Stochastic homogeneous freezing of supercooled droplets in mixed-phase clouds in particle-based idealised microphysics framework (exemplified with PySDM v3.0)

Abstract. Homogeneous freezing of supercooled cloud droplets is an important process governing ice formation during the transition from mixed-phase clouds to pure ice-phase clouds in the upper troposphere. In this study, we implement a stochastic representation of homogeneous freezing in the particle-based aerosol–cloud microphysics model PySDM, treating freezing as a Poisson process dependent on droplet volume, time step, and the nucleation rate. We compare two parameterisations of the nucleation rate: a temperature-dependent formulation and a saturation-dependent formulation. Using an idealised adiabatically ascending air-parcel framework, we investigate the distribution of freezing temperatures and the resulting ice number concentrations across ensembles that vary updraft speed, cloud condensation nuclei number concentration, droplet size distribution, and the number of super-particles. Simulations are performed both with and without vapour deposition on ice, enabling assessment of the role of the Wegener-Bergeron-Findeisen process. We find that homogeneous freezing occurs over a broad temperature range rather than at a single threshold, with freezing temperatures strongly controlled by cooling rate and droplet size. When vapour deposition on ice is active, early stochastic freezing events dominate the evolution of the frozen droplet fraction and substantially reduce the fraction of droplets that ultimately freeze. The two nucleation-rate formulations produce similar behaviour near water saturation but diverge significantly when supersaturation or subsaturation with respect to water develops, leading to pronounced differences in freezing temperatures and ice number concentrations. Our results highlight the importance of stochastic freezing formulations and nucleation-rate choice for representing cloud glaciation in models.