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 f_ice (T) as a function of decreasing temperature, and the corresponding cumulative freezing spectra N_m (T) computed using Valis methodology. The differential freezing spectrum n_m (T) is an approximant to the underlying distribution of heterogeneous ice nucleation temperatures P_u (T) that represents the characteristic freezing temperatures of all IN in the sample. However, N_m (T) can be noisy, resulting in a differential form n_m (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 n_m (T) that represents the underlying distribution P_u (T). Here, we present the HUB method and associated Python codes that model (HUB-forward code) and interpret (HUB-backward code) the results of drop-freezing experiments. HUB-forward predicts f_ice (T) and N_m (T) from a proposed distribution P_u (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 n_m (T) from either N_m (T) or f_ice (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 quantify the dependence of their 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 analysed with kinetic models and nucleation theory.