The effects of shape on electromagnetic scattering by ice crystals

The Fredholm integral method is developed in order to do exact scattering calculations for infinite cylinders of various cross sections and for small finite cylinders of circular cross section. It is believed that the latter problem has not heretofore been solved. It is shown that for shapes representative of ice needles and plates (for example, rods and disks), the predictions made here agree very well with recent experimental measurements. The study on infinite cylinders of various cross section shows that shape does not play a significant part so long as the wave number times the size parameter is less than or equal to 0.9. This means that even for the largest ice crystals occurring high in the troposphere, a shape dependence below about 50 GHz is unlikely. This could be extended to 100 HG GHz for smaller crystals. By investigating finite cylinders, it is shown that the Rayleigh approximation for an equivolumetric spheroid is a very good approximation for ice crystals within these frequency ranges and for forward scattering.