Abstract

Problems encountered in the interpretation of results of laser sensing of crystal clouds are considered. The parameters characterizing the cloud particle orientation are determined through the backscattering phase matrix elements. It is demonstrated how these parameters are related to the probability density of particle distribution over the spatial orientation angles. Trends in the change of the backscattering phase matrices attendant to variations of the zenith sensing angle are shown on the example of a monodisperse ice particle ensemble.

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References

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  1. K. Masuda and H. Ishimoto, “Influence of particle orientation on retrieving cirrus cloud properties by use of total and polarized reflectances from satellite measurements,” J. Quant. Spectrosc. Radiat. Transf.85(2), 183–193 (2004).
    [CrossRef]
  2. C. M. R. Platt, “Lidar backscatter from horizontal ice crystal plates,” J. Appl. Meteorol.17(4), 482–488 (1978).
    [CrossRef]
  3. L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus B Chem. Phys. Meterol.42, 2011–2016 (1990).
  4. V. Noel and K. Sassen, “Study of planar ice crystal orientation in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
    [CrossRef]
  5. V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci.61(16), 2073–2081 (2004).
    [CrossRef]
  6. Y. Balin, B. Kaul, G. Kokhanenko, and D. Winker, “Application of circularly polarized laser radiation for sensing of crystal clouds,” Opt. Express17(8), 6849–6859 (2009).
    [CrossRef] [PubMed]
  7. W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
    [CrossRef]
  8. J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci.52(12), 2276–2285 (1995).
    [CrossRef]
  9. B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation,” J. Atmos. Oceanic Opt.16, 866–870 (2005).
  10. M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt.45(20), 4878–4887 (2006).
    [CrossRef] [PubMed]
  11. A. Borovoi and N. Kustova, “Specular scattering by preferentially oriented ice crystals,” Appl. Opt.48(19), 3878–3885 (2009).
    [CrossRef] [PubMed]
  12. A. Borovoi, A. Konoshonkin, N. Kustova, and H. Okamoto, “Backscattering Mueller matrix for quasi-horizontally oriented ice plates of cirrus clouds: application to CALIPSO signals,” Opt. Express20(27), 28222–28233 (2012).
    [CrossRef] [PubMed]
  13. B. V. Kaul, I. V. Samokhvalov, and S. N. Volkov, “Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar,” Appl. Opt.43(36), 6620–6628 (2004).
    [CrossRef] [PubMed]
  14. M. Hayman, S. Spuler, B. Morley, and J. VanAndel, “Polarization lidar operation for measuring backscatter phase matrices of oriented scatterers,” Opt. Express20(28), 29553–29567 (2012).
    [CrossRef] [PubMed]
  15. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957, Dover, New York, 1981).
  16. C. R. Hu, G. W. Kattawar, M. E. Parkin, and P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a non-spherical dielectric scatter,” Appl. Opt.26, 4159–4173 (1987).
  17. J. W. Hovenier and C. V. M. Van Der Mee, “Testing scattering matrices a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transf.55(5), 649–661 (1996).
    [CrossRef]
  18. M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett.20(12), 1356–1358 (1995).
    [CrossRef] [PubMed]
  19. C. J. Flynn, A. Mendoza, Y. Zheng, and S. Mathur, “Novel polarization-sensitive micropulse lidar measurement technique,” Opt. Express15(6), 2785–2790 (2007).
    [CrossRef] [PubMed]
  20. G. G. Gimmestad, “Reexamination of depolarization in lidar measurements,” Appl. Opt.47(21), 3795–3802 (2008).
    [CrossRef] [PubMed]
  21. B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation,” Atmos. Oceanic Opt.19, 38–42 (2006).
  22. B. V. Kaul, “Effect of electric field on orientation of ice cloud particles,” Atmos. Oceanic Opt.19, 751–754 (2006).
  23. H.-R. Cho, J. V. Iribarne, and W. G. Richards, “On the orientation of ice crystals in a cumulo-nimbus cloud,” J. Atmos. Sci.38(5), 1111–1114 (1981).
    [CrossRef]
  24. V. V. Kuznetsov, N. K. Nikiforova, and L. N. Pavlova, “On measuring the microstructure of crystal fogs by an Aspekt-10 television aerosol spectrometer,” Trudy Inst. Eksper. Meteorol.7(112), 101–106 (1983).
  25. M. Kajikawa, “Laboratory measurement of falling velocity of individual ice crystals,” J. Meteor. Soc. Japan51, 263–272 (1972).
  26. K. Sassen, “Remote sensing of planar ice crystals fall attitudes,” J. Meteorol. Soc. Jpn.58, 422–429 (1980).
  27. O. A. Volkovitskii, L. N. Pavlova, and A. G. Petrushin, Optical Properties of Crystal Clouds (Gidrometeoizdat, Leningrad, 1984).
  28. D. N. Romashov, “Backscattering phase matrix of monodisperse ensembles of hexagonal water ice crystals,” Atmos. Oceanic Opt.12, 376–384 (1999).
  29. Yu. S. Balin, B. V. Kaul, and G. P. Kokhanenko, “Observation of specularly reflective particles and layers in crystal clouds,” Atmos. Oceanic Opt.24, 293–299 (2011).
  30. Y. S. Balin, B. V. Kaul, G. P. Kokhanenko, and I. E. Penner, “Observations of specular reflective particles and layers in crystal clouds,” Opt. Express19(7), 6209–6214 (2011).
    [CrossRef] [PubMed]

2012

2011

Y. S. Balin, B. V. Kaul, G. P. Kokhanenko, and I. E. Penner, “Observations of specular reflective particles and layers in crystal clouds,” Opt. Express19(7), 6209–6214 (2011).
[CrossRef] [PubMed]

Yu. S. Balin, B. V. Kaul, and G. P. Kokhanenko, “Observation of specularly reflective particles and layers in crystal clouds,” Atmos. Oceanic Opt.24, 293–299 (2011).

2009

2008

2007

2006

M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt.45(20), 4878–4887 (2006).
[CrossRef] [PubMed]

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation,” Atmos. Oceanic Opt.19, 38–42 (2006).

B. V. Kaul, “Effect of electric field on orientation of ice cloud particles,” Atmos. Oceanic Opt.19, 751–754 (2006).

2005

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation,” J. Atmos. Oceanic Opt.16, 866–870 (2005).

V. Noel and K. Sassen, “Study of planar ice crystal orientation in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
[CrossRef]

2004

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci.61(16), 2073–2081 (2004).
[CrossRef]

K. Masuda and H. Ishimoto, “Influence of particle orientation on retrieving cirrus cloud properties by use of total and polarized reflectances from satellite measurements,” J. Quant. Spectrosc. Radiat. Transf.85(2), 183–193 (2004).
[CrossRef]

B. V. Kaul, I. V. Samokhvalov, and S. N. Volkov, “Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar,” Appl. Opt.43(36), 6620–6628 (2004).
[CrossRef] [PubMed]

1999

D. N. Romashov, “Backscattering phase matrix of monodisperse ensembles of hexagonal water ice crystals,” Atmos. Oceanic Opt.12, 376–384 (1999).

1996

J. W. Hovenier and C. V. M. Van Der Mee, “Testing scattering matrices a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transf.55(5), 649–661 (1996).
[CrossRef]

1995

1990

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus B Chem. Phys. Meterol.42, 2011–2016 (1990).

1987

1983

V. V. Kuznetsov, N. K. Nikiforova, and L. N. Pavlova, “On measuring the microstructure of crystal fogs by an Aspekt-10 television aerosol spectrometer,” Trudy Inst. Eksper. Meteorol.7(112), 101–106 (1983).

1981

H.-R. Cho, J. V. Iribarne, and W. G. Richards, “On the orientation of ice crystals in a cumulo-nimbus cloud,” J. Atmos. Sci.38(5), 1111–1114 (1981).
[CrossRef]

1980

K. Sassen, “Remote sensing of planar ice crystals fall attitudes,” J. Meteorol. Soc. Jpn.58, 422–429 (1980).

1978

C. M. R. Platt, “Lidar backscatter from horizontal ice crystal plates,” J. Appl. Meteorol.17(4), 482–488 (1978).
[CrossRef]

1972

M. Kajikawa, “Laboratory measurement of falling velocity of individual ice crystals,” J. Meteor. Soc. Japan51, 263–272 (1972).

Balin, Y.

Balin, Y. S.

Balin, Yu. S.

Yu. S. Balin, B. V. Kaul, and G. P. Kokhanenko, “Observation of specularly reflective particles and layers in crystal clouds,” Atmos. Oceanic Opt.24, 293–299 (2011).

Borovoi, A.

Cartwright, J. C.

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus B Chem. Phys. Meterol.42, 2011–2016 (1990).

Castagnoli, F.

Chepfer, H.

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci.61(16), 2073–2081 (2004).
[CrossRef]

Cho, H.-R.

H.-R. Cho, J. V. Iribarne, and W. G. Richards, “On the orientation of ice crystals in a cumulo-nimbus cloud,” J. Atmos. Sci.38(5), 1111–1114 (1981).
[CrossRef]

Del Guasta, M.

Flynn, C. J.

Gimmestad, G. G.

Hayman, M.

Herb, P.

Hovenier, J. W.

J. W. Hovenier and C. V. M. Van Der Mee, “Testing scattering matrices a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transf.55(5), 649–661 (1996).
[CrossRef]

M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett.20(12), 1356–1358 (1995).
[CrossRef] [PubMed]

Hu, C. R.

Hunt, W. H.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Iribarne, J. V.

H.-R. Cho, J. V. Iribarne, and W. G. Richards, “On the orientation of ice crystals in a cumulo-nimbus cloud,” J. Atmos. Sci.38(5), 1111–1114 (1981).
[CrossRef]

Ishimoto, H.

K. Masuda and H. Ishimoto, “Influence of particle orientation on retrieving cirrus cloud properties by use of total and polarized reflectances from satellite measurements,” J. Quant. Spectrosc. Radiat. Transf.85(2), 183–193 (2004).
[CrossRef]

Kajikawa, M.

M. Kajikawa, “Laboratory measurement of falling velocity of individual ice crystals,” J. Meteor. Soc. Japan51, 263–272 (1972).

Kattawar, G. W.

Kaul, B.

Kaul, B. V.

Yu. S. Balin, B. V. Kaul, and G. P. Kokhanenko, “Observation of specularly reflective particles and layers in crystal clouds,” Atmos. Oceanic Opt.24, 293–299 (2011).

Y. S. Balin, B. V. Kaul, G. P. Kokhanenko, and I. E. Penner, “Observations of specular reflective particles and layers in crystal clouds,” Opt. Express19(7), 6209–6214 (2011).
[CrossRef] [PubMed]

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation,” Atmos. Oceanic Opt.19, 38–42 (2006).

B. V. Kaul, “Effect of electric field on orientation of ice cloud particles,” Atmos. Oceanic Opt.19, 751–754 (2006).

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation,” J. Atmos. Oceanic Opt.16, 866–870 (2005).

B. V. Kaul, I. V. Samokhvalov, and S. N. Volkov, “Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar,” Appl. Opt.43(36), 6620–6628 (2004).
[CrossRef] [PubMed]

Klett, J. D.

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci.52(12), 2276–2285 (1995).
[CrossRef]

Kokhanenko, G.

Kokhanenko, G. P.

Yu. S. Balin, B. V. Kaul, and G. P. Kokhanenko, “Observation of specularly reflective particles and layers in crystal clouds,” Atmos. Oceanic Opt.24, 293–299 (2011).

Y. S. Balin, B. V. Kaul, G. P. Kokhanenko, and I. E. Penner, “Observations of specular reflective particles and layers in crystal clouds,” Opt. Express19(7), 6209–6214 (2011).
[CrossRef] [PubMed]

Konoshonkin, A.

Kustova, N.

Kuznetsov, V. V.

V. V. Kuznetsov, N. K. Nikiforova, and L. N. Pavlova, “On measuring the microstructure of crystal fogs by an Aspekt-10 television aerosol spectrometer,” Trudy Inst. Eksper. Meteorol.7(112), 101–106 (1983).

Lucker, P. L.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Masuda, K.

K. Masuda and H. Ishimoto, “Influence of particle orientation on retrieving cirrus cloud properties by use of total and polarized reflectances from satellite measurements,” J. Quant. Spectrosc. Radiat. Transf.85(2), 183–193 (2004).
[CrossRef]

Mathur, S.

Mendoza, A.

Mishchenko, M. I.

Morandi, M.

Morley, B.

Nikiforova, N. K.

V. V. Kuznetsov, N. K. Nikiforova, and L. N. Pavlova, “On measuring the microstructure of crystal fogs by an Aspekt-10 television aerosol spectrometer,” Trudy Inst. Eksper. Meteorol.7(112), 101–106 (1983).

Noel, V.

V. Noel and K. Sassen, “Study of planar ice crystal orientation in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
[CrossRef]

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci.61(16), 2073–2081 (2004).
[CrossRef]

Okamoto, H.

Parkin, M. E.

Pavlova, L. N.

V. V. Kuznetsov, N. K. Nikiforova, and L. N. Pavlova, “On measuring the microstructure of crystal fogs by an Aspekt-10 television aerosol spectrometer,” Trudy Inst. Eksper. Meteorol.7(112), 101–106 (1983).

Penner, I. E.

Platt, C. M. R.

C. M. R. Platt, “Lidar backscatter from horizontal ice crystal plates,” J. Appl. Meteorol.17(4), 482–488 (1978).
[CrossRef]

Powell, K. A.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Richards, W. G.

H.-R. Cho, J. V. Iribarne, and W. G. Richards, “On the orientation of ice crystals in a cumulo-nimbus cloud,” J. Atmos. Sci.38(5), 1111–1114 (1981).
[CrossRef]

Riviere, O.

Romashov, D. N.

D. N. Romashov, “Backscattering phase matrix of monodisperse ensembles of hexagonal water ice crystals,” Atmos. Oceanic Opt.12, 376–384 (1999).

Samokhvalov, I. V.

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation,” Atmos. Oceanic Opt.19, 38–42 (2006).

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation,” J. Atmos. Oceanic Opt.16, 866–870 (2005).

B. V. Kaul, I. V. Samokhvalov, and S. N. Volkov, “Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar,” Appl. Opt.43(36), 6620–6628 (2004).
[CrossRef] [PubMed]

Sassen, K.

V. Noel and K. Sassen, “Study of planar ice crystal orientation in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
[CrossRef]

K. Sassen, “Remote sensing of planar ice crystals fall attitudes,” J. Meteorol. Soc. Jpn.58, 422–429 (1980).

Spuler, S.

Thomas, L.

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus B Chem. Phys. Meterol.42, 2011–2016 (1990).

Vallar, E.

Van Der Mee, C. V. M.

J. W. Hovenier and C. V. M. Van Der Mee, “Testing scattering matrices a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transf.55(5), 649–661 (1996).
[CrossRef]

VanAndel, J.

Vaughan, M. A.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Venturi, V.

Volkov, S. N.

Wareing, D. P.

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus B Chem. Phys. Meterol.42, 2011–2016 (1990).

Weimer, C.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Winker, D.

Winker, D. M.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Zheng, Y.

Appl. Opt.

Atmos. Oceanic Opt.

D. N. Romashov, “Backscattering phase matrix of monodisperse ensembles of hexagonal water ice crystals,” Atmos. Oceanic Opt.12, 376–384 (1999).

Yu. S. Balin, B. V. Kaul, and G. P. Kokhanenko, “Observation of specularly reflective particles and layers in crystal clouds,” Atmos. Oceanic Opt.24, 293–299 (2011).

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation,” Atmos. Oceanic Opt.19, 38–42 (2006).

B. V. Kaul, “Effect of electric field on orientation of ice cloud particles,” Atmos. Oceanic Opt.19, 751–754 (2006).

J. Appl. Meteorol.

C. M. R. Platt, “Lidar backscatter from horizontal ice crystal plates,” J. Appl. Meteorol.17(4), 482–488 (1978).
[CrossRef]

V. Noel and K. Sassen, “Study of planar ice crystal orientation in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
[CrossRef]

J. Atmos. Ocean. Technol.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

J. Atmos. Oceanic Opt.

B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation,” J. Atmos. Oceanic Opt.16, 866–870 (2005).

J. Atmos. Sci.

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci.52(12), 2276–2285 (1995).
[CrossRef]

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci.61(16), 2073–2081 (2004).
[CrossRef]

H.-R. Cho, J. V. Iribarne, and W. G. Richards, “On the orientation of ice crystals in a cumulo-nimbus cloud,” J. Atmos. Sci.38(5), 1111–1114 (1981).
[CrossRef]

J. Meteor. Soc. Japan

M. Kajikawa, “Laboratory measurement of falling velocity of individual ice crystals,” J. Meteor. Soc. Japan51, 263–272 (1972).

J. Meteorol. Soc. Jpn.

K. Sassen, “Remote sensing of planar ice crystals fall attitudes,” J. Meteorol. Soc. Jpn.58, 422–429 (1980).

J. Quant. Spectrosc. Radiat. Transf.

K. Masuda and H. Ishimoto, “Influence of particle orientation on retrieving cirrus cloud properties by use of total and polarized reflectances from satellite measurements,” J. Quant. Spectrosc. Radiat. Transf.85(2), 183–193 (2004).
[CrossRef]

J. W. Hovenier and C. V. M. Van Der Mee, “Testing scattering matrices a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transf.55(5), 649–661 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Tellus B Chem. Phys. Meterol.

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus B Chem. Phys. Meterol.42, 2011–2016 (1990).

Trudy Inst. Eksper. Meteorol.

V. V. Kuznetsov, N. K. Nikiforova, and L. N. Pavlova, “On measuring the microstructure of crystal fogs by an Aspekt-10 television aerosol spectrometer,” Trudy Inst. Eksper. Meteorol.7(112), 101–106 (1983).

Other

O. A. Volkovitskii, L. N. Pavlova, and A. G. Petrushin, Optical Properties of Crystal Clouds (Gidrometeoizdat, Leningrad, 1984).

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957, Dover, New York, 1981).

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Figures (4)

Fig. 1
Fig. 1

Hexagonal crystal orientation angles: θ, φ are polar and azimuth angles and γ is the angle of rotation about the hexagonal axis. Radiation is propagated along the z axis.

Fig. 2
Fig. 2

Element М11 of the BSPM for hexagonal ice plates (height L = 30.64 μm, base diameter а = 200 μm, λ= 0.55 μm, and refractive index n = 1.311; the left ordinate) and normalized elements М12 and М44 (the right ordinate).

Fig. 3
Fig. 3

Dependence of the reflected signal intensity (element М11) and normalized diagonal BSPM elements with increase in k – the parameter of the distribution function over the polar orientation angles – for sensing in the zenith or nadir direction.

Fig. 4
Fig. 4

Dependence of the normalized BSPM elements and parameter χ (see Eq. (6)) on the zenith sensing angle β for a strong degree of particle orientation. Closed symbols – k = 10, open ones – k = 500.

Tables (3)

Tables Icon

Table 1 Dependence of the distribution parameter k on the maximum particle diameter d for five values of the energy dissipation rate ε. The upper values here are for plates, and the lower values are for columns.

Tables Icon

Table 2 Standard deviation σ of plates from horizontal position, in degrees, for the indicated values of the distribution parameter k.

Tables Icon

Table 3 Elements of the normalized BSPM and parameter χ (see Eq. (6)) as functions of the zenith sensing angle β (in degrees) for the indicated values of the parameter k of the distribution function over orientation angles.

Equations (19)

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S= 1 r 2 M S 0 ΔV.
M mod =R( φ 0 ) M exp R( φ 0 )= M 11 ( 1 m 12 0 m 14 m 21 m 22 0 0 0 0 m 33 m 34 m 41 0 m 43 m 44 ),
m 12 = m 21 , m 13 = m 31 , m 14 = m 41 , m 23 = m 32 , m 24 = m 42 , m 34 = m 43 ,
m 11 m 22 + m 33 m 44 =0
M= M 11 ( 1 0 0 m 14 0 1d 0 0 0 0 d1 0 m 41 0 0 2d1 ),
χ= m 22 + m 33 1+ m 44
M(0,θ)= 3 π 0 π/3 M (0,θ,γ)γdγ.
M(n)=n 0 2π 0 π 2 R(φ)M(0,θ) R(φ)f(φ,θ)sinθdθdφ.
f(θ)dθ= 2e kcos(2θ) π I 0 (k) dθ, θ[ 0,π/2 ] ,
k= Λ p,c A 2 d 2b /4 νε ,
f(φ,θ)sinθdθdφ= 1 2πB(k) 2exp[ kcos2θ ] π I 0 (k) sinθdθdφ,
M (n)=n 0 2π 0 π 2 R( φ )M(0, θ ) R( φ )f( φ , θ )sin θ d θ d φ .
f(φ,θ)=f(π,β).
( cosβ 0 sinβ 0 1 0 sinβ 0 cosβ )( sinθcosφ sinθsinφ) cosθ )=( cosβsinθcosφ+sinβcosθ sinθsinφ sinβsinθcosφ+cosβcosθ ).
θ (φ,θ)=acos(sinβsinθcosφ+cosβcosθ),
φ (φ,θ)=acos( cosβsinθcosφ+sinβcosθ (cosβsinθcosφ+sinβcosθ) 2 +(sinθ (sinφ) 2 ).
d l = 2δ 1+δ ,
δ= 1 m 22 1+2 m 12 + m 22 ,
q= m 12 + m 22 1+ m 12 , d l =1q.

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