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A new Monte Carlo/geometric ray-tracing method has been developed for the computation of the scattering, absorption, and polarization properties of ice crystals with various irregular structure, including hollow columns, bullet rosettes, dendrites, and capped columns. The shapes of these ice crystals are defined by appropriate geometric models and incident coordinate systems. The incident photons are traced with a hit-and-miss Monte Carlo method and followed by geometric reflection and refraction on the crystal boundary. Absorption has been accounted for by means of stochastic procedures. Computation of the phase matrix elements and normalization of the phase function have been carried out using the results derived from rays that undergo reflections and refractions and from Fraunhofer diffraction using projected cross section areas for irregular ice crystals. Numerical results are presented for visible and near-infrared wavelengths. It is shown that irregular ice crystals scatter more in forward directions than do solid columns and plates and the single scattering albedo becomes larger when a crystal becomes more complex in shape. Results simulated for randomly oriented hollow columns can be used to interpret lidar backscattering observations. Moreover, the authors further illustrate that the computed phase matrix values for randomly oriented dendrites closely match with 1aboratory observed data for plate-type crystals generated in cold chambers. It is also shown that using equal volume or equal projected-area spheres 1eads to significant errors in the computation of scattering, absorption, and polarization properties for irregular ice crystals. The phase functions, the single scattering albedos and their parameterizations, as well as the polarization patterns presented in this paper are significant in terms of the interpretation of radiance and flux observations from the ground, the air, and space in cirrus cloudy conditions and for remote sensing applications.
Takano et al. (Sat,) studied this question.