The authors use a fully coupled climate model to evaluate the response of permafrost under temperature stabilization and overshoot scenarios. The methods appear rigorous, and the manuscript is well-written. However, the manuscript could be improved by discussing the implications of some of the feedbacks being modeled. Substantial revisions to some sections of the text and figures could further improve the overall clarity of the manuscript and link it more directly to existing literature.

Major comments:

• Line 92 and throughout: Yedoma represents a significant, deep proportion of the permafrost carbon stock in some regions and was formed over extremely long timescales. Given the focus on differences between overshoot and stabilization scenarios, a greater discussion of this limitation could be included in the methods and conclusions.
• Line 90 – 103: More background on the UVICC ESM permafrost carbon model, validation, and perturbed parameter approach would be particularly useful to readers.
• Line 129 – 136: More clarity is needed about this aspect of the method and the interaction with any permafrost feedback loops. It appears these experiments were done to create drivers for the overshoot scenarios (i.e. the proportional control scheme is not active when the final model runs for analysis are done). It then appears based on this text and the text in section 3.2 that any permafrost carbon fluxes would be tacked onto the emissions and removals needed to accomplish these scenarios. Significant edits are needed here for clarity. The additional warming in Figure 5 also appears well-suited for additional discussion.
• Line 159 – 169: I appreciate the perturbed parameter approach that’s been taken here. It’s presented well as uncertainty bounds in the text but includes some cues about the quantity of runs used and uncertainty bounds in more key figures would highlight it. Moreover, I recommend some discussion of any overlapping trajectories given the range of parameter uncertainty. Otherwise, these aspects of the manuscript may not be as apparent to the reader.
• Line 200: Greater elaboration on this result could be valuable. Assessing this impact at the year 2300 seems reasonable, however, given enough time will all the overshoot scenarios eventually converge with SWL-1.5?
• Line 220 and throughout: There is a substantial body of literature related to the response of arctic vegetation to climate change and the processes represented therein. Providing the reader with additional information on the vegetation model within UVICC ESM, the processes represented, limitations therein, including some information about the response of vegetation productivity and framing these results in that context would enhance their presentation. Additional background on the permafrost model would add additional clarity as to why permafrost carbon inputs do not appear to follow the same trajectory as soil carbon.

Minor comments:

• Abstract: for clarity suggest reducing the use of acronyms in the abstract and possibly parts of the text.
• Line 25: gradual and abrupt seem to refer to the rate of carbon loss suggest revision to distinguish this from the processes of gradual and abrupt thaw.
• Line 50: suggest adding further discission of the mechanism behind the presence or absence of hysteresis behavior in different processes as this is useful background.
• Line 229: Suggest clarifying the timescale being discussed in this summary information. It reads very similarly to the sentence immediately prior.

Overall:

This study "aims to fill these gaps using an Earth system model of intermediate complexity to systematically assess the permafrost response and feedback under temperature stabilization or overshoot scenarios achieving various GWLs. " I think it is an interesting paper and recommend publication, but I also think it could make some clearer points, as I discuss below.

Based on that stated aim, I expected to see one or more figures with total permafrost carbon losses plotted as a function of the GWL for both the stabilization and overshoot cases. I.e., is the permafrost carbon loss linear? Are there thresholds or tipping points? Figure 6a shows the areal loss as a function of global warming level, but why are carbon variables not quantified in this way? Does the permafrost carbon feedback strength (in units of Pg C / degree Celsius warming) show a similar nonlinearity as the SPAW shown in f.g 6a with maximum losses per unit warming in the 1.5-2 degree C range? Figure 3b seems to show that the highest sensitivity is in the ~3 degree warming range, but it is difficult to see quantitatively. Likewise it would be interesting to se the radiative forcing as well. So I'd recommend an additional figure with panels along the lines of 6a that allows the reader to trace how the (non-)linearity of each of these permafrost metrics as a function of global warming levels for the stabilization and overshoot cases changes between permafrost area, permafrost carbon, and permafrost radiative forcing.

Further, given the possibility of perturbing parameters due to the relatively low cost of running UVic-ESCM, I had expected to see if any of those parameters introduced nonlinearities or substantially changed the magnitude of the results. But I just see median lines. So it is hard to know how important the uncertainty is. I suggest showing the uncertainty via translucent colored plumes in all figures.

Comments

line 36: the 1.5 degree budget will be exhausted within the next few years, but not the 2 degree budget. Please clarify.

Paragraph starting line 142: This is great that you were able to perturb these key parameters. But I don't see any uncertainty plumes in any of the figures, only the median values. I think it would be informative to the reader to see the partameter uncertainty plumes plotted on all figures.

fig. 2b: Why doesn't the permafrost area recover all the way under the overshoot scenarios? Are there regional changes to the northern high latitude climate that are responsible for the differing permafrost amounts at a given GWL? If so, what are the drivers of that regional change? It might help to add a panel with the regional temperature difference to see whether it behaves differently from the global mean. 

Line 321: This paper doesn't really establish anything about the realism of the model, since there are no model-data comparisons, so suggest reword or provide citations to the papers that have shown this.

Data availability: I downloaded some of the data files in Cui et al., 2024, but they aren't clearly described and don't include any further details than what is in the paper (e.g., spatial information). This strikes me as a fairly minimal data archival effort.