General comments:

The authors present open access Python code to estimate the subpopulations of potential ice nucleating substances from data obtained by drop freezing assays. They present codes that have the potential to be quite important in further discussing the ice-nucleating ability of ambient samples from mineral dust to organic aerosols. I command the others for this important detailed work and for their clear writing. I’d like to raise a few discussion points and point out a few minor issues to be addressed prior to publication.

I’d first like to highlight what I thought were the most important contributions within this paper.

1. Clearly articulated problem to be addressed when using frozen fraction data (for example lines 15-16, 57-58, 75-80)
2. The dilution discussion (section 3.1) is particularly valuable, and the authors can make specific recommendations for the community to move forward in their data analysis.
3. The use of the HUB-forward code to estimate the presence of subpopulations.

Here are my recommendations for improvement:

I struggled a little with the chosen terminology of the code. Why use the term “HUB”? What does the “underlying-based” mean in atmospheric science and/or in statistics? The forward/backward terminology was also not intuitive to me, and it’s not clear why these terms pointing to a direction were used. Could there be better terms to be used such as “subpopulation determination” for HUB-forward? For example, the term could focus on the outcome of the code?

I’d like to challenge an assumption made in the manuscript (for example on lines 138-139) about the role of dilutions. I think the presented data analysis method is best applied to ice nucleating substances that are intact. For example, mineral dust and P. Syringae proteins. However, there is literature on organic matter and dilution series where dilutions can potentially change the shape, form and composition of ice-nucleating sites. For example, (Bogler and Borduas-Dedekind, 2020) showed that dilutions of the macromolecule lignin influences the mass-normalized ice nucleating ability of the material. I would recommend that the authors expand on the idea that this dilution method is for intact ice-nucleating ability. Alternatively, the authors could also use the open access lignin data and see how their code performs (that would be cool actually!).

I also wonder about the choice of Gaussian distributions (Eq3) for the freezing temperatures of populations of IN. Why not log normal? Lines 123-124 mention that other types of normalized distributions could be used, so it would be important to justify this choice. From my own understanding, ambient samples/datasets are typically log normal. See also (Andersson, 2021).

The manuscript is well written and well-motivated. The flow could be improved with more subsections to be able to find the information rapidly for the future reader. For instance, after reading the paragraph at lines 178-186 – I would have been interested to see this code applied in the following section. There could also be a Method section for the details of the math and then a Results and Discussion section with subsections for categories related to recommendations like dilutions series, subpopulations, etc. Subsections within pages 9-10-11 would also help the flow.

There are additional references that I would encourage the authors to consider and I’ve added them throughout my specific comments below.

Specific comments:

Title: The title might be improved by specifying the types of ice nuclei as well as either defining HUB or removing the acronym.

Lines 32-36 has a rather random assortment of references of some drop freezing assays. I can refer the authors to a < 2021 comprehensive table of reported techniques: Table 1 in (Miller et al., 2021)

Line 36: I would also comment that many drop freezing techniques are also used for ambient measurements with unknown concentrations and unknown surface area like sea surface samples and ambient aerosols. How would the authors use their code on these types of samples?

Lines 42-46 discuss the role of cooling rate which is important in data evaluation. I would encourage the authors to comment and reference (Wright et al., 2013). Also relevant to the discussion on lines 440-447.

Eq1b and differential freezing spectra have been discussed previously in (Creamean et al., 2019) and so this reference should be added and discussed.

Scheme 1: “I_u” is not defined. I also think this scheme could be improved by using graphics instead of terms. In other words, the authors could show a frozen fraction graph and show the type of graphs that may be generated based on their code. (especially since different research groups use different terms, a graphical visualization would be helpful – and could also serve as a TOC graphic)

Lines 102-109 could be omitted entirely as these sentences are redundant (more appropriate for a thesis rather than a manuscript)

The idea of Eq2 and the sum of all parts has been nicely discussed in (Steinke et al., 2020) and the authors should consider mentioning this work.

Figure 1 – PMF should also be defined in the text. It’s also difficult to see the black line in figure 1. Perhaps making it bold would help?

Would it be worth relegating the tables to the SI? Some of the values could be added directly onto the graphs for instance.

Line 330-331 – there is much value in having code now to support this claim! Well done to the authors.

Lines 335-343 – excellent recommendations

Figure 6 – specify in the caption the difference between panels A, B, C and D.

Line 368-369: it would be worth describing how the choice of “2 subpopulations” was made. If I understood correctly, it was previously optimized? Or are the authors sourcing this information another way? It would be worth clarifying.

Figure 8 – there’s an error on the panel labels in the caption. ABC should be ACD.

Line 386-387 – why were some points omitted from the optimization procedure?

Figure 9 Panel A is arguably an important graph and would benefit from being highlighted separately (perhaps moving the other panels to the SI?).

References:

Andersson, A.: Mechanisms for log normal concentration distributions in the environment, Sci Rep, 11, 16418, https://doi.org/10.1038/s41598-021-96010-6, 2021.

Bogler, S. and Borduas-Dedekind, N.: Lignin’s ability to nucleate ice via immersion freezing and its stability towards physicochemical treatments and atmospheric processing, Atmospheric Chemistry and Physics, 20, 14509–14522, https://doi.org/10.5194/acp-20-14509-2020, 2020.

Creamean, J. M., Mignani, C., Bukowiecki, N., and Conen, F.: Using freezing spectra characteristics to identify ice-nucleating particle populations during the winter in the Alps, Atmospheric Chemistry and Physics, 19, 8123–8140, https://doi.org/10.5194/acp-19-8123-2019, 2019.

Miller, A. J., Brennan, K. P., Mignani, C., Wieder, J., David, R. O., and Borduas-Dedekind, N.: Development of the drop Freezing Ice Nuclei Counter (FINC), intercomparison of droplet freezing techniques, and use of soluble lignin as an atmospheric ice nucleation standard, Atmospheric Measurement Techniques, 14, 3131–3151, https://doi.org/10.5194/amt-14-3131-2021, 2021.

Steinke, I., Hiranuma, N., Funk, R., Höhler, K., Tüllmann, N., Umo, N. S., Weidler, P. G., Möhler, O., and Leisner, T.: Complex plant-derived organic aerosol as ice-nucleating particles – more than the sums of their parts?, Atmospheric Chemistry and Physics, 20, 11387–11397, https://doi.org/10.5194/acp-20-11387-2020, 2020.

Wright, T. P., Petters, M. D., Hader, J. D., Morton, T., and Holder, A. L.: Minimal cooling rate dependence of ice nuclei activity in the immersion mode, Journal of Geophysical Research: Atmospheres, 118, 10,535-10,543, https://doi.org/10.1002/jgrd.50810, 2013.

The manuscript, “HUB: A method to model and extract the distribution of ice nucleation temperatures from drop-freezing experiments”, presents a way to simulate droplet freezing to calculate frozen fractios and ice active site density. As stated by the authors, their main goal is to link data to theory using 1 or more probability distributions. Also, they aim to described how to sufficiently sample the ice nucleation spectrum, which is interpreted as using a certain number of droplets in experiments and performing dilutions series. This will result in not too much noise in the calculated cumulative or differential ice nucleation spectra. They analyze previous data to show that a distribution of freezing events can change when solution pH changes and when cooling rate changes.

Unfortunately, I see minimal merit for publishing this study and cannot reccomend publication, unless significant revision is made. Perhaps a complete resubmission should be done. A Monte Carlo simulation to predict frozen fraction and n_s or n_m is not new and their main goals have already been accomplished by other work (Vali, 1971; Wright and Petters, 2013; Knopf and Alpert, 2013; Herbert et al., 2014; Vali, 2019; Fahy et al., 2022a; Fahy et al., 2022b). By no means is this list of references complete, the authors can look up their cited references and other studies that cite these to find numerous other models. Furthermore, the authors provide no quantitative uncertainty and no error bars, confidence intervals or prediction bands of the simulated experiments, therefore, no assessment of accuracy in this work. I did find simulating a dilution series and previous data with different pH interesting. The other new aspect is showing that the 3 probability distributions for cholesterol freezing is time dependent. For this paper to be acceptable, the authors should greatly expand their work. A resubmission should include a reproduction of other ice nucleation Monte Carlo models. To relate data and theory, they should derive a mathematical link between their model and theory as this is only discussed in a few sentences in passing despite being a main goal. Finally, they should include an uncertainty analysis of both model and experimental results, and provide new data to test their model. new data could be droplet freezing experiments and dilution series data where they know exactly what the subpopulations are before they start an experiment.

Major Comments

1) l. 18 “first available code”. This is not the first available code to predict frozen fraction or cumulative ice nucleation spectra from a probability distribution. In addition, many of other authors have made their code available, as it is a requirement for data and code availability in most journals and research grants. Therefore, this phrase or anything else similar must be removed from the manuscript.

More generally, it is likely the first time something has been done when a manuscript is published. Yes, how the authors define their probability distribution is unique, but it is distracting and unnecessary to say it is the “first time”.

l. 15-16 “no rigorous statistical analysis…to obtain a well-converged n_m that represents the underlying distribution P_u(T).”. This is not true. Uncertainty are calculated by the previously mentioned studies as well, and with them one can know what is or is not in agreement, what is representative or converged or not. What the authors considers as well-converged is their opinion as there is no uncertainty estimation to claim agreement or not.

2) l. 13 “Underlying distribution” The word underlying has the meaning of something that is real or fundamental to nature. Defining probability distribution of different populations whether this is one, two or ten populations is not demonstrated here to be anything fundamental or real. “Underlying distribution” also has the meaning of something that is not immediately obvious. Whether there is one or more than one distribution (subpopulation) of freezing temperatures is always pre-defined by the authors. In other words, they authors no not derive the number of subpopulations, it is always prescribed for their forward and backward code. This is assumed not underlying.

3) Units. I cannot understand the units in Eqn 5. I know the units of n_m as Mass^-1, and the units of the differential spectrum N_m as Mass^-1 Temperature^-1. In Eqn 5, the unit of Pmax then has to be Temperature^-1 for the frozen fraction to be dimensionless? Would the authors include an equation of Pmax in the manuscript, and check units throughout.

4) There are no uncertainty estimate in this manuscript.

Minor Comments

1) It is common practice, that the cumulative spectra is a lower case n(T). When normalized to mass, it is n_m and when normalized to surface area it is n_s. Please change this accordingly.

2) l. 55-60 How a probability distribution connects ice nucleation experiments and theory needs to be cited and derived. This statement is unsupported. The number of freezing events defines uncertainty, and how many droplets is or is not good enough is opinion without a rigorous definition.

3) l. 70 “based on empirical bootstrapping” What was the most important in (Fahy et al., 2022a) is the non-parameteric bootstrapping was used, i.e. without any prior probability distributions needed. Here, the authors need to assume a distribution (l. 121) and already puts in bias to their methods. They have to define the number of subpopulations (l. 171), again biasing their model.

4) l. 77 The authors are not the first with a way to quantify subpopulations or different types of ice active sites or multi-component freezing to put it another way. There are too many studies to cite about mineral dust, pollen, bacteria, sea spray aerosol particles, washing water etc… A method to quantify subpopulations was done as early as 4 decades ago (Yankofsky et al., 1981).

5) l. 99 What is the difference between an underlying distribution and a true underlying distribution. Is there a false or untrue underlying distribution?

6) l. 121 Why Gaussian and why not something else? I think any distribution could be assumed. If I assumed subpopulations to exist, perhaps a Gaussian is not the best when the mean is centered on a relatively high temperature. There may be chance of sampling freezing temperatures > 0C? Of course these can be simply removed, but this would imply a bias in the subpopulation freezing behavior.

7) Too often in a section, the authors refer to later sections. Please minimize these instances, as it is distracting.

8) l. 299-301 This is circular reasoning. The authors will test the droplets and IN concentrations, to test the sensitivity of Nm to the droplets and IN concentrations?

9) l. 313 What is the authors definition of an “absolute calibration”. How does this differ from a “calibration”.

10) l. 374-375 What is important about looking at a log or linear scale for the y-axis of a graph. If a graph looks better or worse on either scale, what is this telling the reader? This should be clarified.

11) l. 377-379 What is the authors quantitative criteria for “almost identical” and “unnecessary”? How much data variability is explained when two, three or more subpopulations are included? Is the number of subpopulations sufficient when 99% of the variability is explained?

On the other hand, could two different types of ice nucleating particles exist (different populations) in the same drop, but have the same distribution? This code then would mistake these 2 subpopulation as a single subpopulation. This would then misrepresent the ice nucleating subpopulations?

12) l. 424-425 Here, is it assumed that pH can change the position, width and amplitude of the distributions. This is certainly important, but I am wondering how valid is the assumption that pH only changes the amplitude, but keeping the mean and standard deviation the same? As the authors prepare their resubmission and include an uncertainty analysis, I would highly recommend the authors to fit the ice nucleation data for all pH for a common mean and standard deviation, allowing only the amplitude to be a function of pH. Then evaluate if the result is somehow within the predicted and experimental error. One could surmise that a surfaces ability to nucleate ice may or may not be pH dependent, but perhaps pH would destroy active sites instead.

13) Please check references for consistency with doi format, URLs, use of italics, use of the correct journal and journal abbreviations.

Fahy, W. D., Shalizi, C. R., and Sullivan, R. C.: A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments, Atmos. Meas. Tech., 15, 6819-6836, 10.5194/amt-15-6819-2022, 2022a.

Fahy, W. D., Maters, E. C., Giese Miranda, R., Adams, M. P., Jahn, L. G., Sullivan, R. C., and Murray, B. J.: Volcanic ash ice nucleation activity is variably reduced by aging in water and sulfuric acid: the effects of leaching, dissolution, and precipitation, Environ. Sci.: Atmos., 2, 85-99, 10.1039/D1EA00071C, 2022b.

Herbert, R. J., Murray, B. J., Whale, T. F., Dobbie, S. J., and Atkinson, J. D.: Representing time-dependent freezing behaviour in immersion mode ice nucleation, Atmos. Chem. Phys., 14, 8501-8520, 10.5194/acp-14-8501-2014, 2014.

Knopf, D. A. and Alpert, P. A.: Water Activity Based Model of Heterogeneous Ice Nucleation Kinetics for Freezing of Water and Aqueous Solution Droplets, Faraday Discuss., 165, 513-534, 10.1039/C3FD00035D, 2013.

Vali, G.: Quantitative Evaluation of Experimental Results an the Heterogeneous Freezing Nucleation of Supercooled Liquids, J. Atmos. Sci., 28, 402-409, 10.1175/1520-0469(1971)028%3C0402:QEOERA%3E2.0.CO;2, 1971.

Vali, G.: Revisiting the differential freezing nucleus spectra derived from drop-freezing experiments: methods of calculation, applications, and confidence limits, Atmos. Meas. Tech., 12, 1219-1231, 10.5194/amt-12-1219-2019, 2019.

Wright, T. P. and Petters, M. D.: The role of time in heterogeneous freezing nucleation, J. Geophys. Res.-Atmos., 118, 3731-3743, 10.1002/jgrd.50365, 2013.

Yankofsky, S. A., Levin, Z., Bertold, T., and Sandlerman, N.: Some Basic Characteristics of Bacterial Freezing Nuclei, Journal of Applied Meteorology and Climatology, 20, 1013-1019, 10.1175/1520-0450(1981)020<1013:Sbcobf>2.0.Co;2, 1981.