Calculating the millimetre‐wave scattering phase function of snowflakes using the self‐similar Rayleigh–Gans Approximation

Abstract

Exploitation of millimetre‐wave radiometer and radar observations of ice clouds and snow requires the ability to model the scattering properties of snowflakes. This article extends the Self‐Similar Rayleigh–Gans Approximation (SSRGA) for rapid computation of the backscatter cross‐section of ice aggregates, to compute the full scattering phase function, the scattering and absorption cross‐sections and the asymmetry factor. We also show that the Rayleigh–Gans Approximation (RGA) may be improved to represent the enhanced scattering and absorption when the monomers from which the aggregate is composed are non‐spherical. The new model is shown to perform well when compared to benchmark 94 and 183 GHz Discrete Dipole Approximation (DDA) calculations of the scattering by simulated unrimed aggregates of maximum dimension up to 1 cm that have a mass–size relationship in the range observed from aircraft. For denser particles, such as would result from riming, the validity of the underlying RGA becomes questionable and both the backscatter and scattering cross‐sections can be underestimated by a factor of 2.