This is the review of the revised version of the manuscript now entitled “Effect of particle surface area on ice active site densities retrieved from droplet freezing spectra” by Beydoum et al.
This manuscript has greatly improved in clarity and data discussion. Inclusion of an additional co-author is justified. In general, I applaud the authors for the efforts responding to my comments, adding new experimental data, and make changes to the manuscript. Having said this, I am still not convinced that the ice nucleation data is sufficiently accurate to allow for such a study and its interpretation. The mathematical procedure is now much clearer, but I still have my doubts about its meaningfulness which will be substantiated below in more detail. Active sites may actually play a role in nucleation, however, I am not convinced that the presented exercise is sufficient to resolve this issue. Overall, I am not against publishing this work since it will hopefully stimulate more discussion in this direction. However, the authors should include the points and caveats mentioned below. Doing so will not change the novel analytical procedure, but may render some aspects more “relative” and maybe more “honest” what new science can be derived from these kinds of experiments and analysis.
As I worked through this revision, I came across a study by Alpert and Knopf (2016) which made me also read Knopf and Alpert (2013) and Hartmann et al. (2016). Alpert and Knopf apply a stochastic freezing model and analyze surface area uncertainty for a variety of ice nucleation experiments including the cold stage experiment. They also include a discussion of the Hiranuma et al. (2015) intercomparison data. Hartmann et al. also point out the surface area uncertainty for CFDC experiments and also discuss the divergence in active site number densities as particle surface area varies.
Beydoum et al. mention the stochastic nature of the freezing process several times in the manuscript. Alpert and Knopf show that results are statistically significant when a minimum numbers of freezing events are observed. They find that the Broadley et al. (2012) data using about 60 freezing events for a frozen fraction curve is not very statistically significant (Fornea et al.: 125 freezing events). In other words, the frozen fraction curves are prone to large uncertainties. They also show that in most experiments, surface area is likely uncertain by 1-2 orders of magnitude. For this manuscript, e.g., if actual surface area uncertainty were accounted for in the data of Fig. 5, all frozen fraction curves would be indistinguishable. When including the stochastic uncertainty and uncertainties in temperature, this would be even more indistinguishable within the error. For the newly presented experiments, the numbers of observed freezing events are not given. Also, the variation in droplet sizes, 200-300 nm and 500-600 nm, results in surface area uncertainties of more and less a factor 2-3. Again, this is an experimental issue and not necessarily one of the presented mathematical procedure.
As I read through these papers, I realized that Knopf and Alpert (2013) also investigated illite surface area dependent immersion freezing including below critical surface area data by Broadley et al. (2012). In their 2016 paper they are able to describe illite freezing data by Diehl et al. having large illite surface areas with the method published in 2013. What does this mean? Using nucleation rate coefficients instead of active site number density, seems to avoid the issue of particle surface area dependent active site number density? I think, at least these other methods/approaches must be briefly mentioned in the introduction and discussion sections.
Regarding the mathematical procedure and its much improved presentation: g(overline) is determined for large surface areas. Interestingly, when you have a small number of draws (ndraws <25, p. 18, l. 9), then the freezing curve will have a broader shape, but when ndraws>25 the shape will be the same (i.e. the g* distribution is the same as g(overline)). What does this drawing from g(overline) to make a discrete distribution g* really tell us? For lower surface areas, the distribution has to become broader, resulting in a broader frozen fraction curve to represent the data. Instead of fitting a new distribution to that case of smaller surface area, by drawing, the authors use only certain pieces of g(overline) and discard the remaining values of g(overline). Now this discrete distribution g* (which are the pieces of the continuous g(overline)), contains certain values which are “forced” to be chosen. For this reason, when sampling again randomly from g*, the values of g* will contribute much more compared to the original g(overline). In fact, doing so, g* is an entirely new distribution analytically different to the original g(overline). This also means that g* provides an increasing chance for larger and smaller contact angles to be used, compared to the g(overline). All that is happening is that a broader distribution is used that can better predict the data. In fact, the authors state this themselves: using ndraws>25 and sampling from the resulting discrete g* distribution is basically identical to sampling from the continuous g(overline) distribution. This is obvious, since with a large numbers of draws, the majority of g(overline) is resembled by g*.
So, if this is what mathematically is happening, this approach has no relation to active sites or internal and external mixtures. This is because this is only a mathematical procedure, i.e. find g(overline) then change the distribution to find g*. There is no surprise, when manipulating a distribution in above described way, that it becomes broader and better represents the data (which is likely not sufficiently constraint with respect to surface area and statistics as described above). I recommend being much more careful in the interpretation/statements of this mathematical procedure, in particular in the light if the Hartmann et al. and Alpert and Knopf studies are correct. I would defer making statements such as on p. 18, l. 23: “Thus it follows that there is a wider spread in the freezing curves for these droplets, as their freezing temperature is highly sensitive to the presence of moderately strong active sites. This expresses a greater diversity in external variability – the active site density possessed by individual particles from the same particle source.”
As a consequence of above said is, that all the apparent explanations such as stated "wider diversity in activity", "contain rare sites", "strong external variability", "strong nucleators at warm temperatures” are all non-testable statements. In summary, the reason that the frozen fraction curves are broader is because of the mathematical construct of the fitting including the number of draws. It is entirely due to this method of drawing to change the distribution from which frozen fractions are sampled. Lastly, all cumulative distributions ascend in a similar way due to the applied mathematical design and not because of some active sites. This seems not very “notable” to me (p. 18, l. 11).
One could play devil’s advocate and conclude that this paper nicely shows, that the concept of active site number density is not suitable at all to capture immersion freezing in a consistent sense. At a critical surface area (this depends how well known this property is), the active site number density “jumps” and thus has to be corrected by choosing contact angles that fit to the data (i.e. new g* distribution). Furthermore, this seems different for different compounds. One could argue that this is not very satisfying when describing a physical process.
More specific comments:
p. 3, l. 10: I would re-word this, since “stochastic” does not assume “randomness”: The stochastic framework is based on freezing events that occur randomly across a particle’s surface and can be constrained with a temperature dependent nucleation rate (Pruppacher and Klett, 1997).
p. 3, l. 28 – p. 4, l. 7: There are more papers discussing this issue than Ervens and Feingold. It may be fair to include others.
P. 8, l. 7: Is it justified to smooth the Fornea et al. frozen fraction curve? Looking at their Fig. 6, there are much more bumps in the frozen fraction curve due to the limited number of freezing events. This may affect the fit parameters/interpretation?
p. 9, l. 23-26: In fact, vice versa is also true and maybe even more important: the model parameters are only valid for those specific experimental conditions, since they are derived from a fit.
p. 10, l. 2-5: This sentence is too speculative. One could leave this out without losing anything.
p. 11, l. 15-23: How is theta_c1 derived?
p. 13, l. 1-6: And this is prone to large uncertainties as discussed above.
p. 13, l. 12: You do not know the number of particles in the droplets, but later in the manuscript use these arguments to talk/speculate about internal and external variability. See also p. 14, l. 10-14.
p. 14., l. 26 …: Having a factor ~2 in droplet diameter variation, results in large uncertainty of surface area excluding variations on the nanoscale. See general comment.
p. 14, l. 6: This threshold “concentration” in surface area 7.42x10-6 cm2 is different than the 2x10-6 cm2?
p. 15, l. 18: Here it is stated 450-550 micrometer in diameter, but figure captions say otherwise. What are the uncertainties in solution concentrations? How much does this result in variation of surface area?
p. 15, l. 28: Please add new work on Pseudomonas syringae by Pandey et al. (2016).
p. 16, l. 7-9: I would expect that with given stochastic and experimental uncertainty, these curves cannot be discriminated. How does this affect your discussion?
p. 16, l. 21-24: Compared to previous discussion in this manuscript, one would say that the predictions differ from the data, in particular the predictions do not catch the median freezing temperature.
p. 20, l. 11-14: “Further analysis will show this is not due to an enhancement of ice nucleating activity per surface area but is actually a product of external variability causing a broadening of the ice nucleating spectrum within the droplet ensemble when total surface area is below the critical area threshold.”
See also general comments. This is very speculative and not testable. In fact, following the analysis, it should read: “Further analysis will show this is not due to an enhancement of ice nucleating activity per surface area but is actually a product of changing the distribution to g*.”
p. 20, l. 15-23: Here and at other places: Hartmann et al. (2016) also observed this effect of diverging active site number densities. This study deserves to be cited. Also these authors attribute this to erroneous surface areas, similar to the case made by Alpert and Knopf (2016). This also holds for the conclusion section, p. 32, l. 6-8. Hartmann et al. (2016) pointed it already out and gave a convincing argument for it.
p. 22, l. 4-6: This is confusing. At the end it is a surface area effect that governs nucleation. High mass concentration may alter the surface area as stated on lines 18-20.
p. 24, l. 4-6: “…along with finding the critical area, 𝐴c, and ndraws”.
p. 24, l. 25 and following: The papers by Knopf and Alpert and Alpert and Knopf could be discussed/mentioned.
p. 24, l. 26-29: These cited CFDC studies likely applied erroneous surface areas that have to be corrected as outlined by Hartmann et al. (2016).
p. 25, l. 23: You mean fig. 9?
p. 26, l. 6: You mean fig. 10?
p. 25, l. 7: You mean fig. 6?
p. 25, l. 21-24: For this, the number and size (surface) for particles in each droplet needs to be known which is not the case.
p. 28, l. 19: You mean fig. 11?
p. 28, l. 19: There are no gold and green rectangles.
p. 28, l. 28: You mean brown hexagon?
p. 29, l. 4: Alternative explanation given by Alpert and Knopf (2016) could be briefly stated.
Technical corrections:
p. 13, l. 21: “for an ensemble”
p. 18, l. 19: “attributed”
p. 42, l. 19: Only circles are from CMU?
p. 43, l. 6: Only circles are from CMU?
p. 45, l. 11: Brown hexagons?
References:
Knopf, D. A. and Alpert, P. A.: A water activity based model of heterogeneous ice nucleation kinetics for freezing of water and aqueous solution droplets, Farad. Discuss., 165, 513–534, doi:10.1039/c3fd00035d, 2013.
Hartmann, S., Wex, H., Clauss, T., Augustin-Bauditz, S., Niedermeier, D., Rösch, M., and Stratmann, F.: Immersion freezing of kaolinite: Scaling with particle surface area, J. Atmos. Sci., 73, 263–278, doi:10.1175/JAS-D-15-0057.1, 2016.
Alpert, P. A. and Knopf, D. A.: Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model, Atmos. Chem. Phys., 16, 2083–2107, 2016, doi:10.5194/acp-16-2083-2016.
Pandey, R., Usui, K., Livingstone, R. A., Fischer, S. A., Pfaendtner, J., Backus, E. H. G., Nagata, Y., Fröhlich-Nowoisky, J., Schmüser, L., Mauri, S., Scheel, J. F., Knopf, D. A., Pöschl, U., Bonn, M., and Weidner, T.: Ice-nucleating bacteria control the order and dynamics of interfacial water, Science Advances, 2, 4, e1501630, doi: 10.1126/sciadv.1501630, 2016. |