Comparison of the pseudo-spectral time domain method and the discrete dipole approximation for light scattering by ice spheres

Abstract

The pseudo-spectral time domain method (PSTD) and the discrete dipole approximation (DDA) are two popular numerically rigorous methods used to model the single-scattering properties of arbitrarily shaped dielectric particles. Stemming from a previous comparison made between the PSTD and DDA for non-absorptive particles, this study expands the comparison to include absorptive cases, and shows the relative strengths of the two methods for application to ice crystal light scattering. The scattering properties of spheres with realistic ice refractive indice, whose analytic solutions can be obtained by using the Lorenz–Mie theory, are considered. Refractive indices of ice at 30 wavelengths ranging from 0.2µm to 100µm are separated into three groups based on the imaginary parts of the refractive indices (i.e., mi<10−3, 10−3≤mi≤10−1, and mi>10−1). The two methods are compared in terms of the computational time needed to reach the same accuracy. This study indicates that the performance of either the PSTD or DDA depends on both the real part and the imaginary part of the particle refractive index. For ice spheres with the imaginary part of the refractive index less than 10−3 and at size parameters exceeding 40, the PSTD is more efficient than the DDA. The PSTD also has a wider capability range for particles at larger sizes. At wavelengths where ice is moderately absorptive (10−3<mi<10−1 in this study), the critical size parameter decreases as the real part of the refractive index increases. At size parameters below the critical size parameter, the DDA outperforms the PSTD. Furthermore, when the ice becomes strongly absorptive, the DDA is approximately twice as fast as the PSTD for particles with size parameters reaching up to 100.