Backscattering enhancement on spheroid-shaped hydrometeors: Considerations in water and ice particles of uniform size and Marshall-Palmer distributed rains

A second-order scattering theory is derived for uniformly oriented spheroidal hydrometeors with a general drop size distribution in a single layer. Effects of backscattering enhancement are evaluated for a nadir pointing radar with a finite beam width at millimeter wave frequencies. Spheroids of uniform size are first studied to characterize the deviations from the spherical theories. For water spheroids, the difference between the cross term (backscattering enhancement term) and the ladder term (conventional multiscattering term) becomes larger as the spheroids deviate from the spherical shape. On the contrary, for ice spheroids, this difference is negligible. Marshall-Palmer distributed rains with Pruppacher-Pitter-form drops are studied using the spheroidal approximation. The results confirm the validity of the spherical approximation used in the preceding works within the accuracy limit of measurement. In the Marshall-Palmer distributed rains, the second-order scattering effect becomes serious as the footprint radius increases. Hence the second-order scattering is to be taken into account for accurate measurement of hydrometeor reflectivity for a spaceborne radar because of its large footprint radius.