Abstract

The effect of ice crystal size and shape on the relation between radar reflectivity and optical extinction is examined. Discrete-dipole approximation calculations of 95-GHz radar reflectivity and ray-tracing calculations are applied to ice crystals of various habits and sizes. Ray tracing was used primarily to calculate optical extinction and to provide approximate information on the lidar backscatter cross section. The results of the combined calculations are compared with Mie calculations applied to collections of different types of equivalent spheres. Various equivalent sphere formulations are considered, including equivalent radar-lidar spheres; equivalent maximum dimension spheres; equivalent area spheres, and equivalent volume and equivalent effective radius spheres. Marked differences are found with respect to the accuracy of different formulations, and certain types of equivalent spheres can be used for useful prediction of both the radar reflectivity at 95 GHz and the optical extinction (but not lidar backscatter cross section) over a wide range of particle sizes. The implications of these results on combined lidar-radar ice cloud remote sensing are discussed.

© 2004 Optical Society of America

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    [CrossRef]
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  34. M. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving delta-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
    [CrossRef]
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    [CrossRef]
  38. A. Ansmann, “Molecular-backscatter profiling of the volume-scattering coefficient in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 197–210.
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2003 (2)

S. P. Neshyba, T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres: 2. Hexagonal columns and plates,” J. Geophys. Res. 108, 4448, doi: 10.1029/2002JD003302 (2003).

D. P. Donovan, “Ice-cloud effective particle size parameterization based on combined lidar, radar and mean Doppler velocity measurements,” J. Geophys. Res. 108, 4573, doi: 10.1029/2003JD003469 (2003).

2002 (1)

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

2001 (2)

D. P. Donovan, A. C. A. P. Van Lammeren, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 1, theory and examples,” J. Geophys. Res. 106, 27425–27448 (2001).
[CrossRef]

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

1999 (4)

D. P. Wylie, W. P. Menzel, “Eight years of high cloud statistics using HIRS,” J. Clim. 12, 170–184 (1999).
[CrossRef]

H. Lemke, M. Quante, “Backscatter characteristics of nonspherical ice crystals: assessing the potential of polarimetric radar measurements,” J. Geophys. Res. 104, 31739–31752 (1999).
[CrossRef]

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce haloes?” Appl. Opt. 38, 1626–1629 (1999).
[CrossRef]

1998 (3)

M. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving delta-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multispectral reflectance measurements during EURCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

H. Lemke, H. Okamoto, M. Quante, “Comment on Error analysis of backscatter from discrete dipole approximation for different ice particle shapes,” Atmos. Res. 49, 189–197 (1998).

1997 (2)

A. J. Gibson, L. Thomas, S. K. Bhattacharyya, “Some characteristics of cirrus clouds deduced from laser radar observations at different elevation angles,” J. Atmos. Terr. Phys. 29, 657–660 (1997).

K. Aydin, C. Tang, “Millimeter wave radar scattering from model ice crystal distributions,” IEEE Trans. Geosci. Remote Sens. 35, 140–146 (1997).
[CrossRef]

1996 (2)

A. Macke, J. Müller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

P.-H. Wang, P. Minnis, M. P. McCormick, G. S. Kent, K. M. Skeens, “A 6-year climatology of cloud occurrence frequency from Stratospheric Aerosol and Gas Experiment II observations (1985–1990),” J. Geophys. Res. 101, 29407–20429 (1996).
[CrossRef]

1995 (6)

D. Atlas, S. Y. Matrosov, A. J. Heymsfield, M.-D. Chou, D. B. Wolff, “Radar and radiation properties of ice clouds,” J. Appl. Meteorol. 34, 2329–2345 (1995).
[CrossRef]

A. Macke, M. I. Michshenko, K. Miunonen, 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]

Y. Tanaka, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

T. L. Schneider, G. L. Stephens, “Theoretical aspects of modeling backscattering by cirrus ice particles at millimeter wavelength,” J. Atmos. Sci. 52, 4367–4385 (1995).
[CrossRef]

H. Okamoto, A. Macke, M. Quante, E. Raschke, “Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94 GHz. An error analysis,” Contrib. Atmos. Phys. 68, 319–334 (1995).

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. 12, 162–176 (1995).
[CrossRef]

1994 (3)

P. Piironen, E. W. Eloranta, “Demonstration of a high-spectral-resolution lidar based on an iodine absorption filter,” Opt. Lett. 19, 234–236 (1994).
[CrossRef] [PubMed]

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

S. Y. Matrosov, B. W. Orr, R. A. Kropfli, J. B. Snider, “Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements,” J. Appl. Meteorol. 33, 617–626 (1994).
[CrossRef]

1993 (2)

C. E. Dungey, C. F. Bohren, “Backscattering by nonspherical hydrometeors as calculated by the coupled-dipole method; an application in radar meteorology,” J. Atmos. Ocean. Technol. 10, 526–532 (1993).
[CrossRef]

Y. X. Hu, K. Stamnes, “An accurate parameterization of the radiative properties of water clouds suitable for use in climate models,” J. Clim. 6, 728–742 (1993).
[CrossRef]

1991 (1)

A. Arking, “The radiative effects of clouds and their impact on climate,” Bull. Am. Meteorol Soc. 72, 795–813 (1991).
[CrossRef]

1990 (1)

L. Thomas, J. C. Cartwright, D. P. Wakeling, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211–216 (1990).

1984 (1)

1978 (1)

C. M. R. Platt, N. Abshire, G. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally aligned crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[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]

1954 (1)

D. Atlas, M. Kerker, W. Hitschfeld, “Scattering and attenuation by non-spherical atmospheric particles,” J. Atmos. Terr. Phys. 3, 108–119 (1954).
[CrossRef]

Abshire, N.

C. M. R. Platt, N. Abshire, G. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally aligned crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

Ansmann, A.

A. Ansmann, “Molecular-backscatter profiling of the volume-scattering coefficient in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 197–210.

Apituley, A.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Arking, A.

A. Arking, “The radiative effects of clouds and their impact on climate,” Bull. Am. Meteorol Soc. 72, 795–813 (1991).
[CrossRef]

Arnott, W. P.

J. Hallett, W. P. Arnott, M. P. Bailey, J. T. Hallet, “Ice crystals in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 41–77.

Atlas, D.

D. Atlas, S. Y. Matrosov, A. J. Heymsfield, M.-D. Chou, D. B. Wolff, “Radar and radiation properties of ice clouds,” J. Appl. Meteorol. 34, 2329–2345 (1995).
[CrossRef]

D. Atlas, M. Kerker, W. Hitschfeld, “Scattering and attenuation by non-spherical atmospheric particles,” J. Atmos. Terr. Phys. 3, 108–119 (1954).
[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]

Austin, R.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Aydin, K.

K. Aydin, C. Tang, “Millimeter wave radar scattering from model ice crystal distributions,” IEEE Trans. Geosci. Remote Sens. 35, 140–146 (1997).
[CrossRef]

Bailey, M. P.

J. Hallett, W. P. Arnott, M. P. Bailey, J. T. Hallet, “Ice crystals in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 41–77.

Benedetti, A.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Bhattacharyya, S. K.

A. J. Gibson, L. Thomas, S. K. Bhattacharyya, “Some characteristics of cirrus clouds deduced from laser radar observations at different elevation angles,” J. Atmos. Terr. Phys. 29, 657–660 (1997).

Boain, R.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Bohren, C. F.

C. E. Dungey, C. F. Bohren, “Backscattering by nonspherical hydrometeors as calculated by the coupled-dipole method; an application in radar meteorology,” J. Atmos. Ocean. Technol. 10, 526–532 (1993).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Carlson, B. E.

Cartwright, J. C.

L. Thomas, J. C. Cartwright, D. P. Wakeling, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211–216 (1990).

Chou, M.-D.

D. Atlas, S. Y. Matrosov, A. J. Heymsfield, M.-D. Chou, D. B. Wolff, “Radar and radiation properties of ice clouds,” J. Appl. Meteorol. 34, 2329–2345 (1995).
[CrossRef]

Donovan, D. P.

D. P. Donovan, “Ice-cloud effective particle size parameterization based on combined lidar, radar and mean Doppler velocity measurements,” J. Geophys. Res. 108, 4573, doi: 10.1029/2003JD003469 (2003).

D. P. Donovan, A. C. A. P. Van Lammeren, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 1, theory and examples,” J. Geophys. Res. 106, 27425–27448 (2001).
[CrossRef]

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Draine, B. T.

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

Dungey, C. E.

C. E. Dungey, C. F. Bohren, “Backscattering by nonspherical hydrometeors as calculated by the coupled-dipole method; an application in radar meteorology,” J. Atmos. Ocean. Technol. 10, 526–532 (1993).
[CrossRef]

Durden, S. L.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Eloranta, E. W.

Flatau, P. J.

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

Francis, P.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Francis, P. N.

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multispectral reflectance measurements during EURCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Gibson, A. J.

A. J. Gibson, L. Thomas, S. K. Bhattacharyya, “Some characteristics of cirrus clouds deduced from laser radar observations at different elevation angles,” J. Atmos. Terr. Phys. 29, 657–660 (1997).

Goddard, J.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Grenfell, T. C.

S. P. Neshyba, T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres: 2. Hexagonal columns and plates,” J. Geophys. Res. 108, 4448, doi: 10.1029/2002JD003302 (2003).

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

Hallet, J. T.

J. Hallett, W. P. Arnott, M. P. Bailey, J. T. Hallet, “Ice crystals in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 41–77.

Hallett, J.

J. Hallett, W. P. Arnott, M. P. Bailey, J. T. Hallet, “Ice crystals in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 41–77.

Heymsfield, A. J.

D. Atlas, S. Y. Matrosov, A. J. Heymsfield, M.-D. Chou, D. B. Wolff, “Radar and radiation properties of ice clouds,” J. Appl. Meteorol. 34, 2329–2345 (1995).
[CrossRef]

A. J. Heymsfield, G. M. McFarquhar, “Midlatitude and tropical, cirrus microphysical properties,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 78–101.

Hignett, P.

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multispectral reflectance measurements during EURCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Hitschfeld, W.

D. Atlas, M. Kerker, W. Hitschfeld, “Scattering and attenuation by non-spherical atmospheric particles,” J. Atmos. Terr. Phys. 3, 108–119 (1954).
[CrossRef]

Hogan, R. J.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Hu, Y. X.

Y. X. Hu, K. Stamnes, “An accurate parameterization of the radiative properties of water clouds suitable for use in climate models,” J. Clim. 6, 728–742 (1993).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hulst Van De, H. V.

H. V. Hulst Van De, Light Scattering by Small Particles (Dover, New York, 1981), pp. 85–101.

Illingworth, A.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Kent, G. S.

P.-H. Wang, P. Minnis, M. P. McCormick, G. S. Kent, K. M. Skeens, “A 6-year climatology of cloud occurrence frequency from Stratospheric Aerosol and Gas Experiment II observations (1985–1990),” J. Geophys. Res. 101, 29407–20429 (1996).
[CrossRef]

Kerker, M.

D. Atlas, M. Kerker, W. Hitschfeld, “Scattering and attenuation by non-spherical atmospheric particles,” J. Atmos. Terr. Phys. 3, 108–119 (1954).
[CrossRef]

Kropfli, R. A.

S. Y. Matrosov, B. W. Orr, R. A. Kropfli, J. B. Snider, “Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements,” J. Appl. Meteorol. 33, 617–626 (1994).
[CrossRef]

Lammeren, A. C. A. P. Van

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Lemke, H.

H. Lemke, M. Quante, “Backscatter characteristics of nonspherical ice crystals: assessing the potential of polarimetric radar measurements,” J. Geophys. Res. 104, 31739–31752 (1999).
[CrossRef]

H. Lemke, H. Okamoto, M. Quante, “Comment on Error analysis of backscatter from discrete dipole approximation for different ice particle shapes,” Atmos. Res. 49, 189–197 (1998).

Liou, K. N.

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. 12, 162–176 (1995).
[CrossRef]

Y. Tanaka, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

Mace, G.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Macke, A.

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce haloes?” Appl. Opt. 38, 1626–1629 (1999).
[CrossRef]

M. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving delta-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multispectral reflectance measurements during EURCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

A. Macke, J. Müller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

H. Okamoto, A. Macke, M. Quante, E. Raschke, “Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94 GHz. An error analysis,” Contrib. Atmos. Phys. 68, 319–334 (1995).

A. Macke, M. I. Michshenko, K. Miunonen, 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]

Matrosov, S. Y.

D. Atlas, S. Y. Matrosov, A. J. Heymsfield, M.-D. Chou, D. B. Wolff, “Radar and radiation properties of ice clouds,” J. Appl. Meteorol. 34, 2329–2345 (1995).
[CrossRef]

S. Y. Matrosov, B. W. Orr, R. A. Kropfli, J. B. Snider, “Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements,” J. Appl. Meteorol. 33, 617–626 (1994).
[CrossRef]

McCormick, M. P.

P.-H. Wang, P. Minnis, M. P. McCormick, G. S. Kent, K. M. Skeens, “A 6-year climatology of cloud occurrence frequency from Stratospheric Aerosol and Gas Experiment II observations (1985–1990),” J. Geophys. Res. 101, 29407–20429 (1996).
[CrossRef]

McFarquhar, G. M.

A. J. Heymsfield, G. M. McFarquhar, “Midlatitude and tropical, cirrus microphysical properties,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 78–101.

McNice, G.

C. M. R. Platt, N. Abshire, G. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally aligned crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

Menzel, W. P.

D. P. Wylie, W. P. Menzel, “Eight years of high cloud statistics using HIRS,” J. Clim. 12, 170–184 (1999).
[CrossRef]

Michshenko, M. I.

Miller, S.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Minnis, P.

P.-H. Wang, P. Minnis, M. P. McCormick, G. S. Kent, K. M. Skeens, “A 6-year climatology of cloud occurrence frequency from Stratospheric Aerosol and Gas Experiment II observations (1985–1990),” J. Geophys. Res. 101, 29407–20429 (1996).
[CrossRef]

Mishchenko, M.

M. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving delta-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

Mishchenko, M. I.

Mitrescu, C.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Miunonen, K.

Müller, J.

A. Macke, J. Müller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Neshyba, S. P.

S. P. Neshyba, T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres: 2. Hexagonal columns and plates,” J. Geophys. Res. 108, 4448, doi: 10.1029/2002JD003302 (2003).

O’Connor, E.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Okamoto, H.

H. Lemke, H. Okamoto, M. Quante, “Comment on Error analysis of backscatter from discrete dipole approximation for different ice particle shapes,” Atmos. Res. 49, 189–197 (1998).

H. Okamoto, A. Macke, M. Quante, E. Raschke, “Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94 GHz. An error analysis,” Contrib. Atmos. Phys. 68, 319–334 (1995).

Orr, B. W.

S. Y. Matrosov, B. W. Orr, R. A. Kropfli, J. B. Snider, “Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements,” J. Appl. Meteorol. 33, 617–626 (1994).
[CrossRef]

Pelon, J.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Piironen, P.

Platt, C. M. R.

C. M. R. Platt, N. Abshire, G. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally aligned crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

Quante, M.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

H. Lemke, M. Quante, “Backscatter characteristics of nonspherical ice crystals: assessing the potential of polarimetric radar measurements,” J. Geophys. Res. 104, 31739–31752 (1999).
[CrossRef]

H. Lemke, H. Okamoto, M. Quante, “Comment on Error analysis of backscatter from discrete dipole approximation for different ice particle shapes,” Atmos. Res. 49, 189–197 (1998).

H. Okamoto, A. Macke, M. Quante, E. Raschke, “Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94 GHz. An error analysis,” Contrib. Atmos. Phys. 68, 319–334 (1995).

Raschke, E.

A. Macke, J. Müller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

H. Okamoto, A. Macke, M. Quante, E. Raschke, “Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94 GHz. An error analysis,” Contrib. Atmos. Phys. 68, 319–334 (1995).

Rossow, W.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Russchenberg, H. W. J.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Sassen, K.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Schneider, T. L.

T. L. Schneider, G. L. Stephens, “Theoretical aspects of modeling backscattering by cirrus ice particles at millimeter wavelength,” J. Atmos. Sci. 52, 4367–4385 (1995).
[CrossRef]

Skeens, K. M.

P.-H. Wang, P. Minnis, M. P. McCormick, G. S. Kent, K. M. Skeens, “A 6-year climatology of cloud occurrence frequency from Stratospheric Aerosol and Gas Experiment II observations (1985–1990),” J. Geophys. Res. 101, 29407–20429 (1996).
[CrossRef]

Snider, J. B.

S. Y. Matrosov, B. W. Orr, R. A. Kropfli, J. B. Snider, “Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements,” J. Appl. Meteorol. 33, 617–626 (1994).
[CrossRef]

Stamnes, K.

Y. X. Hu, K. Stamnes, “An accurate parameterization of the radiative properties of water clouds suitable for use in climate models,” J. Clim. 6, 728–742 (1993).
[CrossRef]

Stephens, G. L.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

T. L. Schneider, G. L. Stephens, “Theoretical aspects of modeling backscattering by cirrus ice particles at millimeter wavelength,” J. Atmos. Sci. 52, 4367–4385 (1995).
[CrossRef]

Tanaka, Y.

Y. Tanaka, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

Tang, C.

K. Aydin, C. Tang, “Millimeter wave radar scattering from model ice crystal distributions,” IEEE Trans. Geosci. Remote Sens. 35, 140–146 (1997).
[CrossRef]

Testud, J.

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

Thomas, L.

A. J. Gibson, L. Thomas, S. K. Bhattacharyya, “Some characteristics of cirrus clouds deduced from laser radar observations at different elevation angles,” J. Atmos. Terr. Phys. 29, 657–660 (1997).

L. Thomas, J. C. Cartwright, D. P. Wakeling, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211–216 (1990).

Van Lammeren, A. C. A. P.

D. P. Donovan, A. C. A. P. Van Lammeren, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 1, theory and examples,” J. Geophys. Res. 106, 27425–27448 (2001).
[CrossRef]

Vane, D. G.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Veal, D. L.

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

Wakeling, D. P.

L. Thomas, J. C. Cartwright, D. P. Wakeling, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211–216 (1990).

Wang, P.-H.

P.-H. Wang, P. Minnis, M. P. McCormick, G. S. Kent, K. M. Skeens, “A 6-year climatology of cloud occurrence frequency from Stratospheric Aerosol and Gas Experiment II observations (1985–1990),” J. Geophys. Res. 101, 29407–20429 (1996).
[CrossRef]

Wang, Z.

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Warren, S. G.

S. P. Neshyba, T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres: 2. Hexagonal columns and plates,” J. Geophys. Res. 108, 4448, doi: 10.1029/2002JD003302 (2003).

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

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

Wolff, D. B.

D. Atlas, S. Y. Matrosov, A. J. Heymsfield, M.-D. Chou, D. B. Wolff, “Radar and radiation properties of ice clouds,” J. Appl. Meteorol. 34, 2329–2345 (1995).
[CrossRef]

Wylie, D. P.

D. P. Wylie, W. P. Menzel, “Eight years of high cloud statistics using HIRS,” J. Clim. 12, 170–184 (1999).
[CrossRef]

Yang, P.

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. 12, 162–176 (1995).
[CrossRef]

Appl. Opt. (2)

Atmos. Res. (1)

H. Lemke, H. Okamoto, M. Quante, “Comment on Error analysis of backscatter from discrete dipole approximation for different ice particle shapes,” Atmos. Res. 49, 189–197 (1998).

Bull. Am. Meteor. Soc. (1)

G. L. Stephens, D. G. Vane, R. Boain, G. Mace, K. Sassen, Z. Wang, A. Illingworth, E. O’Connor, W. Rossow, S. L. Durden, S. Miller, R. Austin, A. Benedetti, C. Mitrescuthe CloudSat Science Team, “The CloudSat Mission and the EOS Constellation: a new dimension of space-based observations of clouds and precipitation,” Bull. Am. Meteor. Soc. 83, 1771–1790 (2002).
[CrossRef]

Bull. Am. Meteorol Soc. (1)

A. Arking, “The radiative effects of clouds and their impact on climate,” Bull. Am. Meteorol Soc. 72, 795–813 (1991).
[CrossRef]

Contrib. Atmos. Phys. (1)

H. Okamoto, A. Macke, M. Quante, E. Raschke, “Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94 GHz. An error analysis,” Contrib. Atmos. Phys. 68, 319–334 (1995).

IEEE Trans. Geosci. Remote Sens. (1)

K. Aydin, C. Tang, “Millimeter wave radar scattering from model ice crystal distributions,” IEEE Trans. Geosci. Remote Sens. 35, 140–146 (1997).
[CrossRef]

J. Appl. Meteorol. (3)

D. Atlas, S. Y. Matrosov, A. J. Heymsfield, M.-D. Chou, D. B. Wolff, “Radar and radiation properties of ice clouds,” J. Appl. Meteorol. 34, 2329–2345 (1995).
[CrossRef]

S. Y. Matrosov, B. W. Orr, R. A. Kropfli, J. B. Snider, “Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements,” J. Appl. Meteorol. 33, 617–626 (1994).
[CrossRef]

C. M. R. Platt, N. Abshire, G. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally aligned crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

C. E. Dungey, C. F. Bohren, “Backscattering by nonspherical hydrometeors as calculated by the coupled-dipole method; an application in radar meteorology,” J. Atmos. Ocean. Technol. 10, 526–532 (1993).
[CrossRef]

J. Atmos. Sci. (4)

T. L. Schneider, G. L. Stephens, “Theoretical aspects of modeling backscattering by cirrus ice particles at millimeter wavelength,” J. Atmos. Sci. 52, 4367–4385 (1995).
[CrossRef]

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

Y. Tanaka, 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. Müller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

J. Atmos. Terr. Phys. (2)

D. Atlas, M. Kerker, W. Hitschfeld, “Scattering and attenuation by non-spherical atmospheric particles,” J. Atmos. Terr. Phys. 3, 108–119 (1954).
[CrossRef]

A. J. Gibson, L. Thomas, S. K. Bhattacharyya, “Some characteristics of cirrus clouds deduced from laser radar observations at different elevation angles,” J. Atmos. Terr. Phys. 29, 657–660 (1997).

J. Clim. (2)

Y. X. Hu, K. Stamnes, “An accurate parameterization of the radiative properties of water clouds suitable for use in climate models,” J. Clim. 6, 728–742 (1993).
[CrossRef]

D. P. Wylie, W. P. Menzel, “Eight years of high cloud statistics using HIRS,” J. Clim. 12, 170–184 (1999).
[CrossRef]

J. Geophys. Res. (8)

P.-H. Wang, P. Minnis, M. P. McCormick, G. S. Kent, K. M. Skeens, “A 6-year climatology of cloud occurrence frequency from Stratospheric Aerosol and Gas Experiment II observations (1985–1990),” J. Geophys. Res. 101, 29407–20429 (1996).
[CrossRef]

D. P. Donovan, A. C. A. P. Van Lammeren, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 1, theory and examples,” J. Geophys. Res. 106, 27425–27448 (2001).
[CrossRef]

D. P. Donovan, A. C. A. P. Van Lammeren, R. J. Hogan, H. W. J. Russchenberg, A. Apituley, P. Francis, J. Testud, J. Pelon, M. Quante, J. Goddard, “Cloud effective particle size and water content profile retrievals using combined lidar and radar observations, 2, comparison with IR radiometer and in situ measurements of ice clouds,” J. Geophys. Res. 106, 27449–27464 (2001).
[CrossRef]

T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres,” J. Geophys. Res. 104, 31697–31709 (1999).
[CrossRef]

S. P. Neshyba, T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by an assembly of spheres: 2. Hexagonal columns and plates,” J. Geophys. Res. 108, 4448, doi: 10.1029/2002JD003302 (2003).

H. Lemke, M. Quante, “Backscatter characteristics of nonspherical ice crystals: assessing the potential of polarimetric radar measurements,” J. Geophys. Res. 104, 31739–31752 (1999).
[CrossRef]

D. P. Donovan, “Ice-cloud effective particle size parameterization based on combined lidar, radar and mean Doppler velocity measurements,” J. Geophys. Res. 108, 4573, doi: 10.1029/2003JD003469 (2003).

M. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving delta-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

J. Opt. Soc. Am. (2)

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. 12, 162–176 (1995).
[CrossRef]

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

Opt. Lett. (2)

Q. J. R. Meteorol. Soc. (1)

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multispectral reflectance measurements during EURCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Tellus (1)

L. Thomas, J. C. Cartwright, D. P. Wakeling, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211–216 (1990).

Other (6)

A. Ansmann, “Molecular-backscatter profiling of the volume-scattering coefficient in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 197–210.

H. V. Hulst Van De, Light Scattering by Small Particles (Dover, New York, 1981), pp. 85–101.

ESA (European Space Agency), The Five Candidate Earth Explorer Missions—EarthCare—Earth Clouds, Aerosols and Radiation ExplorerESA SP-1257(1), (ESA/ESTEC, Noordwijk, The Netherlands, 2001).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

J. Hallett, W. P. Arnott, M. P. Bailey, J. T. Hallet, “Ice crystals in cirrus,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 41–77.

A. J. Heymsfield, G. M. McFarquhar, “Midlatitude and tropical, cirrus microphysical properties,” in Cirrus, D. K. Lynch, K. Sassen, D. Starr, G. Stephens, eds. (Oxford U. Press, New York, 2002), pp. 78–101.

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Figures (14)

Fig. 1
Fig. 1

Ratio of 355-nm extinction to 95-GHz radar reflectivity for size distributions of ice spheres for two values of γ (2 and 7) as a function of R eff (left) and Reff (right).

Fig. 2
Fig. 2

Definition of mean diameter (D m ). For a given ice crystal in this study, D m is constructed from the average over all possible crystal orientations.

Fig. 3
Fig. 3

Various types of equivalent spheres considered in this study.

Fig. 4
Fig. 4

Reflectivity as a function of particle radius for ice spheres and a radar wavelength of 95 GHz calculated with Mie theory and predicted by the Rayleigh scattering approximation.

Fig. 5
Fig. 5

Crystal habits considered in this study.

Fig. 6
Fig. 6

Aspect ratios for plates and columns used here.

Fig. 7
Fig. 7

Size equivalent spheres for various equivalent sphere approaches: top left, columns; top right, plates; bottom left, broad-branched stellars; bottom right, narrow-branched stellars. Here D refers to the maximum dimension (L in the case of columns and 2a in the case of plates and distance between opposite tip vertices for the stellar crystals).

Fig. 8
Fig. 8

Reflectivity calculated by DDA theory applied to 3-D randomly oriented crystals of different sizes and habits compared with reflectivity calculated with Mie theory applied to equivalent volume R v spheres. Top left, columns; top right, plates; bottom left, broad-branched stellars; bottom right, narrow branched stellars.

Fig. 9
Fig. 9

Radar reflectivity (95 GHz) calculated with Mie theory applied to different equivalent sphere formulations to DDA-calculated reflectivity values. Here random 3-D orientation has been assumed. Note the change in size axis range between the hexagonal crystals (columns and plates) and the stellars.

Fig. 10
Fig. 10

Ratio of 95-GHz radar reflectivity to 355-nm lidar extinction coefficient for two families of size distribution (columns) as defined by use of Eq. (8) with γ = 2 and γ = 6 (as in Fig. 1) as a function of R v , R eff, and R eff. The lighter lines show the results for spheres (generated with Mie theory for both the radar reflectivity and the 355-nm extinction), whereas the dark lines show the results for 3-D randomly oriented ice crystals generated with DDA results for the reflectivity and the assumption that the extinction is equal to twice the average cross-sectional area.

Fig. 11
Fig. 11

Ratio of 95-GHz Radar reflectivity to 355-nm lidar extinction coefficient ratio as a function of R eff for size distribution of randomly oriented columns, plates, and stellars (wavelengths and γ values as in Fig. 10). Top left, columns; top right, plates; bottom left, broad-branched stellars; bottom right, narrow-branched stellars.

Fig. 12
Fig. 12

Ratio of 95-GHz radar reflectivity to 355-nm lidar backscatter coefficient as a function of R eff for the same families of size distribution of plates (right) and columns (left) as used in Fig. 11 (dark lines). The lighter lines show the corresponding results for ice spheres (wavelengths and γ values as in Fig. 10).

Fig. 13
Fig. 13

Ratio of reflectivity for 2-D-oriented crystals to 3-D randomly oriented crystals.

Fig. 14
Fig. 14

Ratio of extinction for 2-D-oriented crystals to 3-D randomly oriented crystals. In the case of the 2-D-oriented crystals the extinction refers to a beam of light perpendicular to the plane of orientation.

Equations (16)

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Z=λ6π6|K|2i NDi|SDi|2orn,
|SDi|264|K|2π6λ6MDi/ρi,s4π/32,
Z64NoMD/ρi,s4π/32,
Z=NoD6.
α2NoAcD,
Reff=34ρi,sMDAcD.
Reff=916πMD/ρi,s2AcD1/4.
ND=NoRm1ΓγrRmγ-1 exp-r/Rm,
Ze=|K||Kw|2Z,
ZNoDv6.
ZNo1ρi,s2 ρi,aDa2Da6,
ZNo1|K|2 |Ki,a|Da2Da6,
ρi,aρi,s=|Ki,a||K|,
Z64 i NReffDiReffDi6,
NReffDi=NDiDvDi2ReffDi6.
Zα=CReff4,

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