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


  • Thomas C. Grenfell,

  • Stephen G. Warren


The use of “equivalent” spheres to represent the scattering and absorption properties of nonspherical particles has been unsatisfactory in the past because the sphere of equal volume has too little surface area and thus too little scattering, whereas the sphere of equal area has too much volume giving too much absorption. Their asymmetry factors are also too large. These problems can largely be avoided if the real cloud of nonspherical particles is represented by a model cloud of spheres where the model cloud contains the same total surface area as well as the same total volume. Each nonspherical particle is then represented not by just one sphere but rather by a collection 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 long circular cylinders are used as a test case because an exact solution is available for all size parameters. The extinction efficiency and single-scattering coalbedo are closely approximated by the values for equal-V/A spheres across the ultraviolet, visible, and infrared from 0.2 to 50 μm wavelength; the asymmetry factor is matched somewhat less well. Errors in hemispheric reflectance, absorptance, and transmittance are calculated for horizontally homogeneous clouds which cover the range of crystal sizes and optical depths from polar stratospheric clouds through cirrus clouds to surface snow. The errors are less than 0.05 at all wavelengths over most of this space.