Knowledge of optical properties of ice crystal particles of cirrus clouds is a challenging problem of atmospheric optics.
Cirrus clouds cover, in average, 20%-30% of Earth's surface that leads to their essential impact of climate. Therefore
these optical properties are needed for incorporation in up-to-date models of Earth's radiation budget and, consequently,
they should be used in numerical models of climate prediction or climate change.
The optical properties of ice crystal particles have been calculated for recent 20-30 years by a lot of authors under an
assumption of 3-D orientation. However, the crystals often reveal a tendency to be oriented in the horizontal plane
because of aerodynamic laws.
Phase functions for light scattering by horizontally and preferably oriented hexagonal ice plates and columns are
numerically calculated within the framework of geometric optics. The main quantitative properties of the halos (sundog,
parhelion 120°, suncave Parry arc, sunvex Parry arc, and others) are obtained for a number of both incident light
directions and aspect ratios of the plates and columns respectively. A parameterization of the phase functions in the
parhelic, subparhelic and circumzenithal (circumhorizonthal) circles for the plates and all scattered energy for the
columns are proposed based on the integral contributions of the narrow angular peaks (halos) that are tabulated as the
Our results can be used for atmospheric lidar observation for determining of size, shape distributions of the ice crystals
particles in cirrus clouds.
A method for retrieving aspect ratios of the plates by means of polarization measurements is discussed.