To simulate passive microwave radiances in all-sky conditions requires better knowledge of the scattering properties of frozen hydrometeors. Typically, snow particles are represented as spheres and their scattering properties are calculated using Mie theory, but this is unrealistic and, particularly in deep-convective areas, it produces too much scattering in mid-frequencies (e. g. 30-50 GHz) and too little scattering at high frequencies (e. g. 150-183 GHz). These problems make it hard to assimilate microwave observations in numerical weather prediction (NWP) models, particularly in situations where scattering effects are most important, such as over land surfaces or in moisture sounding channels. Using the discrete dipole approximation to compute scattering properties, more accurate results can be generated by modelling frozen particles as ice rosettes or simplified snowflakes, though hexagonal plates and columns often give worse results than Mie spheres. To objectively decide on the best particle shape (and size distribution) this study uses global forecast departures from an NWP system (e. g. observation minus forecast differences) to indicate the quality of agreement between model and observations. It is easy to improve results in one situation but worsen them in others, so a rigorous method is needed: four different statistics are checked; these statistics are required to stay the same or improve in all channels between 10 GHz and 183 GHz and in all weather situations globally. The optimal choice of snow particle shape and size distribution is better across all frequencies and all weather conditions, giving confidence in its physical realism. Compared to the Mie sphere, most of the systematic error is removed and departure statistics are improved by 10 to 60%. However, this improvement is achieved with a simple "one-size-fits-all" shape for snow; there is little additional benefit in choosing the particle shape according to the precipitation type. These developments have improved the accuracy of scattering radiative transfer sufficiently that microwave all-sky assimilation is being extended to land surfaces, to higher frequencies and to sounding channels.
