A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments

Abstract

Abstract. A suite of generally applicable statistical methods based on empirical bootstrapping is presented for calculating uncertainty and testing the significance of quantitative differences in temperature and/or ice active site densities between ice nucleation temperature spectra derived from droplet freezing experiments. Such experiments are widely used to determine the heterogeneous ice nucleation properties and ice nucleation particle concentration spectra of different particle samples, as well as in studies of homogeneous freezing. Our methods avoid most of the assumptions and approximations inherent to existing approaches, and when sufficiently large sample sizes are used (approximately >150 droplets and >=1000 bootstrap samples in our system), can capture the full range of random variability and error in ice nucleation spectra. Applications include calculation of accurate confidence intervals and confidence bands, quantitative statistical testing of differences between observed freezing spectra, accurate subtraction of the background filtered water freezing signal, and calculation of a range of statistical parameters using data from a single droplet array freezing experiment if necessary. By providing additional statistical tools to the community, this work will improve the quality and accuracy of statistical tests and representations of uncertainty in future ice nucleation research, and will allow quantitative comparisons of the ice nucleation ability of different particles and surfaces.

A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments

“…The bootstrapping approach could be particularly useful for incorporating uncertainty in IN activity into advanced atmospheric models, as a full distribution of IN activity at each temperature can be easily estimated from simulations. To facilitate adoption of these statistics, all code developed for this project along with documentation and data to recreate the figures in this paper are available in archived form as was used at the time of writing at KiltHub (Fahy et al, 2022a) or in a living GitHub repository where updates or additional information may be added in the fu-ture (https://github.com/wdfahy/CMU-INstats, last access: 7 November 2022).…”

HUB: a method to model and extract the distribution of ice nucleation temperatures from drop-freezing experiments

“…Variability in the temperature, volume, and amount of icenucleating particles per droplet can also contribute to the dispersion of freezing temperatures (Vali, 2019;Knopf et al, 2020). There is consensus now that both stochastic effects and sample heterogeneities contribute to the distribution of freezing temperatures, and both approaches are used for the modeling of drop-freezing experiments (Vali, 1971;Marcolli et al, 2007;Niedermeier et al, 2011;Murray et al, 2011;Broadley et al, 2012;Herbert et al, 2014;Harrison et al, 2016;Alpert and Knopf, 2016;Vali, 2019;Fahy et al, 2022b). Stochastic modeling of the freezing curves is based on predicting the survival probability of liquid water containing INs as a function of supercooling, and it requires a model for the temperature dependence of the nucleation rate of the IN components.…”

Comment on “A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments” by Fahy et al. (2022)

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The analysis methods in Fahy et al (2022) and their interpretation of experiments with water drops containing ice-nucleating particles raise some technical issues and prompt a discussion of the principles involved in the use of differential spectra.

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