Quantifying land carbon cycle feedbacks under negative CO<sub>2</sub> emissions

Chimuka, V. Rachel; Nzotungicimpaye, Claude-Michel; Zickfeld, Kirsten

doi:https://doi.org/10.5194/bg-2022-168

Preprints

https://doi.org/10.5194/bg-2022-168

Preprints

05 Sep 2022

| 05 Sep 2022

Status: a revised version of this preprint was accepted for the journal BG and is expected to appear here in due course.

Quantifying land carbon cycle feedbacks under negative CO₂ emissions

V. Rachel Chimuka, Claude-Michel Nzotungicimpaye, and Kirsten Zickfeld

Abstract. Land and ocean carbon sinks play a major role in regulating atmospheric CO₂ concentration and climate. However, their future efficiency depends on feedbacks in response to changes in atmospheric CO₂ concentration and climate, namely the concentration-carbon and climate-carbon feedbacks. Since carbon dioxide removal is a key mitigation measure in emission scenarios consistent with global temperature goals in the Paris agreement, understanding carbon cycle feedbacks under negative CO₂ emissions is essential. This study investigates land carbon cycle feedbacks under positive and negative CO₂ emissions using an Earth system model driven with idealized scenarios of atmospheric CO₂ increase and decrease, run in three modes. Our results show that the magnitude of carbon cycle feedbacks differs between the atmospheric CO₂ ramp-up (positive emissions) and ramp-down (negative emissions) phases. These differences are likely largely due to climate system inertia: the response in the ramp-down phase represents the response to both the prior positive emissions and negative emissions. To isolate carbon cycle feedbacks under negative emissions and quantify these feedbacks more accurately, we propose a novel approach that uses zero emissions simulations to reduce this inertia. We find that the magnitudes of the concentration-carbon and climate-carbon feedbacks under negative emissions are larger in our novel approach than in the standard approach. This has two implications: using feedback parameters from the standard approach will (1) underestimate carbon release under negative emissions due to the concentration-carbon feedback, and (2) underestimate carbon gain due to the climate-carbon feedback. Given that the concentration-carbon feedback is the dominant feedback, quantifying carbon cycle feedbacks with the standard approach will result in the underestimation of carbon loss under negative emissions, thereby overestimating the effectiveness of negative emissions in drawing down CO₂.

Received: 25 Aug 2022 – Discussion started: 05 Sep 2022

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V. Rachel Chimuka et al.

Status: closed

RC1:
'Comment on bg-2022-168', Anonymous Referee #1, 04 Oct 2022

The comment was uploaded in the form of a supplement: https://bg.copernicus.org/preprints/bg-2022-168/bg-2022-168-RC1-supplement.pdf

Citation: https://doi.org/10.5194/bg-2022-168-RC1
- AC1: 'Reply on RC1', Rachel Chimuka, 16 Nov 2022
  
  Please see the attached document for our response to Anonymous Referee #1.
  
  Citation: https://doi.org/10.5194/bg-2022-168-AC1
CC1:
'Comment on bg-2022-168', Irina Melnikova, 12 Oct 2022
The authors explore carbon cycle feedbacks under an idealized 1%CO2-CDR overshoot scenario using an intermediate complexity model UVic ESCM and introduce a novel approach that uses zero emissions simulations to reduce the climate system inertia when quantifying feedback parameters during the ramp-down period.
I and other co-authors of a closely-related study (Melnikova et al., 2021, hereafter M21) would like to draw the authors’ attention to our study as it may have been overlooked when the authors say:
L85: "Our study complements the only existing study on ocean carbon cycle feedbacks under negative emissions (Schwinger & Tjiputra, 2018) by exploring the behaviour of these feedbacks on land.”
It would be interesting to see a comparison of the analysis of the carbon cycle feedbacks under the idealized 1%CO2-CDR scenario with SSP5-3.4-OS scenario, and I would be pleased to provide the data if the authors are interested.
Particularly, in M21 (section “4.2. The Peaks of Land and Ocean Carbon Uptakes”), we discuss the balance between GPP and TER that could be useful for the proposed analysis by the authors on balance between NPP and soil respiration.
Most importantly, the conclusions of this new study sound somewhat opposite to the conclusions of M21 where we stated that: “The carbon cycle feedback parameters amplify after the CO₂ concentration and temperature peaks … so that land and ocean absorb more carbon per unit change in the atmospheric CO₂ change (stronger negative feedback) and lose more carbon per unit temperature change (stronger positive feedback) compared to if the feedbacks stayed unchanged”. In contrast, the study by Chimuka et al. concludes on a “reduced carbon loss due to the concentration-carbon feedback and reduced carbon gain due to the climate-carbon feedback.”
I am curious about what drove the discrepancy in the conclusions and encourage the authors to add some discussion that could be useful for the scientific community and could prevent any confusion about the conclusions.
While I am not sure for the reasons that drove the discrepancy, I speculate it could be (i) the methodology used to calculate the feedback parameters (i.e., in this study, “Feedbacks under negative emissions are computed at the return to preindustrial levels (end of ramp-down phase) using changes in carbon pools, atmospheric CO2 concentration, and surface air temperature computed relative to the time of peak atmospheric CO2”, while M21 computed them relative to piControl). In fact, for our M21 analysis we considered using (1) piControl, (2) time of CO₂ and temperature peaks, and (3) “new equilibrium state” at the end of the simulation. However, we chose (1) because using (2) in the more “realistic” SSP scenario would result in too small values of ∆CO₂ and temperature during most part of the ramp-down phase, resulting in ill-defined quantities. Besides, UVic ESCM shows no lag between the peaks of CO₂ concentration and global surface temperature but it is not the case in some of the more complex models (e.g., Boucher et al., 2012, shows a lag of temperature peak over the ocean; in M21, the lag of temperature peak is up to 30 years, depending on the ESM). The discrepancy in conclusions of the two studies could also be due to (ii) the proposed method to remove the impact of climate inertia by using additional zero-emission simulations. Finally, (iii) the discrepancy could root in the difference between the idealized 1%CO2-CDR and SSP5-3.4-OS scenarios (e.g., due to scenario dependency of feedback parameters). I suggest adding discussion on this matter, especially in terms of the implications of translating the conclusions from the idealized scenarios to the more socially-relevant ones.

Other comments are :
L341: “Surface air temperature remains relatively constant in the BGC mode. In the FULL mode, the land switches into a source of carbon after missions cease, consistent with the behaviour of the UVic ESCM in the Zero Emissions Commitment Model Intercomparison Project (ZECMIP)”
Yes, but there is a variety of responses among models in ZECMIP. The UVic’s behavior in ZECMIP is somewhat different from the majority of models (see figures 2.d and 3.a of MacDougall et al 2020). Could some discussion be added?
Also, we would appreciate seeing a comparison of the 'standard' ꞵ and γ (under 1%CO2 experiments) by UVic to the CMIP6 ensemble in a table or figure to get a better idea of where this version of UVic stands.

L426: “Models without a nitrogen cycle exhibit greater land carbon gain under positive emissions relative to other CMIP5 and CMIP6 models, that is, the concentration-carbon feedback parameter is more positive (Table S2). They also exhibit greater carbon loss under positive emissions, that is, the climate-carbon feedback parameter is more negative.”
I am concerned that the authors ignore that the climate-carbon feedback may be both positive (i.e., amplifying climate change) and negative in the colder regions.

L12: “This study investigates land carbon cycle feedbacks under positive and negative CO2 emissions using an Earth system model”
The fact that UVic is not an ESM but EMIC should be made clear throughout the manuscript.

I hope these comments are useful.
Irina Melnikova, with the inputs of co-authors of Melnikova et al. (2021)

References:
Boucher, O., Halloran, P.R., Burke, E.J., Doutriaux-Boucher, M., Jones, C.D., Lowe, J., Ringer, M.A., Robertson, E. and Wu, P., 2012. Reversibility in an Earth System model in response to CO2 concentration changes. Environmental Research Letters, 7(2), p.024013. http://dx.doi.org/10.1088/1748-9326/7/2/024013

MacDougall, A. H., Frölicher, T. L., Jones, C. D., Rogelj, J., Matthews, H. D., Zickfeld, K., Arora, V. K., Barrett, N. J., Brovkin, V., Burger, F. A., Eby, M., Eliseev, A. V., Hajima, T., Holden, P. B., Jeltsch-Thömmes, A., Koven, C., Mengis, N., Menviel, L., Michou, M., Mokhov, I. I., Oka, A., Schwinger, J., Séférian, R., Shaffer, G., Sokolov, A., Tachiiri, K., Tjiputra , J., Wiltshire, A., and Ziehn, T., 2020. Is there warming in the pipeline? A multi-model analysis of the Zero Emissions Commitment from CO2, Biogeosciences, 17, 2987–3016, https://doi.org/10.5194/bg-17-2987-2020

Melnikova, I., Boucher, O., Cadule, P., Ciais, P., Gasser, T., Quilcaille, Y., Shiogama, H., Tachiiri, K., Yokohata, T. and Tanaka, K., 2021. Carbon cycle response to temperature overshoot beyond 2°C: An analysis of CMIP6 models. Earth's Future, 9, e2020EF001967. https://doi.org/10.1029/2020EF001967
Citation: https://doi.org/10.5194/bg-2022-168-CC1
- AC2: 'Reply on CC1', Rachel Chimuka, 16 Nov 2022
  
  Please see the attached document for our response to Irina Melnikova and co-authors of Melnikova et al. (2021)
  
  Citation: https://doi.org/10.5194/bg-2022-168-AC2
RC2:
'Reviewer comment on bg-2022-168', Anonymous Referee #2, 13 Oct 2022
Authors quantify carbon-concentration and carbon-climate feedback for negative emissions for an idealized scenario and compare the magnitude of these feedbacks for the positive emissions part of an idealized scenario. The manuscript is relatively well written and in principle it all makes sense. However, I would suggest improving the manuscript in the following ways.

Please include equations in the main text that should clarify your methodology (where you subtract the effect of zero emissions run on quantities considered during the ramp-down phase). If a picture is worth 500 words, an equation is worth at least 200 words. In the absence of the equations, it is difficult to understand your methodology.

Please introduce your sign notation in the beginning and then use it consistently throughout the manuscript. Recall that carbon-concentration feedback is negative from the atmosphere’s perspective because it reduces atmospheric CO₂ If you use the term “when carbon is gained” then please clarify explicitly which component is gaining carbon - land/ocean or the atmosphere.

Near lines 308-313, I was confused with the sign notation even more because it seems, as you interpret it, sign notation reverses during the ramp-down phase. This needs to be better explained because I am unable to understand why sign notation reversal is needed. If carbon-concentration feedback is negative from an atmosphere’s perspective (let’s say a value of -1.0 Pg C/ppm) this implies that an increase in atmospheric CO2 concentration will be reduced from its initial amount due to this negative feedback. The corollary of this is that if atmospheric CO2 is reducing then the change in CO2 is negative (say -2 ppm) which when multiplied by -1.0 Pg C/ppm yields +2.0 Pg C implying 2 Pg C is added to the atmosphere. All this makes sense in my mind. So why is reversal of sign notation needed?

I would also like to note that feedback parameters are most “realistic” or “relevant” when found using FULL and BGC runs. The real world operates like a fully-coupled simulation. For finding feedback parameters in addition to FULL we need a BGC or RAD simulation. Since the carbon-concentration feedback is the dominant feedback perhaps it makes more sense to use the BGC simulation.

Finally, my last major comment is that when in the real world we do ramp down emissions then, at that point in time, the land and ocean C cycles won’t be in equilibrium with the atmospheric CO2. There will be inertia in the real system, and the response of land and ocean at the time will be affected by this inertia. So is the purpose of attempting to correct the feedback parameters for this inertia on the ramp-down side only to compare them with their ramp-up counterparts?

Minor comments

1. I realize the purpose of Figure 1 is to clarify things but for me text for easier to follow. Perhaps you can try to improve Figure 1.

2. Line 107, “generates permafrost”. Please reword this sentence. I think it is incorrect to say “generate permafrost”. Permafrost is a state which results from sub-zero temperatures.

3. Lines 145-152 need equations to clarify the methodology used.

4. Line 172. “This temperature change is driven by biophysical responses to increasing CO2”. Please add another sentence of explanation at the end of this sentence for completeness.

5. Please put a zero line in Figures 3c,d,e,f, and Figures 4a,b.

6. Lines 258-261 read “ … except in the vegetation carbon pool where the width of the hysteresis increases throughout the simulation (figure 5(c)). The land and ocean carbon pools in the RAD mode also exhibit hysteresis (figure 6). The hysteresis in the land carbon pool is dominated by the soil carbon pool (figure 5(d)), and the width of the hysteresis appears to increase throughout the simulation for all carbon pools except the vegetation carbon, which shows nearly constant hysteresis”.

I am confused here. Please reword clearly. Hysteresis is defined as the difference in paths going up and down. Isn’t hysteresis zero at the point of turn? With this in mind please reword the above sentences.

7. Lines 273-274 read “The ocean holds only 70PgC less than at preindustrial, but unlike the land carbon pool, a miniscule amount of ocean carbon is regained in the ramp-down phase (figure 5d)”.

But Figure 5d is the soil C figure. Please refer to the correct figure.

8. Line 308 reads “For positive emissions, feedback parameters are positive (negative) for a gain (loss) of carbon”. Please consider not using sentences that use pair of parentheses to note two points. This can get very confusing. Also, please clarify whether the gain or loss is by which component – land/ocean or the atmosphere.

9. Line 309 reads “ … resulting in a negative denominator (see supplementary equations 3.3 – 3.6)”.

There is no denominator in these equations. I think I know what’s implied here but it may not be obvious to other readers.

10. Lines 308 – 313. Please use equations here because the sign convention is becoming confusing.

11. Comparison of Figure 5a and S4a shows there’s more hysteresis in BGC run than in the FULL run. Can this be explained? Isn’t this a good reason to use the FULL simulation to find feedback parameters on the ramp-up and ramp-down portions?

12. What does “All” means in Figure 7a legend?

13. Zero emissions runs were initialized from the end of ramp-up. What does BGC and RAD mean for these runs? Do the RAD and BGC runs in Figure 7, see and not see temperature change, respectively, relative to end of the ramp-up or relative to the pre-industrial state? Please clarify.

14. Lines 375-377 read “Under negative emissions, the magnitudes of b[eta] and g[amma] from our novel approach are larger compared to those from the “CDR-reversibility” simulation WHEN RAMPING UP (CORRECT?), implying greater carbon loss due to the concentration-carbon feedback and greater carbon gain due to the climate-carbon feedback under negative emissions”.

“Greater carbon loss” and “greater carbon gain” for what component – land/ocean or atmosphere?

15. Lines 383-384 read “… due to the concentration-carbon feedback, carbon pools take up carbon in the ramp-up phase, continue to take up carbon in the early ramp-down phase.”

Actually, it’s the other way around. Carbon pools don’t behave according to the feedbacks but rather feedbacks are derived from the behavior of the C pools. Please consider rewording.

16. Next two sentences …

“Due to the climate-carbon feedback, carbon pools lose carbon in the ramp-up phase, continue to lose carbon in the ramp-down phase, then switch into carbon sinks”

“… suggesting that land and ocean carbon changes due to carbon cycle feedbacks …”

Here too, please consider rewording.

17. Lines 404-405 read “ … we subtract the zero emissions simulations from the “CDR-reversibility” simulations …”.

Please use equations to show how.

18. Lines 427-428 read “… concentration-carbon feedback parameter is more positive (Table S2)”.

Please clarify if this is from the land’s perspective. Please use a single notation consistently.

19. Lines 428-429 read … “They [i.e. land models with N cycle] also exhibit greater carbon loss under positive emissions, that is, the climate-carbon feedback parameter is more negative”.

This seems incorrect. Note that land models with N cycle typically have a smaller absolute magnitude of carbon-climate feedback because increase in temperature promotes vegetation growth due to enhanced N mineralization which somewhat compensates for increased soil C respiratory losses.

20. Lines 433 – 435 read “With the consideration of nitrogen limitation, the already weakened CO2 fertilization effect under declining CO2 concentrations would be further constrained, exacerbating the carbon loss due to the concentration-carbon feedback”.

This seems like a bit of speculation. Why would this be? It could be the other way around too. If increasing CO2 causes C:N ratios to increase and constrain photosynthesis, more than the case when the N cycle is not represented, then decreasing CO2 should lower C:N ratio and help vegetation photosynthesize a bit more (compared to when the N cycle is not represented).

Of course, overall photosynthesis will still be reducing since CO2 is going down but off the top of my head it’s difficult for me to imagine the effect of N cycle when CO2 is reducing. Perhaps is prudent to not speculate.

21. Finally, what is the CDR-reversibility simulation? Does this refer to both the ramp-up and ramp-down portions or just the ramp-down portion? Note that the ramp-up portion already has a standard experiment name i.e. 1pctCO2. Please clarify this in the beginning and then use the correct terminology throughout the rest of the manuscript.
Citation: https://doi.org/10.5194/bg-2022-168-RC2
- AC3: 'Reply on RC2', Rachel Chimuka, 16 Nov 2022
  
  Please see the attached document for our response to Anonymous Referee #2.
  
  Citation: https://doi.org/10.5194/bg-2022-168-AC3

Status: closed

RC1:
'Comment on bg-2022-168', Anonymous Referee #1, 04 Oct 2022

The comment was uploaded in the form of a supplement: https://bg.copernicus.org/preprints/bg-2022-168/bg-2022-168-RC1-supplement.pdf

Citation: https://doi.org/10.5194/bg-2022-168-RC1
- AC1: 'Reply on RC1', Rachel Chimuka, 16 Nov 2022
  
  Please see the attached document for our response to Anonymous Referee #1.
  
  Citation: https://doi.org/10.5194/bg-2022-168-AC1
CC1:
'Comment on bg-2022-168', Irina Melnikova, 12 Oct 2022
The authors explore carbon cycle feedbacks under an idealized 1%CO2-CDR overshoot scenario using an intermediate complexity model UVic ESCM and introduce a novel approach that uses zero emissions simulations to reduce the climate system inertia when quantifying feedback parameters during the ramp-down period.
I and other co-authors of a closely-related study (Melnikova et al., 2021, hereafter M21) would like to draw the authors’ attention to our study as it may have been overlooked when the authors say:
L85: "Our study complements the only existing study on ocean carbon cycle feedbacks under negative emissions (Schwinger & Tjiputra, 2018) by exploring the behaviour of these feedbacks on land.”
It would be interesting to see a comparison of the analysis of the carbon cycle feedbacks under the idealized 1%CO2-CDR scenario with SSP5-3.4-OS scenario, and I would be pleased to provide the data if the authors are interested.
Particularly, in M21 (section “4.2. The Peaks of Land and Ocean Carbon Uptakes”), we discuss the balance between GPP and TER that could be useful for the proposed analysis by the authors on balance between NPP and soil respiration.
Most importantly, the conclusions of this new study sound somewhat opposite to the conclusions of M21 where we stated that: “The carbon cycle feedback parameters amplify after the CO₂ concentration and temperature peaks … so that land and ocean absorb more carbon per unit change in the atmospheric CO₂ change (stronger negative feedback) and lose more carbon per unit temperature change (stronger positive feedback) compared to if the feedbacks stayed unchanged”. In contrast, the study by Chimuka et al. concludes on a “reduced carbon loss due to the concentration-carbon feedback and reduced carbon gain due to the climate-carbon feedback.”
I am curious about what drove the discrepancy in the conclusions and encourage the authors to add some discussion that could be useful for the scientific community and could prevent any confusion about the conclusions.
While I am not sure for the reasons that drove the discrepancy, I speculate it could be (i) the methodology used to calculate the feedback parameters (i.e., in this study, “Feedbacks under negative emissions are computed at the return to preindustrial levels (end of ramp-down phase) using changes in carbon pools, atmospheric CO2 concentration, and surface air temperature computed relative to the time of peak atmospheric CO2”, while M21 computed them relative to piControl). In fact, for our M21 analysis we considered using (1) piControl, (2) time of CO₂ and temperature peaks, and (3) “new equilibrium state” at the end of the simulation. However, we chose (1) because using (2) in the more “realistic” SSP scenario would result in too small values of ∆CO₂ and temperature during most part of the ramp-down phase, resulting in ill-defined quantities. Besides, UVic ESCM shows no lag between the peaks of CO₂ concentration and global surface temperature but it is not the case in some of the more complex models (e.g., Boucher et al., 2012, shows a lag of temperature peak over the ocean; in M21, the lag of temperature peak is up to 30 years, depending on the ESM). The discrepancy in conclusions of the two studies could also be due to (ii) the proposed method to remove the impact of climate inertia by using additional zero-emission simulations. Finally, (iii) the discrepancy could root in the difference between the idealized 1%CO2-CDR and SSP5-3.4-OS scenarios (e.g., due to scenario dependency of feedback parameters). I suggest adding discussion on this matter, especially in terms of the implications of translating the conclusions from the idealized scenarios to the more socially-relevant ones.

Other comments are :
L341: “Surface air temperature remains relatively constant in the BGC mode. In the FULL mode, the land switches into a source of carbon after missions cease, consistent with the behaviour of the UVic ESCM in the Zero Emissions Commitment Model Intercomparison Project (ZECMIP)”
Yes, but there is a variety of responses among models in ZECMIP. The UVic’s behavior in ZECMIP is somewhat different from the majority of models (see figures 2.d and 3.a of MacDougall et al 2020). Could some discussion be added?
Also, we would appreciate seeing a comparison of the 'standard' ꞵ and γ (under 1%CO2 experiments) by UVic to the CMIP6 ensemble in a table or figure to get a better idea of where this version of UVic stands.

L426: “Models without a nitrogen cycle exhibit greater land carbon gain under positive emissions relative to other CMIP5 and CMIP6 models, that is, the concentration-carbon feedback parameter is more positive (Table S2). They also exhibit greater carbon loss under positive emissions, that is, the climate-carbon feedback parameter is more negative.”
I am concerned that the authors ignore that the climate-carbon feedback may be both positive (i.e., amplifying climate change) and negative in the colder regions.

L12: “This study investigates land carbon cycle feedbacks under positive and negative CO2 emissions using an Earth system model”
The fact that UVic is not an ESM but EMIC should be made clear throughout the manuscript.

I hope these comments are useful.
Irina Melnikova, with the inputs of co-authors of Melnikova et al. (2021)

References:
Boucher, O., Halloran, P.R., Burke, E.J., Doutriaux-Boucher, M., Jones, C.D., Lowe, J., Ringer, M.A., Robertson, E. and Wu, P., 2012. Reversibility in an Earth System model in response to CO2 concentration changes. Environmental Research Letters, 7(2), p.024013. http://dx.doi.org/10.1088/1748-9326/7/2/024013

MacDougall, A. H., Frölicher, T. L., Jones, C. D., Rogelj, J., Matthews, H. D., Zickfeld, K., Arora, V. K., Barrett, N. J., Brovkin, V., Burger, F. A., Eby, M., Eliseev, A. V., Hajima, T., Holden, P. B., Jeltsch-Thömmes, A., Koven, C., Mengis, N., Menviel, L., Michou, M., Mokhov, I. I., Oka, A., Schwinger, J., Séférian, R., Shaffer, G., Sokolov, A., Tachiiri, K., Tjiputra , J., Wiltshire, A., and Ziehn, T., 2020. Is there warming in the pipeline? A multi-model analysis of the Zero Emissions Commitment from CO2, Biogeosciences, 17, 2987–3016, https://doi.org/10.5194/bg-17-2987-2020

Melnikova, I., Boucher, O., Cadule, P., Ciais, P., Gasser, T., Quilcaille, Y., Shiogama, H., Tachiiri, K., Yokohata, T. and Tanaka, K., 2021. Carbon cycle response to temperature overshoot beyond 2°C: An analysis of CMIP6 models. Earth's Future, 9, e2020EF001967. https://doi.org/10.1029/2020EF001967
Citation: https://doi.org/10.5194/bg-2022-168-CC1
- AC2: 'Reply on CC1', Rachel Chimuka, 16 Nov 2022
  
  Please see the attached document for our response to Irina Melnikova and co-authors of Melnikova et al. (2021)
  
  Citation: https://doi.org/10.5194/bg-2022-168-AC2
RC2:
'Reviewer comment on bg-2022-168', Anonymous Referee #2, 13 Oct 2022
Authors quantify carbon-concentration and carbon-climate feedback for negative emissions for an idealized scenario and compare the magnitude of these feedbacks for the positive emissions part of an idealized scenario. The manuscript is relatively well written and in principle it all makes sense. However, I would suggest improving the manuscript in the following ways.

Please include equations in the main text that should clarify your methodology (where you subtract the effect of zero emissions run on quantities considered during the ramp-down phase). If a picture is worth 500 words, an equation is worth at least 200 words. In the absence of the equations, it is difficult to understand your methodology.

Please introduce your sign notation in the beginning and then use it consistently throughout the manuscript. Recall that carbon-concentration feedback is negative from the atmosphere’s perspective because it reduces atmospheric CO₂ If you use the term “when carbon is gained” then please clarify explicitly which component is gaining carbon - land/ocean or the atmosphere.

Near lines 308-313, I was confused with the sign notation even more because it seems, as you interpret it, sign notation reverses during the ramp-down phase. This needs to be better explained because I am unable to understand why sign notation reversal is needed. If carbon-concentration feedback is negative from an atmosphere’s perspective (let’s say a value of -1.0 Pg C/ppm) this implies that an increase in atmospheric CO2 concentration will be reduced from its initial amount due to this negative feedback. The corollary of this is that if atmospheric CO2 is reducing then the change in CO2 is negative (say -2 ppm) which when multiplied by -1.0 Pg C/ppm yields +2.0 Pg C implying 2 Pg C is added to the atmosphere. All this makes sense in my mind. So why is reversal of sign notation needed?

I would also like to note that feedback parameters are most “realistic” or “relevant” when found using FULL and BGC runs. The real world operates like a fully-coupled simulation. For finding feedback parameters in addition to FULL we need a BGC or RAD simulation. Since the carbon-concentration feedback is the dominant feedback perhaps it makes more sense to use the BGC simulation.

Finally, my last major comment is that when in the real world we do ramp down emissions then, at that point in time, the land and ocean C cycles won’t be in equilibrium with the atmospheric CO2. There will be inertia in the real system, and the response of land and ocean at the time will be affected by this inertia. So is the purpose of attempting to correct the feedback parameters for this inertia on the ramp-down side only to compare them with their ramp-up counterparts?

Minor comments

1. I realize the purpose of Figure 1 is to clarify things but for me text for easier to follow. Perhaps you can try to improve Figure 1.

2. Line 107, “generates permafrost”. Please reword this sentence. I think it is incorrect to say “generate permafrost”. Permafrost is a state which results from sub-zero temperatures.

3. Lines 145-152 need equations to clarify the methodology used.

4. Line 172. “This temperature change is driven by biophysical responses to increasing CO2”. Please add another sentence of explanation at the end of this sentence for completeness.

5. Please put a zero line in Figures 3c,d,e,f, and Figures 4a,b.

6. Lines 258-261 read “ … except in the vegetation carbon pool where the width of the hysteresis increases throughout the simulation (figure 5(c)). The land and ocean carbon pools in the RAD mode also exhibit hysteresis (figure 6). The hysteresis in the land carbon pool is dominated by the soil carbon pool (figure 5(d)), and the width of the hysteresis appears to increase throughout the simulation for all carbon pools except the vegetation carbon, which shows nearly constant hysteresis”.

I am confused here. Please reword clearly. Hysteresis is defined as the difference in paths going up and down. Isn’t hysteresis zero at the point of turn? With this in mind please reword the above sentences.

7. Lines 273-274 read “The ocean holds only 70PgC less than at preindustrial, but unlike the land carbon pool, a miniscule amount of ocean carbon is regained in the ramp-down phase (figure 5d)”.

But Figure 5d is the soil C figure. Please refer to the correct figure.

8. Line 308 reads “For positive emissions, feedback parameters are positive (negative) for a gain (loss) of carbon”. Please consider not using sentences that use pair of parentheses to note two points. This can get very confusing. Also, please clarify whether the gain or loss is by which component – land/ocean or the atmosphere.

9. Line 309 reads “ … resulting in a negative denominator (see supplementary equations 3.3 – 3.6)”.

There is no denominator in these equations. I think I know what’s implied here but it may not be obvious to other readers.

10. Lines 308 – 313. Please use equations here because the sign convention is becoming confusing.

11. Comparison of Figure 5a and S4a shows there’s more hysteresis in BGC run than in the FULL run. Can this be explained? Isn’t this a good reason to use the FULL simulation to find feedback parameters on the ramp-up and ramp-down portions?

12. What does “All” means in Figure 7a legend?

13. Zero emissions runs were initialized from the end of ramp-up. What does BGC and RAD mean for these runs? Do the RAD and BGC runs in Figure 7, see and not see temperature change, respectively, relative to end of the ramp-up or relative to the pre-industrial state? Please clarify.

14. Lines 375-377 read “Under negative emissions, the magnitudes of b[eta] and g[amma] from our novel approach are larger compared to those from the “CDR-reversibility” simulation WHEN RAMPING UP (CORRECT?), implying greater carbon loss due to the concentration-carbon feedback and greater carbon gain due to the climate-carbon feedback under negative emissions”.

“Greater carbon loss” and “greater carbon gain” for what component – land/ocean or atmosphere?

15. Lines 383-384 read “… due to the concentration-carbon feedback, carbon pools take up carbon in the ramp-up phase, continue to take up carbon in the early ramp-down phase.”

Actually, it’s the other way around. Carbon pools don’t behave according to the feedbacks but rather feedbacks are derived from the behavior of the C pools. Please consider rewording.

16. Next two sentences …

“Due to the climate-carbon feedback, carbon pools lose carbon in the ramp-up phase, continue to lose carbon in the ramp-down phase, then switch into carbon sinks”

“… suggesting that land and ocean carbon changes due to carbon cycle feedbacks …”

Here too, please consider rewording.

17. Lines 404-405 read “ … we subtract the zero emissions simulations from the “CDR-reversibility” simulations …”.

Please use equations to show how.

18. Lines 427-428 read “… concentration-carbon feedback parameter is more positive (Table S2)”.

Please clarify if this is from the land’s perspective. Please use a single notation consistently.

19. Lines 428-429 read … “They [i.e. land models with N cycle] also exhibit greater carbon loss under positive emissions, that is, the climate-carbon feedback parameter is more negative”.

This seems incorrect. Note that land models with N cycle typically have a smaller absolute magnitude of carbon-climate feedback because increase in temperature promotes vegetation growth due to enhanced N mineralization which somewhat compensates for increased soil C respiratory losses.

20. Lines 433 – 435 read “With the consideration of nitrogen limitation, the already weakened CO2 fertilization effect under declining CO2 concentrations would be further constrained, exacerbating the carbon loss due to the concentration-carbon feedback”.

This seems like a bit of speculation. Why would this be? It could be the other way around too. If increasing CO2 causes C:N ratios to increase and constrain photosynthesis, more than the case when the N cycle is not represented, then decreasing CO2 should lower C:N ratio and help vegetation photosynthesize a bit more (compared to when the N cycle is not represented).

Of course, overall photosynthesis will still be reducing since CO2 is going down but off the top of my head it’s difficult for me to imagine the effect of N cycle when CO2 is reducing. Perhaps is prudent to not speculate.

21. Finally, what is the CDR-reversibility simulation? Does this refer to both the ramp-up and ramp-down portions or just the ramp-down portion? Note that the ramp-up portion already has a standard experiment name i.e. 1pctCO2. Please clarify this in the beginning and then use the correct terminology throughout the rest of the manuscript.
Citation: https://doi.org/10.5194/bg-2022-168-RC2
- AC3: 'Reply on RC2', Rachel Chimuka, 16 Nov 2022
  
  Please see the attached document for our response to Anonymous Referee #2.
  
  Citation: https://doi.org/10.5194/bg-2022-168-AC3

V. Rachel Chimuka et al.

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V. Rachel Chimuka et al.

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Co-editor-in-chief

This study is the first to quantify land carbon cycle feedbacks under decreasing atmospheric CO2 concentration following negative CO2 emissions and compare them to feedbacks under positive emissions. The novel approach presented here reduces the carbon cycle inertia in the phase where atmospheric CO2 concentration decreases in order to improve the quantification of carbon cycle feedbacks under negative emissions. This approach reduced the effectivity of negative emissions in reducing atmospheric CO2, due to larger concentration-carbon and climate-carbon feedbacks.

Short summary

Our findings suggest that carbon cycle feedbacks differ under increasing and decreasing atmospheric CO₂ levels, and the sign and magnitude of the differences depends on the approach taken to quantify the feedbacks. Our study proposes a more accurate approach for quantifying carbon cycle feedbacks under decreasing CO₂ levels and provides insights into the role of carbon cycle feedbacks in determining the effectiveness of carbon dioxide removal in reducing CO₂ levels.


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Quantifying land carbon cycle feedbacks under negative CO2 emissions

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Quantifying land carbon cycle feedbacks under negative CO₂ emissions