A time-dependent multiple scattering theory for a pulsed radar with a finite beam width

Multiple scattering returns from spherical water particles of uniform diameter are studied for pulsed radar operation. The Gaussian transverse beam-profile and the rectangular pulse-duration are taken into account. A second-order analytical solution is derived for a single layer structure, based on the time-dependent radiative transfer theory. The method itself can be extended to higher-order scatterings in a multiple layered structure with general drop size distributions. The calculation results show that the effect of second-order scattering becomes larger, as the footprint radius, range, and range resolution, which are normalized by the mean free path, increase.