The theory of ice nucleation by heterogeneous freezing of deliquescent mixed CCN. Part I: Critical radius, energy, and nucleation rate

This paper extends previous work on the theory of heterogenous ice nucleation. The goals of this analysis are to explain empirical observations of ice nucleation and to provide a suitable framework for modeling and parameterizing the ice nucleation process in cloud-scale and large-scale atmospheric models. Considered are the processes of heterogeneous freezing of deliquescent mixed cloud condensation nuclei that may serve as ice nuclei, and the properties of an ice germ critical radius, energy, and nucleation rate of ice crystals are examined as functions of temperature and supersaturation. Expressions for nucleation in a polydisperse aerosol for the deliquescence-freezing mode are developed. Equations are derived for the threshold and critical saturation ratios as functions of temperature and nucleation rate, and for the threshold and critical temperatures as functions of saturation ratio. Equivalence of the new formulation for the freezing point depression with traditional expressions is shown and the concepts of the effective temperature and supercooling are introduced. These new formulations are used in a companion paper for simulations of ice nucleation using a cloud parcel model.