Optimal numerical methods for determining the orientation averages of single-scattering properties of atmospheric ice crystals

The optimal orientation averaging scheme (regular lattice grid scheme or quasi Monte Carlo (QMC) method), the minimum number of orientations, and the corresponding computing time required to calculate the average single-scattering properties (i.e., asymmetry parameter (g), single-scattering albedo (_ωo), extinction efficiency (Q_ext), scattering efficiency (Q_sca), absorption efficiency (Q_abs), and scattering phase function at scattering angles of 90° (P₁₁ (90°)), and 180° (P₁₁ (180°))) within a predefined accuracy level (i.e., 1.0%) were determined for four different nonspherical atmospheric ice crystal models (Gaussian random sphere, droxtal, budding Bucky ball, and column) with maximum dimension D = 10 μm using the Amsterdam discrete dipole approximation at λ = 0.55, 3.78, and 11.0 μm.The QMC required fewer orientations and less computing time than the lattice grid. The calculations of P₁₁ (90°) and P₁₁ (180°) required more orientations than the calculations of integrated scattering properties (i.e., g, _ωo, Q_ext, Q_sca, and Q_abs) regardless of the orientation average scheme. The fewest orientations were required for calculating g and _ωo. The minimum number of orientations and the corresponding computing time for single-scattering calculations decreased with an increase of wavelength, whereas they increased with the surface-area ratio that defines particle nonsphericity.