Analytic investigation of condensational process in a mixed-phase adiabatic parcel

The condensation process in mixed phase adiabatic cloudy parcels is investigated analytically using two new equations, namely: the equation of the coexistence of liquid water and ice and the mass balance equation. Regimes of liquid-ice coexistence that may form in an adiabatic parcel ascending at constant velocity are investigated. The existence of four zones with different microphysical structures following one after another along the vertical direction has been found. The necessary and sufficient conditions for formation of liquid water within an ascending ice parcel are derived. The analytic expressions for the glaciation time for a vertically moving adiabatic cloud parcel are derived. The effect of the vertical velocity, liquid water content, concentrations of ice particles and liquid droplets, temperature and other parameters on the glaciation process is discussed. It is shown analytically that the glaciation time depends only on the vertical displacement of the parcel and does not depend on the trajectory along which the cloud parcel moves towards glaciation point. The analytic dependencies of glaciation time and the altitude of glaciation on vertical velocity are presented. The role of the Wegener–Bergeron–Findeisen mechanism in the phase transformation is analyzed. Analytic results demonstrate a good agreement with those obtained using a parcel model. The results can be useful for analysis and interpretation of observations in mixed-phase clouds.