Natalia Kustova

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 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.

Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation

This paper is a revision of a paper presented at the SPIE conference on Laser Radar Technology for Remote Sensing, Sep. 2003, Barcelona, Spain. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 5240. Light scattering by large, as compared to wavelength, ice crystal particles is considered within the framework of geometric optics. Certain general equations for the scattering matrices and for an averaging procedure over an arbitrary distribution of particle orientations are considered. The appearance of a strong backscattering peak is explained by the occurrence of right dihedral angles in the crystals. An analytical equation for the peak including the polarization properties is proposed.

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.

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.

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.

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.

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.

Beam splitting algorithm for the problem of light scattering by atmospheric ice crystals. part 1. theoretical foundations of the algorithm

The beam splitting algorithm permitting one to obtain a solution of the problem of light scattering by atmospheric crystalline ice particles in the geometrical optics approximation is presented. The construction of Jones and Mueller matrices is considered in detail as a basis of the algorithm. Special attention is paid to the interface of the program implementation of the algorithm, which facilitates its introduction in a thirdparty project. The developed algorithm is freely available as an open source software.

Limits to applicability of geometrical optics approximation to light backscattering by quasihorizontally oriented hexagonal ice plates

Quasihorizontally oriented ice crystals of cirrus clouds became an object of active study in recent times. Experimental observations are made with the use of multiwavelength and polarization lidars; their signals are interpreted on the basis of solutions obtained in the approximation of physical or geometrical optics. In this work, we compare these approximations for solution of the problem of light backscattering by quasihorizontally oriented hexagonal ice plates. Special attention is paid to the limits to applicability of geometrical optics approach to solution of such problems.