The relation between the orientation of particles in ice-crystal clouds and backscattering phase matrices (BSPMs) is considered. Parameters characterizing the predominant orientation of particles in the azimuthal direction and in the horizontal position are presented. The parameters are expressed through BSPM elements. A technique for measuring BSPM elements with lidar is described. Examples of some measurements are presented along with a statistical generalization of the results from more than 400 BSPM measurements. It is found that the orientation of coarse particles with large diameters in an azimuthal direction and in a horizontal position is more probable than in a random direction. However, the orientation of large particles is often masked by small particles that are not subject to the effect of orienting factors. Thus the mean parameters characterizing the state of orientation of particles in clouds as a whole correspond to weak orientation. It is supposed that the orientation of particles in the azimuthal direction is caused by wind-velocity pulsations.

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Lidar equation has been derived for the case when the anisotropy of a scattering medium is assumed to be weak to introduce any essential distortions into the wave front of a sounding radiation. It is shown in the paper that this equation may successfully be used when interpreting data of lidar sensing of crystal clouds in the atmosphere.

The application of circularly polarized laser radiation and measurement of the fourth Stokes parameter of scattered radiation considerably reduce the probability of obtaining ambiguous results for radiation depolarization in laser sensing of crystal clouds. The uncertainty arises when cloud particles appear partially oriented by their large diameters along a certain azimuth direction. Approximately in 30% of all cases, the measured depolarization depends noticeably on the orientation of the lidar reference plane with respect to the particle orientation direction. In this case, the corridor of the most probable depolarization values is about 0.1-0.15, but in individual cases, it can be noticeably wider. The present article considers theoretical aspects of this phenomenon and configuration of a lidar capable of measuring the fourth Stokes parameter together with an algorithm of lidar signal processing in the presence of optically thin cloudiness when molecular scattering cannot be neglected. It is demonstrated that the element ?44 of the normalized backscattering phase matrix (BSPM) can be measured. Results of measurements are independent of the presence or absence of azimuthal particle orientation. For sensing in the zenith or nadir, this element characterizes the degree of horizontal orientation of long particle diameters under the action of aerodynamic forces arising during free fall of particles.

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