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Atmospheric and Oceanic Optics

, Volume 32, Issue 2, pp 117–123 | Cite as

Extinction Matrix of Atmospheric Ice Crystals with Their Preferred Spatial Orientation for the Visible and IR Regions

  • N. V. KustovaEmail author
  • A. V. KonoshonkinEmail author
  • D. N. TimofeevEmail author
  • V. A. ShishkoEmail author
OPTICAL WAVES PROPAGATION
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Abstract

The extinction matrix for an ensemble of hexagonal ice plates and columns is presented. The extinction matrix for droxtal and bullet crystals has been estimated. The calculations have been carried out for particles with characteristic dimensions from 10 to 100 μm and wavelengths from 0.3 to 10 μm assuming a gamma distribution of particle size with a width parameter μ < 4. It has been found that the extinction matrix of an ensemble of atmospheric ice crystals in the visible wavelength region is a unit matrix with a coefficient equal to the doubled area of the particle projection. The error of this representation does not exceed tenths of a percent and does not depend on the type of crystals and their spatial orientation. It has also been found that such a representation of the extinction matrix in the IR region is possible only for hexagonal columns, bullets, and similar crystals with a characteristic size greater than 20 μm for wavelengths less than 8 μm.

Keywords:

extinction coefficient extinction matrix cirrus clouds physical optics light scattering ice crystals 

Notes

ACKNOWLEDGMENTS

This work was supported by the Russian Foundation for Basic Research (project nos. 16-35-60 089, 18‑05-00568, and 18-55-53 046), President of the Russian Federation (grant no. MK-2495.2017.5), and Mendeleev Foundation of Tomsk State University. Calculations of the quasi-horizontally oriented column were supported by the Russian Science Foundation (agreement no. 18-77-10 035).

REFERENCES

  1. 1.
    Climate Change 2007: The Physical Science Basis: Contribution of Working Group I to the Fourth Assessment Report of the IPCC (Cambridge University Press, Cambridge, 2007).Google Scholar
  2. 2.
    M. Hayman, S. Spuler, and B. Morley, “Polarization lidar observations of backscatter phase matrices from oriented ice crystals and rain,” Opt. Express 22, 16976–16990 (2014).ADSCrossRefGoogle Scholar
  3. 3.
    M. Hayman and J. P. Thayer, “General description of polarization in lidar using stokes vectors and polar decomposition of mueller matrices,” J. Opt. Soc. Am., A 29, 400–409 (2012).ADSCrossRefGoogle Scholar
  4. 4.
    J. Reichardt, U. Wandinger, V. Klein, I. Mattis, B. Hilber, and R. Begbie, “RAMSES: German meteorological service autonomous Raman lidar for water vapor, temperature, aerosol, and cloud measurements,” Appl. Opt. 51, 8111–8131 (2012).ADSCrossRefGoogle Scholar
  5. 5.
    A. Borovoy, N. Kustova, and A. Konoshonkin, “Interference phenomena at backscattering by ice crystals of cirrus clouds,” Opt. Express 23, 24 557–24 571 (2015).CrossRefGoogle Scholar
  6. 6.
    A. V. Konoshonkin, N. V. Kustova, V. A. Shishko, and A. G. Borovoy, “The technique for solving the problem of light backscattering by ice crystals of cirrus clouds by the physical optics method for a lidar with zenith scanning,” Atmos. Ocean. Opt. 29 (3), 252–263 (2016).CrossRefGoogle Scholar
  7. 7.
    C. Zhou and P. Yang, “Backscattering peak of ice cloud particles,” Opt. Express 23, 11 995–12 003 (2015).CrossRefGoogle Scholar
  8. 8.
    G. Mie, “Beitrage Zur Optik Truber Medien, Speziell Kolloidaler Metallosungen,” Ann. Phys. (New York) 25, 377–445 (1908).ADSzbMATHGoogle Scholar
  9. 9.
    P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev., D 3, 825–839 (1971).ADSCrossRefGoogle Scholar
  10. 10.
    B. Peterson and S. Strom, “T-matrix formulation of electromagnetic scattering from multilayered scatterers,” Phys. Rev., D 10, 2670–2684 (1974).ADSCrossRefGoogle Scholar
  11. 11.
    K. S. Kunz and R. J. Luebbers, Finite Difference Time Domain Method for Electromagnetics (FL: CRC Press, Boca Raton, FL, 1993).Google Scholar
  12. 12.
    A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 1998).zbMATHGoogle Scholar
  13. 13.
    E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).ADSCrossRefGoogle Scholar
  14. 14.
    M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106, 546–557 (2007).ADSCrossRefGoogle Scholar
  15. 15.
    A. A. Popov, Avtoref. Doctoral Dissertation in Mathematics and Physics (Tomsk, 1992).Google Scholar
  16. 16.
    M. Del Guasta, “Simulation of lidar returns from pristine and deformed hexagonal ice prisms in cold cirrus by means of “face-tracing”,” J. Geophys. Res. 106, 12 589–12 602 (2001).ADSCrossRefGoogle Scholar
  17. 17.
    L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).ADSCrossRefGoogle Scholar
  18. 18.
    A. Borovoy, A. Konoshonkin, and N. Kustova, “The physics-optics approximation and its application to light backscattering by hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 146, 181–189 (2014).ADSCrossRefGoogle Scholar
  19. 19.
    A. A. Popov, “Polarized radiation extinction and backscattering cross-sections by a round plate in the physical optics approximation,” Opt. Atmos. Okeana 1 (5), 19–24 (1988).Google Scholar
  20. 20.
    A. A. Popov and O. V. Shefer, “An analytical expression for the coefficient of optical attenuation by a polydisperse plate crystal system,” Opt. Atmos. Okeana 2 (5), 532–535 (1989).Google Scholar
  21. 21.
    A. A. Popov and O. V. Shefer, “Estimate of the extinction of optical radiation by crystals lacking plane-parallel faces,” Opt. Atmos. Okeana 3 (5), 456–461 (1990).Google Scholar
  22. 22.
    A. V. Konoshonkin, N. V. Kustova, and A. G. Borovoy, “Beam-splitting code for light scattering by ice crystal particles within geometric-optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 164, 175–183 (2015).ADSCrossRefGoogle Scholar
  23. 23.
    A. V. Konoshonkin, N. V. Kustova, and A. G. Borovoi, “Beam splitting algorithm for the problem of light scattering by atmospheric ice crystals. Part 2. Comparison with the ray tracing algorithm,” Atmos. Oceanic Opt. 28 (5), 448–454 (2015).CrossRefGoogle Scholar
  24. 24.
    A. G. Borovoy, A. A. Popov, and O. V. Shefer, “Theoretical investigation of the spectral behavior of the optical radiation extinction coefficient of a system of oriented ice plates,” Opt. Atmos. Okeana 4 (9), 899–906 (1991).Google Scholar
  25. 25.
    O. V. Shefer, “Energy and polarization characteristics of optical radiation scattered forward by a plane crystal,” Atmos. Ocean. Opt. 19 (4), 244–248 (2006).Google Scholar
  26. 26.
    A. A. Popov and O. V. Shefer, “Numerical study of the extinction matrix for a plate crystal,” Rus. Phys. J. 52 (8), 850–861 (2009).CrossRefzbMATHGoogle Scholar
  27. 27.
    O. Shefer and A. Popov, “Extinction and small angle scattering by thin plate crystals,” Appl. Opt. 49 (8), 1434–1445 (2010).ADSCrossRefGoogle Scholar
  28. 28.
    O. V. Shefer, “Special features of the extinction matrix for preferably oriented plate crystals,” Rus. Phys. J. 55 (5), 40–48 (2012).CrossRefzbMATHGoogle Scholar
  29. 29.
    O. Shefer, “Numerical study of extinction of visible and infrared radiation transformed by preferentially oriented plate crystals,” J. Quant. Spectrosc. Radiat. Transfer 117, 104–113 (2013).ADSCrossRefGoogle Scholar
  30. 30.
    G. M. McFarquhar, T.-L. Hsieh, M. Freer, J. Mascio, and B. F. Jewett, “The characterization of ice hydrometeor gamma size distributions as volumes in N0–λ–μ phase space: Implications for microphysical process modeling,” J. Atmos. Sci. 72 (2), 892–909 (2015).ADSCrossRefGoogle Scholar
  31. 31.
    O. V. Shefer, “Energy and polarization features of the extinction of visible and near-IR wavelengths by large crystals,” Izv. Vyssh. Ucheb. Zaved., Fiz. 57 (10), 61–68 (2014).Google Scholar
  32. 32.
    O. Shefer, “Extinction of radiant energy by large atmospheric crystals with different shapes,” J. Quant. Spectrosc. Radiat. Transfer 178, 350–360 (2016).ADSCrossRefGoogle Scholar
  33. 33.
    O. Shefer, “Numerical study of influence of different dispersed components of crystal cloud on transmission of radiant energy,” J. Quant. Spectrosc. Radiat. Transfer 201, 148–155 (2017).ADSCrossRefGoogle Scholar
  34. 34.
    L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).Google Scholar
  35. 35.
    H. C. van de Hulst, Light Scattering by Small Particles (Willey, New York, 1957).CrossRefGoogle Scholar
  36. 36.
    N. V. Kustova and A. G. Borovoy, “The shadow function method in aureole scattering,” Atmos. Ocean. Opt. 19 (10), 778–783 (2006).Google Scholar
  37. 37.
    A. H. Auer and D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 29, 311–317 (1970).ADSCrossRefGoogle Scholar
  38. 38.
    D. L. Mitchell, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part 1. Microphysics,” J. Atmos. Sci. 51, 797–816 (1994).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of SciencesTomskRussia
  2. 2.Tomsk State UniversityTomskRussia

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