This paper presents the results of calculations and analyzes the backscattering matrices of random oriented ice crystals, typical for cirrus clouds. The backscattering matrices were calculated within the physical optics approximation for lidar (wavelength 0.355 μm) and the discrete dipole approximation for 94 GHz radar (wavelength 3189 μm) with the refractive indices of ice – 1.3249+0i and 1.7864+0.0032i respectively. For the first time, it was possible to correctly calculate the ratio of radar and lidar signals in the direction of backscatter, called the radar-lidar ratio. The radar-lidar ratio is obtained for a wide particle size distribution for typical ice crystal shapes in cirrus clouds: hexagonal column and plate, bullet, droxtal, aggregate, bullet-rosette, arbitrary shape and sphere. As a result, it is shown that the radar-lidar ratio can be used to estimate the ice crystals size in cirrus clouds. The radar-lidar ratio for the EarthCARE satellite was unambiguously obtained for an adequate model of the sizes and shapes of ice crystals of a cirrus cloud.
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