Modeling homogeneous ice nucleation from drop-freezing experiments: Impact of droplet volume dispersion and cooling rates

Homogeneous nucleation is the prominent mechanism of glaciation in cirrus and other high-altitude clouds. Ice nucleation rates can be studied in laboratory assays that gradually lower the temperature of pure water droplets. These experiments can be performed with different cooling rates, different droplet sizes, and often with a distribution of droplet sizes. We combine nucleation theory, survival probability analysis, and published data on the fraction of frozen droplets as a function of temperature to understand how cooling rate, droplet size, and size dispersity influence the nucleation rates. The framework, implemented in the Python code AINTBAD, provides a temperature dependent nucleation rate on a per volume basis, in terms of approximately temperature-independent prefactor (A) and barrier (B) parameters. We find that less than an order of magnitude dispersion in droplet diameters, if not properly included in the analysis, can cause apparent nucleation barriers to be underestimated by 50\%. This result highlights the importance of droplet size-dispersion in efforts to model glaciation in the polydisperse droplets of clouds. We also developed a theoretical framework, implemented in the Python code IPA, to predict the fraction of frozen droplets at each temperature for arbitrary droplet size dispersions and cooling rates. Finally, we present a sensitivity analysis for the effect of temperature uncertainty on the nucleation spectrum. Our framework can improve models for ice nucleation in clouds by explicitly accounting for droplet polydispersity and cooling rates.