Multiple Scattering of Polarized Light in Cirrus Clouds.

The correct formula for superimposing diffracted and reflected/refracted light rays is derived on the basis of the geometric ray technique for light scattering by hexagonal ice crystals. The scattering phase matrix for randomly oriented ice crystals, including the effect of birefringence, is formulated. In addition, a new theory for the symmetrical property of the scattering phase matrix for horizontally oriented ice crystals is presented. Computations of the scattering phase matrix for randomly and horizontally oriented ice crystals are then carried out and the results are presented and physically discussed. Using the resulting single-scattering properties derived from the present study, the radiative transfer of polarized light through randomly and horizontally oriented ice crystals is theoretically formulated and numerically computed. A comparison is made between the radiative properties of randomly oriented ice crystals, area equivalent ice spheres, and horizontally oriented ice crystals. Based on the computed results, new knowledge and understanding of the intensity field for randomly and horizontally oriented ice crystal clouds is derived, leading to explanations of numerous atmospheric optical phenomena associated with ice crystal clouds. The computational scheme and results presented in this study could be useful for the development of parameterizations for the radiative properties of cirrus clouds in climate models, as well as remote sensing of the composition and structure of cirrus clouds by meteorological satellites.