Reply to RC1:

Thanks for your generous comments and for supporting the argument about data handling.

The second issue, that of discrete versus continuous spectra, is indeed worth more discussion than what's in my Comment. The question has to be looked at from two different perspectives. My Comment focused on the mathematical issue. The definition of the differential spectrum clearly allows for discrete values, since no other quantity appears in the equation than the parameters at the temperature considered. This was the point I wanted to make in the Comment.

The other dimension of the question is what can be expected for INPs in a real sample. That problem was not addressed in the Comment and, as the reviewer points out, it well could be the subject of a separate publication. As a quick reflection, I surmise, that for a sample containing INPs with a large range of characteristic temperatures, it is unlikely that there will be major gaps in activity. Even with INPs from a single substance there are variations in nucleating sites that lead to such a diversity of nucleation temperatures. However, one can imagine that once we learn how to create sites of specific characteristics they may have well-defined precise characteristic temperatures with only small random variations about them in an experiment. That would be manifested as a single peak in the differential spectrum.

Reply to Markus Petters:

Thanks for providing more insight and for opening the topic for further discussion.

Regarding the numerical procedure, I agree, and said so in the Comment, that in most practical cases the differences between fixed and variable binning will be minor. The reviewer's point about zeroes is correct and that adds more weight to the conclusion that dynamic binning should be discouraged on the basis of principle. No claim is made that binning at any given bin width is optimal for the representation of measurement results. That analysis, taking both empirical and statistical considerations into account, is awaiting future investigation. For now, the choice of what bin intervals to use remains a subjective compromise between several factors; for that reason no recommendation is made for any specific value.

The issue of continuity of the spectra has two parts. The computation of the spectra has no inherent requirement for continuity across a large temperature range and that was the main point in the Comment. The physical reasons for continuity are less clear. Indeed there is a degree of spread about characteristic nucleation temperatures from the site nucleation rate function. However, this would only come into play when combining several repetitions and will not be seen in the differential spectrum for any one realization (experimental run). Beyond that, it is clear from wide experience that, even with samples containing INPs from one given substance, there is a large range of observed nucleation temperatures and that no large gaps are found if sample sizes are large. This arises, principally, from variations in site configurations. Thus, I agree that continuous differential spectra are more the general rule. A clear example of the opposite is the mix of two sources of INPs as in the spectra plotted in the Comment and in the Reviewer's Fig. 1. So, while there is room for arguments about the physical processes, the definition of the differential spectrum clearly allows for discrete values and for gaps. The question of continuity was brought up in the Comment because it is assumed for much of the development in F22 and it needed to be said that continuity may be valid for some data sets but it is not an a priori property of the differential spectra.

Reply is attached as a PDF