This is a rather important paper, neatly discussing the assumption behind SOCOL microphysical scheme and how changes in the assumptions that are valid in background conditions need to be re-assessed for simulations of SAI. The addition of the Pinatubo simulations and their discussion in light of the SAI finding is very nicely done. The manuscript is perfect for GMD and is exceptionally well written, so I think it should be promptly published. I have a just a few minor comments below.

Great abstract. I would suggest using terms now more widely used, like Solar Radiation Modification and just SRM (or SAI) instead of strat-SRM, which is confusing (in my opinion). You also never use the term “strat-SRM” in the manuscript, so a bit pointless.

Line 112: “Neighboring size bins differ by molecule number doubling” this description is slightly confusing, suggest a rewrite…

Line 182: Do they actually follow G4? G4 didn’t explicitly mention how to inject (only indicating to do it just like in the models’ simulations of Pinatubo), and used RCP4.5, while  SSP5-8.5 is more recent than that. Are you talking about G6, which is based on SSP5-8.5 but goes to SSP2-4.5 surface temperatures, and prescribed injections at 10N-10S? If so, need to correct here. Right reference is more correctly Kravitz et al. (2015).

Line 277-290: Again, some clarity needed in which scenario you used.

Line 345: why only the “extreme” one? You also consider a 5 Tg case which is not extreme by Pinatubo-like eruption standards.

Line 361: use exponential notation to avoid confusion here please (as you do elsewhere!).

Line 369: a good example “of” how…

Line 450: old habits die hard… you use “solar geoengineering” here while saying it’s a misleading term in line 34 and promising you’ll use the term “climate intervention” in your work. I don’t mind “geoengineering” as a term, but if you – and free to do so – then abide by the promise not to use it, so as to not to confuse the reader!

The paper by Vattioni et al on the different handling of the operator splitting of nucleation and condensation and, sub-timestepping handles an important aspect of uncertainties in the evolution of sulfate aerosols in the stratosphere. The paper is well written and needs minor revisions.

My main comments are related to the last section. My recommendation is to discuss your work in more detail in relation to Wan et al (2013,2023), not just to the schemes in HAM 1 and HAM2, but also in relation to their method that solves production,

condensation and nucleation simultaneously. You see, somehow, similar problems, and their article provides a solution. It may be difficult to upgrade your model, but you should discuss the conclusion that it would be better to solve multiple processes simultaneously. It may be good to add a figure of the nucleation rates as well.

Can you give a recommendation how to proceed? What is the best option for simulations of SAI or volcanic eruptions? Will this also apply to other models?

Line 7 and 10: 'of of'

Line 38: The aerosol scatter

Line 140: How do you handle other processes, e.g. sedimentation? A long timestep (2h) may reduce sedimentation artificially in case the aerosols sediment into the next gridbox only.

2.2 Socolv4: Changing the resolution of the model changes transport (e.g. Niemeier et al, 2020). This should be kept in mind.

Line 235 pp: There is a mismatch of the names. You write very often CN and CN. One should be NC.

Fig 3: You average between 30N to 30S in Fig 2. Fig 3 shows a global average. To see the differences between the simulations you may add a 30N to 30S average in Fig 3.

Line 301 - 303: This is not true for Fig 4c. CN_20 is more similar to CN_200 compared to the burden plot. Why?

Line 312: Less time for ozone formation or stronger meridional transport? The last might be quite important.

Line 321-322: Where? 6 to 24 DU are the values for the hemisphere, not at high latitudes.

Section 3.5: Pinatubo is not a good analogue for SAI. The injection rate is much higher as are the SO2 concentrations. It might be of interest for you to compare with Wrana et al (2023). After the eruption of Ulawun, satellite data show a decrease in particle size. So nucleation after the eruption is important to get a good agreement between model and data.

Line 399pp: Wan et al 2013 offer a solution of your problem: 'These errors can be significantly reduced by employing solvers that handle production, condensation and nucleation at the same time.' You should discuss this - employing in the model might be an even better solution. You may have a look for Wan et al (2023) as well (https://doi.org/10.48550/arXiv.2306.05377).

Line 412-414: This is not true in general, only for the specific setup of the modes in combination with the injection strategy used in Laakso et al (2022).

Line 415-416: spread: How is this related to this work. Aren't you comparing apples and pears here?

Line 424: As far as I understand Laakso (2022), SALSA does not use Vehkamäki. Nucleation in SALSA is much stronger than in HAM.

Line 426: The collision rate is important for high SO2 concentrations. Otherwise the parameterizations of Vehkamäki (2002) might be not valid at all grid points. However, this is not well published. Määtänen et al (2018) is an upgrade and includes the collision rate. It might be worth to think about an implementation in your model.

Line 443: Can you relate your results to Yu et al (2023)? You get very different answers with one nucleation parameterization, but different substepping etc. So, I wonder if this very general conclusion of Yu et al (2023) holds for your results. In Wrana et al (2023) we use Määtänen et al (2018). This parameterization reproduces the particle size after the Raikoke and Ulawun eruptions quite well. These small eruptions are much closer to SAI because they have a more similar eruption rate than the Pinatubo eruption. I recommend that you do a simulation, even if you do not want to include the results in this paper. You may gain more confidence, which is the better way to continue. 

References

Määtänen, A., Merikanto, J., Henschel, H., Duplissy, J., Makkonen, R., Ortega, I. K., and Vehkamaki, H.: New Parameterizations for Neutral and Ion-Induced Sulfuric Acid-Water Particle Formation in Nucleation and Kinetic Regimes, J. Geophys. Res.-Atmos., 123, 1269–1296, https://doi.org/10.1002/2017JD027429, 2018.

Niemeier, U., Richter, J. H., and Tilmes, S.: Differing responses of the quasi-biennial oscillation to artificial SO2 injections in two global models, Atmos. Chem. Phys., 20, 8975–8987, doi.org/10.5194/acp-20-8975-2020, 2020.

Wrana, F., Niemeier, U., Thomason, L. W., Wallis, S., and von Savigny, C.: Stratospheric aerosol size reduction after volcanic eruptions, Atmos. Chem. Phys., 23, 9725–9743, https://doi.org/10.5194/acp-23-9725-2023, 2023.

The manuscript authored by Vattioni, Stenke, et al. examines the impact of sequential operator splitting and the number/length of time steps on the simulated outcomes of climate intervention through stratospheric sulfur injections. Authors say in the manuscript that “The intention of this paper is to raise awareness within the (aerosol) modelling community for potential numerical problems within conventional aerosol microphysics modules” and it does that very well. The key finding and message for the modeling community is that, even when simulating the same scenario with an identical model and identical lines of code, results can vary significantly (in this instance, ranging from a radiative forcing of -2.3 Wm-2 to -5.3 Wm-2) due to the order in which the two processes are calculated. The aspect of this  “choice” is a detail  which is quite often overlooked in studies related to stratospheric aerosol injection and model intercomparison studies. Furthermore, the manuscript is exceptionally well-written, making it straightforward to read and devoid of any major issues. Consequently, I strongly recommend the publication of this manuscript.

I have only some minor comments or corrections. First more general ones:

I would like to see some discussion from the authors about the role of the coagulation in all of this. It clearly had an impact in Pinatubo simulations (which was a nice point by the way!), but does it have a major impact in the case of stratospheric aerosol injections? In these simulations coagulation was included in the microphysical subloop. What do you think, would it have had a major impact if the number of steps would have been increased only for nucleation and condensation, but not coagulation? And just to be sure: I do not expect to see any additional simulation or analysis on this, but it would be just interesting to know if the authors would have any thoughts about this. Usually coagulation is a computationally heavy process (however probably not that much in SOCOL, where the coagulation kernel is not calculated inside the subloop) and thus not wanted to be calculated more than is needed. 

Authors also mentioned about the sensitivity of results to the chosen injection scenario, but this could be discussed little more in respect to take home messages of this study. What I mean is that e.g. increasing the number of timesteps, or calling nucleation routine first, had a large impact on S25 simulations but rather small for S5 simulations. Thus someone might think that this issue of calculating microphysics does not matter for 5 Tg(S)/yr injections. However, in this study the injections were done in a quite wide area/band (30 N - 30 S latitudes) and I assume there would have been a larger difference if the injections would have been done to a narrower band. This was actually shown more or less by ESM SOCOLc4 simulations for S5p. 

Some specific comments:

Some lines in the text there are “CN” while it was clearly referring to “nucleation first”/NC. Please check these (or neglect me if I have understood something wrong):

P9 L209 "nucleation first" (CN) -> "nucleation first" (NC) 

P9 L214 “of the CN and CN simulations” -> “of the CN and NC simulations” 

P10 L239 “CN and CN” -> “CN and NC”

P10 L245 “(CN, “ -> “(NC, “

P11 L251 “CN and CN” ->”CN and NC”

P12 L253 “CN_20 setting” ->”NC_20 setting”

P12 L265 “sequence (CN_20)” -> 

P12 L282, P13 L294, 

P14 L335, L247, 

P16 L355, L361, 363-365

Fig5 text

P18 L416

I noticed that this is something that Daniele (RC1) commented on already but I will mention it anyway: In the introduction it is said that “climate intervention” is used instead of “geoengineering”, but still “geoengineering” is used in a couple of lines in the text. 

P1 L15 “25 MT/yr” -> “25 Tg(S)/yr” and  “timesetp” -> “timestep”

P5 L137 “H_2O_2” -> “H_2O”?

P6 L159 Maybe you could add that one major difference between SOCOL model versions is also the atmospheric model (ECHAM5 / ECHAM6). If I am not totally wrong.

P7 L177-184 I have to admit that I don't always completely remember all GeoMIP scenarios but here it is said that the simulated point scenarios are following the G4 GeoMIP scenario of Kravitz 2011. However G4 is based on RCP4.5 and 5 Tg SO2/yr is injected (= 2.5 Tg(S)/yr). I assume you meant to refer to some other GeoMIP experiment? I was also thinking that “point” might be slightly misleading as the injections are done along several grid points along the meridian and thus it is different from in Pinatubo simulation. But there is no perfect way to name these and I do not have a better suggestion for the name.

P 7 L 190-193 You could describe the Pinatubo experiment also here in text as it is done in Table 1. I mean how much SO2 is injected, which altitude and which ISAMIP experiment you are referring to. You could also mention why you chose “low-shallow-injection scenario”. 

P10, Fig. 2 Please check that (a)-(f) in the text (description of the figure) corresponds to the ones in the figure. 

P11, Fig. 11. I recommend using some other color than light blue for optimal effective radii or at least make it darker. I did not see it when I printed the manuscript and it is not very clear in the pdf. 

P11, Fig. 11 or P12 L260, This probably would  not need new figures and can be just mentioned in the text but it would be really interesting to see individual radiative forcing for shortwave and longwave radiation separately. I would be expecting that the difference in LW radiative forcing between simulations is relatively small. By the way, if radiative forcing is calculated as difference of radiative fluxes between perturbed and control/background scenarios, and not by e.g. double radiation call with and without aerosols, you might see some change in LW radiative forcing due to the land temperature adjustment which might be relatively large in case of 25 Tg(S)/yr injections. Of course this is something that does not affect your conclusions, but good to consider.   

P12 L284 This is more just a comment, but it is really interesting that the difference in temperature response between CN and NC scenarios is quite large here. As I mentioned above, I am expecting the difference to be caused by the fact that the latitude band is narrower than for SOCOL-AERv2 simulations. In Laakso et al. 2022 point injection led to more similar response between SALSA (prefers nucleation) and M7 (prefers condensation), but there sulfur was injected to the one model grid point which probably gave nucleation more suitable conditions to fight against condensation in M7 simulations. 

P13 L317 I am not sure if I understood how nudging of winds was done. I assume it was not fully nudged if there are changes in atmospheric circulation?

P18 L414. Actually, in M7 simulations of Laakso et al. 2022 growth of the particles in accumulation mode was not restricted, but the size of the accumulation mode was. I mean that accumulation mode was in its maximum size, and when particles in accumulation mode grew up (by condensation or coagulation), they were transferred to coarse mode. This created a gap between these two modes.