Representing time-dependent freezing behaviour in immersion mode ice nucleation

In order to understand the impact of ice formation in clouds, a quantitative understanding of ice nucleation is required, along with an accurate and efficient representation for use in cloud resolving models. Ice nucleation by atmospherically relevant particle types is complicated by interparticle variability in nucleating ability, as well as a stochastic, time-dependent, nature inherent to nucleation. Here we present a new and computationally efficient Framework for Reconciling Observable Stochastic Time-dependence (FROST) in immersion mode ice nucleation. This framework is underpinned by the finding that the temperature dependence of the nucleation-rate coefficient controls the residence-time and cooling-rate dependence of freezing. It is shown that this framework can be used to reconcile experimental data obtained on different timescales with different experimental systems, and it also provides a simple way of representing the complexities of ice nucleation in cloud resolving models. The routine testing and reporting of time-dependent behaviour in future experimental studies is recommended, along with the practice of presenting normalised data sets following the methods outlined here.