Estimating ice particle scattering properties using a modified Rayleigh‐Gans approximation

A modification to the Rayleigh-Gans approximation is made that includes self-interactions between different parts of an ice crystal, which both improves the accuracy of the Rayleigh-Gans approximation and extends its applicability to polarization-dependent parameters. This modified Rayleigh-Gans approximation is both efficient and reasonably accurate for particles with at least one dimension much smaller than the wavelength (e. g., dendrites at millimeter or longer wavelengths) or particles with sparse structures (e. g., low-density aggregates). Relative to the Generalized Multiparticle Mie method, backscattering reflectivities at horizontal transmit and receive polarization (HH) (Z(HH)) computed with this modified Rayleigh-Gans approach are about 3 dB more accurate than with the traditional Rayleigh-Gans approximation. For realistic particle size distributions and pristine ice crystals the modified Rayleigh-Gans approach agrees with the Generalized Multiparticle Mie method to within 0.5 dB for Z(HH) whereas for the polarimetric radar observables differential reflectivity (Z(DR)) and specific differential phase (K-DP) agreement is generally within 0.7 dB and 13%, respectively. Compared to the A-DDA code, the modified Rayleigh-Gans approximation is several to tens of times faster if scattering properties for different incident angles and particle orientations are calculated. These accuracies and computational efficiencies are sufficient to make this modified Rayleigh-Gans approach a viable alternative to the Rayleigh-Gans approximation in some applications such as millimeter to centimeter wavelength radars and to other methods that assume simpler, less accurate shapes for ice crystals. This method should not be used on materials with dielectric properties much different from ice and on compact particles much larger than the wavelength.