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Immersion freezing is an important ice nucleation pathway\udinvolved in the formation of cirrus and mixed-phase clouds. Laboratory\udimmersion freezing experiments are necessary to determine the range in\udtemperature, T, and relative humidity, RH, at which ice\udnucleation occurs and to quantify the associated nucleation\udkinetics. Typically, isothermal (applying a constant temperature) and\udcooling-rate-dependent immersion freezing experiments are\udconducted. In these experiments it is usually assumed that the\uddroplets containing ice nucleating particles (INPs) all have the same INP surface area\ud(ISA); however, the validity of this assumption or the impact it may\udhave on analysis and interpretation of the experimental data is rarely\udquestioned. Descriptions of ice active sites and variability of contact angles have been\udsuccessfully formulated to describe ice nucleation experimental data in previous\udresearch;\udhowever, we consider the ability of a stochastic freezing model founded on classical nucleation\udtheory to reproduce previous results and to explain experimental uncertainties and data scatter.\udA stochastic immersion freezing model based on first\udprinciples of statistics is presented, which accounts for variable ISA\udper droplet and uses parameters including the\udtotal number of droplets, Ntot, and the heterogeneous ice\udnucleation rate coefficient, Jhet(T). This model is\udapplied to address if (i) a time and ISA-dependent stochastic\udimmersion freezing process can explain laboratory immersion freezing\uddata for different experimental methods and (ii) the assumption that\udall droplets contain identical ISA is a valid conjecture with\udsubsequent consequences for analysis and interpretation of immersion\udfreezing.\ud\ud \ud\ud\udThe simple stochastic model can reproduce the observed time and\udsurface area dependence in immersion freezing experiments for\uda variety of methods such as: droplets on a cold-stage exposed to air\udor surrounded by an oil matrix, wind and acoustically levitated\uddroplets, droplets in a continuous-flow diffusion chamber (CFDC), the\udLeipzig aerosol cloud interaction simulator (LACIS), and the aerosol\udinteraction and dynamics in the atmosphere (AIDA) cloud\udchamber. Observed time-dependent isothermal frozen fractions\udexhibiting non-exponential behavior can be readily explained\udby this model considering varying ISA. An apparent cooling-rate dependence of Jhet is explained by assuming identical ISA\udin each droplet. When accounting for ISA variability, the cooling-rate\uddependence of ice nucleation kinetics vanishes as expected from\udclassical nucleation theory. The model simulations allow for\uda quantitative experimental uncertainty analysis for parameters\udNtot, T, RH, and the ISA variability. The implications of our results for\udexperimental analysis and interpretation of the immersion freezing\udprocess are discussed

Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model