Multiple-scattering formulation of pulsed beam waves in hydrometeors and its application to millimeter-wave weather radar

This letter deals with the backscattering of millimeter pulsed beam waves from hydrometeors. A new approach is presented for a solution of time-dependent three-dimensional vector radiative transfer equation for the Stokes vectors to study the multiple-scattering effects of beam waves on radar echoes. General solutions for beam waves are derived in an integral form without any approximation. They are given in numerically tractable forms representing the scattering process in the space and time domain. Time-dependent second-order solutions for radar echoes of pulsed beam waves are straightforwardly obtained to predict multiple-scattering effects depending on the variation of an incident beam size. It is shown that the inhomogeneity of the radial direction of beam waves causes the mode coupling of waves between the azimuth directions in the scattering matrix, and that the mode coupling depends on the ratio of the incident beam size to the total mean free path length of the medium.