Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation

The use of "equivalent" spheres to represent the scattering and absorption properties of nonspherical particles has been unsatisfactory in the past be cause the sphere of equal volume has too little surface area and thus too l ittle scattering, whereas the sphere of equal area has too much volume givi ng too much absorption. Their asymmetry factors are also too large. These p roblems can largely be avoided if the real cloud of nonspherical particles is represented by a model cloud of spheres where the model cloud contains t he same total surface area as well as the same total volume. Each nonspheri cal particle is then represented not by just one sphere but rather by a col lection of independent spheres that has the same volume-to-surface-area (V/ A) ratio as the nonspherical particle. To demonstrate the broad utility of this approach, we show results for ice, whose absorption coefficient varies with wavelength by 8 orders of magnitude. Randomly oriented infinitely lon g circular cylinders are used as a test case because an exact solution is a vailable for all size parameters. The extinction efficiency and single-scat tering coalbedo are closely approximated by the values for equal-V/A sphere s across the ultraviolet, visible, and infrared from 0.2 to 50 mu m wavelen gth; the asymmetry factor is matched somewhat less well. Errors in hemisphe ric reflectance, absorptance, and transmittance are calculated for horizont ally homogeneous clouds which cover the range of crystal sizes and optical depths from polar stratospheric clouds through cirrus clouds to surface sno w. The errors are less than 0.05 at all wavelengths over most of this space .