Formation of atmospheric halos and applicability of geometric optics for calculating single-scattering properties of hexagonal ice crystals: Impacts of aspect ratio and ice crystal size

In order to determine the threshold sizes at which hexagonal ice crystals begin to form atmospheric halos (i.e., 22° and 46° halos) and the applicability of the conventional geometric optics method (GOM), the single-scattering properties (i.e., phase matrix, asymmetry parameter g, and extinction efficiency Q_ext) of randomly oriented hexagonal ice crystals were calculated using the Amsterdam discrete dipole approximation (ADDA) and conventional GOM at a wavelength λ=0.55μm. For these calculations, a width (W) of up to 36μm and a length (L) of up to 48μm of hexagonal ice crystals with aspect ratios (AR=L/W) of 0.1, 0.25, 0.5, 1.0, 2.0, and 4.0 were used. Further, a halo ratio and power spillover index (Ψ) were used to quantify the intensity of 22° and 46° atmospheric halos as functions of sizes and ARs of hexagonal ice crystals. The phase matrixes, g, and Q_ext, calculated using ADDA and conventional GOM became closer as the crystal size increased for all six ARs. There was better agreement between ADDA and GOM simulations at smaller sizes for hexagonal crystals with compact shapes (e.g., AR=1.0) compared to that for crystals with either oblate (e.g., AR=0.1) or prolate (e.g., AR=4.0) shapes. The errors in the conventional GOM were ~1.2% (7.0%) for g (Q_ext) of hexagonal crystals with volume-equivalent-sphere size parameter (χ_veq) of 90 for all ARs, whereas they were ~0.8% (3.3%) for hexagonal crystals with χ_veq=100. It was shown that the lower size limit of the applicability of conventional GOM depends on particle shape.The 22° and 46° halos were produced at smaller crystal sizes and the intensity of a halo was more pronounced at a given size for crystals with a compact shape compared to those with more prolate or oblate shapes. The calculated 22° halo forming sizes of hexagonal crystals with AR=0.1 (0.25; 0.5; 1.0; 2.0; 4.0) were ~52 (60; 58; 49; 61; 77) for χ_veq: these halo forming sizes vary for different definitions of size parameter and were ~74 (72; 64; 53; 69; 93) for surface-equivalent-sphere size parameter (χ_seq) and ~103 (90; 68; 45; 91; 182) for conventional size parameter (χ_D). The calculated 46° halo forming χ_veq of hexagonal crystals with AR=0.5 (1.0; 2.0) were ~58 (49; 92), ~64 (53; 112) for χ_seq, and ~68 (45; 223) for χ_D. The intensities of the 22° and 46° halos increased with crystal size for all six ARs. The calculations of Ψ of 22° and 46° halos showed that hexagonal ice crystals with much larger sizes were required to produce well-defined 46° halos compared with 22° halos. However, large crystals tend to have preferred orientations that prevent formation of halos, which might be why 46° halos are much less frequent than 22° halos in the atmosphere.