Error analysis of backscatter from discrete dipole approximation for different ice particle shapes

Ice sphere backscatter has been calculated using both Mie theory and the discrete dipole approximation (DDA) at a wavelength of 3.2 mm (94 GHz). The electric dipole, magnetic dipole and electric quadrupole contributions to spherical particle backscatter have been analyzed. The results show that there is a resonance area around particle size parameter of 1.5, where the calculated backscatter errors are very large due to the neglect of the magnetic dipole, and this is confirmed by applying Mie theory to 8.66 mm (35 GHz) and 3.21 cm (X-band) wavelengths. Based on the backscatter calculation using a cube and a hexagon column randomly oriented in space, it was found that the backscatter error from the inaccurate representation of the particle surface shape is much smaller than that from the neglect of the magnetic dipole, and the resonance occurs at different particle sizes depending upon the exact particle shapes. At a wavelength of 3.2 mm, the particle shape has little effect on backscatter when volume-equivalent spherical particle radius r_v < 500 μm, and Rayleigh backscatter can be used as a reasonable approximation for r_v < 300 μm.