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Heterogeneous ice formation by immersion freezing in mixed-phaseclouds can be parameterized in general circulation models (GCMs) by classicalnucleation theory (CNT). CNT parameterization schemes describe immersionfreezing as a stochastic process, including the properties of insolubleaerosol particles in the droplets. There are different ways to parameterizethe properties of aerosol particles (i.e., contact angle schemes), which arecompiled and tested in this paper. The goal of this study is to find aparameterization scheme for GCMs to describe immersion freezing with theability to shift and adjust the slope of the freezing curve compared tohomogeneous freezing to match experimental data.  We showed in a previous publication that the resulting freezing curves fromCNT are very sensitive to unconstrained kinetic and thermodynamic parametersin the case of homogeneous freezing. Here we investigate how sensitive theoutcome of a parameter estimation for contact angle schemes from experimentaldata is to unconstrained kinetic and thermodynamic parameters. We demonstratethat the parameters describing the contact angle schemes can mask theuncertainty in thermodynamic and kinetic parameters.  Different CNT formulations are fitted to an extensive immersion freezingdataset consisting of size-selected measurements as a function of temperatureand time for different mineral dust types, namely kaolinite, illite,montmorillonite, microcline (K-feldspar), and Arizona test dust. Weinvestigated how accurate different CNT formulations (with estimated fitparameters for different contact angle schemes) reproduce the measuredfreezing data, especially the time and particle size dependence of thefreezing process. The results are compared to a simplified deterministicfreezing scheme. In this context, we evaluated which CNT-basedparameterization scheme able to represent particle properties is the bestchoice to describe immersion freezing in a GCM

Classical nucleation theory of immersion freezing: sensitivity of contact angle schemes to thermodynamic and kinetic parameters