Light backscattering by randomly oriented hexagonal ice crystals of cirrus clouds is considered within the framework of the physical-optics approximation. The fine angular structure of all elements of the Mueller matrix in the vicinity of the exact backward direction is first calculated and discussed. In particular, an approximate equation for the differential scattering cross section is obtained. Its simple spectral dependence is discussed. Also, a hollow of the linear depolarization ratio around the exact backward direction inherent to the long hexagonal columns is revealed.

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We investigated the use of backscatter properties of atmospheric ice particles for space-borne lidar applications. We estimated the average backscattering coefficient (β), backscatter color ratio (χ), and depolarization ratio (δ) for ice particles with a wide range of effective radii for five randomly oriented three-dimensional (3D) and three quasi-horizontally oriented two-dimensional (2D) types of ice particle using physical optics and geometrical integral equation methods. This is the first study to estimate the lidar backscattering properties of quasi-horizontally oriented non-pristine ice crystals. We found that the χ–δ relationship was useful for discriminating particle types using Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data. The lidar ratio (S)–δ relationship, which is determined using space-borne high-spectral-resolution lidar products such as EarthCARE ATLID or future space-borne lidar missions, may also produce robust classification of ice particle types because it is complementary to the χ–δ relationship.