Power laws for backscattering by ice crystals of cirrus clouds.

The backscattering Mueller matrix for the typical shapes of ice crystals of cirrus (hexagonal columns and plates, bullets and droxtals) in the case of their random orientations has been approximately presented as the power functions of the crystal size from 10 µm to 1000 µm. The coefficients of the power functions have been found. Four commonly used backscatter ratios used in lidar research (depolarization, lidar, color and backscatter-to-IWC ratios) have been calculated for the first time as the functions of the modal crystal size at the conventional lidar wavelengths of 0.355, 0.532 and 1.064 µm.