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Heterogeneous ice formation by immersion freezing in mixed-phase clouds can be parameterized in general circulation models (GCMs) by classical nucleation theory (CNT). CNT parameterization schemes describe immersion freezing as a stochastic process, including the properties of insoluble aerosol particles in the droplets. There are different ways to parameterize the properties of aerosol particles (i.e., contact angle schemes), which are compiled and tested in this paper. The goal of this study is to find a parameterization scheme for GCMs to describe immersion freezing with the ability to shift and adjust the slope of the freezing curve compared to homogeneous freezing to match experimental data.

We showed in a previous publication that the resulting freezing curves from CNT are very sensitive to unconstrained kinetic and thermodynamic parameters in the case of homogeneous freezing. Here we investigate how sensitive the outcome of a parameter estimation for contact angle schemes from experimental data is to unconstrained kinetic and thermodynamic parameters. We demonstrate that the parameters describing the contact angle schemes can mask the uncertainty in thermodynamic and kinetic parameters.

Different CNT formulations are fitted to an extensive immersion freezing dataset consisting of size-selected measurements as a function of temperature and time for different mineral dust types, namely kaolinite, illite, montmorillonite, microcline (K-feldspar), and Arizona test dust. We investigated how accurate different CNT formulations (with estimated fit parameters for different contact angle schemes) reproduce the measured freezing data, especially the time and particle size dependence of the freezing process. The results are compared to a simplified deterministic freezing scheme. In this context, we evaluated which CNT-based parameterization scheme able to represent particle properties is the best choice to describe immersion freezing in a GCM.