The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.

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.

A general view of the backscattering Mueller matrix for the quasi-horizontally oriented hexagonal ice crystals of cirrus clouds has been obtained in the case of tilted and scanning lidars. It is shown that the main properties of this matrix are caused by contributions from two qualitatively different components referred to the specular and corner-reflection terms. The numerical calculation of the matrix is worked out in the physical optics approximation. These matrices calculated for two wavelengths and two tilt angles (initial and present) of CALIPSO lidar are presented as a data bank. The depolarization and color ratios for these data have been obtained and discussed.

The backscattering coefficient (β), lidar ratio (S), and depolarization ratio (δ) of ice particles were estimated over a wide range of effective radii to interpret spaceborne 355-nm high-spectral-resolution lidar data from the ATLID sensor onboard the EarthCARE satellite. Five randomly oriented ice particle shapes (3D ice) and two quasi-horizontally oriented particle types (2D ice) were analyzed using five effective angles. The size dependence of β, S, and δ was examined using physical optics and geometrical optics integral equation methods. Differences in β for the same effective radius and ice water content among particle types exceeded one order of magnitude. S-δ relations are useful for inferring ice particle habit and orientation using ATLID data from EarthCARE.

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.

Intensity of light scattered by a large randomly oriented particle of irregular faceted shape at the backscattering cone of [170°, 180°] is calculated using the physical-optics approximation. It is shown that the backscattered light for a single large particle of irregular shape is split into the coherent and incoherent parts similarly to the phenomena well-known for multiple scattering media. For the model of irregular faceted particles assumed in the paper, the coherent part creates the coherent backscattering peak whose angular width is equal approximately to the ratio of wavelength/(particle size). The incoherent part approaches to the smoothed geometric-optics solution. For other models of faceted particles where the dihedral angle of 90° among the facets is essential, the incoherent part creates as well the incoherent backscattering peak with another angular width.