Using the general equations derived in Chapter 9 based on extended classical nucleation theory, parameterizations are derived suitable for use in cloud and climate models with sufficiently large time steps. Heterogeneous freezing of haze particles and drops caused by supersaturation and temperature variations are considered in Sections 10.1 and 10.2, and similar parameterizations of the deposition nucleation is derived in Sections 10.3. In particular, it is shown that the functional forms of previous empirical or semi-empirical parameterizations described in Section 9.4 can be obtained and generalized from these theoretical parameterizations based on classical nucleation theory, and their empirical parameters can be expressed via the fundamental atmospheric parameters and aerosol properties.

In the next three sections, Sections 10.4–10.6, contact ice nucleation mode is described, its general properties, the three major mechanisms of aerosol scavenging by drops that may lead to contact nucleation, the collection rates, probabilities of freezing, and scavenging in polydisperse ensembles of drops and aerosols.