Applicability of the Rayleigh-Gans approximation for scattering by snowflakes at microwave frequencies in vertical incidence

[1] The applicability of the Rayleigh-Gans approximation (RGA) for scattering by snowflakes is studied in the microwave region of the electromagnetic spectrum. Both the shapes of the single ice crystals, or monomers, and their amounts in the modeled snowflakes are varied. For reference, the discrete-dipole approximation (DDA) is used to produce numerically accurate solutions to the single-scattering properties, such as the backscattering and extinction cross-sections, single-scattering albedo, and the asymmetry parameter. We find that the single-scattering albedo is the most accurate with only about 10% relative bias at maximum. The asymmetry parameter has about 0.12 absolute bias at maximum. The backscattering and extinction cross-sections show about –65% relative biases at maximum, corresponding to about –4.6 dB difference. Overall, the RGA agrees well with the DDA computations for all the cases studied and is more accurate for the integrated quantities, such as the single-scattering albedo and the asymmetry parameter than the cross-sections for the same snowflakes. The accuracy of the RGA seems to improve, when the number of monomers is increased in an aggregate, and decrease, when the frequency increases. It is also more accurate for less dense monomer shapes, such as stellar dendrites. The DDA and RGA results are well correlated; the sample correlation coefficients of those are close to unity throughout the study. Therefore, the accuracy of the RGA could be improved by applying appropriate correction factors.