Calculating the millimetre‐wave scattering phase function of snowflakes using the self‐similar Rayleigh–Gans Approximation

Abstract

Exploitation of millimetre-wave radiometer and radar observations of ice clouds and snow requires the ability to model the scattering properties of snowflakes. This article extends the Self-Similar Rayleigh-Gans Approximation (SSRGA) for rapid computation of the backscatter cross-section of ice aggregates, to compute the full scattering phase function, the scattering and absorption cross-sections and the asymmetry factor. We also show that the Rayleigh-Gans Approximation (RGA) may be improved to represent the enhanced scattering and absorption when the monomers from which the aggregate is composed are non-spherical. The new model is shown to perform well when compared to benchmark 94 and 183 GHz Discrete Dipole Approximation (DDA) calculations of the scattering by simulated unrimed aggregates of maximum dimension up to 1 cm that have a mass-size relationship in the range observed from aircraft. For denser particles, such as would result from riming, the validity of the underlying RGA becomes questionable and both the backscatter and scattering cross-sections can be underestimated by a factor of 2.

Using snowflake surface-area-to-volume ratio to model and interpret snowfall triple-frequency radar signatures

“…4.2 show similar characteristic differences with respect to triple-frequency radar signatures modeled for collections of randomly distributed ice spheres and for soft spheres and spheroids as the differences found for snowflake size distributions spanning the total analyzed range of diameters up to D max = 23.6 mm. Therefore, application of the two SSRGA snowflake parameterizations beyond the size range they were originally derived for by Hogan et al (2017) is not expected to significantly affect the corresponding analysis results and conclusions in this study.…”

“…For comparison, the analysis also includes massequivalent soft (mixed ice-air) oblate spheroids and snowflakes modeled according to the self-similar RayleighGans approximation (SSRGA; Hogan and Westbrook, 2014;Hogan et al, 2017). Backscatter cross sections of randomly oriented soft spheroids with major axis length D are calculated with the T-matrix method (Waterman, 1971), using the implementation of Mishchenko and Travis (1998) within the PyTMatrix software package of Leinonen (2014).…”

“…Here, the SSRGA is applied to snowflake masses derived by Eqs. (3) and (4) and for complex refractive indices n ice,λ of pure ice, using the parameterizations listed by Hogan et al (2017) for synthetic aggregate snowflakes that were generated according to Westbrook et al (2004), abbreviated as "W04" throughout the text, and according to Nowell et al (2013), abbreviated as "N13".…”

“…6. The N13 and W04 snowflake parameterizations according to the SSRGA used in this study were originally derived for snowflake 3-D shape models with diameters D 10 mm by Hogan et al (2017). Nonetheless, these SSRGA parameterizations are applied to snowflake diameters up to D max = 23.6 mm in the presented analysis to allow a direct comparison with modeled backscatter by collections of randomly distributed ice spheres and by soft spheres and spheroids (this extension of the SSRGA validity range is briefly discussed below).…”

“…4. The analysis includes a comparison with snowfall triple-frequency radar signatures determined for soft spheroids and for snowflakes modeled according to the selfsimilar Rayleigh-Gans approximation (Hogan and Westbrook, 2014;Hogan et al, 2017). Additionally, snowflake complexity values obtained from MASC images are used as an indicator of snowflake SAV to derive snowfall triplefrequency radar signatures.…”