Dear authors,

As you may find that some reviewers still had major concerns about the revised manuscript. Please carefully check and respond to these remaining comments/suggestions.

Sincerely,

Hang Su

Dear authors,
Thanks for submitting your paper. I would like to accept your paper for publication in ACP if the final comments can be properly addressed and implemented.

As you may find in the course of the peer review, the following points were still concerned by the referee.

Use of data below detection limit.
With respect to using measurements below the limit of detection (LOD) of the system. The authors' have made the statement that “The analysis is consistent for Na+ concentrations over the full Na+ measurement range, including below our assigned Na+ LOD.” If a measurement is below its LOD it is not considered reliable, since it is within a signal-to-noise ratio of 3 to 1. When the signal is near the intensity of the noise a number of factors can lead to issues. The authors’ claim that researchers define LOD in different ways, but for a standard analytical measurement, such as chromatography, there is an accepted definition that is broadly used and which should be here. The fact that the data is consistent with data above the LOD, is still not a good reason for using this data. Frankly data below the limit of quantification (LOQ) (10:1) shouldn’t be used, but signal should at least be > 3:1 to be used. The authors’ do not seem willing to only use properly quality controlled data, which should be the standard in a high quality journal like ACP.

Use of inferred Na+
- Inferred Na+: The other major issue is the use of “Inferred Na+”, which I am still uncomfortable with. First, “Inferred Na+” should be renamed since it accounts for all NVCs, not just sodium. Perhaps “Inferred NVCs”? Secondly, as one of the reviewers noted, inferred Na+ is a bit of a circular argument and somewhat misleading. In prior work, the authors’ have argued that proxy methods, such as molar ratio and ion balance have significant shortcomings, but to my understanding “inferred Na+” uses the same basic concept since inferred Na+ is used to help explain the ammonium-to-sulfate ratios, even when the actual Na+ data don’t match that. Maybe this could be reframed with a different name to help the issue. However, introducing a fudge factor and implying it has a real meaning (e.g. Na+ concentration) to account for the fact that the measurements of Na+ (which have their own issues) don’t match the inferred value necessary to have NVCs explain the R ratio, is not strong support for the authors’ hypothesis and argument that NVCs explain the ammonium-sulfate ratio.

Exclusion of Organic Films, Glassy Aerosols, or other Possibilities
The abstract and paper overall still very much imply that the authors’ hypothesis about NVCs is the only reasonable explanation for overprediction of R values. However, given the issues with the Na+ data (below LOD) and the need to use inferred Na+ values higher than what is measured to make the hypothesis work, the strength of the authors’ arguments against organic properties/films or other explanations does not appear sufficiently justified and should be weakened (as noted in previously).

Here is my view and suggestions.
(1) Not using data below LOD or at least clearly marked all data points of which the calculations/predictions were based on data below LOD.
“Na+ data below the LOD is used in the analysis to increase the size of the data set”, this seems to be the reason why the authors used the data below LOD and tried to justify its use. If the data above LOD produce the same result, using data below LOD in my opinion will only weaken the paper, giving an impression that the conclusion is based on highly uncertain data. Besides, predictions based on measured Na+ below LOD give an R ~ 2 (Fig. 1f, if I understand correctly), which seems to support the finding of early studies that low NVC cannot explain the measured low R, and challenge the conclusion of this study. Therefore, avoid using these data will eventually strengthen this paper.
(2) Weaken the argument against other explanations.
I appreciate the confidence of the authors on their explanations but I am not convinced that it is the only explanation especially given the large uncertainties of measurements. Also in Fig. 4, the comparison of r2 between Na+ and OA seems not really fair, because the former effect has been considered but not the effect of kinetic mass transfer limitations induced by organics. Comparison of the gray points seems more meaningful but both data seems to be quite scattered, surely with r2<0.93. What if NVC explains 80% of the variations of R while other explanation explains 20%? I would suggest the authors to weaken their argument, e.g., use formulation “tentative” or “possible” explanation, or something like that.


Concerning the comments from the community, I also read the paper of Silvern et al. (2017)and here is my impression. Silvern et al. found a low R, tried to explain it by examining different factors (including alkaline cations), and finally provided a tentative explanation. From the text “concentrations of alkaline cations other than ammonium (e.g., Ca2+, Mg2+) are also too low to significantly affect the charge balance, as previously shown by Kim et al. (2015). Concentrations of these other alkaline cations are reported at the CSN sites, and we find for the ensemble of CSN sites in Fig. 2 that they would modify R on average by 0.11 mol mol−1”, they seem to have examined NVCs but found little effect based on their data. From the text “a possible role of organic aerosol” and “A tentative explanation is that sulfate particles are increasingly coated by organic material”, it seems that they wanted to find an explanation for the observed R, rather than to use R to prove their explanation. I understand that people may have different interpretation of the same paper. But in case of double or split interpretations, I would suggest using or quoting more original text to be more objective and toavoid debates.

Best regards

Hang Su