Scattering of Light by Raindrops with Single-Mode Oscillations

Abstract

Light scattering by oscillating raindrops is studied theoretically in the ray optics approximation. The effects of oscillation mode, amplitude, time dependence, drop size, and size distribution on the light scattering are studied. The oscillations are modeled as individual spherical harmonics modes with sinusoidal time dependence, and an example size-dependent oscillation scheme is created for size distribution simulations. Marshall?Palmer (M?P) and gamma size distributions are used to represent continuous frontal rain and convective showers, respectively. Lognormal distribution is used in studying the effect of the width of the distribution on light scattering. It is shown that the introduction of studied oscillation modes (2,?0), (2,?1), and (3,?1) change the scattering properties of equilibrium raindrops differently and are thus, in principle, recognizable by light-scattering measurements. Further, individual oscillation modes introduce new features in the scattering pattern, unlike the Gaussian random oscillations that tend to smooth it. Even a population of differently oscillating drops causes relatively little smoothing as long as each drop has only one oscillation mode. The M?P and gamma size distributions, although remarkably different, smooth the scattering patterns in a very similar manner, making the derivation of raindrop size distribution as an inverse light-scattering problem very difficult. The time dependence of scattering is found to be quite strong. The location of the so-called 90° rainbow depends strongly on the drop size. As a result, realistic M?P and gamma size distributions effectively smooth away the bow, whereas it is clearly seen in narrow lognormal distributions with drop size centered around d = 2.0 mm. As instantaneous size distributions are observed to be more monodisperse than the averaged distributions, it is thus possible that in some rare conditions this novel feature could be seen in nature.