This study compares a series of global and box model simulations with varying DMS chemistry mechanisms to the long-term trend in ice core trends in MSA at Denali and Summit (where bio-sulfate was also estimated from measurements). They find that no scheme is able to reproduce the observed trends. They explore the role of oxidants, lifetime, and indirectly, deposition schemes on their results. They also compare simulated present-day concentrations with observed MSA, DMS, and MSA/sulfate ratios. The study is thorough and detailed. While the authors were not able to fully explain the observed trend with any of their model schemes, the study explores a range of sensitivities and remains a valuable contribution to the literature. I include comments below largely to improve the readability of the manuscript.

Major comments:

1. The discussion of 3.2 is challenging to follow with all the various model versions and time intervals. And given that no model is able to fully reproduce the observed trends, I would suggest that the authors consider separating their discussion into two time horizons: 1750-1979 and then 1979-2007.
2. Line 9-10; line 269, line 424, line 424: These statements are not correct. Based on Figure 4, no model can fully reproduce the observed trends at Dinali or Summit. There are some schemes that have success in reproducing some of the trend (e.g. 1750 to 1979, but not 1979 to 2007), or the overall tendency (if not magnitude) in some species, but not others. More broadly, the authors should be clear that the models all do simulate an increasing role for NO3 oxidation of DMS, but this does not produce the observed decline in MSA and therefore does not directly support their hypothesis (lines 426-428 are incorrect – no model reproduces the observed decrease in MSA at Denali and only some models reproduce the decrease in MSA at Summit from 1750-1979, but do not capture the increase from 1979-2007). Additional text that mischaracterizes the results:
   • Line 210-211: nitrate did not plateau from 1979-2007 in v13.2.1
   • Lines 227-228: the box model using Cala and Tashmim mechanisms and GC13 only reproduce the 1750 to 1979 trend, they do not represent the increase from 1979 to 2007.
   • Line 286-287: This statement is incorrect: despite the consistent increasing trend in NO3 in Figure 5, Figure 4 shows that, in none of the simulations does bioSO4 increase monotonically, nor does MSA decrease monotonically over time.
   • Line 369, line 439: It’s not clear from Figure 4 that GC13 outperforms GC12 in comparison to the ice core observations. For MSA, GC13 is superior to GC12 at Summit, but worse at Denali. The performance for bioSO4 at Summit is poor for both. These statements should be corrected.

Minor comments:

1. All figure captions: please specify what “model results” are being compared. Concentrations? Deposition?
2. Line 14 and 449: while much of the chemistry goes via an aqueous pathway, this sentence seems to suggest that it is that part of the chemical processing which is uncertain. While this may be true for aqueous phase MSA production, it seems more likely that rather than the aqueous conversion of SO2 to sulfate, it is the gas-phase chemistry that precedes this step that is uncertain. Perhaps this statements should be modified to be more specific to the aqueous pathways of interest?
3. Lines 143-144: Not including MSA+OH does not seem very well justified. Is there any literature to support this decision beyond it being “overly efficient” in the Tashmim mechanism? Perhaps the authors could discuss the uncertainty in the rate? MSA is overestimated in many of the simulations shown in Figure 8 and it seems like this loss would ameliorate some of these comparisons. It would be nice to see some further discussion of this.
4. Line 174-183: what are the uncertainties on all of these measurements?
5. Lines 189-190: what is the uncertainty associated with this comparison of grid cell average deposition at 4x5? Can the authors comments on the possible impact of uncertainties in transport, deposition, and inability to reproduce gradients at this very coarse horizontal resolution?
6. Figure 6b: The large percentages here are largely over low deposition regions (differences of small numbers). Presumably at lower deposition, uncertainties may be larger? Can the authors comment on this.
7. Figure 8, 9, 10: The authors might choose colours to better distinguish GC12 and GC 13 (e.g. warm colours for GC13, cold colours for GC12) to improve ease of interpretation.

This study has used two versions of GEOS-Chem with four different DMS oxidation mechanisms implemented (in total 5 different simulations) to investigate how the oxidation mechanisms influences the long-term trend in DMS derived sulphate and MSA and compare the results to ice core observations. The trends differ, depending on the mechanisms included and the model version used (with different atmospheric oxidant concentrations), highlighting the importance of the sulphur chemistry. None of the simulations could reproduce both the long-term trend and the seasonality in in situ measurements. For aerosol-cloud interaction, the natural aerosols background level is important, and hence better understanding of the natural sulphur cycle is important.

The study is well defined and highlights important issues in atmospheric chemistry modelling. Some improvement to the method sections to make the set up clearer is needed. And the flow in the results section could be improved. The results section is sometimes hard to follow, but the authors have added a summary section at the end of each section which is good. The conclusion sections put the results in a broader context. One more issue that is worth mentioned the role of DMS on the effect of the IMO2020 ship emission regulation, as shown in Jin et al. (2018).

Below are my specific comments to the manuscript:

L95: As I was very curious about the difference between the two GEOS-chem versions, I would have rearranged the first paragraph in section 2.1. First present GEOS-chem and at the end the two different models and how they differ. Do you know what else is different than wet deposition? The natural emissions are also identical in the two model versions.

L106 and several other places you refer to the model versions 13.2.1 or 12.9.3. Stick to GC12 and GC13 as they are defined.

L110: Clearly define the abbreviations for the chemistry schemes before they are used. It may be useful to refer to Table 1 here and maybe skip the details of the chemistry here and leave that for section 2.2. And why is only one scheme used in both models?

L116: Ice cover is also equal in all simulations? Ice cover was mentioned in the Introduction.

L122: Can you add the total DMS emissions in the model simulations here? And how it compares to other studies.

L130: Add also range of absolute numbers in emissions? And what is the source of these emissions?

L135: Table 2 with the time periods simulated should be referred to in the previous section, and keep this section only for describing the oxidation mechanisms.

Figure 1: In the figure caption, can the abbreviation be used instead of references? And more clearly state what part of the figures that are not included in the different schemes? The figures does not tell about the differences between the schemes, so a reference to the supplementary figures at the end of the table caption could be good. And regarding the supplementary figures: Is there no abstraction branch in J. Chen and Cala? Could the figures have a similar layout, so it is easier to visually grasp the differences? Can the numbers below the arrows in Fig. 1 be added to these supplementary figures?

L165: “isolate the impacts of changing oxidant concentrations on trends in MSA and bioSO4” In the full simulations, what else are impacting? Add advantages of using box-model compared to the full model.

L197: For clarity, state what chemistry scheme is used in these simulations as listed in Table 1. Does the different schemes have any impact at all on these values? I guess not. Maybe the default scheme in the two model versions can be mentioned in the GEOS-chem section.

L206: Can you describe the Cl trend in Zhai et al?

L218: Can you put your results in the context of the more recent multi model intercomparison AerChemMIP as well? (Griffiths et al., 2021)

L224: Here as well, you can refer to more recent multi model studies (Stevenson et al., 2020) from AerChemMIP.

L229 and L235: “some simulations” This is a bit vague. Maybe skip and write which capture the observed trend and which do not.

I also struggle a bit with the box model vs. the model results. Can why they differ (for components and sites) be explained? Near L370 transport and deposition is mentioned. Can this be brought in earlier in the text.

L269: Can you bring in results from Denali in the summary as well?

L286: Fig 5b ->  Fig 5a?

L305: In the section above, you have presented each of the figure panels separately. Possible to combine this presentation, and highlight differences.

L321: Add a description of the trend in the ice core records from the previous studies.

L367: “In summary, the overall similarity between box model results (Fig. 4) and GEOS-Chem.. (Fig. 7)”  I can not see that you have discussed Fig. 4 or the box model results in the section above. Can you please help the reader describe this?

Figure 8 and Figure 9: Add time period in the figure captions.

Figure 10: Add time period for the observations in the figure.

L421: The in situ observations is used for comparing the model results for present day and not over the industrial era. Consider rewriting. Maybe introduce the in situ in L431?

L435: Remind the reader that these two model versions have different oxidant concentrations.

L444: “but does not explicitly account for the formation of HPMTF and other short-lived isomerization pathway intermediates” add “as included in Tashmim” (if correct)

L446: “some simulations” list which ones.

Table 2 and 3 in the supplement, burden has unit mass, but given in these tables as mass per year, please check. And how is the lifetime calculated?

Technical comments:

L39-40: “with updated DMS oxidation chemistry” mentioned twice.

L304: No Fig 5e.

L332: “lifetime can offset or amplify a trend in that occurs due” delete in.

L397: “Observed DMS missing ratio is at a maximum” -> mixing I guess.

L429: “increase in BrO drives an increase the production of MSA” -> delete the.

Figure 2: a), b), c) etc. missing in the figure.

Figure 4d: a triangle is shown.

References:

Griffiths, P. T., Murray, L. T., Zeng, G., Shin, Y. M., Abraham, N. L., Archibald, A. T., Deushi, M., Emmons, L. K., Galbally, I. E., Hassler, B., Horowitz, L. W., Keeble, J., Liu, J., Moeini, O., Naik, V., O'Connor, F. M., Oshima, N., Tarasick, D., Tilmes, S., Turnock, S. T., Wild, O., Young, P. J., and Zanis, P.: Tropospheric ozone in CMIP6 simulations, Atmos. Chem. Phys., 21,4187-4218, 10.5194/acp-21-4187-2021, 2021.

Jin, Q., Grandey, B. S., Rothenberg, D., Avramov, A., and Wang, C.: Impacts on cloud radiative effects induced by coexisting aerosols converted from international shipping and maritime DMS emissions, Atmos. Chem. Phys., 18,16793-16808, 10.5194/acp-18-16793-2018, 2018.

Stevenson, D. S., Zhao, A., Naik, V., O'Connor, F. M., Tilmes, S., Zeng, G., Murray, L. T., Collins, W. J., Griffiths, P. T., Shim, S., Horowitz, L. W., Sentman, L. T., and Emmons, L.: Trends in global tropospheric hydroxyl radical and methane lifetime since 1850 from AerChemMIP, Atmos. Chem. Phys., 20,12905-12920, 10.5194/acp-20-12905-2020, 2020.