Radar meteorological equations for bistatic/multistatic weather radar systems detecting small spheroid raindrops

Expressions for the directivity function of a small spheroid particle and its side-scattering cross-section are obtained and then sets of radar meteorological equations for bistatic and multistatic weather radar systems are given for the cases that the orientation of the detected small spheroid particle is uniquely upward and omnidirection-distributed, respectively, as well as the polarization of the transmitted radar wave is horizontal and vertical, respectively. The main results include that (1) the 3 components of dipole moment can be generated because of the radar waves incident from arbitrary azimuth and elevation, which leads the directional function of particle scattering to depending on not only the scattering direction but also the relationship between the two respective coordinates of the radar antenna and the particle;（2）the side-scattering cross-section of the particle is the sum of the side-scattering cross-sections for all the 3 components of the scattering waves;（3）the difference in radar meteorological equations between the bi static radar system and the mono-based radar system are caused by the difference between the side-scattering cross-section and the back-scattering cross-section in addition to the difference between their effective volumes and the difference between their antenna directional functions; （4） the side-scattering cross-section in radar meteorological equations is the sum of the side-scattering cross-sections for all the 3 components of the scattering waves and is sensitive to the polarization manner of the incident wave;（5）the obtained bistatic radar meteorological equations for the case in which the orientation of all the spheroids is uniquely vertical are classified according to both the polarization manner of the incident wave and the directional feature of the transmitting antenna; the elevation of the incident wave may make the side-scattering cross-section of the spheroids consist of 3 orthogonal components, one of which must be vertical in case the incident wave is vertical polarized, but the scattered power is independent of the transmitting antenna elevation if the incident wave is horizontal polarized; （6） the obtained bistatic radar meteorological equations for the case in which the orientation of all the spheroids is omnidirection distributed depend on the directional feature of the transmitting antenna but independent of the elevation and polarization manner of the incident wave.