The authors explore how land and ocean carbon sinks react to rising and falling atmospheric CO2 levels and associated temperature changes in five Earth System Models. They examine both a stylized scenario and a more realistic overshoot scenario, finding a large hysteresis in the sink response and an ill-definement of the metrics when atmospheric CO2 approaches its initial level.

General comments

Overall, the paper is well-written and involves a large amount of work. I believe it is suitable for publication in Biogeosciences after some revisions. Here are some suggestions to improve the manuscript:

• I am sceptical on how the authors tried to remove the effects from land-use change. Firstly, instead of removing gridcells with cropland fractions above a specific threshold (thereby removing gridcells with stable land cover over time), wouldn’t it make more sense to remove gridcells with large changes in cropland fraction? Secondly, it seems the authors only considered croplands but not grazing land. Depending on how the ESMs implemented transitions between natural land and grazing land, this might cause substantial land-use emissions or carbon uptake (from forest regrowth on abandoned grazing land) in some regions. Thirdly, it would be good to compare your calculated metrics for the selected gridcells to all gridcells in the idealized simulations to see whether the selected gridcells are indeed representative for the entire globe.
• The authors find a large hysteresis in the sink response to declining atmospheric CO2 levels. This is likely a result of sinks responding not only to decreasing CO2 but are also still affected by the previous CO2 increase (e.g. Chen et al., 2019; Chimuka et al., 2023; Krause et al., 2020). It would be good to discuss (and if feasible investigate) this more in the paper.

Specific comments

L19: I wonder whether the 1.5° target is still realistically feasible, I suggest to change “1.5” to “well below 2°”

L31: Does this mean the growth is the same everywhere or that there are spatial variations but all models show the same patterns?

L107: I thought the Arctic is warming at least 3x faster, please double-check. Also the references seem to be model-based.

L118ff: Include Chimuka et al. (2023). Also it’s not entirely clear to me how the study goes beyond those previous studies (e.g. SSP535 is also used in Melnikova et al.). Can you elaborate a bit more?

L169: “gases”

L239: Maximum for the average over the whole time period or maximum of individual years?

L239: “cropland”

L240: remove comma

L254: This seems a major limitation, I assume models without dynamic vegetation to have a lower hysteresis. In general, in addition to calculating the different terms (Fig. 7), can you say more on which differences in modelled processes you think drive the differences in the carbon response to decreasing CO2?

L256: Remove comma.

L268: Another comma I think should be removed.

Fig. 1: Please use consistent names (not only here but throughout the manuscript – there is a mixture e.g. of “SSP5-3.4-OS”, “ssp534-os” and “ssp534-over”), avoid too many abbreviations (“ROC”), use subscripts for CO₂. “1pctCO2” is instead a combination of “1pctCO2” and “1pctCO2-cdr”, I don’t think this has been made clear. Maybe term this combination “1pctCO2-1pctCO2cdr” (or simply “1pctCO2-cdr” as it is an extension of “1pctCO2”) and use this name throughout the manuscript?

L326: “(Fig. 2c,d)” should be moved to end of the sentence.

L329ff: Not sure I understand this interpretation, it sounds as if the carbon does not need to be released without climate warming. I think what you mean instead is that more initial carbon uptake happens in the BGC simulation and this extra carbon is then released? Also I think warming reduces the land carbon sink in SSP5-3.4-OS rather than increasing the source?

L332: Remove second comma.

L414ff: I find this unclear. Is the mechanism that “cropland grid cells” in this scenario tend to keep/increase their cropland fraction until the end of the century so they don’t benefit much from CO2 fertilization?

L416: I understand what you mean but one could argue land-use change is affected by atmospheric CO2. Change e.g. to “We note that land use change is an input rather than a feedback process in our simulations.”

L431: I am not sure I understood how the numbers were calculated. Is it the cumulative carbon flux between year 70 and 210 (so without hysteresis and perfect reversibility it would be 0)?

Fig. 5,8: Are b) and e) really needed?

Fig. 7c:  “.ppm” should be “/ppm”. Can you also add a legend?

Fig. 8: Change “fdbk” to “feedback”.

L628: But other carbon losses would likely also increase for a higher TCR, so the contribution might be the same?

L629: Typo NortESM2-LM.

Fig. 9: The white areas (croplands) in the right figure are hardly distinguishable from areas with small changes. Consider using grey colour instead.

L686: These grid cells seem pretty far north to be used for croplands. Can you checker whether there is indeed some cropland expansion happening there? Could it also be related to wood harvest which may only be represented in UKESM and CanESM?

L733: “in the SSP5-3.4-OS scenario”. Do you have an idea why the uptake does not occur in 1pctCO2?

L743: This section is very long for a summary and conclusion section. Consider shortening.

L799: Is this really a negative feedback or rather a lag in a positive feedback?

L840: Do you have suggestions for such experiments?

L844f: I don’t understand, isn’t it these interactions that make SSP5-3.4 so difficult to interpret? Why would it not be possible to include e.g. afforestation?

References

Chen et al. (2019): Vegetation structural change since 1981 significantly enhanced the terrestrial carbon sink, Nature Communications, 10, doi: 10.1038/s41467-019-12257-8

Chimuka et al. (2023): Quantifying land carbon cycle feedbacks under negative CO2 emissions, Biogeosciences, 20, doi: 10.5194/bg-20-2283-2023

Krause et al. (2020): Legacy Effects from Historical Environmental Changes Dominate Future Terrestrial Carbon Uptake, Earth’s Future, 8, 10.1029/2020EF001674

Asaadi et al. quantify carbon cycle feedback in scenarios with positive and negative emissions using an ensemble of ESMs. They use cumulative and flux-based carbon cycle feedback metrics to quantify global as well as regional carbon cycle feedbacks. They also use a decomposition approach to quantify the contribution of various carbon cycle processes to carbon-concentration feedback strength. They find that the carbon-concentration and carbon-climate feedbacks as well as the uncertainty in these feedbacks increase during the negative emissions phase.

The manuscript is a valuable contribution to a small existing body literature on carbon-cycle feedbacks under negative CO2 emissions. It is mostly well written, clearly structured and informative. There are, however, several aspects that need to be addressed before the paper is acceptable for publication in Biogeociences.

• Non-CO2 radiative forcing in SSP3.4-OS simulations. The inclusion of non-CO2 radiative forcing in SSP5-3.4OS simulations hampers the comparability of carbon cycle feedbacks with the idealized 1pctco2 simulation. The temperature changes induced by non-CO2 forcings are significant in some models and the response to these changes in the BGC simulations confounds the response to changes in atmospheric CO2. Given this complication, along with the effect of residual land-use changes and the small period of net negative emissions in SSP5-3.4OS, I would like to encourage the authors to think about whether inclusion of this scenario in the paper is warranted. The paper is quite long and a stronger focus would be beneficial. If the authors decide to retain analysis of the SSP3.4-OS simulations in the manuscript, a more in-depth discussion of the non-CO2 induced temperature effects is needed.
• Hysteresis: The manuscript describes in the hysteresis in the integrated land and ocean carbon flux response to changes in CO2 and temperature, but misses to provide an explanation for why this hysteresis may occur. Identification of possible causes (e.g. lagged response to forcing) could help to explain some effects described in the paper (see specific comments).
• Calculation of feedback metrics: The authors chose to calculate the feedback metrics during the negative emissions phase using the same reference year (pre-industrial) as for the positive emissions phase. This leads to feedback metrics being ill-defined as the pre-industrial state is approached in the ramp-down phase of the 1pctco2 simulation. An alternative approach has been proposed (Chimuka et al., 2023) that uses the time of transition from positive to net negative emissions as the reference year. The advantage of such an approach is that it quantifies carbon cycle feedbacks specifically under conditions of declining atmospheric and cooling, which is consistent with the stated objective of the manuscript (l. 134-145). These alternative approaches should at least be acknowledged and discussed.
• Description of model results lacks precision in some instances (see specific comments).

Specific comments

l 19: The goal of the Paris Agreement is to limit warming to “well below 2°C” above pre-industrial levels.

l 45, “exhausted within the next few decades”. Decades -> years. Include reference to updated carbon budget estimates in Forster et al., 2023.

l 50-51: Include more recent references, e.g. IPCC Synthesis Report, State of CDR report (Smith et al., 2023).

l 118: A recently published study by Chimuka et al. explores land carbon cycle feedbacks under negative emissions. Please include reference.

l 138-139: “We briefly explore … the impact of alternative metrics”. The need for alternative metrics in mentioned in the Conclusions, but the paper does not include an exploration of these metrics. Please rephrase.

l 173-174: Please clarify whether the assumption DT_BGC=0 was used in the calculation of feedback metrics for 1pctCO2 and SSP5-3.4-OS simulations; for the latter this assumption is not justified due to non-CO2 forcings applied in the BGC simulation.

l 306: “smaller magnitude of the temperature anomaly”. I think this should read “larger magnitude”.

l 308-309; “suggests that a substantial part of the carbon-climate feedback…”. Unclear how you reach this conclusion. Please explain.

l 324-325: “the terrestrial CO2 source … is larger….”: Models with a larger terrestrial sink have a larger source in the ramp-down phase of the BGC simulation. This suggests that these models have a larger sensitivity (DC_L/DCO2) to both atmospheric CO2 increase and decrease.

l 369: Which “simulations”?

l 372 (and elsewhere in sections 3.2.1 and 3.2.): “the ocean carbon-concentration feedback is larger…”. Need to explain how the magnitude of feedbacks is inferred. I assume you are using the slope but his needs to be clarified.

l 408: It is worth pointing out that, in contrast to the ocean, the integrated atmosphere-land flux starts to increase, albeit with a lag, in response to cooling in the negative emissions phase in most models.

l 411-413: “This is because…”. This needs to be explained and justified more clearly. Are you saying that because “cropland grid cells” have a smaller cumulative flux in the SSP-3.4-OS simulations, this can also be expected for grid cells with a cropland fraction <25%?

l 415: “driver”: How about the role of non-CO2 forcings in SSP5-3.4-OS?

l 424: “remains very similar”: Several models show significant differences (MIROC, CanESM, UKESM).

l 439-442: It would be helpful if the authors could point to potential causes for the hysteresis, such as lagged response to forcing and/or tipping points/state changes. This could also help with the interpretation of results. E.g. if the larger concentration-carbon feedback in some models is dominated by tree-PFTs (which appears to be the case based on the statement in l. 658-659), the longer response timescale of these PFTs could explain why models with a larger carbon-concentration feedback also have larger hysteresis.

l 509-510: “This implies …”: The fact that feedback metrics as calculated in this study become ill-defined at the end of the 1pctCO2 simulation is not a problem of the metrics themselves, but the choice of reference year used for the calculation of the anomalies in the ramp-down phase. An alternative that addresses this problem is to use the transition year from positive to negative emissions as reference year (see Chimuka et al., 2023).

l 516-517: To interpret this increase in model uncertainty it would be valuable if the authors could address the additional processes that become relevant in ramp-down phase. E.g. the uncertainties would be expected to increase if models exhibits different lag times in response to the prior CO2 increase.

l 654.: “consistent with the lagged response”: this is the first time a lagged response is mentioned. The possibility of such responses should be discussed earlier in the context of hysteresis.

l 683-685: This inference is incorrect. Calculating the metrics assuming DT_BGC=0 changes the value of the feedback parameter, but does not remove the confounding effect of non-CO2 induced warming on beta.

l 685-687: It would be helpful if cropland grid cells that were omitted in the global feedback metric calculations could be clearly identified in the maps in Figs. 9 and 10 for both the 1pctco2 and SSp5-3.4-OS simulations (e.g. by a contour line delineating these grid cells).

l 700-701: “predominantly negative value of gamma_o”: by closely looking at the maps it looks like gamma_o exhibits a banded pattern of positive and negative values.

l 756-757: “Hysteresis is stronger relative..”. Sentence unclear. Please rephrase.

l 774-775: The singularity of beta and gamma at the end of the 1pctco2 simulation is not a problem of the experimental design but the choice of reference year.

l 782-783: Unclear what is meant by “relative strength of the feedback”.

l 798-790: This “additional component of uncertainty” could be the different response timescales exhibited by the models in response to prior forcing. See earlier comment.

l 799: “strong negative feedback”: Unclear which feedback you are referring to.

l 805: Given these complications as well as the complications arising due to inclusion of non-CO2 forcing, what is the value of including these simulations in the feedback analysis?

l 825: “these metrics become difficult to interpret”: discuss alternative approaches proposed in Chimuka et al., 2023.

References

Chimuka et al., 2023. Quantifying land carbon cycle feedbacks under negative CO2 emissions. Biogeosciences. 20: 2283–2299, https://doi.org/10.5194/bg-20-2283-2023.

Forster et al., 2023. (2023). Indicators of Global Climate Change 2022: annual update of large-scale indicators of the state of the climate system and human influence. Earth System Science Data. 15: 2295–2327, https://doi.org/10.5194/essd-15-2295-2023.

Smith et al., 2023, Ths state of carbon dioxide removal, https://www.stateofcdr.org/