Backscattering properties of randomly oriented hexagonal hollow columns for lidar application.

The study of the optical properties of cirrus clouds is necessary to improve the accuracy of interpreting data from space lidars and ground-based lidar networks. Existing databases of backscattering properties do not include data on hollow columns. In this paper, the backscattering properties of randomly oriented hollow column ice crystal particles in cirrus at wavelengths of 355 nm, 532 nm, and 1064 nm have been investigated. The backscattering cross section (M11), depolarization ratio (δ), lidar ratio (S), and color ratio (χ) of randomly oriented hollow columns with sizes ranging from 10-316.23 µm are calculated within the framework of the physical optical approximation (PO). For the first time, we introduce the concept of modal hollow columns (MHC) suitable for mid-latitude regions, which simplifies the description of hollow ice crystals in nature. It is found that when the mixing proportion of MHC and solid columns (SC) reaches 50%, the mixing ratio can be distinguished by the lidar ratio for a wavelength of 1064 nm and by the χ(1064,532)-δ(532) relation.

Degree of linear polarization of light at backscattering by a single large particle of irregular shape.

Light backscattering by large randomly oriented particles of irregular shape is calculated using the physical optics approximation (PhOA). It is shown that the degree of linear polarization reveals the polarization surge because of the coherent backscattering. The sign of the polarization surge for pairs of conjugate beams can be either negative or positive depending on the shape of the photon trajectory that predominantly contributes to backscattering. Summing up the surges, we conclude that the conventional negative polarization phenomena are not obligatory in the case of a single backscattering particle.

Lidar backscatter simulation for angular scanning of cirrus clouds with quasi-horizontally oriented ice crystals.

Backscattering properties of ice crystals are numerically investigated in the case of plate-like quasi-horizontally oriented crystals of cirrus clouds. In this case, a vertically oriented lidar detects the specular reflection from the clouds while a lidar with angular scanning allows one to infer the microphysical properties like the transverse shape of the crystals. It is shown that the depolarization ratio as a function of the lidar tilt reveals a step at a lidar tilt of about 30° from the vertical. This step has been observed experimentally. Appearance of this step indicates that the transverse shapes of the plate-like crystals are regular.

Radar-lidar ratio for ice crystals of cirrus clouds.

Simultaneous measurement of lidar and radar signals returned from the same cirrus clouds is a prospective method for retrieving the cloud microphysics, i.e. size and shape of the ice crystals constituting the clouds. In this study, the ratio of the backscattered signals of lidar and radar called the radar-lidar ratio has been calculated for the first time for typical shapes of ice crystals and wide distribution of the crystals over their sizes. It is shown that it is the lidar-radar ratio that is most sensitive to crystal sizes while the lidar depolarization ratio is most sensitive to crystal shapes.

Wavelength dependence of ice cloud backscatter properties for space-borne polarization lidar applications.

We investigated the use of backscatter properties of atmospheric ice particles for space-borne lidar applications. We estimated the average backscattering coefficient (ß), 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.

Interpretation of lidar ratio and depolarization ratio of ice clouds using spaceborne high-spectral-resolution polarization lidar.

The backscattering coefficient (ß), 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 ß, S, and δ was examined using physical optics and geometrical optics integral equation methods. Differences in ß 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.

Coherent and incoherent backscattering by a single large particle of irregular shape.

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.

Extinction matrix for cirrus clouds in the visible and infrared regions.

The extinction matrix for cirrus clouds has been calculated for the visible and infrared regions using the physical optics approximation. The cirrus clouds are modeled as a statistical ensemble of the hexagonal ice plates, distributed over their size and orientations by the gamma and Gaussian laws, respectively. Then, the extinction matrixes as the functions of the incident wavelength, incident direction, crystal size, and crystal orientation are numerically calculated for the first time. It is shown that the off-diagonal elements of the matrix are negligible. Therefore, the extinction in cirrus clouds is described with good accuracy by the scalar exponential law.

Power laws for backscattering by ice crystals of cirrus clouds.

The backscattering Mueller matrix for the typical shapes of ice crystals of cirrus (hexagonal columns and plates, bullets and droxtals) in the case of their random orientations has been approximately presented as the power functions of the crystal size from 10 µm to 1000 µm. The coefficients of the power functions have been found. Four commonly used backscatter ratios used in lidar research (depolarization, lidar, color and backscatter-to-IWC ratios) have been calculated for the first time as the functions of the modal crystal size at the conventional lidar wavelengths of 0.355, 0.532 and 1.064 µm.

Backscatter by azimuthally oriented ice crystals of cirrus clouds.

The backscattering Mueller matrix has been calculated for the first time for the hexagonal ice columns and plates with both zenith and azimuth preferential orientations. The possibility of a vertically pointing polarization lidar measuring the full Mueller matrix for retrieving the orientation distributions of the crystals is considered. It is shown that the element m44 or, equivalently, the circular depolarization ratio distinguishes between the low and high zenith tilts of the crystals. Then, at their low or high zenith tilts, either the element m22 or m34, respectively, should be measured to retrieve the azimuth tilts.

Interference phenomena at backscattering by ice crystals of cirrus clouds.

It is shown that light backscattering by hexagonal ice crystals of cirrus clouds is formed within the physical-optics approximation by both diffraction and interference phenomena. Diffraction determines the angular width of the backscattering peak and interference produces the interference rings inside the peak. By use of a simple model for distortion of the pristine hexagonal shape, we show that the shape distortion leads to both oscillations of the scattering (Mueller) matrix within the backscattering peak and to a strong increase of the depolarization, color, and lidar ratios needed for interpretation of lidar signals.

Backscatter ratios for arbitrary oriented hexagonal ice crystals of cirrus clouds.

Three dimensionless ratios widely used for interpretation of lidar signals, i.e., the color ratio, lidar ratio, and depolarization ratio, have been calculated for hexagonal ice crystals of cirrus clouds as functions of their spatial orientation. The physical-optics algorithm developed earlier by the authors is applied. It is shown that these ratios are minimal at the horizontal crystal orientation. Then these quantities increase with the effective tilt angle approaching the asymptotic values of the random particle orientation. The values obtained are consistent with the available experimental data.

Layers of quasi-horizontally oriented ice crystals in cirrus clouds observed by a two-wavelength polarization lidar.

Layers of quasi-horizontally oriented ice crystals in cirrus clouds are observed by a two-wavelength polarization lidar. These layers of thickness of several hundred meters are identified by three attributes: the backscatter reveals a sharp ridge while the depolarization ratio and color ratio become deep minima. These attributes have been justified by theoretical calculations of these quantities within the framework of the physical-optics approximation.

Backscattering by hexagonal ice crystals of cirrus clouds.

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.

Backscattering reciprocity for large particles.

The backscattering reciprocity theorem is considered for large particles as compared with the incident wavelength particles of arbitrary shape. It is shown that, in the specific case of faceted particles, this theorem is provided by the appearance of pairs of conjugate backscattered beams. A parameter characterizing a deviation of any approximation from the reciprocity theorem is proposed, and it is used for estimation of reliability for the physical-optics approximation.

Backscattering Mueller matrix for quasi-horizontally oriented ice plates of cirrus clouds: application to CALIPSO signals.

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.

Specular scattering by preferentially oriented ice crystals.

Scattered light for preferentially oriented ice crystals is divided into specular and diffuse components, where the specular scattering is created by horizontally oriented facets of fluttering crystals. The specular component for a fluttering thin plate modeling these crystals is found analytically. The solution obtained is a two-dimensional (2D) convolution of a geometric optics pattern depending only on flutter and an independent diffraction function. The geometric optics pattern is explicitly expressed through the probability density for particle tilts, and the diffraction function is taken in the Fraunhofer diffraction approximation. The 2D convolution calculated numerically reveals a cumulative enhancement of scattered light in the scattering domain center. Certain possibilities to retrieve both flutter parameters and particle sizes from the specular patterns are discussed.

Statistical approach to light scattering by convex ice crystals.

Within the geometric optics approximation, the phase functions of randomly oriented ice crystals are calculated as a series relative to multiplicity of internal collisions of light inside the particles. In the case of convex crystals, it is shown that the coefficients of the series provide the most information about the crystal shapes, while the angular functions of this series are weakly dependent on the shapes. The prevailing role of the term corresponding to one internal collision is emphasized. Three numbers describing a distribution of the single-collision scattered light among the aureole and halos of 22 degrees and 46 degrees prove to be the basic parameters by which to characterize scattering by hexagonal ice crystals.