Dear Dr. William Wieder,

It's our great pleasure to see your positive comment. We appreciate your posting.

> I'd really love to see individual model results shown for Fig 3b

As you may have already noticed, the historical evolution of CO2 concentration for individual models is presented in Fig.10a, and a similar plot has already been made in the IPCC-AR6 report (Ch.4, Fig.4.3). In addition, Liddicoat et al. (2021) J.Clim. investigated concentration-driven historical simulations, showing the time series of compatible fossil fuel emissions and other carbon fluxes. We believe these existing figures could be good references for you. If we have misunderstood your point, we would be very grateful if you could let me know.

Hajima and coauthors look at evolution of atmospheric CO2 simulated in the CMIP6 ESM experiments and identified potential sources of bias in simulated CO2 concentrations for individual models.  The work is timely, given interest in emission driven scenarios for the FastTrack experiments for CMIP7.  Moreover, the high level finding that CO2 simulated in the E-hist experiments for CMIP6 models seem reasonable is very encouraging. Discussion about uncertainty in land use change emissions is highly relevant and helps set the stage for CMIP7 analysis (although the insight may come too late for much model development).

[Response] We would like to thank you for undertaking peer review of our manuscript, and we greatly appreciate your positive comments.

Broader suggestions and concerns.

What’s the take home message in Section 4.1 & 4.4? To be honest, I found this paper a bit long and hard to wade through.  Is information in these sections critical to the main points being made in this analysis?  More specific comments follow for each section below.

[Response] Thank you for your perspective on this aspect of the manuscript. Based on your feedback and comments received from your fellow reviewer, we would like to consider removing sections 4.1 and 4.4 from the main text. However, we agree with you that some of the analyses presented in sections 4.1 and 4.4 will be useful for modeling centers. Therefore, we suggest that the relevant aspects should be retained in the appendices or supplementary material of the revised manuscript.

Section 4.1

On one hand, I like the idea of helping to guide developers at modeling centers about potential biases in their CMIP6 results.  At the same time, I don’t completely understand this section or why the authors assume that ESMs should be trying to replicate results from the global carbon budget (GCB) experiments?  My understanding of the GCB experiments is that these are concentration driven land and ocean model simulations that are run offline (data rather than model atmosphere boundary conditions).  The explanation for ACCESS (Fig 8a) seems to make sense, a larger LULCC source of CO2 and stronger land C uptake are both needed for this model, but the analysis suggests the model will still have a high bias in CO2 concentration at the end of the E-hist period.   “Improving” land use change emissions that are consistent with GCB estimates for other models really takes them far away from desirable CO2 concentrations (e.g. CNRM).  Why is the GCB C-cycle assumed to be more correct than the CMIP6 models?  Moreover, I’d assume there’s some overlap between GCB and CMIP6 models, does this just mean we’re pseudoreplicating results?

[Response] Thank you for recognizing the potential scientific significance of the content of section 4.1. Although section 4.1 will be removed in the revised manuscript, we would like to address some of your concerns.

- Regarding the assumption that the GCB results are more correct than those of the ESM:

Yes, we also recognize that the GCB estimation might have errors or systematic biases because the estimation relies on offline models. However, the GCB offline models are driven by meteorological fields based on reanalysis datasets, which are surely more accurate than the climate fields reproduced by ESMs. Additionally, the GCB estimation of the ocean C sink is based not only on offline models but also on observation-based data products. We agree that the GCB estimation might have scope for improvement, but the GCB is likely the best current aggregation of scientific knowledge regarding the global carbon budget. Based on this idea, we tried to visualize the discrepancies between the GCB and the ESM to provide hints for further improvement of ESMs.

- Regarding why the ACCESS model would have a positive concentration bias even if it could reproduce the same C budget as the GCB:

It can be seen from Fig. 8a that the current status of ACCESS (black circle in Fig. 8a) is indicated by its position above the multimodel regression line (black line), which suggests that ACCESS currently simulates higher CO2 concentration in E-HIST than that expected from compatible emissions in C-HIST. Thus, this model is unable to accurately simulate CO2 concentration in E-HIST, even if the model could perfectly mimic the global carbon budget as presented by GCB2021. A similar feature can be found in MIROC, i.e., the model plots below the regression line, which suggests that it produces lower CO2 concentration than that expected from the compatible emissions in C-HIST.

The reasons why two models plot away from the regression line remain unclear. A possible explanation is different behavior in the carbon cycle between C-HIST and E-HIST (e.g., the magnitude of the natural C sink differs between the two experiments). The important finding of this analysis is that ACCESS and MIROC would retain a certain amount of CO2 concentration bias, even if they could perfectly mimic the global C budget as presented by GCB2021.

- Regarding why the CNRM model would have a worse CO2 concentration if it acquired the same C budget as GCB:

Although the CNRM model showed the best performances regarding CO2 concentration and compatible fossil fuel emissions (Fig. 5), this model had the lowest emissions from LUC (i.e., 23.5 PgC, Table 4). Thus, having larger LUC emissions in this model should be accompanied by enhancement of CO2 concentration and reduction in compatible fossil fuel emissions, as depicted in Fig. 8. In the CMIP6 run, this model assumed a large amount of net C input to the system from external natural sources (i.e., “IB” in Table4), which likely compensated the lower LUC emissions in this model.

To me, the big take home message from 4.1 is that some models have strong biases in land use change emissions and natural land C sinks (brown and green arrows Fig 8).  Could the same point be made by placing a vertical line for the estimates of LUC emissions and natural land update (+ uncertainty) from the GCB models on fig 9? Combined with this suggestion, would it make more sense to present the ideas in section 4.2 first, before diving into particulars for each model (currently in 4.1; e.g., swap figs 8-9 and sections 4.1 and 4.2?)

[Response] Thank you for the suggestions. Although section 4.1 will be removed in the revised manuscript, we agree that the idea of showing the GCB range in Fig. 9 would be informative for readers; therefore, we will modify Fig. 9 as you suggested.

Section 4.4

This one really lost me.  By differencing a host of different CMIP experiments the results seem to suggest that the only two models with enough data to analyze are different, mainly because of nebulous non-CO2 effects, and those differences change over time (Fig 11). The authors speculate may be related to N biogeochemistry in MIROC, but in general I found this section vague, speculative, and difficult to try and understand.  In the conclusion (section 5), the non-CO2 effects seem to be the most relevant part of the analysis.  I wonder if focusing on this result would be more helpful.  Specifically, I found the Era analysis in Fig 10 to be helpful, but the subsequent waterfall figure (Fig 11) was too busy to add much clarity.  Perhaps focusing on Table 5 and clarifying the methods used and causes for non-CO2 effects would be helpful here?

[Response] Thank you for your constructive comments. Based on your feedback and the comments of your fellow reviewer, we have decided that this part will be shortened or removed from the main text; at the very least, we will focus more on Table 5 and move Fig. 11 to the supplementary material.

Minor and editorial comments:

This is more of a stylistic comment, but I found the introduction a bit long and wandering.  There’s good information in here, especially on the differences and advantages of emission driven and concentration driven scenarios, but is there extraneous information in the text that’s distracting or confusing?  Specifically, I wondered in the global carbon budget (GCB) discussion was necessarily germane to the CMIP-focused analysis that’s central to the work being presented here?

[Response] We agree that the introduction section is overlong and could be a burden on readers. In the revised manuscript, this section will be made as concise as possible. However, we think that the discussion on GCB remains necessary because it highlights the current best science of the global carbon budget, which is the main focus of our manuscript.

I like the use of Figs 1-2 to communicate the rather complicated story that’s being presented in the results.

[Response] Thank you for your positive comment on this aspect. In the revised manuscript, these figures will be modified based on comments received from your fellow reviewer.

Line 440-445 (and associated paragraph).  I’m struck that in the ESM runs (E-hist) there are feedbacks between freely evolving atmospheric CO2 concentrations and land or ocean C update.  These feedbacks are absent in the C-Hist experiments.  Indeed, differences in atmospheric CO2 concentration between C-hist and E-hist experiment (Table 4) do seem positively correlated with differences in ocean and land C updake from these two experiments (and maybe more strongly for ocean C update).  This suggests that feedbacks in ocean and land sinks may help keep atmospheric CO2 ‘on track’ the emissions forced runs (Fig 3a)?    Should this point be made in Fig 4?  Note, this this also seems to be related to ideas about land use change emissions (around line 640).

[Response] Thank you very much for highlighting these important points. Yes, we agree that there was no statement indicating that “the fully active carbon cycle processes in simulations (i.e., E-HIST) can make the trajectory of atmospheric CO2 concentration more realistic, by buffering the biases of CO2 concentration and C fluxes among carbon cycle components.” This point will be mentioned explicitly in the revised manuscript.

Line 451-453 should this redundant text (and short paragraph) be deleted?

[Response] Thank you for identifying the redundant text. The duplicated sentences will be deleted.

Should panels 7a & 7b be switched, to match the order ocean and land are discussed in the text (lines 530-550)

[Response] The panels will be switched in the revised manuscript as you suggested.

In section 5 I feel like references to display items would be helpful (in addition to statistical results).

[Response] Thank you for this suggestion and we will modify the manuscript accordingly.

Line 904 should this refer to section 4.4?

[Response] Yes, it was typo and it will be changed to 4.4.

While CMIP data are freely available, I’m surprised authors don’t make any of their code available. (line 1015)

[Response] Following requests made via community comments on the interactive discussion page, we plan to share the time series of global C budget in each model in tabular text format. We believe that a text file would be most useful in helping interested readers conduct their own further studies.

Dear Dr. Stephen E. Schwartz

Thank you for your interest in our manuscript. We also appreciate your supplemental explanation of Dr. William Wieder's comments.

In light of both your and Dr. William Wieder's comments, we would like to submit, in the 2nd revision stage, both 1) figures and 2) tabular text data that can confirm the results of each model for the concentration-driven and emission-driven experiments. Please wait for our second manuscript to be submitted.

I appreciate the feedback on your interactive discussion.

General Comments:

The authors present a comparison of carbon budgets in two types of Earth system model simulations, one in which the carbon cycle is freely evolving in response to specified emissions of fossil fuels with prognostic atmospheric CO2 content, and another in which the carbon cycle is diagnostic in response to specified atmospheric CO2 content. They find that in the mutli-model mean the answers are relatively comparable, but that there are distinct differences between the behavior of individual components. In particular they find that the treatment of carbon fluxes associated with land use and land cover change generates much of the difference.

In general this is an important topic and I think that the analysis makes a useful contribution to the literature. I thank the authors for doing the analysis and reporting their findings.

[Response] We would like to thank you for undertaking peer review of our manuscript, and we are greatly appreciative of your recognition of the value of our work.

Specific Comments:My main suggestion is that the paper would benefit from some streamlining. It is currently quite long, and contains a large number and variety of types of analysis wich loosely tie together. I think the authors could work to trim the manuscript to focus on the most important points, so that these main points stand out more clearly. I have suggested a few places where parts of the analysis seem less central.

[Response] Thank you for your constructive comments. Based on your feedback and comments received from your fellow reviewer, the length of the manuscript will be reduced in the revised version. Specifically, sections 4.1 and/or 4.4 will be removed or substantially reduced in length.

Even as someone working in this field I found the terminology hard to follow sometimes. I think one simple improvement would be to make the language in the manuscript more active throughout. A second would be to label the figures with the terms that are used in the text. It is hard to keep translating back and forth between the symbols (CL for example) to the words used on figure axes labels. The authors could include both the current words and the symbols in parentheses. This applies to figures 4,5,7,9 (at least).

[Response] We apologize for the inconvenience caused by the terminology adopted in the original manuscript. In the revised version, we will modify the forms of expression as appropriate. Additionally, as you suggested, the figures will be modified to display the symbols together with the relevant wording.

There is a distinct focus on comparing models with GCB2021, and a result of finding that the behavior of carbon cycling in ESMs is heavily dependent on modeled land use change fluxes. I would appreciate seeing some further language about the uncertainties in assessed "truth" of observed land use change fluxes. For example, in the conclusions line 906-907 some comment on the reason for differences would be helpful (or perhaps earlier on, the authors can figure out the placement).

[Response] Thank you for your suggestion regarding the focus on land use change emissions in the conclusion section. In the revised manuscript, the conclusion section will mention the “truth” of land use change fluxes (i.e., the value with an uncertainty range as estimated by GCB2021), which is mentioned in section 3.1 of the original manuscript.

I would like to see a version of Figure 3 with the spagetti lines for all models plotted. This is a figure I would like to show in presentations! I am wondering if you can have both versions, the current Fig 3, and an alternate with a line plotted for each model. Or perhaps just the spagetti version. I also suggest adding the data from GCB2021 because it is discussed extensively in the text in comparison to this figure, but the data is not shown here.

[Response] Thank you for your suggestions. We also received a similar idea via the community comments. Therefore, we will include the “spaghetti” version of the plots (perhaps in the appendices or supplementary material because the spaghetti figure looks quite “busy”). We will also try to include the GCB range in Fig. 3.

Technical Comments:

line 60 - "alters" perhaps "adjusts" would be more accurate here

[Response] It will be corrected as you suggested.

line 112-114 - "results of a C-driven experiment allow a posteriori diagnosis of fossil fuel CO2 emission" I don’t thnk that this is a reason c-driven is preferred (which is the original statement at the beginning of this list). This is a way that we can assess the consequences of c-drien as an experimental design choice, but I don’t see why this is an argument for c-driven. Can it be removed from the list and prefaced differently?  “Although not a direct benefit, the results…” The next paragraph shows why this isn’t directly a benefit.

[Response] In future scenarios, the translation of the CO2 emission to the concentration relies heavily on simple climate models (emulators). Thus, as we understand, the calculation of compatible fossil fuel emissions by ESMs and the comparison with the emulators should have scientific significance (Liddicoat et al. 2020). In CMIP5, in particular, scenarios called “Representative Concentration Pathways” were used, and the CO2 concentration pathways were assumed prior to the emissions. Thus, elucidating the emissions that realize the concentrations of the RCPs was one of the necessary challenges at that time. We will continue to consider this issue carefully, and modifications will be made in the revised manuscript as necessary. We are greatly appreciative that you highlighted this issue.

line 121 - consider adding "despite the lack of a fully coupled carbon cycle" at the end of this sentence.

[Response] Thank you for this suggestion; the amendment will be made as you suggested.

line 142-143 -"whereas many CMIP6 experiments are designed to be performed with C-driven setting for many of the reasons mentioned above" - I found this a little confusing, consider just dropping this clause here.

[Response] It will be removed as you suggested.

line 146 - "identifying the carbon cycle processes that are inadequately simulated in each model"  this needs an example.

[Response] We plan to modify the sentence as follows: “identifying the carbon cycle processes that are inadequately simulated in each model (i.e., the magnitudes of land use change emissions, and natural carbon sinks of the land and the ocean)”.

Figure 1 and Figure 2 - I'm not sure that these figures are necessary. If authors choose to keep them I suggest some changes to the visual appearance. I think that colors could be used instead of or in addition to shading. The numbers in parentheses need more white space and consistent spacing from the arrows. Figure 2 explains the reason for each comparison, but there is not a parallel in figure 1.

[Response] Considering the comment from your fellow reviewer, we would like to retain these workflow diagrams in the revised manuscript. However, the figures will be modified in accordance with your suggestions.

line 323 - "measured" they are not really measured. I think "diagnosed" would be more appropriate.

[Response] It will be corrected as you suggested.

line 337 - add a reference to Fig. 3a at the end of the sentence that starts with "First", and appropriate sub-figure references for the following sentences.

[Response] It will be corrected as you suggested (perhaps you intended L356 rather than L337).

line 451-453 - these sentences seems to repeat the few before them on lines 445-448.

[Response] Yes, this was an editorial error that will be corrected in the revised manuscript.

line 485-486 - this sentence says what is observed, but not why. Why does including land use reduce the correlation?

[Response] Thank you for identifying that this sentence lacked explanation of the underlying reason. In the revised manuscript, the sentence will be replaced as follows: “In E-HIST, the strength of carbon cycle feedbacks plus the LUC emissions in models determine the CO2 concentrations (y-axis of Fig. 5). Meanwhile in C-HIST, their magnitudes (feedbacks and LUC emission) are aggregated into the compatible fossil fuel emission (x-axis of Fig. 5) as per the definition (Eq. 3a). Thus, using only the compatible fossil fuel emission of C-HIST better explains the magnitude of the CO2 concentration in E-HIST.”

section 4.1 starting line 468 - There needs to be a more clear statement about what this analysis is useful for. I think it is to get better adjusted diagnosed emissions from C-HIST, but that isn't actually stated. Without a strong argument for why this is useful I would suggest that this is a section that could be removed from the manuscript.

[Response] Based on your feedback and the comments of your fellow reviewer, we will remove this section partly, or move it to the appendices or supplementary material in the revised manuscript.

line 476 - "ACCESS-ESM1.5 should increase land use emissions" do the authors mean that the model should be adjusting this internally? I don't think that makes sense, so I find this language confusing. I'm guessing that the authors mean that the output from this model should be adjusted after the fact? At what time point? Does this apply only to the present day or historical? Again, I'm not sure what the point of this analysis is.

[Response] In the revised manuscript, we will remove this section (or move it to the supplementary material).

The section was intended to provide hints for improvement of the models regarding the global carbon budget by showing the gap between each ESM and GCB2021. In ACCESS-ESM1.5, the land use change emission was diagnosed at only 26 PgC in terms of the cumulative value (Table 4), which was the second lowest among all the models and much smaller than the GCB estimate (180 PgC). This suggests that ACCESS-ESM1.5 has scope for improvement regarding land use change emissions.

Line 644-645 – C_O^E-HIST is listed twice – I assume one of them is a typo.

[Response] Thank you for identifying this typo. The correct sentence is “C_O^E-HIST … is correlated more with E_LUC^C-HIST …. than with C_O^C-HIST”.

section 4.4, starting line 748 - This comparison seems to be a bit of a tangent to the main line of analysis in the manuscript. Given that the whole manuscript is quite long the authors should consider reducing or removing this section, or reserving it for another paper which can investigate nutrient cycling in greater detail.

[Response] Based on your feedback and the comments of your fellow reviewer, this section will be removed partly or moved to the supplementary material in the revised manuscript.

line 877 - "model improvement"- there are several vague references to model improvement. Can the authors be more specific or give examples?

[Response] This paragraph is linked to section 4.1 and it will be removed in the revised manuscript.

line 945 - "simulated CO2 concentration" do the authors mean using emissions-driven runs? It would be helpful to say so explicitly.

[Response] It will be corrected as you suggested.