This study estimated a large set of marginal abatement cost (MAC) curves based on the output of IAMs in the ENGAGE Scenario Explorer and the GET model. The MAC curves were then applied to the emulator for Integrated Assessment Models (emIAM) and coupled to a simple climate model, ACC2. The test results showed that emIAM was able to reproduce the original IAM emission outcomes under similar conditions. The topic provided rich information about MAC curves under various IAMs, as well as different regions evaluated in the manuscript. While I agree with the authors that the analysis provided by the authors is certainly of general interest to climate-economic model developers and climate-focused researchers, I unfortunately cannot recommend publication of the manuscript in its present form. Here are my concerns:

First, the authors reviewed a range of existing literature about the categories of MAC curves and different MAC curves estimated under various backgrounds. However, the results and analysis generally focused on the outcome of this study. I recommend adding a comparison between the estimated MAC curves in this study and those presented in existing studies, including differences in function forms, appropriate interpretation of parameters, and other major differences compared to existing estimates.

Second, the ENGAGE Scenario dataset includes a wide range of outputs from various IAMs and regions. I am not quite sure about the reasons why the output of a separate GET model was also used for estimating the MAC curves. An explanation of the necessity of adding the output of the GET model is needed for readers to understand the framework of this study more clearly.

Third, the manuscript mentions that the emIAM-ACC2 model minimized total abatement costs to obtain possible emission pathways for reproducing the outcomes from other IAMs. More information about how this process works is needed, including the necessary equations and the objective function for minimizing.

Fourth, this study provided many figures (some of which are similar) to present the estimations of the MAC curves and the emulating results, especially in the Supplement. While these figures provide visual information to present relevant results, there are too many figures stacked together, making it difficult for readers to find the information they need. An appropriate way to manage these figures, such as indexing them using tables or other means of relevance, should be added.

Xiong et al have developed an emulator for integrated assessment models (IAMs) using a "marginal abatement cost (MAC)" approach. The emulator uses a large set of MACs derived from IAM-based scenarios in an existing database to reproduce most original IAM emission outcomes at a much lower computational cost than the original model. Additionally, the emulator can be coupled to a simple climate model to generate emission pathways for a specific temperature target. In general, this is a positive modeling development, as emulators are common in various fields, including climate models, but are currently lacking in the IAM field. As IAMs continue to advance in complexity, emulators could be valuable in scenario discovery.

While this study represents one of the first attempts to develop an IAM emulator, there are three main areas for improvement, as summarized below and discussed in detail.

Firstly, the overall flow should be better. Sometimes, the details are provided before a general overview, creating challenges for readers.

Secondly, the visualization could be improved. Many figures are too busy to deliver the critical message.

Lastly, while I appreciate the massive details and results provided by authors, most of the result text was just purely describing the results, without a high-level generalization or explanation of the reason behind the findings. There is little discussion about the model structures, which might help explain the results.

Detailed comments:

1. Line 108: please explain what’s the NPi2100 scenario. Previous sentences mentioned other scenarios like NPi2020 and INDCi2030, but not NPi2100.
2. Section 2 breaks the entire flow. First, it’s unclear what precisely the MAC is in this context. Some experienced readers might generally know a MAC as a function between the carbon price and % emission reductions. Still, different kinds of literature might have different definitions (i.e., carbon price or emission price) or sectoral and gas specifications. This critical “background” information did not show up until Section 3.1. So before diving into the IAM and overwhelming scenarios definitions, this paper could benefit from a high-level schematic showing the entire working flow. (BTW, the current Fig.1 is overwhelming, with many texts and details but somewhat unclear logic).
3. From section 2, It’s unclear why this paper needs the GET model in addition to the ENGAGE scenario database.
4. Line 157: “if there are non-zero carbon prices in baseline, we subtracted them from the carbon price in mitigation scenarios”, is this implicitly assuming a linear relationship between CO2 price and emission reductions? i.e., a linear MAC?
5. Line 163: I know the term “portfolio” is clearly defined in the GET modeling part in Section 2.2, but what does the “portfolio” mean in the ENGAGE scenario database?
6. Line 165 and below: what exactly does this functional form mean? Again, this is breaking the flow, as I saw additional explanations 30 lines below in line 192.
7. Line 165, where is the carbon price in this equation (1)? I guess the carbon price is f(x), but the text below, albeit with many details embedded, did not indicate which term represents the carbon price.
8. Line 199, “performing consistently the best for all IAMs (see the Zenodo repository)”. This crucial result needs at least a supplementary table or figure or even a main figure/table.
9. Line 208-209: why do the maximum first and second derivatives of temporal change in abatement levels correspond roughly to the limit of the technological change rate and the socio-economic inertia?
10. 1, can you show the x- and y-axis in the same scale? (so that we can see how MACs shift in time)
11. Line 248: “crosses in the right panel of Figure 1” --- I cannot find crosses in the right panel because they are too small.
12. In figure 2, the authors pointed out different models show very different carbon prices for the same level of reduction. For example, when reaching a 100% reduction, the corresponding price is about $150, while POLES is about $1000. However, this could be the masked effect of the single fitted line on a wide range of scenarios. Even the fitted value for POLES indicated an ~$1000 to achieve a 100% reduction, there are individual data points (scenarios) reaching 100% reduction with much lower prices. For this type of data and distribution, perhaps the MAC approach is not suitable because of the nature of some particular models.
13. Section 3.2.2 discussed the role of the first and second derivatives of the abatement changes, which is interesting, but I still don’t fully understand its value. I.e., do they have physical meanings? (see my comment # 8). Also, what if those upper limits for the first and second derivatives were removed? How could that change the fitted models?
14. Fig 4 seems to capture the model differences. However, the true question is to what extent are these differences because of the model’s structural differences or differences in the scenarios simulated by different models? Each model may contribute varying numbers of scenarios to the database with unevenly distributed scenario narratives. Thus, the differences here might be driven by the artificial selection of the training sample. I hope the authors can share some thoughts on this. Also, is there any notable structural differences that might be helpful to explain the observations in line 320-329?
15. Table 2, why do some models have huge coefficients for a and c? For example, the “a” parameter for REMIND CH4 or the “c” parameter for WITCH CH4 and N2O? Is this because of the model itself, or were the scenarios chosen for fitting? Also, the main text did not make any comment on Table 2.
16. Line 366: “They are further compared with the Global MAC curves for energy-related CO2 emissions from ENGAGE IAMs.”
17. Figures 7 and 8: Given the current presentation, there’s no way to check the model performance for emIAM-ACC2 visually. Please avoid showing so many lines/dots in one figure; this busy chart provides minimal information.
18. Technically, the entire validation test (section 4) is performed in the “training set”. Ideally, this should be done in a validation set outside the training set. Authors could 1) try to select scenarios from another scenario database, such as IPCC AR6, with the same set of models and selected scenarios as validation, or 2) just randomly choose a part of the ENGAGE scenarios as the training set to fit MACs (if there’s enough sample size), then use the remaining ENGAGE scenarios as the validation set.
19. Comparing Figures 10 and 11, I wonder why COFFEE performed well in the global test but poorly for most regions for CO2. Are they consistent?
20. Line 623 “The results showed that the original emission pathways were reproduced reasonably well in a majority of cases.” This is oversimplified. The performance depends on the gas, model, and maybe other features (if Figures 7 and 8 could have been clearer). Here needs a better summary of the findings.
21. Line 626, “Materials that are required for making such decisions are systematically presented in Supplement and our Zenodo repository.” This is essential information; the authors should provide a couple of high-level bullet points.
22. Line 627, “Some IAMs were more easily emulated than other IAMs. The goodness of fit of the MAC curves depends on gases and regions.” Again, this is another place that should have provided richer information beyond the current simple comment (which readers would even know before reading this paper).

Summary:

The paper describes an emulator for Integrated Assessment Models (IAMs) based on an aggregation of MAC curves of different models, regions, time points and greenhouse gases. The idea is interesting and useful, because it allows for quick assessments of abatement given different carbon prices, for which running IAMs may be computationally costly. The paper focuses on the calculation of these MAC curves, on which the authors are thorough, and on the validation of the resulting emulator in comparison to the output of the IAMs that the authors started with.

General comments

While the idea of this emulator is interesting and useful, I unfortunately do not recommend publication in the paper’s current form and am providing a few suggestions below that may be used for major revision.

• The scenarios used as input are merely listed, but little motivation is given why the ENGAGE database is chosen, while I think this is key to the resulting MAC curves in the emIAM. My suggestion would be to at least motivate why the ENGAGE database is suitable for this exercise, and why the authors are not using the full AR6 scenario database that came out last year.
• A major concern is the lack of discussion in this paper. The paper contains a lot of detailed description of results, along with many detailed figures, but lacks broader discussion. For example, where to the gas differences in Fig. 4 or the regional differences in Fig. 5 come from? Could we have expected them beforehand? And what do the significant model differences in Fig. 2 imply for the ultimate results?
• The paper can be written more concise and requires a bit more flow to guide the reader throughout the steps. Also, the paper contains too many figures/panels which are not well readable, especially when it comes to symbols (circles/triangles, etc.) and scenario labels. The authors may consider moving some to the SI.
• More details on the uncertainty of this approach is needed. Clearly, the results are gas, model, region and time dependent, while some of these things are actually aggregated into a single MAC in emIAM. What does this imply for the end results? Perhaps work with uncertainty bars in a summarizing plots in the end to give the reader a feeling for the uncertainty of emIAM. Similar for the parametric uncertainties in the values of a, b, c and d when fitting, which may require a sensitivity analysis.
• The authors have chosen to work with percentage abatement w.r.t. baselines rather than absolute abatement. I understand the reasoning, but it is not trivial that this choice fully counteracts the lack of temporal dependency in the analysis (e.g., in the form of learning by doing), even though this is (perhaps even coincidentally) visible when comparing the percentage versions versus the absolute versions. Moreover, baselines significantly differ among models, which introduces another source of uncertainty. A discussion on this would be helpful in the paper.
• The numbers in Fig. 10 and 11 are difficult to judge purely on their numerics. It would be useful to provide an example and focus on a number of key ingredients of emission pathways rather than pure correlations: how do the 2030 emissions differ, the netzero years, and the required negative emissions in overshoot scenarios? I guess that it is almost trivial to have a high correlation in general, because in all scenarios, emissions go down over time. Hence, to convince the reader, focusing on comparisons beyond mere correlation metrics would be useful.
• Perhaps more generally and related to aforementioned points: the MAC curve deductions themselves are interesting and a lot of insights can be obtained from them. However the analysis also reveals that “We do not provide specific recommendations on the appropriateness of the use of each MAC curve and leave the users to decide which MAC curves to apply” (p. 31), suggesting that the many differences between the MAC curves limit the universal applicability of emIAM. Potential users need to be guided better: which results are generalizable, what are the main uncertainties? A discussion section, looking at this question from a helicopter point-of-view may help in this respect, which is currently missing. This paper may be a first step in the direction of IAM-emulators, but then the authors are invited to write a bit more about what the next steps should be.

Minor comments

• The portfolios for GET are described only qualitatively. The choices (p. 5) even seem arbitrary – e.g., why did the authors use the numbers of 100% larger and 50% smaller bioenergy constraints in the respective portfolios?
• Unclear: in Section 4, also the regional MAC curves from emIAM are used, while on p. 6 a regional independence is assumed. What is it you are actually using in section 4?
• Could you elaborate a bit on Fig. 6 and where these points come from?
• Second derivative unit should be % / year^2 I guess, or are the numbers of the fractional order 1e-4?