Using global climate model simulations, this study estimates the effective radiative forcing of changes in SO2 due to the IMO 2020 sulfur regulation, which limits the sulfur content in international shipping fuel from 3.5% to 0.5% by mass. The results show the magnitude of the ERF due to 2020 sulfur regulation is 0.073 W m⁻², which is within the range of 0.03 to 0.33 W m⁻² in the literature. This study advances our understanding of the ERF magnitude of international shipping induced SO2 changes before and after 2020. Overall, it is a high-quality manuscript with clear representation, robust analysis, and interesting results. I have one major comments for the authors to be addressed:

                  In the Discussion and conclusion section, the role of DMS in estimation of shipping induced ERF is discussed. I am wondering if the DMS emissions in each model simulations could be derived and compared. The differences of DMS among these model simulations could help explain the spread of the estimated shipping ERF among the ensemble members. I expect to see smaller magnitudes of the ERF in simulations with larger DMS emissions.

Minor comments:

1. Near Line 20: delete “fuel” in “fuel (IMO, 2018)”.
2. Line 20: please cite reference about the 77% reduction. How was this number calculated?
3. Line 47: The forcing should be 0.18 W m⁻² in Jin et al (2018).
4. Figure 2: Many dots are broken. I guess the broken dots have the same meaning with the remaining full dots. If so, please correct the broken dots. Otherwise, please explicitly indicate the meaning of the broken dots.
5. Currently, only two figures in the main text and many figures are organized in the supplementary materials, which makes the audience to refer to the supplementary figures frequently. I suggest the authors move some of the suppl. figures to the main text.

This is a multi-model estimate of how the 2020 IMO ship fuel regulation has affected global climate. While the motivation for reduced sulfur fuel content is air quality, the regulation has become an important indicator of human impacts on global climate via aerosols. A constraint on the full impact also helps understand the causes of recent interannual temperature shifts. There have been several evaluations of this ship fuel change but I have seen no multi-model attempts like this and feel the study is fitting for ACP. I do however feel the authors aren’t strongly leveraging the benefits of a multi-model approach. I would like to ask the authors if they can provide more assessment of what processes are driving the forcing and its intermodel spread, and for clarification on the quite narrow uncertainty range they estimate.

Major comments

It would be nice if there were deeper context on the model results, as the Results section is quite thin so I feel the study isn’t leveraging the breadth of model output the authors have available. For instance I wonder if the authors can provide any information on what processes drive the forcing in the assessed models? E.g. division between ACI and ARI and between RF and ERF. For instance, most models have estimates of cloud radiative effects, which could be used to decompose the contribution of cloud forcing changes, even if ‘cloud masking’ of non-cloud changes makes this a rough estimate. Second, the GISS model is often run with the Ghan ‘clean’ (aerosol free) double-radiation call, so if this was done for the simulations here the aerosol direct effect and a more representative cloud radiative forcing can be separated out from the output of what is here treated as two models. Much of the advantage of a multi-model study is that it can be set up to enable process-based comparisons among the models. So I’d encourage the authors to add any indication whether the ERF and its spread are dominated by any particular term, or otherwise to add more of a process-based story to this evaluation.

The stated ERF range of 0.06-0.09 Wm-2 is quite narrow and at odds with the “large uncertainties” assertion in the manuscript’s last sentence. So I wonder if this is an accurate portrayal of the uncertainty. For one, each of the models in Fig. 1 has a larger uncertainty than the multi-model uncertainty, which gives the sense there is more uncertainty than depicted here. I wonder if the authors can instead give an uncertainty range that combines the evaluated factors? Also, I wonder if the authors can comment on features of the models that make their ERFs similar. For instance, if the ACI RF (first indirect effect) were the leading factor, could it be that the models have similar CCN parameterizations? The Abdul-Razzak and Ghan parameterization is ubiquitous, which might explain some of the intermodel similarity.

Could the authors please add context on how their results are different or improved from other recent studies on the climatic impact of the ship fuel regulation? Currently much of the Discussion section summarizes past studies, and feels more suited to the Introduction. I’d like to see more context on how the current study advances the field.

Specific comments

Lines 25-6: I’d like the ERF and RF (defined in Line 140 but first used in 72) to be explained in the Introduction, especially since “effective radiative forcing” is prominently in the title. Can the authors please briefly describe the terms in each, and which are expected to be relevant? For instance, is it expected for the semi-direct effect (the ERF ARI – RF ARI) to be a contributor, or is sulfate not sufficiently absorbing?

Line 29: The cited “total aerosol ERF” as stated in the reference refers to the change “over the industrial era (1750–2014)”. Since this doesn’t significantly include natural aerosol, the description would be clearer by specifying this as a “total anthropogenic aerosol ERF” or similar. Natural aerosols can also be assessed to have an ERF.

Line 34: “Assuming” makes it sound like the 80% reduction was a completely arbitrary choice. Maybe “approximating” is better, or this can be reworded another way?

Lines 43-51: Because there is already a range of forcing estimates for the same case, can the authors please briefly say in the Introduction how the present study is an improvement or at least a worthwhile addition to this literature?

Methods, generally: Can the authors please add a bit of info on whether the aerosol radiative effects and/or CCN activation schemes are different between the models in any way that matters? Conversely, if these models are highly similar, the intermodel range might not represent an accurate representation of current process uncertainties.

Line 63: When the authors say they “perform two atmosphere-only simulations”, for most models they seem to actually mean four, given the two ensemble members. Maybe change to “two types of atmosphere-only” simulations or clarify this another way?

Line 72: RF is used here but has not yet been defined.

Lines 72-4: Can the authors please briefly explain in the text why they have chosen to use a CTM? Is there an added benefit over the GCMs, which presumably could be nudged in a way that mimics the CTM’s being driven by meteorology? Or it’s predominantly just to have one more model?

Table 1 caption: Can the authors please say in the manuscript why the CTM is only one year? Is this because the CTM is constrained by meteorological inputs and hence less susceptible to noise? I think this would look better in the text rather than the caption, but leave it to the authors to decide.

Lines 85-6: The same info on the climatology seems to be repeated for each model, as it appears in Lines 99-100 and Lines 109-110. I’d encourage the authors to avoid repeats by describing common setup information at the start of the Methods rather than in each model description.

Lines 92-7: The ModelE citations are confusing. Since the version used is E2.1, can the authors please cite Bauer et al 2020 more centrally and omit references to older model versions not used here, which are cited in the Bauer paper anyhow?

Line 98: Can the authors please explain why/how they expect the two ModelE versions to perform differently? Does this mostly stem from differences in sulfate size from its fixed value in OMA (which ideally would be stated) and the interactive value in MATRIX?

Line 97: Do the authors expect the lifetime effect (which should be briefly described) would contribute much? There’s a brief reference near the end of the manuscript but I feel this should be indicated sooner.

Line 118: Is the OsloCTM3 aerosol module one-moment or two?

Fig. 1: Does it really make sense for the range from multiple models to be smaller than the range from any single model? I would expect there to be compounding uncertainties.

Lines 142: Can the authors estimate RF ARI and RF ACI in any other models for comparison to these OsloCTM3 values? Or generally make any apples-to-apples comparisons between the models for anything other than the full simulated effect?

Fig. 2: Given there are only two figures in the manuscript, it would make sense to at least make this a compound figure with one of the Supplementary figures, if there isn’t anything more directly relevant to show here.

Line 168: Please give a brief rationale of why this study, which generally agrees with the others, is different or original from the previous attempts.

Lines 180-185: I find this paragraph confusing to read. This makes it sound like DMS is being released from ships, but these references are about naturally emitted DMS, right? I’d like to see this more clearly delineated.

Line 195: “modelled emissions” of what?

Lines 195-6: “showed that the cloud droplet numbers respond linearly” to “showed that cloud droplet number responds linearly”

Line 200: I think the “liquid water path adjustments” is the second indirect effect that is indirectly hinted at when Line 97 mentions the GISS model has only a “first indirect effect” (Line 97), but I’d like to see this effect briefly explained early in the article and then described consistently.

Line 202: Is the cloud fraction impact separate or heavily linked to the liquid water path adjustment? Clouds with less cloud fraction tend to have less liquid water path if not normalizing by the fraction. I see this is following the language of observational studies, but find it a bit confusing.

Line 208-9: The stated “large uncertainties” are what I’d expect but this article’s main conclusion is a 0.06-0.09 Wm-2 uncertainty range, which is quite small. Please reconcile.

Typographic or minor errors

Line 63: “is used to” to “are used to”

Line 186: “include” to “includes”

Line 195: “reanalysis wind” to “reanalysis winds”

Table 1: “#Ensemble members” could at least be “# of ensemble members”.