On the calculation of single-scattering properties of frozen droplets and frozen droplet aggregates observed in deep convective clouds

Abstract. During multiple field campaigns, small quasi-spherical ice crystals, commonly referred to as frozen droplets (FDs), and their aggregates (frozen droplet aggregates (FDAs)), have been identified as the predominant habits in the upper regions of deep convective clouds (DCCs) and their associated anvils. These findings highlight the significance of FDs and FDAs for understanding the microphysics and radiative properties of DCCs. Despite the prevalence of FDs and FDAs at the tops of DCCs where they directly contribute to cloud radiative forcing, the detailed single-scattering properties (e.g., scattering-phase function P₁₁ and asymmetry parameter g) of FDs and FDAs remain highly uncertain. This uncertainty is mainly due to insufficient in situ measurements and the resolution of cloud probes, which hinder the development of idealized shape models for FDs and FDAs. In this study, two shape models, the Gaussian random sphere (GS) and droxtal (DX), are proposed as possible representations for the shapes of in-situ measured FDs and FDAs. A total of 120 individual models of GSs and 129 models of DXs were generated by varying their shapes. Furthermore, by attaching these individual models in both homogeneous or heterogeneous manners, three different types and a total of 315 models of FDAs were created: (1) aggregates of GSs; (2) aggregates of DXs; and (3) combinations of GSs and DXs which are called habit mixtures (HMs). The P₁₁ and g of the developed models were calculated using a geometric optics method at a wavelength of 0.80 μm and then compared with those obtained using a Polar Nephelometer (PN) during the CIRCLE−2 field campaign to assess the models. Both individual component ice crystals (i.e., either GS or DX) and homogeneous component aggregates (i.e., either aggregates of GSs or aggregates of DXs) showed substantial differences compared with the PN measurements, whereas the P₁₁ of the HMs was found to match most accurately the in situ measured P₁₁, reducing the differences to 0.87 %, 0.88 %, and 5.37 % in the forward, lateral, and backward scattering regions, respectively. The g of the HMs was found to be 0.80 which falls within the range of the PN measurement (0.78 ± 0.04). The root mean square error for the HM was minimized to a value of 0.0427. It was shown that the novel HMs developed in this study demonstrated better performance than in previous research where HMs were developed indirectly by weighting the calculated P₁₁ of shape models to interpret in situ measurement. The result of this study carries important implications for enhancing the calculation of single-scattering properties of DCCs.