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

The heterogeneous nucleation of ice is an important atmospheric process facilitated by a wide range of aerosols. Drop-freezing experiments are key for the determination of the ice nucleation activity of biotic and abiotic ice nucleators (INs). The results of these experiments are reported as the fraction of frozen droplets fice( T) as a function of decreasing temperature and the corresponding cumulative freezing spectra Nm( T) computed using Gabor Vali's methodology. The differential freezing spectrum nm( T) is an approximant to the underlying distribution of heterogeneous ice nucleation temperatures Pu( T) that represents the characteristic freezing temperatures of all INs in the sample. However, Nm( T) can be noisy, resulting in a differential form nm ( T) that is challenging to interpret. Furthermore, there is no rigorous statistical analysis of how many droplets and dilutions are needed to obtain a well-converged nm( T) that represents the underlying distribution Pu( T). Here, we present the HUB (heterogeneous underlying-based) method and associated Python codes that model (HUBforward code) and interpret (HUB-backward code) the results of drop-freezing experiments. HUB-forward predicts fice( T) and Nm( T) from a proposed distribution Pu( T) of IN temperatures, allowing its users to test hypotheses regarding the role of subpopulations of nuclei in freezing spectra and providing a guide for a more efficient collection of freezing data. HUB-backward uses a stochastic optimization method to compute nm( T) from either Nm( T) or fice( T). The differential spectrum computed with HUB-backward is an analytical function that can be used to reveal and characterize the underlying number of IN subpopulations of complex biological samples (e.g., ice-nucleating bacteria, fungi, pollen) and to quantify the dependence of these subpopulations on environmental variables. By delivering a way to compute the differential spectrum from drop-freezing data, and vice versa, the HUB-forward and HUB-backward codes provide a hub to connect experiments and interpretative physical quantities that can be analyzed with kinetic models and nucleation theory.

Automated summary

The heterogeneous nucleation of ice is a significant atmospheric process, and drop-freezing experiments are crucial for determining the ice nucleation activity. However, interpreting and analyzing the results of these experiments can be challenging, as noise may be present and there is a lack of rigorous statistical analysis regarding the necessary number of droplets and dilutions.