Light scattering by absorbing hexagonal ice crystals in cirrus clouds.

An improved ray-optics theory for single scattering and polarization of hexagonal columns and plates randomly oriented in space has been developed by considering absorption and by using the Chebyshev solution for diffraction integrals. The vector-tracing method and statistics technique of random sampling are employed. The equivalent forms of Snell's law and Fresnel formulas for absorbing ice crystals are derived, and two equivalent optical constants, m' and m″, are obtained. Comparison is made of the computed results of our model and the Takano and Liou model for asymmetry factors, single-scattering albedos, and scattering phase matrix elements. Some characteristics of our model are discussed, and these analyses demonstrate that our ray-optics model is practical and much improved.