Review of “Asymmetry in carbon cycle feedbacks and transient climate response under positive and negative CO₂ emissions” by Chimuka and Zickfeld.

This is a clear and well written manuscript that explores the symmetry of response of the carbon cycle under positive or negative emissions of CO₂. This is an important question, and one of increasing interest as both science and policy are required to think more about aspects of overshoot and reversibility. Much more is known about the climate system in a steadily warming world than one where CO₂ removal leads to cooling. This manuscript contributes to a research agenda to better address this issue.

The paper uses the UVic earth system model of intermediate complexity. This is a model widely used in the literature and suited to exploring this question. While the results from this model are interesting, and the analysis sheds light on processes involved, I find the value of the paper is more in terms of testing an experimental design which could be adopted more widely by other models. We know that such responses are model-dependent and even the sign of behaviour of terms such as ZEC can vary from model to model. So it is not so much that these results are definitive, but that they lead the way for other models to follow and for a wider research initiative into symmetry and reversibility.

I have some minor comments which I list below which I hope the authors find useful to clarify some points.

I do, though, have a major comment about the design and intent of the paper. The more I think about this question, the more I realise that there is a difference between “symmetry” and “reversibility”. It may feel nuanced, but I believe it is important.

The difference is that “symmetry” - as defined in this study - is asking the question “do we see the same response if we go upwards from a starting point or downwards from that same point?”, whereas “reversibility” would ask “do we see the same response going up from one point to another as we do going back down from the second point back to the first?”

Previous studies of reversibility (e.g. Boucher et al 2012, or CDRMIP simulations) have addressed the question of “going back down again”, BUT they have been contaminated by the problem that they have very large legacy effects on the way down because the simulation follows immediately from very strong upwards forcing and is not in steady state. The current authors know this well and discuss it in detail in Chimuka et al (2023). The present study therefore represents a novel experiment design and analysis by equilibrating at a higher level (here 2xCO2), thus avoiding the legacy response in the negative emissions phase. I think this is vital and a very nice experimental design.

However, if the question of interest is whether or not we can recover a previous climate state by the same path in reverse (i.e. does TCRR = TCRE?) then I am not sure that the current experiment answers exactly that question. The asymmetry found in this paper may be because the system response differs above 2xCO2 from below. For example, if TCRE is state-dependent (e.g. lets assume the TCRE gradient gets less steep at higher warming), then we would expect TCRE measured above 2xCO2 to be lower than TCRE measured up to 2xCO2. This would manifest as an asymmetry about 2xCO2 – that’s true. But it does not necessarily imply that reversibility is along different lines. TCRR and TCRE could still be identical to each other. Does that make sense?

A more direct answer to the reversibility question would be to compare your ramp-down experiments here with the ramp-up from 1xCO2 up to 2xCO2. So you can measure a TCRE going from 1xCO2 up to 2xCO2, and then a TCRR going back down (but from an equilibrated state at 2xCO2). I think this then answers the reversibility question.

I think you must have such experiments, but I realise that requesting them (and new analysis) to be added here is a big task. As the manuscript stands it does indeed answer the stated question regarding “symmetry”. But my challenge to the authors is whether or not that is really the target question? Given that work like this will undoubtedly be influential in experimental design for CMIP (CMIP7 and beyond), then making sure that we address the correct questions is as important as making sure we design the experiments to answer them. One option is to keep the present manuscript and be clear that the question asked is on symmetry but does not necessarily reflect reversibility. This opens up the opportunity for a follow-on paper on reversibility. Or a second option would be to add to the current study an analysis of positive vs negative emissions up vs down between the same points.

I appreciate a request for extra analysis is never welcome, but I hope the authors see this a constructive suggestion.

Chris Jones

Minor comments/suggestions:

• Have you thought about pitching the experiments in emissions rather than concentration forcing? I have been a proponent of using concentration-driven runs to diagnose the alpha/beta/gamma feedback metrics because they are in units of “per ppm” so prescribing concentration as the boundary condition makes sense. But for metrics like TCRE/TCRR which are “per GtC of emission”, then prescribing emissions makes sense as a boundary condition. Then it is relatively easy to prescribe simulations with symmetric positive/negative emissions. The consequence here of imposing symmetric % change in concentration is very unsymmetric emissions rates (your fig 1b).
• The fact that it only needs 43 years to reach 3xCO2 feels very short – are you comfortable this is long enough for a reliable signal? Potentially should we look at lower rates and longer runs? If this experiment was adopted for example in ESMs with significant internal variability would this be long enough to robustly diagnose T and carbon fluxes?
• Figure 5 is useful – can you include alpha on here too?
• Sec 3.3 on quantifying the asymmetry and using Jones & Friedlingstein framework. I think you could be clearer here that the J&F framework is simply a way to break open TCRE to see which components matter – but yes it might be approximate. The delta-T/CE and delta-T/CR remain the correct answer and the actual definition of TCRE and TCRR (you say “conventional calculation” – I would make this stronger and say “known values” or similar). Just to be clear that J&F isn’t a rival definition, just a means of understanding
• Fig 6 – instead of plotting these vs time, I wonder if plotting vs Emissions is more relevant? We know the diagnosed emissions are not symmetric so we wouldn’t expect the T vs time to be the same even if TCRE=TCRR. So maybe plotting in emissions space here makes more sense

Review of "Asymmetry in carbon cycle feedbacks and transient climate response under positive and negative CO2 emissions"

Overall assessment:

The study devises a novel experiment design to assess the asymmetry in positive and negative TCRE. This is done by spinning-up an Earth System Model (ESM) at 2X pre-industrial CO2 concentration and carrying out positive and negative emissions experiments from climate equilibrium. Biogeochemically and radiatively coupled CO2 experiments are conducted to decompose the components of the carbon cycle feedbacks. The paper finds that there are substantial asymmetries in positive and negative TCRE driven by complex Earth system responses. Overall the paper is well thought out, thorough and a valuable contribution to negative emissions research. I recommend that the paper undergo minor revisions.

General Comments:

(1) While the need for a new experiment design to quantify asymmetry in TCRE is clearly explained in the introduction, you do not give a clear rationale specifically for your new experimental design. Why is starting simulations from 2X CO2 a good idea? Why not  start at pre-industrial conditions? 

While dropping down to zero CO2 concentration would clearly cause catastrophic strain on any ESMs numerics, you need to explain to the reader why this is a bad experiment design, and why this justifies starting from 2X CO2.

(2) You need to establish that TCRE exists in 2X CO2 world (I highly suspect it does). To do this simple conducted flat-5, flat-10 and flat-15 experiments from the 2XCO2 equilibrium state to 2000 PgC, and make sure that the cumulative emissions vs. temperature curve is linear and path-independent. You can place the figure in the supplementary and add a sentence or two in the main text saying that you checked this.  

Specific comments:

Line 25: Change to either 'year 2100' or '2100 CE'

Line 112: 'several millennia' be specific, give actual numbers.

Line 124: Explanation here can be improved. It is unclear what 'symmetrically' means in this context. 

Line 130: Change 'real world' to 'natural world'

Figure 1b: What are there tails on the flat-10 experiment?

Line 183: Should 'modes' be 'models'? If not a typo please explain more.

Line 260: Please write our 'positive emissions' and 'negative emissions'. 'PE' and 'NE' are not improving the readability of the paper.

Line 261:  Change 'logarithmic' to 'approximately logarithmic'

Figure 4: Please write out all of the abbreviations in the figure legend.

Figure 5: I would suggest using Kelvin units in place of ºC. Have C for carbon and ºC in the same units can lead to confusion.

Figure 6a: Again Kelvin would be preferable. 'TCRE/TCRR' could be written 'TCRE or TCRR' to avoid readers interpreting the former as a division operation.

Line 490: Write out RF and AF. Many readers will read RF as 'radiative forcing'

Line 496: Change 'real world' to 'natural word'

Line 503: Change 'real world' to 'present day' or 'pre-industrial world'. Many paleoclimate states have been close to 2XCO2.

Line 518 to 520: There are versions of the UVic ESCM with fully coupled nitrogen cycle (De Sisto et al. 2024). This should be mentioned here. 

References:

De Sisto, M.L., C. Somes, A. Landolfi, and A. H. MacDougall, 2024: Projecting atmospheric N2O rise until the end of the 21st century: an Earth System Model study, Environmental Research Letters, (12), 124036

This is a review of the manuscript entitled “Asymmetry in carbon cycle feedbacks and transient climate response under positive and negative CO₂ emissions” by Rachel Chimuka and Kirsten Zickfeld. The authors aim to quantify asymmetries in the land and ocean carbon feedbacks and TCRE/TCRR, and test their initial state and rate dependency. They firstly look at the symmetry in response to positive emissions on a 1pctCO2 trajectory from  2 to 3xCO2 and the response to negative emissions from 2 to 1xCO2 (PI). They find that there are asymmetries in the feedback parameters and TCRE and attribute those to the land/ocean processes underlying the changes in carbon inventories and the atmospheric fraction as well as climate sensitivity.

The paper is well written and clear in its methodology and results layout. The approach is novel and UVic provides a testbed to assess its usefulness. To that extent I do not have major comments.  I would like to highlight a few points, some of which the authors already address, perhaps a little in passing, so I would welcome some comments on those points.

• The UVic model and its low-complexity structure with regards to the atmospheric component is casting some uncertainty at how much these results are robust and generalizable. Some missing processes here with regards to the physical climate, e.g. storm track representation, biases in air-sea fluxes, overly stable AMOC, etc make in the sensitivity of the feedback parameters to changes in the climate somewhat uncertain. I would like to know what the feedback parameters & TCRE are in this model compared to the CMIP6/5 ensemble.
• I also wonder how the relative significance of β and γ estimates under fast or slow warming rate as shown in Fig. 5 would compare given the spread of these parameters in models (Arora et al 2020 Fig. 5 -even though they are computed at different levels). In other words, the rate-dependency (especially for the climate-carbon feedback) may not be conclusive if the spread of all the CMIP6 models is considered. Perhaps in subsequent applications of this framework the 3 to 4xCO2 pathway is chosen to make this comparison more straight forward with, say Arora 2020. Similarly, a future application of this framework could be to start the esm-flat10-conc simulations from PI to 1000PgC to make the comparison with temperature and land/ocean carbon responses comparable to other models that performed the flat10 simulations (as in Sanderson et al 2025).
• I am somewhat perplexed about the AMOC in Fig. S1.2. First, maybe a more conventional notation can be used, such as 18Sv rather than 1.8 x10-7 m3/s. Secondly, it seems that at 2xCO2 equilibrium, the AMOC is quite strong. I suppose it weakened with prior emissions (if I judge from the response to subsequent positive emissions) but recovered during the equilibration period? While this makes sense, I am wondering if that maybe masking the response to positive emissions. Typically, the air-sea flux of CO2 saturates somewhere between 2 and 3xCO2 forcing on the 1pct scenario (at least in most models), but if the ocean is left to equilibrate, is the air-sea flux further reduced during the equilibration period? Maybe that is why the ocean sink changes so much slower than the land sink in Fig. 3b and picks up again as the AMOC responds to positive emissions (delayed response compared to the negative emissions). The ocean resists taking up more carbon but gives it up easier. It should be noted also, that equilibrated simulations at high levels of CO2 are difficult to do in ESMs, due to computational cost, if that framework were to be adopted. And that brings me to my last comment.
• If mitigation is to occur, it will probably happen on a transient trajectory rather on an equilibrated trajectory (as in the simulations here). How do we translate the responses of an equilibrated system to those of a transient system which experiences negative emissions. I understand the framework needs equilibrium states to produce “clean” feedback parameters, free from the system’s inertia, but we will have to account for this in the actual system’s response to CDR, for example. Perhaps using this framework in conjunction with Chimuka 2023? Some discussion on these last two points would be very helpful. 

Overall, I think this is an important contribution that aims to untangle the system’s responses to positive and negative emissions, TCRE and TCRR.

Review of "Asymmetry in carbon cycle feedbacks and transient climate response under positive and negative CO₂ emissions" by Chimuka and Zickfeld 

The authors present novel simulations with an Earth system model of intermediate complexity, that allow to determine the asymmetry of carbon cycle feedbacks and TCRE/TCRR under positive and negative emissions. They investigate the rate and state-dependency of their results with additional simulations. They find large asymmetries in all of the metrics investigated and a clear rate-dependance. The manuscript is well written, the experimental design is novel and very relevant to address some of the knowledge gaps surrounding carbon dioxide removal (CDR). I did not find any major problems with the manuscript, and I would recommend publication in Biogeosciences after a few comments and suggestions have been addressed by the authors.

General comments: 

I was a bit disappointed about the discussion related to a comparison of results to the previous study by Chimuka et al. (2023). The authors use only two short sentences on this, stating that the results are inconsistent. Given that the same model was used by the same authors, I would have been curious to learn more. Particularly, since I believe that the setup of Chimuka et al. 2023, i.e. running a zero-emission simulation as a reference to single out the committed changes from previous positive emissions, is much better suited for multi-model studies with full ESMs. I agree that the set-up with a 2x-CO2 reference state used in the present study is a very clean experimental design, but I doubt that CMIP modelling groups will be willing to do a full >1000 year spinup at 2xCO2 as a prerequisite for these experiments. Therefore, it would be extremely valuable to learn more about the reason why the results from these two kinds of experiments are different, and I would encourage the authors to add a more details on this in the  Discussions section.

I was also a bit confused about the definition of the sign of asymmetry. I would suggest to help the reader by including a definition in terms of an Equation. Also, currently, the definition is somewhat hidden in section 3.2.1. I would suggest to move the definition to the beginning of section 3.2 (also since it applies to both land and ocean).

Specific comments:

line 129-130: "that cannot yet be achieved in the real world" This sounds as if the authors would be confident that these levels of negative emission could be achieved in the future. I'm not sure this is intended, and I would suggest to reword this sentence.

line 160 and 164: "twice the preindustrial CO₂ concentration for both simulations" This doesn't hold for the 3xCO₂ and 4xCO₂ simulations, so maybe better "the CO₂ concentration of the respective equilibrium state from which the simulations were branched off" or similar?

line 203-204: "However, this warming is considered negligible in this feedback framework". Arora et al. 2020 and Asaadi et al. 2024 (both cited) have looked at the assumption ΔT_BGC=0 and found that the effect is indeed relatively small.

Equations 7 and 8: I guess ΔT_BGC=0 is assumed also here, too (as in Equations 3 and 4)? I would suggest to adjust Equations 7 and 8 accordingly to not confuse the reader.

lines 238-239: "All changes in variables were calculated relative to the 2xCO₂ (twice the preindustrial CO₂ concentration) equilibrium state." See my comment above, this doesn't hold for the 3x and 4xCO₂.

line 261-262: The logarithmic relationship is not only used by UVic, but widely used in climate sciences (Myre et al. 1998; Etminan et al. 2016). 

line 345: Here you could in addition cite Schwinger et al. 2014 (which is already cited before, note that it is missing in the list of references)

line 355-361: This paragraph is largely repetition of what has been said before for the FULL, because the difference between FULL and BGC is so small. I would suggest to shorten this.

line 373: Delete "land" before "climate-carbon feedback"

lines 388-389: I cannot follow this argument. A larger temperature change under negative emissions means that the land and ocean carbon cycle have actually seen these colder temperatures. A smaller gamma means that land and ocean have reacted less to this cooling per degree of cooling compared to warming. I do not see that the way of calculating would "favour a smaller gamma under negative emissions". Please double check this logic.

line 396: The results on the rate dependency (for positive emissions) are consistent with the early results of Gregory et al. 2009 (cited), this could be mentioned.

line 405: As far as I can see from Fig. S1.3 is at least the sign of the asymmetry the same for both land and ocean across all equilibrium states?

line 474: The correct reference is "Schwinger and Tjiputra (2018)"

line 504: Isn't the sign of the asymmetry robust, as seen from Fig. S1.3?

References:

Etminan, M., G. Myhre, E. J. Highwood, and K. P. Shine (2016), Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the

methane radiative forcing, Geophys. Res. Lett., 43, 12,614–12,623, doi:10.1002/2016GL071930.

Myhre, G., E. Highwood, K. Shine, and F. Stordal (1998), New estimates of radiative forcing due to well mixed greenhouse gases, Geophys. Res.

Lett., 25(14), 2715–2718, doi:10.1029/98GL01908.