A statistical model for ice growth in the bulk region of mixed-phase clouds.*

Mixed-phase clouds, responsible for most planet precipitations, are three-phase atmospheric systems containing ice, supercooled droplets, and water vapor.

In particular, the behavior of a suspension of ice and liquid water droplets is different from pure water droplets suspended in the air. In mixed-phase clouds, indeed, rain formation is driven by the Wegener-Bergeron-Findeisen process, where ice crystals condensate at the expense of liquid droplets because ambient vapor pressure falls between the saturation water vapor pressure in liquids and the lower saturation vapor pressure over ice. This work aims to investigate how small-scale isotropic turbulence, a critical factor in the glaciation of ice particles, affects the process using a statistical model validated against data from Direct Numerical Simulations (DNS) and existing literature. The main assumption to derive the model is that the Lagrangian supersaturation fluctuations are Gaussian distributed in the bulk of the cloud. While this hypothesis may not be accurate at the cloud edge, the model can be easily extended to deal with non-Gaussian distribution following our previous work on warm clouds. Preliminary results indicate that turbulence does not affect mean values, e.g., glaciation time and average particle sizes, but contributes to the shape of the droplet and ice size distributions.