The revised manuscript is clearly improved compared with the initial submission. The authors have taken the concerns of the anonymous reviewers seriously and modified the manuscript accordingly. The writing of the manuscript has been improved and imprecise formulations have been reformulated more clearly. The reasoning of the authors can now be followed throughout the manuscript and the aims and purpose of the study have become clearer. Specifically, the following improvements have been made:
- The relevant literature is discussed more fully in the revised manuscript.
- A detailed discussion of the composition of the different aerosol classes has been added. Although the physicochemical characterization given in the revised Table 1 exhibits some gaps, it helps to better classify and compare the different samples. It is more clearly discussed to what extent the analyzed sample types are able to represent the proposed aerosol classes.
- Statistical tests have been added to analyze whether the samples exhibit significantly different freezing spectra.
- The addition of a pure water-freezing curve helps to judge that there is no relevant influence of the background signal on the freezing spectra of the samples.
- A discussion of the origin of time dependence was added and it was concluded that the time dependence is mostly stochastic.
- The empirical approach to treat the time dependence is now explained better. An appendix with a table containing the definition of the mathematical symbols has been added that helps to understand the equations.
- The conclusions have been extended. Most importantly it is explicitly stated that the stochastic component of immersion freezing is minor compared with the temperature dependence of INP freezing. This is an important finding of this study, in view of a purely stochastic representation of immersion freezing that has been proposed in a recent study (Knopf et al., 2020).
Yet, the valuable input from Gabor Vali has only partially been considered in the manuscript revisions. The suggestion to show the results in terms of the freezing rate, i.e. fraction of unfrozen droplets that freeze per time, has been taken up in Fig. 11 by adding a panel (b) displaying the freezing rates of the samples. Unfortunately, throughout the rest of the manuscript, the authors stuck to an analysis in terms of their fractional freezing rate, which has much less physical meaning. Yet, even if the authors do not want to convert their fractional freezing rate to the real freezing rate, the revised manuscript can be published after the following minor revisions:
Abstract: The abstract could be extended by a sentence that the authors have added to the conclusion section in the revised manuscript: “Any purely stochastic model of INP activity, assuming that the fractional freezing rate of all unfrozen drops is constant, would predict very high frozen fractions after a certain time, which would be inconsistent with our measurements. Instead, the statistical variability of efficiencies among INPs must be accounted for with any application of stochastic theory.” Or a similar statement.
Line 18: it should be mentioned that all samples were collected at the same station. The name of the sampling station could also be given.
Line 75: “since INPs influence the ice concentration observed” instead of “since INPs determine the ice concentration observed” would be more precise since updraft velocity is also a major determinant of ice crystal number density in clouds.
Line 76: do you mean here secondary ice production? If yes, it should be stated explicitly.
Line 77: It is more than “beneficial” to simulate the first ice in mixed-phase clouds accurately. Consider to replace “beneficial” by “crucial” or something similar.
Lines 104–105: do you mean here that also the freezing rate should decline exponentially? Yet, for stochastic freezing, the freezing rate, i.e. the fraction of unfrozen droplets that freeze per time, remains constant. Just the absolute number of droplets that freeze per time decline together with the number of unfrozen droplets. In your terminology, the freezing rate seems to be termed a fractional rate. Then. it is absolutely unclear what you mean by “freezing rate”. As your terminology differs from the common terminology, there are many sources for confusion. If you want to stick to your terminology, it might be best to just remove “freezing rate” from the sentence.
Line 106: It should be added "for immersion freezing" after “This is seldom observed”, to make clear that this sentence does not refer to homogeneous ice nucleation, which is indisputable stochastic.
Lines 259–260: SiO2, CaO, and Al2O3 are not minerals present in mineral dusts but the oxides that form after ignition of the samples, which is performed to determine the elemental composition. Mineral composition of dusts can e.g. be found in Murray et al. (2012), Kaufmann et al. (2016), and Boose et al. (2016).
Line 290 and Table 1: The PM10 and ACSM derived aerosol concentrations are not always consistent. E.g. PM10 of the combustion dominated sample is 20.85 ug/m3, but the sum of Org, NH4, Cl, NO3, and SO4 adds up to 24.5 ug/m3. The reason for such discrepancies should be discussed.
Line 326: “aerosol components” might be a more appropriate wording than “aerosol properties”.
Lines 473 – 477: this discussion is quite confuse and should be formulated clearer.
Table 1: Bio Trak OPC showed elevated number concentration during the dust event from February 20 to 26. As mineral dusts can also be fluorescing, the Bio Trak signal should not be directly identified with PBAP in the presence of mineral dust as it is done in Table 1.
Lines 492–494: what is meant by “relatively small”? Please specify. What is meant by “a likely candidate”? The marine biogenic components? If yes, it should be “candidates”.
Line 563 and Figure 8: it might be more meaningful to indicate the min–max value range rather than one standard deviation.
Line 579: again, it might be meaningful to also state the min–max difference.
Line 594–596: the definition of fice(t*) seems imprecise. More precisely, it should be "the fraction of droplets freezing starting from the isothermal phase (i.e. fice(t*=0) = 0).
Line 605: The fractional rate of freezing of unfrozen drops is the freezing rate! Please change accordingly.
Line 606: should this be fice(t*)/dt* as on line 603?
Lines 606–608 and Figure 11b: the presentation of the data in terms of the freezing fraction per fraction of unfrozen drops makes more sense than the presentation per fraction of frozen droplets, as the former represents the freezing rate, which should remain constant for stochastic freezing. It should be discussed why this quantity increases again for times since the start of the isothermal phase larger than 103 s for most samples. Also check for correctness as this behavior seems inconsistent with Fig. 9. Maybe discuss the uncertainty of the data points. Was this evaluation done for the averaged (yellow) data points shown in Fig. 9? If yes, you should consider smoothing them before analysis. As it seems, their scatter is increased compared with the individual datasets through averaging the datasets.
Lines 614–615: what chemical kinetics are meant here? This should be explained.
Line 616: what is the “natural time scale of freezing”? This should also be explained.
Line 626–627: this sentence is confusing. Do you mean: “such less efficient drops” instead of “such less efficient INPs”?
Lines 654–657: Making the fraction of droplets freezing per time interval a function of the unfrozen droplet fraction would indeed be a physically more meaningful formulation. If it were formulated like this, 1/tau(t*) could indeed be viewed as the probability of unfozen drops freezing during the isothermal phase. Consider to revise the manuscript in this respect.
Line 709: what is meant by “somehow”? Please specify.
Line 710: the way the equation is formulated, the temperature shift in Eq. (4) applies to all INPs. Shouldn’t it then be “applied to all INPs”? The sentence should be changed accordingly or it should be commented why only “most INPs”.
Line 831–832: this sentence is not complete.
Line 964: Does the statement in the bracket refer to the treatment of temperature dependence suggested in this study? Please clarify.
Line 974–976: this last sentence should be formulated in view of the discussion above, because it sounds as if the temperature dependence could indeed account for the observations of Westbrook and Illingworth.
Table 2: it should be stated whether low or high numbers stand for uniqueness.
Table B1: The parameter “Q” should be explained better in the list of symbols: “passive tracer of what?” What is meant by “freezing level”? Why does Q have units of kg[air]-1? On line 836, a value of Q is given without units.
Figure 9b: Axis labels in panels (b) need to be enlarged to the size shown in panels (a).
Table 3: chi for the mineral dust influenced sample should be 1.48 instead of 1.5.
Line 59: The meaning of PK97 should be given here, at the first mentioning of Pruppacher and Klett, and not on line 91.
Line 585: “time increases” instead of “times increase”.
Table 4: the upper value of the continental pristine sample is not correctly displayed.
Table 5: “°C” should be removed from “-16.3°C”. The line numbers appear within the table.
Boose, Y., Welti, A., Atkinson, J., Ramelli, F., Danielczok, A., Bingemer, H. G., Plötze, M., Sierau, B., Kanji, Z. A., and Lohmann, U.: Heterogeneous ice nucleation on dust particles sourced from 9 deserts worldwide – Part 1: Immersion freezing, Atmos. Chem. Phys., 16, 15075–15095, https://doi.org/10.5194/acp-16-15075-2016, 2016.
Kaufmann, L., Marcolli, C., Hofer, J., Pinti, V., Hoyle, C. R., and Peter, T.: Ice nucleation efficiency of natural dust samples in the immersion mode, Atmos. Chem. Phys., 16, 11177–11206, https://doi.org/10.5194/acp-16-11177-2016, 2016.
Murray, B. J., O’Sullivan, D., Atkinson, J. D., and Webb, M. E.: Ice nucleation by particles immersed in supercooled cloud droplets,
Chem. Soc. Rev., 41, 6519–6554, doiI:10.1039/c2cs35200a, 2012.