Vol. 36, issue 12, article # 8

Konoshonkin A. V., Kustova N. V., Shishko V. A., Timofeev D. N., Tkachev I. V., Bakute E., Babinovich A. E., Zhu X., Wang Zhenzhu. Properties of light backscattering on hollow hexagonal ice columns for optical models of cirrus clouds. // Optika Atmosfery i Okeana. 2023. V. 36. No. 12. P. 1013–1019. DOI: 10.15372/AOO20231208 [in Russian].
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Cirrus clouds have a significant impact on the radiation balance of our planet and play a crucial role in climate formation. To study their optical properties, it is necessary to address the issue of light scattering by nonspherical ice particles. This article focuses on the numerical simulation of the characteristics of light backscattering for hollow hexagonal columns using the physical optics method. The study examines particles ranging in size from 10 to 316 mm, with wavelengths of 0.355, 0.532, and 1.064 mm. The findings reveal that as the cavity of hexagonal columns increases, the backscattering peak caused by corner reflection rapidly decreases, then several secondary maxima appear, which account for up to 10% of the main peak. At the same time, the position of these secondary maxima remains unaffected by particle size and incident wavelength but is significantly influenced by the particle's shape. These results are valuable for developing an optical model of cirrus clouds and for laser sounding of the atmosphere.


light scattering, physical optics method, atmospheric ice crystal, cirrus cloud, hollow hexagonal column



1. Mischenko M., Hovenier J.W., Travis L.D. Light scattering by nonspherical particles. San Diego: Academic press, 2000. 720 p.
2. Liou K.N. Influence of cirrus clouds on weather and climate processes – a global perspective // Mon. Weather. Rev. 1986. V. 114, N 6. P. 1167–1199.
3. Jacobowitz H. A method for computing the transfer of solar radiation through clouds of hexagonal ice crystals // J. Quant. Spectrosc. Radiat. Transfer. 1971. V. 11, N 6. P. 691–695.
4. Sun W.B., Loeb N.G., Tanev S., Videen G. Finite-difference time-domain solution of light scattering by an infinite dielectric column immersed in an absorbing medium // Appl. Opt. 2005. V. 44, N 10. P. 1977–1983.
5. Yang P., Liou K.N. Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space // J. Opt. Soc. Am. A. 1996. V. 13, N. 10. P. 2072–2085.
6. Yee K. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media // IEEE Trans. Antennas Propag. 1996. V. 14, N 3. P. 302–307.
7. Yurkin M.A., Maltsev V.P., Hoekstra A.G. The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength // J. Quant. Spectrosc. Radiat. Transfer. 2007. V. 106, N 1. P. 546–557.
8. Zubko E., Shkuratov Y., Videen G. Effect of morphology on light scattering by agglomerates // J. Quant. Spectrosc. Radiat. Transfer. 2015. V. 150. P. 42–54.
9. Zubko E., Kimura H., Shkuratov Y., Muinonen K., Yamamoto T., Okamoto H., Videen G. Effect of absorption on light scattering by agglomerated debris particles // J. Quant. Spectrosc. Radiat. Transfer. V. 110, N 14. P. 1741–1749.
10. Noel V., Ledanois G., Chepfer H., Flamant P.H. Computation of a single-scattering matrix for nonspherical particles randomly or horizontally oriented in space // Appl. Opt. 2001. V. 40, N 24. P. 4365–4375.
11. Mishchenko M.I., Macke A. Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving d-function transmission // J. Geophys. Res.: Atmos. 1998. V. 103, N D2. P. 1799–1805.
12. Cai Q., Liou K.N. Polarized – light scattering by hexagonal ice crystals – Theory // Appl. Opt. 1982. V. 21, N 19. P. 3569–3580.
13. Borovoi A.G., Kustova N.V., Oppel U.G. Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation // Opt. Eng. 2005. V. 44, N 7. P. 071208.
14. Konoshonkin A.V., Kustova N.V., Osipov V.A., Borovoj A.G., Masuda K., Ishimoto H., Okamoto H. Metod fizicheskoj optiki dlya resheniya zadachi rasseyaniya sveta na kristallicheskikh ledyanykh chastitsakh: sravnenie difraktsionnykh formul // Optika atmosf. i okeana. 2015. V. 28, N 9. P. 830–843.
15. Borovoi A., Konoshonkin A., Kustova N. The physical-optics approximation and its application to light backscattering by hexagonal ice crystals // J. Quant. Spectrosc. Radiat. Transfer. 2014. V. 146. P. 181–189.
16. Konoshonkin A.V., Kustova N.V., Borovoi A.G. Beam-splitting code for light scattering by ice crystal particles within geometric-optics approximation // J. Quant. Spectrosc. Radiat. Transfer. 2015. V. 164. P. 175–183.
17. Okamoto H., Sato K., Borovoi A., Ishimoto H., Masuda K., Konoshonkin A., Kustova N. Interpretation of lidar ratio and depolarization ratio of ice clouds using spaceborne high-spectral-resolution polarization lidar // Opt. Express. 2019. V. 27, N 25. P. 36587–36600.
18. Baum B.A., Heymsfield A.J., Yang P., Bedka S.T. Bulk scattering properties for the remote sensing of ice clouds. Part I: Microphysical data and models // J. Appl. Meteorol. 2005. V. 44, N 12. P. 1885–1895.
19. Schmitt C.G., Heymsfield A.J. On the occurrence of hollow bullet rosette- and column-shaped ice crystals in midlatitude cirrus // J. Atmos. Sci. 2007. V. 64, N 12. P. 4514–4519.
20. Miloshevich L.M., Heymsfield A.J. A balloon-borne continuous cloud particle replicator for measuring vertical profiles of cloud microphysical properties: Instrument design, performance, and collection efficiency analysis // J. Atmos. Ocean. Technol. 1997. V. 14, N 4. P. 753–768.
21. Takano Y., Liou K.N. Radiative-transfer in cirrus clouds. 3. Light-scattering by irregular ice crystals // J. Atmos. Sci. 1995. V. 52, N 7. P. 818–837.
22. Smith H.R., Connolly P.J., Baran A.J., Hesse E., Smedley A.R.D., Webb A.R. Cloud chamber laboratory investigations into scattering properties of hollow ice particles // J. Quant. Spectrosc. Radiat. Transfer. 2015. V. 157. P. 106–118.
23. Timofeev D.N., Konoshonkin A.V., Kustova N.V. Algoritm Modified Beam-Splitting 1 (MBS-1) dlya resheniya zadachi rasseyaniya sveta na nevypuklykh ledyanykh atmosfernykh chastitsakh // Optika atmosf. i okeana. 2018. V. 31, N 6. P. 473–480; Timofeev D.N., Konoshonkin A.V., Kustova N.V. Modified Beam-Splitting 1 (MBS-1) algorithm for solving the problem of light scattering by nonconvex atmospheric ice particles // Atmos. Ocean. Opt. 2018. V. 31, N 6. P. 642–649.
24. Chiruta M. The capacitance of solid and hollow hexagonal ice columns // Geophys. Res. Lett. 2005. V. 32, N 5. P. L05803.
25. Mitchell D.L., Arnott W.P. A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology // J. Atmos. Sci. 1994. V. 51, N 6. P. 817–832.
26. Heymsfield A. Ice crystal terminal velocities // J. Atmos. Sci. 1972. V. 29, N 7. P. 1348–1357.
27. Auer A.H., Veal D.L. The dimension of ice crystals in natural clouds // J. Atmos. Sci. 1970. V. 27, N 6. P. 919–926.
28. Warren S.G., Brandt R.E. Optical constants of ice from the ultraviolet to the microwave: A revised compilation // J. Geophys. Res. 2008. V. 113. P. D14.
29. Timofeev D.N., Konoshonkin A.V., Kustova N.V., Shishko V.A., Borovoi A.G. Otsenka vliyaniya pogloshcheniya na rasseyanie sveta na atmosfernykh ledyanykh chastitsakh dlya dlin voln, kharakternykh dlya zadach lazernogo zondirovaniya atmosfery // Optika atmosf. i okeana. 2019. V. 32, N 5. P. 381–385; Timofeev D.N., Konoshonkin A.V., Kustova N.V., Shishko V.A., Borovoi A.G. Estimation of the absorption effect on light scattering by atmospheric ice crystals for wavelengths typical for problems of laser sounding of the atmosphere // Atmos. Ocean. Opt. 2019. V. 32, N 5. P. 564–568.
30. Konoshonkin A., Borovoi A., Kustova N., Reichardt J. Power laws for backscattering by ice crystals of cirrus clouds // Opt. Express. 2017. V. 25, N 19. P. 22341–22346.
31. Sokovykh O.V., Samokhvalov I.V. Sistemnaya integratsiya eksperimental'nogo oborudovaniya vysotnogo polyarizatsionnogo lidara // Optika atmosf. i okeana. 2013. V. 26, N 10. P. 891–896.
32. Borovoi A.G. Light scattering by large particles: physical optics and the shadow-forming field // Light Scattering Reviews 8: Radiative transfer and light scattering England: Springer, 2013. P. 115–138.
33. Vouk V. Projected Area of Convex Bodies // Nature. 1948. V. 162, N 4113. P. 330–331.
34. McFarquhar G.M., Heymsfield A.J. Parameterization of tropical cirrus ice crystal size distributions and implications for radiative transfer: Results from CEPEX // J. Atmos. Sci. 1997. V. 54, N 17. P. 2187–2200.
35. URL: https://iao.ru/ru/about/ resources/info/cluster (data obrashcheniya: 13.01.2023).