From the journal Environmental Science: Atmospheres Peer review history

21-Dec-2022

Dear Dr Olenius:

Manuscript ID: EA-ART-12-2022-000174
TITLE: Reducing chemical complexity in representation of new-particle formation: Evaluation of simplification approaches

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Associate Editor, Environmental Science: Atmospheres

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Reviewer 1

This paper assesses the merits of methods to reduce the chemical complexity of nanoparticle formation mechanisms. I like the topic of this paper which is definitely something to be reflected upon. More and more studies are claiming that one vapor or another ‘enhances’ nucleation, but how to incorporate all these species into a simplified yet usable framework is not something that is often discussed.
The discussion on simplifying the mechanisms to quasi-unary representations is also valuable since such simplification is very attractive but its performance has not been systematically examined yet. This work certainly enhances our understanding of how far away the base distribution is away from equilibrium.
I am of the opinion that this paper should be published after the following minor comments have been addressed:
1. In the last sentence of abstract, it should be added something like ‘or the concentration of the enhancing species is above a certain limit’.
2. Please make it explicitly clear that the SA monomer concentrations are held constant during the simulations rather than SA + SA1Base1 as was done . At high DMA, EDA concentrations, the sulfuric acid will mostly be in the form of SA1Base1.
3. Page 8,’For the stronger base DMA, underprediction (up to factors of ≲10) and possibly overprediction (up to a factor of ~2)’: This factor of 2 seems to be caused by double-counting SA nucleation when the base is saturated. I suggest the authors make this clear.
4. The authors have been a bit reserved on the typical concentrations of NH3. In polluted environments such as Beijing, the concentration of NH3 can easily go beyond 1010 (0.4 ppb) and even reach 10 ppb level. I would suggest increasing the typical vapor concentration range of ammonia.
5. A table or references summarizing the typical concentrations of bases will help interpret the simulation results.
6. For Table S2, in the lumped cases, is MA+NH3 lumped as MA or NH3 (same question for other species)? Please make this very clear in the caption of table S2 as well as in other places where the lumping approach is discussed.

Technical corrections:
Figure S10 caption: ‘similarly’ should be ‘similar’

Reviewer 2

The authors propose an interesting approach to simplify the considerations for formation rates/cluster concentrations in terms of the so-called summing, lumping and quasi-unary approximations. The approaches in aerosol nucleation simulation field are new and the intention to make the simplifications is worth to be encouraged since so many compounds potentially contribute to nucleation, so the work is definitely deserved to be published.
There are a few comments listed below:
1. I am doubtful about the instructive significance of the approaches since the authors didn’t provide insightful indicators to distinguish different nucleation precursors. In other words, when facing new compounds, such as methanesulfonic acid/dicarboxylic acids and bases, it seems like the uncertainty of simplifications is still unknown as no clear parameters are provided to describe the similarity of different nucleation precursors. So I suggest that more insightful analysis should be made to define what’s called “similarity” for different nucleation precursors to improve the application value of the approaches.
2. There should be two directions for lumping: A is treated as B and B is treated as A. Is there a significant difference between them?
3. What’s the differences between the sum approach with using “ideal cases” of bases with identical thermochemical (e.g. Figure 3) and the lumping approach?
4. In Figure S9, the concentration difference between H2O and H2SO4 is huge, so I think the ODE solving should not be stable. If so, how could we trust the “perfect comparison” in section 3.2.1?

We thank both reviewers for their comments and insights. We have prepared a revised manuscript considering the points brought up by the reviewers, and feel that this has improved and clarified the study. Please find below our point-by-point replies to the comments. The reviewers’ comments are reproduced in blue, and quotes from the revised manuscript are written in red. Changes are marked in the revised manuscript with yellow highlight.

Referee: 1
Comments to the Author
This paper assesses the merits of methods to reduce the chemical complexity of nanoparticle formation mechanisms. I like the topic of this paper which is definitely something to be reflected upon. More and more studies are claiming that one vapor or another ‘enhances’ nucleation, but how to incorporate all these species into a simplified yet usable framework is not something that is often discussed.
The discussion on simplifying the mechanisms to quasi-unary representations is also valuable since such simplification is very attractive but its performance has not been systematically examined yet. This work certainly enhances our understanding of how far away the base distribution is away from equilibrium.
I am of the opinion that this paper should be published after the following minor comments have been addressed:

1. In the last sentence of abstract, it should be added something like ‘or the concentration of the enhancing species is above a certain limit’.

The sentence has been modified to read:
Simplifications in cluster growth dynamics by quasi-unary approaches, on the other hand, are reasonable mainly for strong cluster formation involving very low-evaporating species and at excess concentration of the implicitly treated stabilizing compound.

2. Please make it explicitly clear that the SA monomer concentrations are held constant during the simulations rather than SA + SA1Base1 as was done. At high DMA, EDA concentrations, the sulfuric acid will mostly be in the form of SA1Base1.

In fact, we do define [H2SO4] as the “effective” H2SO4 concentration that includes also H2SO4 molecules that are clustered with one or more base molecules. As the reviewer notes, H2SO4 is likely to form H2SO4•base dimers with strong bases, and these dimers are expected to be included in measured [H2SO4] (Rondo et al., J. Geophys. Res. Atmos. 121, 3036–3049, 2016; Kupiainen-Määttä et al., J. Phys. Chem. A, 117, 14109–14119, 2013). Therefore, we define [H2SO4] as the “measurable” concentration in order to avoid misleading values that may occur especially at high amine concentrations at which the fraction of free H2SO4 monomers may be minor.

We apologize for this unclarity and have now explained this in the model description in Section 2.2:
As H2SO4 molecules tend to cluster with strong bases, we define the H2SO4 vapor concentration as the total concentration of H2SO4 monomers and H2SO4•base, where “base” refers to any base molecule. This is consistent with measurements, as the clustered molecules are expected to contribute to the H2SO4 signal.

3. Page 8,’For the stronger base DMA, underprediction (up to factors of ≲10) and possibly overprediction (up to a factor of ~2)’: This factor of 2 seems to be caused by double-counting SA nucleation when the base is saturated. I suggest the authors make this clear.

Yes, this is correct. The double-counting is now clarified in Section 3.1:
At saturated conditions, the rate is double-counted by ∑J2 comp at base1 ≈ base2, as the explicit formation rate remains the same upon doubling of base concentration.

4. The authors have been a bit reserved on the typical concentrations of NH3. In polluted environments such as Beijing, the concentration of NH3 can easily go beyond 1010 (0.4 ppb) and even reach 10 ppb level. I would suggest increasing the typical vapor concentration range of ammonia.

We agree that it is good to include also higher concentrations, and we have now extended the upper limit of the [NH3] range to ppb levels in Figures 5, 7, S10 and S13. References including such polluted cases have been added to Table 2; see also the reply to comment 5 by reviewer 1.

5. A table or references summarizing the typical concentrations of bases will help interpret the simulation results.

This is a useful suggestion, and we have now added Table 2 in Section 3.1. The table lists typical concentration levels observed in the atmosphere for ammonia and amines, with references to ambient measurements.

6. For Table S2, in the lumped cases, is MA+NH3 lumped as MA or NH3 (same question for other species)? Please make this very clear in the caption of table S2 as well as in other places where the lumping approach is discussed.

We agree that this needs to be clarified, and we have now added the information on the assumed surrogate species in the last column of Table S2. The species are also stated in the captions of the figures depicting the lumping approach. As the choice of the surrogate species is not unambiguous, we chose to use the more common, more often studied atmospheric species that are also more likely to be included in e.g. larger-scale chemical transport models. That is, for the MA–NH3 case NH3 was used as a representative compound, and for the amine cases DMA was used, except for TMA–EDA for which TMA was applied. The implications of these choices are summarized in the reply to comment 2 by reviewer 2.

Technical corrections:
Figure S10 caption: ‘similarly’ should be ‘similar’

This has been fixed.

Referee: 2
Comments to the Author
The authors propose an interesting approach to simplify the considerations for formation rates/cluster concentrations in terms of the so-called summing, lumping and quasi-unary approximations. The approaches in aerosol nucleation simulation field are new and the intention to make the simplifications is worth to be encouraged since so many compounds potentially contribute to nucleation, so the work is definitely deserved to be published.
There are a few comments listed below:

1. I am doubtful about the instructive significance of the approaches since the authors didn’t provide insightful indicators to distinguish different nucleation precursors. In other words, when facing new compounds, such as methanesulfonic acid/dicarboxylic acids and bases, it seems like the uncertainty of simplifications is still unknown as no clear parameters are provided to describe the similarity of different nucleation precursors. So I suggest that more insightful analysis should be made to define what’s called “similarity” for different nucleation precursors to improve the application value of the approaches.

It is correct that quantitative errors due to the simplifications cannot be readily assessed for arbitrary clustering chemistries. However, the main conclusions and the general trends are clear: if given compounds are observed to have different enhancing effects on quantitative formation rates, it is obvious that they cannot be lumped. In this case, the commonly used sum approach can be applied to obtain a lower-limit assessment of the formation rate in the absence of full multi-component data.

We agree that the question of how to define the “similarity” of compounds requires more discussion. A simple indicator for assessing whether given species are similar enough to be lumped is the formation rate (or cluster concentrations from which the formation rate follows; Eq. (2)), either modeled or measured. We compared the quantitative formation rates of the two-component H2SO4–base chemistries within the Kubečka data set, and found that the differences in the rates reflect the lumpability: J (H2SO4–DMA) and J (H2SO4–EDA) are generally similar, but show larger differences to J (H2SO4–TMA) and especially to the other, weaker bases. The results for DMA vs. EDA and DMA vs. TMA are illustrated in Figure R1; the comparison of TMA vs. EDA shows differences of the same order as DMA vs. TMA, and for other pairs of bases within DLPNO_Kubečka the differences are larger.

(Figure R1)
Figure R1: Ratios J (H2SO4–base1) / J (H2SO4–base2) of two-component formation rates for the DLPNO_Kubečka data at different [H2SO4], [base]=[base1]=[base2], T and CS, where base1 and base2 are (1) DMA and EDA (left-hand side panels), and (2) DMA and TMA (right-hand side panels). Note the different color scales. Explanations for markers and shades are as in Figures 2 and 3.

This is now discussed in SI Section 3:
In order to assess whether given species are similar enough to be lumped, we compared (1) the formation rates of 2-component H2SO4–base chemistries, and (2) the clustering efficiency proxy proposed by Chee et al.15 J (H2SO4–DMA) and J (H2SO4–EDA) are relatively close to each other, with differences of less than a factor of 10 at most conditions of Figure 4 (mostly factors of ≲2 and ≲5 at 260 K and 280 K, respectively, which is also the order of error in the corresponding Jlumped). The differences are large (up to a factor of ~10) at 300 K and [base] ≳ 1–10 ppt, reflecting the larger error in Jlumped occurring at these conditions. By contrast, J (H2SO4–TMA) deviates more from DMA and EDA (by factors of up to ~100 at 260–280 K and ~105 at 300 K, reflecting the order of the errors in Jlumped; e.g. Figure S7), and the differences are even larger between other pairs of bases, as expected (from ~2–3 to several orders of magnitude). These comparisons suggest that formation rates can provide a straight-forward means for approximate similarity assessments.

In addition, from the theoretical perspective the so-called normalized heterodimer concentration Φ has been suggested as a metric for assessing the clustering efficiency of acid–base chemistries (Chee et al., Atmos. Chem. Phys. 21, 11637–11654, 2021). Φ requires only the knowledge of the formation free energy of the acid•base heterodimer, that is used as a proxy for particle formation potential. Therefore, we assessed the similarity also by this proxy, and the comparison is discussed in SI Section 3:
The additional cluster formation proxy by Chee et al.,15 referred to as the normalized heterodimer concentration Φ, only requires data for the acid•base heterodimers:
Φ=(([acid][base])/C_ref )^(1/2) exp((-ΔG_heterodimer)/(k_B T)), (S1)
where [acid] and [base] are the vapor concentrations, Cref = Pref / (kB T) is the reference concentration at which the free energies are calculated, T is the temperature and kB is the Boltzmann constant, and ΔGheterodimer is the Gibbs free energy of formation of the dimer. At given acid and base concentrations, the difference in Φ for different chemistries 1 and 2 depends only on the exponential factor:
Φ_2/Φ_1 =exp((-ΔG_heterodimer,2+ΔG_heterodimer,1)/(k_B T)). (S2)
The ratios of Φ (Eq. (S2)) for bases within DLPNO_Kubečka are shown in Table S1. The values reflect the results obtained for the lumping approach (Table S2): Φ for DMA and EDA are very close to each other, with differences of less than a factor of 2, while Φ for TMA differs from the DMA and EDA values by factors of ≳ 10. Values for NH3 and MA are several orders of magnitude lower than those of the stronger bases, and they also differ from each other by a factor of ≳ 10. This suggests that Φ can be used as an additional indicator to characterize the similarity of H2SO4–base chemistries. However, it must be emphasized that Φ does not give information on the binding of larger clusters. For example, compounds that contain sites that do not form hydrogen bonds, such as TMA, may form strongly bound heterodimers but exhibit steric hindrance effects in larger complexes. Therefore, Φ should be considered as an additional indicative metric and applied together with formation rate and/or cluster concentration data.

Table S1: Ratio Φ (base2) / Φ (base1) of the normalized heterodimer concentration Φ for the amines within the DLPNO_Kubečka data set at different temperatures.
(Table S1)

As for non-lumpable chemistries, the reason for the bias of the sum approximation is straight-forward: The underprediction in summed J is due to the total vapor concentration being lower in the isolated chemical systems, and the vapor concentrations at which it occurs depend on the relative strengths of the stabilizing species. Here, [NH3] at which the largest bias occurs in the sum approach for the H2SO4–NH3–DMA system is orders of magnitude higher than [DMA] (Figures 2, S2, and S3), while for the H2SO4–EDA–DMA and H2SO4–TMA–DMA (Figures S6 and S7), the EDA and TMA concentrations with largest bias are of similar orders as that of DMA. The corresponding concentration for MA lies in between those of NH3 and the stronger amines, as expected (not shown). The sum approach was found to cause minor positive bias in only a few specific cases, such as the double-counting of the formation rate at saturated conditions (e.g. Figure 3b; comment 3 by reviewer 1). As the underprediction trend is consistent and related to vapor concentration effects, the same logic can in principle be expected to apply for other interacting chemistries, such as multi-acid cases with different acid strengths.

We have reformulated the text in Section 3.1 to include discussion on the similarity assessments, and to better summarize the general trends and conclusions:
To find indicators for similarity, we compared the formation rates J2 comp of the isolated systems (SI Section 3). The differences in J2 comp generally follow the patterns of the error in the lumped rate Jlumped (e.g. Figure 4); small differences (less than a factor of 10 between H2SO4–DMA and H2SO4–EDA) coincide with low errors in Jlumped. This suggests that the rates can be used as an indicator to assess similarity. In addition, a simple theoretical proxy based on acid•base heterodimer stability36 is in line with the comparisons (SI Section 3), and can thus serve as an additional measure.
(…)
To summarize, the commonly applied sum approach can be expected to give lower-limit assessments of the overall formation rate, here with the largest underprediction by factors of up to ~10–100 (Table S2) occurring at vapor level combinations at which all species are able to contribute (i.e. high and low concentrations for weak and strong clustering agents, respectively). The direction of the bias is consistent, as it follows from the omission of the total vapor concentration and similar behavior can thus be expected for other interacting chemistries. However, if model data and/or observations suggest very similar particle formation rates for stabilizing species with concentrations of the same magnitude, lumping is likely to involve less errors than summing of J.

Finally, the following bullet point has been added to Conclusions:
Similarity can be assessed based on formation rates, and additionally by a theoretical proxy involving the free energies of acid•base heterodimers. Minor differences in these indicators, here approximately by factors of ≲10, suggest similarity.

2. There should be two directions for lumping: A is treated as B and B is treated as A. Is there a significant difference between them?

The choice of the so-called surrogate species can affect the direction of the bias in the lumping approach: if the properties of a stronger stabilizer are assumed for the lumped compound, the approximated formation rate is likely to be overpredicted, while choosing a weaker clustering species can result in underprediction. Here, we simply chose to use the more commonly studied bases as lumped species; see also the reply to comment 6 by reviewer 1. However, when the stabilizing effects of given species are similar enough for lumping to be a reasonable approximation, the absolute differences between choosing either A or B are of course small even if the sign of the bias may differ.

Information on the surrogate species is now included in Table S2, and we have added the following text to SI Section 3:
Here, we chose to use the properties of the more common or more widely studied bases (e.g. NH3 instead of MA, or DMA instead of EDA), as indicated in Table S2.

3. What’s the differences between the sum approach with using “ideal cases” of bases with identical thermochemical (e.g. Figure 3) and the lumping approach?

Perfectly identical compounds are correctly represented by the lumping approach as they are truly “lumpable”, while the sum approach may result in errors as discussed in Sections 2.3.1 and 3.1. The reason for including the synthetic cases with identical base properties is to assess the effect of the sum approach in the “extreme” case with perfectly similar species, compared to the opposite case of e.g. H2SO4–NH3–DMA in which the bases are very different (as well as other cases within the Kubečka et al. multi-base data set with more or less different bases). These assessments form a consistent general picture of the bias as discussed in the reply to comment 1 by reviewer 2.

The applicability of the lumping approach for the ideal cases has now been clarified in Section 2.3.1:
In this case, the three-compound system H2SO4–base1–base2 is correctly described by the lumping approach, (…)
And in Section 3.1:
That is, clusters with equal amounts of H2SO4 and base are assumed similar regardless of whether they contain base1, base2, or both, and the cases are thus correctly represented by lumping.

4. In Figure S9, the concentration difference between H2O and H2SO4 is huge, so I think the ODE solving should not be stable. If so, how could we trust the “perfect comparison” in section 3.2.1?

It is indeed true that the set of differential equations becomes very stiff when there are such extremely large differences in the rate constants. Consequently, the Matlab ode15s solver applied in the simulations sometimes does not find the solution, and the simulation stops with no result. The results shown in Figure S9 correspond to successful simulations.

The validity of the equilibrium assumption for H2O has been previously tested within the study by Paasonen et al. (Atmos. Chem. Phys. 12, 9113–9133, 2012; Section 2.1.3). Here a different approach was taken: instead of simulating a complete cluster set including water, the equilibration with respect to water was studied by simulating individual collision and evaporation processes of hydrated clusters with explicit treatment of H2O molecules. The hydrate distributions and effective rate constants extracted from the explicit simulations were found to follow the equilibrium assumption, and implicit treatment of water was thus considered valid.

21-Jan-2023

Dear Dr Olenius:

Manuscript ID: EA-ART-12-2022-000174.R1
TITLE: Reducing chemical complexity in representation of new-particle formation: Evaluation of simplification approaches

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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Reviewer 2

The concerns about the manuscirpt have been properly addressed, so I recommend the acceptance of the paper.