Critical humidities of homogeneous and heterogeneous ice nucleation: Inferences from extended classical nucleation theory

A generalization of classical ice nucleation theory is used to derive analytical expressions for the critical (threshold) humidities of homogeneous and heterogeneous freezing. The critical radius and energy of an ice embryo and nucleation rates were derived previously by the authors as functions of temperature, pressure, water saturation ratio, and radii of freezing particles. Here we invert the analytical expressions for the nucleation rates and solve them relative to the critical water and ice saturation ratios ( or critical relative humidities). The critical humidities are expressed as analytical functions of temperature, pressure, nucleation or cooling rates, radius of freezing particles and their physico-chemical properties, misfit strain, and activation energy. Calculations of critical ice relative humidities are made using these equations over an extended temperature range down to -75 degrees C and are compared with previous empirical parameterizations and experimental data, and differences are interpreted in the context of variation of the other parameters. It is shown that the critical humidities for heterogeneous ice nucleation are lower than those for homogeneous nucleation; however, this difference is not constant but depends substantially on the temperature and properties of freezing aerosol. Some simple parameterizations for cloud and climate models are suggested.