X. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, "Single-scattering properties of droxtals," J. Quant. Spectrosc. Radiat. Transfer 79-80, 1159-1180 (2003). [CrossRef]
• A. J. Baran, S. Haveman, P. N. Francis, and P. Yang, "A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus," J. Quant. Spectrosc. Radiat. Transfer 70, 505-518 (2001). [CrossRef]
• D. L. Mitchell, W. P. Arnott, C. Schmitt, A. J. Baran, S. Havemann, and Q. Fu, "Contributions of photon tunneling to extinction in laboratory grown hexagonal columns," J. Quant. Spectrosc. Radiat. Transfer 70, 761-776 (2001). [CrossRef]

Mon. Weather Rev.

• S. A. Ackerman, W. L. Smith, J. D. Spinhirne, and H. E. Revercomb, "The 27-28 October 1986 far-IRE IFO cirrus case study: spectral properties of cirrus clouds in the 8-12 µm window," Mon. Weather Rev. 118, 2377-2388 (1990). [CrossRef]

Phys. Rev. Lett.

• H. M. Nussenzveig and W. J. Wiscombe, "Diffraction as tunneling," Phys. Rev. Lett. 59, 1667-1670 (1987). [CrossRef]

Q. J. R. Meteorol. Soc.

• J. S. Foot, "Some observations of the optical properties of clouds: II. Cirrus," Q. J. R. Meteorol. Soc. 114, 145-164 (1988). [CrossRef]
• P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, and 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

• A. Macke, "Monte Carlo calculations of light scattering by large particles with multiple internal inclusions," in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., (Academic, 2000), pp. 309-322.
• K. N. Liou, Y. Takano, and P. Yang, "Light scattering and radiative transfer by ice crystal clouds: applications to climate research," in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 417-449.

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