Stochastic homogeneous freezing of supercooled droplets in particle-based microphysics

Homogeneous freezing of supercooled cloud droplets controls the transition from mixed- to ice-phase regime in the upper troposphere. We discuss a stochastic representation of the process, for use in particle-based aerosol-cloud microphysics models. The embraced Poissonian formulation is governed by droplet volume, model time step, and the homogeneous nucleation rate.

Using an implementation of the model in the PySDM particle-based modelling package, we evaluate two nucleation-rate formulations: a temperature-dependent and a water-activity-based parameterisations, the latter applicable also to aqueous solution droplets.

Using an air-parcel framework, we investigate freezing-temperature distributions and resulting ice number concentrations across ensembles of simulations with varying updraft speeds, CCN concentrations, droplet size distributions, and number of super-particles. The two nucleation-rate parameterisations diverge under super- or subsaturated conditions with respect to water, yielding differences in freezing temperatures and ice number concentrations.

To asses the impact of Wegener-Bergeron-Findeisen process on ice concentrations, we consider simulations with and without vapour deposition on ice. With deposition enabled, early stochastic freezing events dominate the evolution of the frozen droplet fraction and substantially reduce the number of droplets that ultimately freeze.

The developed model allows to validate the common assumption that homogeneous freezing is a threshold phenomenon occurring at ca. 235 K. We find that homogeneous freezing spans a broad temperature range controlled by cooling rate and droplet size, highlight the importance of stochastic freezing formulations and nucleation-rate choice for representing cloud glaciation.