Improved 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 effect, 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 FDs and FDAs measured in situ. 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 a homogeneous and heterogeneous manner, three different types and a total of 404 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 values 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 most accurately match the P11 measured in situ, reducing the differences to +0.87 %, +0.88 %, and −5.37 % in the forward-, lateral-, and backward-scattering regions, respectively. The g value 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 results of this study suggest potential implications for enhancing the calculation of single-scattering properties of ice crystals in DCCs.