Sensitivities of immersion freezing: Transition from classical nucleation theory to deterministic expressions

While many models use deterministic expressions to predict the number concentration of ice particles in the atmosphere only as a function of temperature and sometimes ice nuclei (IN) properties, such a description is in apparent contradiction to classical nucleation theory that implies stochastic, time-dependent freezing behavior. Based on sensitivity studies, we show that indeed freezing is least sensitive to time as compared to other parameters such as temperature, and IN properties (size, contact angle). We develop new CNT-based expressions and quantify the uncertainty that is inferred by neglecting time. These expressions are compared to laboratory-and observationally based deterministic parameterizations. We show general agreement in trends and parameters and discuss the transition from the physically-based CNT to deterministic relationships.