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Owing to the various shapes of ice particles, the relationships between fall velocity, backscattering cross-section, mass, and particle size are complicated. This affects the application of cloud radar Doppler spectral density data in the retrieval of the microphysical properties of ice crystals. In this study, under the assumption of six particle shape types, the relationships between particle mass, fall velocity, backscattering cross-section, and particle size were established based on existing research. Variations of Doppler spectral density with the same particle size distribution (PSD) of different ice particle types are discussed. The radar-retrieved liquid and ice PSDs, water content, and mean volume-weighted particle diameter were compared with airborne in situ observations in the Xingtai, Hebei Province, China, in 2018. The results showed the following. (1) For the particles with the same equivalent diameter (De), the fall velocity of the aggregates was the largest, followed by hexagonal columns, hexagonal plates, sector plates, and stellar crystals, with the ice spheres falling two to three times faster than ice crystals with the same De. Hexagonal columns had the largest backscattering cross-section, followed by stellar crystals and sector plates, and the backscattering cross-sections of hexagonal plates and the two types of aggregates were very close to those of ice spheres. (2) The width of the simulated radar Doppler spectral density generated by various ice crystal types with the same PSD was mainly affected by the particle’s falling velocity, which increased with the particle size. Turbulence had different degrees of influence on the Doppler spectrum of different ice crystals, and it also brought large errors to the PSD retrieval. (3) PSD comparisons showed that each ice crystal type retrieved from the cloud radar corresponded well to aircraft observations within a certain scale range, when assuming that only a certain type of ice crystals existed in the cloud, which could fully prove the feasibility of retrieving ice PSDs from the reflectivity spectral density.

Establishment and Preliminary Application of the Forward Modeling Method for Doppler Spectral Density of Ice Particles