Journal Of Geophysical Research-atmospheres
 A cloud of nonspherical ice particles may be represented in radiation models by a collection of spheres, in which the model cloud contains the same total volume of ice and the same total surface area as the real cloud but not the same number of particles. The spheres then have the same volume-to-area (V/A) ratio as the nonspherical particle. In previous work this approach was shown to work well to represent randomly oriented infinitely long circular cylinders for computation of hemispherical reflectance, transmittance, and absorptance. In this paper the results have been extended to hexagonal columns and plates using a geometric optics technique for large particles and finite-difference-time-domain theory (FDTD) for small particles. The extinction efficiency and single-scattering coalbedo for these prisms are closely approximated by the values for equal-V/A spheres across the ultraviolet, visible, and infrared from 0.2 to 25 mum wavelength. Errors in the asymmetry factor can be significant where ice absorptance is weak, at visible wavelengths for example. These errors are greatest for prisms with aspect ratios close to 1. Errors in hemispheric reflectance, absorptance, and transmittance are calculated for horizontally homogeneous clouds with ice water paths from 0.4 to 200,000 g m(-2) and crystal thicknesses of 1 to 400 mum, to cover the range of crystal sizes and optical depths from polar stratospheric clouds (PSCs) through cirrus clouds to surface snow. The errors are less than 0.05 over most of these ranges at all wavelengths but can be larger at visible wavelengths because of the ideal shapes of the prisms. The method was not tested for, and is not expected to be accurate for, angle-dependent radiances.
Neshyba, Steven P., Tc Grenfell, and Sg Warren. 2003. "Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 2. Hexagonal columns and plates." Journal Of Geophysical Research-atmospheres 108(D15): 4448-4448.