We have developed a theoretical framework for the computation of polarized radiative transfer in cirrus clouds containing randomly and horizontally oriented ice crystals. In the case involving horizontal orientation, the phase matrix corresponding to the Stokes vector consists of 16 nonzero elements in principle and its dependence on directionality cannot be expressed in terms of the scattering angle but must be defined by the incoming and outgoing directions. The physical meanings of optical depth must also be re-defined to account for its dependence on the incoming light beam.

We have demonstrated that polarization of sunlight reflected from clouds can be employed to identify the shape of cloud particles. The polarization patterns located at the well-known rainbow features in the backscattering direction at about 125°-140° can be used to discriminate spherical water droplets (water clouds) and nonspherical ice crystals (ice clouds). Second, we showed that in the case of ice clouds, the ice crystal size and shape can be inferred from linear or full polarization patterns. From the limited polarization observations that were available, we found that a combination of various ice crystal shapes produced the best interpretation. Finally, we illustrated that the reflected polarization from ice clouds contains peak features that can only be produced by horizontally oriented ice columns/plates. Reflected polarization thus provides a means to infer the orientation of nonspherical ice crystals, information that cannot be obtained globally from other remote sensing techniques.