From the journal Environmental Science: Atmospheres Peer review history

20-Apr-2022

Dear Dr Steinke:

Manuscript ID: EA-ART-03-2022-000019
TITLE: Sensitivity of ice nucleation parameterizations to the variability in underlying ice nucleation rate coefficients

Thank you for your submission to Environmental Science: Atmospheres, published by the Royal Society of Chemistry. I sent your manuscript to reviewers and I have now received their reports which are copied below.

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Associate Editor
Environmental Science: Atmospheres
Royal Society of Chemistry

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Reviewer 1

This study examines sensitivity of ice nucleation parameterizations to the variability in underlying ice nucleation rate coefficients. I believe this study adds knowledge to the understanding of the contributions of variability in aerosol surface area and the particle-to-particle differences in freezing efficiency. This study is a good and a decent one. I would recommend it to be published with some improvements and answering of the questions as mentioned below.

1. When J_het is small in Fig. 3, the assumption of log-normal distribution causes significant impacts on f_ice. But for the large J_het in Fig. 4, the relative shift of the median f_ice values is slightly smaller, when comparing between a constant J_het value and log-normal J_het distribution. Can the authors provide physical reasons for the dependence on J_het?
2. In Figure 1, the log-normal distributions are not smooth, especially for N = 100. Why?
3. In Figure 2, why is there no small aerosol surface area for N = 100 in the right panel?

Reviewer 2

In this study the expected variability in droplet fraction frozen caused by four different distributions of heterogeneous nucleation rate on droplet freezing experiments using both a relatively large number of droplets and a relatively small number of droplets are spelled out. The results of this process are used to estimate variability in ice water path that the different representations and droplets numbers would have on a literature parameterisation of ice-water path. The paper is very well written and clear. The results make a great deal of sense. While they are unsurprising having the impact of droplet number and varying rate distribution spelt out is clearly helpful and I think the paper is a valuable contribution. The paper is very nicely written and clear and I recommend publication.

Minor comments: It may be worth briefly mentioning the Monte-Carlo simulations described by Vali(1). A few groups are using simulations of this type to produce confidence intervals on lab and field data and some sort of description of how this process relates to the work described here may be helpful.
Sear(2) used the GEV to describe droplet freezing data also. The paper isn’t entirely relevant to this work but it seems worth mentioning, just in case the authors aren’t aware of it!

1 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, doi:10.5194/amt-12-1219-2019 (2019).
2 Sear, R. P. Generalisation of Levine's prediction for the distribution of freezing temperatures of droplets: a general singular model for ice nucleation. Atmos. Chem. Phys. 13, 7215-7223, doi:10.5194/acp-13-7215-2013 (2013).

Response to reviewer comments on “Sensitivity of ice nucleation parameterizations to the variability in underlying ice nucleation rate coefficients” by Steinke and Burrows (2022)

Dear editor, dear referees,
we would like to thank reviewers for providing valuable feedback and comments. Please find below our responses as well as an indication of changes to the manuscript.

Regards,
Isabelle Steinke

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Referee: 1
========
This study examines sensitivity of ice nucleation parameterizations to the variability in underlying ice nucleation rate coefficients. I believe this study adds knowledge to the understanding of the contributions of variability in aerosol surface area and the particle-to-particle differences in freezing efficiency. This study is a good and a decent one. I would recommend it to be published with some improvements and answering of the questions as mentioned below.
1. When J_het is small in Fig. 3, the assumption of log-normal distribution causes significant impacts on f_ice. But for the large J_het in Fig. 4, the relative shift of the median f_ice values is slightly smaller, when comparing between a constant J_het value and log-normal J_het distribution. Can the authors provide physical reasons for the dependence on J_het?
** Relatively speaking, very ice-active particles (represented by high Jhet values in the tail of the distribution) contribute more to the simulated freezing events when most of the particles are not very ice-active (i.e., for the Jhet distribution with the lower median value). When the median Jhet value increases, the baseline frozen fractions are higher, fewer droplets remain unfrozen, and these particles are less able to cause additional freezing in the population of droplets. This is mathematically expressed by the fact that the frozen fractions depend on Jhet in a nonlinear (i.e., sublinear) way as described by equation 1.
We have now added the following sentence to the manuscript (l. 198 ff):
However, the overall sensitivity to the shape of the Jhet distribution is less pronounced at higher Jhet values due to the sublinear relationship between frozen fractions fice and Jhet.
2. In Figure 1, the log-normal distributions are not smooth, especially for N = 100. Why?
**Due to the low number of droplets and the way the bin sizes were chosen, there are some bins that are less populated because fewer values were drawn from the underlying Jhet distribution. This reflects the random variability in sampling that would be expected in real physical experiments, where randomness is more pronounced when sample sizes are small.
3. In Figure 2, why is there no small aerosol surface area for N = 100 in the right panel?
**Similarly, as in the Jhet distribution shown in Fig. 1, in this specific example, there are no or very few instances when small aerosol surface numbers were drawn randomly from the underlying aerosol size distribution. Therefore, we changed the figure caption to “Exemplary aerosol surface area distributions…[]”.

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Referee: 2
========
In this study the expected variability in droplet fraction frozen caused by four different distributions of heterogeneous nucleation rate on droplet freezing experiments using both a relatively large number of droplets and a relatively small number of droplets are spelled out. The results of this process are used to estimate variability in ice water path that the different representations and droplets numbers would have on a literature parameterisation of ice-water path. The paper is very well written and clear. The results make a great deal of sense. While they are unsurprising having the impact of droplet number and varying rate distribution spelt out is clearly helpful and I think the paper is a valuable contribution. The paper is very nicely written and clear and I recommend publication.

Minor comments: It may be worth briefly mentioning the Monte-Carlo simulations described by Vali(1). A few groups are using simulations of this type to produce confidence intervals on lab and field data and some sort of description of how this process relates to the work described here may be helpful.
Sear(2) used the GEV to describe droplet freezing data also. The paper isn’t entirely relevant to this work but it seems worth mentioning, just in case the authors aren’t aware of it!
1 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, doi:10.5194/amt-12-1219-2019 (2019).
2 Sear, R. P. Generalisation of Levine's prediction for the distribution of freezing temperatures of droplets: a general singular model for ice nucleation. Atmos. Chem. Phys. 13, 7215-7223, doi:10.5194/acp-13-7215-2013 (2013).
**We thank the reviewer for their positive feedback. We have now included references to the two studies highlighted by the reviewer (see lines 130 and 215ff). In addition, we now elaborate that the study by Vali et al. (2019) presents an approximation for large droplet ensemble sizes whereas we explicitly consider the number of droplets in our study.

19-Jun-2022

Dear Dr Steinke:

Manuscript ID: EA-ART-03-2022-000019.R1
TITLE: Sensitivity of ice nucleation parameterizations to the variability in underlying ice nucleation rate coefficients

Thank you for submitting your revised manuscript to Environmental Science: Atmospheres. I am pleased to accept your manuscript for publication in its current form. I have copied any final comments from the reviewer(s) below.

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Dr Tzung-May Fu
Associate Editor
Environmental Science: Atmospheres
Royal Society of Chemistry

Reviewer 2

I'm entirely happy with the revised manuscrip and reccomend publication.