A Unified Formalism of Incoherent, Quasi-coherent, and Coherent Correlation Signals on Pulse-Pair Doppler Operation for a Cloud-Profiling Radar: Aiming for a Space Mission

The correlation signals of the incoherent, quasi-coherent, and coherent backscatterings from clouds have been analytically calculated from a unified formalism based on the Eulerian description for a generic weather radar with pulse-pair function, especially aiming for a space-/airborne mission. The spectral broadening due to Doppler fading and wind shears is calculated from this formalism. Since the coupling of these two effects in the spectral broadening is substantial, a conventional estimation is found not to be adapted for the space-/airborne radar. The condition of pulse-pair interval to make data treatment of this operation correspond to that of the fast Fourier transform (FFT) operation is also derived. Further, comparing the derivation of the quasi-coherent scattering to that of the incoherent scattering within the unified formalism, as concerns the Fraunhofer region, it is proven that the former scattering can be represented in a similar form to the latter one, even for nonuniformly illuminated clouds, despite the difference in scattering properties. In addition, the reestimation of the volumetric reflectivity for the quasi-coherent scattering is performed. Finally, the Doppler correlation signals for the coherent backscattering and for the optical partial reflection from a keen boundary of cloud density are formulated.