4 A pseudo-spectral time domain method for light scattering computation

Atmospheric particles, for example ice crystals, dust, soot, or various chemical crystals , play a significant role in the atmosphere by scattering and absorbing radiation, principally in two bands: incident solar, with peak at about 0.5 µm, and terrestrial thermal emission, with peak at about 10 µm. Knowledge of aerosol scattering properties is a fundamental but challenging aspect of radiative transfer studies and remote sensing applications. In this chapter we consider only scattering by single homogeneous particles, but in the atmosphere particles occur both individually and as constituents of such aerosols as homogeneous or heterogeneous aggregates with other particles and sometimes coated with liquids. The pseudo-spectral time domain method (PSTD) for calculating scattering properties that we discuss, like a number of other methods currently in use, can be used to investigate scattering properties of a wide variety of aerosols, homogeneous or heterogeneous, singly or in aggregate. Even with a narrow focus on single scattering by homogeneous particles, there are significant obstacles remaining to a comprehensive understanding of scattering properties, given the complexity introduced by considerations of particle shape, size, and refractive index. Much of what we know of this complexity comes from numerical work, and the estimation of errors can become quite challenging in the absence of either a known exact solution or observations. The 'gold standard' in single scattering is provided by the Lorenz–Mie theory (Mie, 1908). It provides an exact solution of the scattering problem for a single spherically homogeneous particle of arbitrary size, thereby giving a way of assessing in one special case the faithfulness of numerical methods developed to treat particles of different shapes and compositions, as well as methods designed to work in special particle size regimes. There is of course no guarantee that a method working well in homogenous and spherically symmetric cases will necessarily work well in general cases, but if the method has no built-in preference for spherically symmetric problems (as might be the case, for example, with a spectral method based on spherical harmonics), and the tests applied also have no such prejudice, we have done the best we can to