Vapour density field of mixed-phase clouds

This work presents a theoretical model based on the electrostatic image charges method to calculate the steady-state water vapour density field for a population of supercooled cloud droplets and ice crystals. The model allows a determination of the vapour density among the cloud droplets and ice particles and obtains a representative vapour density of the system which is called the ambient vapour density of the mixed-phase cloud. The results show that the ambient vapour density is close to the saturated value over water in clouds where the cloud droplet concentration is much higher than the ice crystal concentration and close to the ice saturation value in glaciated clouds. A parameterization of the ambient vapour density is given as a function of the sizes and concentrations of the cloud droplets and ice crystals. In addition, the model is used to study the diffusional growth rate of ice crystals immersed in a mixed cloud. The results indicate that the growth of an ice crystal can be reduced by the presence of neighbouring crystals. A mass growth rate equation for diffusional growth was found, which incorporates effects of the ice crystal size, the cloud droplet radius, liquid water content, and ice crystal and droplet concentrations. These studies are of important to considerations in thunderstorm electrification processes, where the mechanism of charge transfer between colliding ice particles and graupel is influenced by growth rate.