Analytical investigation of glaciation time in mixed-phase adiabatic cloud volumes

Glaciation in mixed-phase adiabatic cloudy parcels is investigated analytically using two new equations: the equation for coexistence of liquid water and ice and the mass balance equation. The analysis of glaciation time is performed for a vertically moving adiabatic mixed-phase cloud parcel. The effects of vertical velocity, liquid water content, and concentrations of ice particles, liquid droplets, temperature, and other parameters on the glaciation process are discussed. It is shown analytically that, for a certain envelope of vertical velocities, the glaciation time depends only on the vertical displacement of the parcel and does not depend on the trajectory along which the cloud parcel travels toward the glaciation point. Analytical dependencies of the glaciation time and of the altitude of glaciation on vertical velocity are presented. The results demonstrate a good agreement with those obtained using the corresponding parcel model. The limitations of the newly proposed approach are discussed as well, and it is shown that implementation of a simple correction factor allows one to calculate the glaciation time within a wide range of temperatures, from 0° down to -30°C.