Time-dependent Second Order Scattering Theory for a Weather Radar with a Finite Beam Width

Multiple scattering effects from spherical water particles of uniform diameter are studied for a W-band pulsed radar. The Gaussian transverse beam-profile and the rectangular pulse- duration are used for calculation. An second-order analytical solution is derived for a single layer structure, based on a time- dependent radiative transfer theory. When the range resolution is fixed, increase in footprint radius leads to increase in the second order reflectivity that is defined as the ratio of the second order return to the first order one. This undesirable feature becomes more serious as the range increases. Since the spaceborne millimeter-wavelength radar has a large footprint radius that is competitive to the mean free path, the multiple scattering effect must be taken into account for analysis.