Anticorrelation of Net Uptake of Atmospheric CO<sub>2</sub> by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models

Schwartz, Stephen E.

doi:https://doi.org/10.5194/egusphere-2024-748

Preprints

https://doi.org/10.5194/egusphere-2024-748

Preprints

22 May 2024

| 22 May 2024

Anticorrelation of Net Uptake of Atmospheric CO₂ by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models

Stephen E. Schwartz

Abstract. The rate at which atmospheric carbon dioxide (CO₂) would decrease in response to decrease of anthropogenic emissions or cessation (net zero emissions) is of great scientific and societal interest. Such decrease in atmospheric CO₂ on the centennial scale would be due essentially entirely to transfer of carbon into the world ocean (WO) and the terrestrial biosphere (TB), which are sink compartments on this time scale. The rate of decrease of excess atmospheric CO₂ and the apportionment of this decrease into the two sink compartments has been examined in two prior model intercomparison studies, subsequent either to a pulse emission of CO₂ or to abrupt cessation of anthropogenic CO₂ emissions. The present study examines and quantifies inter-model anticorrelation in those studies in the net rate and extent of uptake of CO₂ into the two sink compartments. Specifically, in each study the time-dependent coefficients characterizing the net transfer rate into the two sink compartments, (evaluated as the net transfer rate normalized to excess atmospheric CO₂ above pre-pulse amount, for the pulse experiment; or as the net transfer rate divided by excess atmospheric CO₂ above preindustrial amount, for the abrupt cessation experiment) was found to exhibit strong anticorrelation across the participating models. That is, models for which the normalized rate of uptake into the WO was high exhibited low uptake rate into the TB, and vice versa. This anticorrelation in net transfer rate results in anticorrelation in net uptake extent into the two compartments that is substantially greater than would be expected simply from competition for excess CO₂ between the two sink compartments. This anticorrelation, which is manifested in diminished inter-model diversity, can lead to artificially enhanced confidence in current understanding of the consequences of potential future reductions of CO₂ emissions and in the global warming potentials of non-CO₂ greenhouse gases relative to that of CO₂.

Received: 13 Mar 2024 – Discussion started: 22 May 2024

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Journal article(s) based on this preprint

15 Nov 2024

Anticorrelation of net uptake of atmospheric CO₂ by the world ocean and terrestrial biosphere in current carbon cycle models

Stephen E. Schwartz

Biogeosciences, 21, 5045–5057, https://doi.org/10.5194/bg-21-5045-2024,https://doi.org/10.5194/bg-21-5045-2024, 2024

Short summary

Stephen E. Schwartz

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-748', Andrew MacDougall, 30 May 2024

Review: Anticorrelation of Net Uptake of Atmospheric CO2 by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models
Overall Evaluation:

The manuscript used results from two prominent model intercomparison projects of Earth system models to show that uptake of carbon by the terrestrial biosphere and ocean are anti-correlated, beyond the degree one would expect from conservation of mass. The analysis is convincing and the the paper is well written. I believe that the paper can be published pending minor revisions.
General Comments:

(1) It would be helpful in the Introduction to briefly describe the principle underlying processes that drive ocean (air-sea gas exchange) and land (photosynthesis and respiration) carbon uptake .
Specific Comments:

Line 82: Please re-write sentence for clarity.
Line 87: J13 has also been used to tune the FAIR climate emulator (e.g. Smith et al. 2018), a very commonly used climate emulator.
Figure 1 (and other in the same format): The extra lines on panel d and e are visually distracting. Though they do add scientific value, the lines obscure the main point of these panels.
Line 231 to 232: Did you intend to refer to Figure 3 here?
Line 269: Note quite correct. Simulations stopped when 1000PgC of cumulative emissions was diagnosed. By coincidence this is almost the same point in time that most models reach 2X CO₂.
Figure 4: Metadata for this figure is visible.
Line 429: Fire is also a major contributing factor to inter-annual variability in the land carbon uptake (e.g. Di Virgilio et al. 2019).
Line 454 to 475: Far too main abbreviations in these two paragraphs. I recommend writing all of them out except 'GWP', which is a common abbreviation.
Line 486 to 496: I suspect tuning models to match the Keeling curves may be the source of the anti-correlation. Virtually all ESM try to replicate the curve as a test of their carbon-cycles.

References:

Smith CJ, Forster PM, Allen M, Leach N, Millar RJ, Passerello GA, Regayre LA. FAIR v1. 3: a simple emissions-based impulse response and carbon cycle model. Geoscientific Model Development. 2018 Jun 18;11(6):2273-97.
Giovanni Di Virgilio, Jason P Evans, Stephanie AP Blake, Matthew Armstrong, Andrew J Dowdy,Jason Sharples, and Rick McRae. Climate change increases the potential for extreme wildfires. Geophysical Research Letters, 46(14):8517–8526, 2019.

Citation: https://doi.org/10.5194/egusphere-2024-748-RC1
- AC2: 'Reply on RC1', Stephen E. Schwartz, 27 Aug 2024
  
  Response (2024-0827) to RC1: 'Comment on egusphere-2024-748', Andrew MacDougall, 30 May 2024
  I appreciate the Reviewer's attention to the manuscript and generally positive and helpful comments. I am especially pleased that the Reviewer finds the analysis convincing and the paper well written.
  Review: Anticorrelation of Net Uptake of Atmospheric CO2 by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models
  
  Overall Evaluation:
  
  The manuscript used results from two prominent model intercomparison projects of Earth system models to show that uptake of carbon by the terrestrial biosphere and ocean are anti-correlated, beyond the degree one would expect from conservation of mass. The analysis is convincing and the the paper is well written. I believe that the paper can be published pending minor revisions.
  
  General Comments:
  
  (1) It would be helpful in the Introduction to briefly describe the principle underlying processes that drive ocean (air-sea gas exchange) and land (photosynthesis and respiration) carbon uptake .
  
  A short para is added describing the underlying processes. I thank the reviewer for the suggestion
  
  Specific Comments:
  
  Line 82: Please re-write sentence for clarity.
  
  The sentence is divided into two.
  
  Line 87: J13 has also been used to tune the FAIR climate emulator (e.g. Smith et al. 2018), a very commonly used climate emulator.
  
  I thank the Reviewer for calling attention to this. A sentence to this effect has been added.
  
  Figure 1 (and other in the same format): The extra lines on panel d and e are visually distracting. Though they do add scientific value, the lines obscure the main point of these panels.
  
  The reviewer notes that the curves (thin curves, green, cyan, brown) that show indivdual instances add scientific value, but he finds them distracting. I would prefer to leave them in the figure as they give a sense of the extent of fluctuations of individual pairings of sets of (k_O, k_T) pairs. I think the reader will figure it out.
  
  Line 231 to 232: Did you intend to refer to Figure 3 here?
  
  Yes. Thank you. Corrected.
  
  Line 269: Note quite correct. Simulations stopped when 1000PgC of cumulative emissions was diagnosed. By coincidence this is almost the same point in time that most models reach 2X CO2.
  
  Corrected
  
  Figure 4: Metadata for this figure is visible.
  
  Will be deleted in the final.
  
  Line 429: Fire is also a major contributing factor to inter-annual variability in the land carbon uptake (e.g. Di Virgilio et al. 2019).
  
  Added (but without citation)
  
  Line 454 to 475: Far too many abbreviations in these two paragraphs. I recommend writing all of them out except 'GWP', which is a common abbreviation.
  
  I have looked over these two paras. The first para (beginning line 545 in the original, 471 in the revision) introduces (and defines) only the abbreviation AGWP, in addition to well known abbreviations IRF and IPCC.
  
  The second para (beginning line 464 in the original, 481 in the revision) introduces (and defines) only ncghg and introduces ghg, in addition to the AGWP, and IPCC previously introduced and GWP, which it specifically defines.
  
  On re-reading these paras, I feel that they do not overly tax the reader and suggest leaving as is.
  
  Line 486 to 496: I suspect tuning models to match the Keeling curves may be the source of the anti-correlation. Virtually all ESM try to replicate the curve as a test of their carbon-cycles.
  
  This comment caused me to think more about the pertinent paragraph. In the revision I avoid the use of the word "tuning" and the phrase "Keeling curve" suggested by the Reviewer. But I note explicitly that in historical runs satisfying the observational requirement of growth in atmospheric CO2 being equal to the difference between emissions and the sum of uptake into the ocean and the TB sets up a potential for anticorrelation in models. I thank the Reviewer for the comment.
  
  I also tightened that paragraph and re-arranged and removed some materials in the section.
  
  References:
  
  Smith CJ, Forster PM, Allen M, Leach N, Millar RJ, Passerello GA, Regayre LA. FAIR v1. 3: a simple emissions-based impulse response and carbon cycle model. Geoscientific Model Development. 2018 Jun 18;11(6):2273-97.
  
  Giovanni Di Virgilio, Jason P Evans, Stephanie AP Blake, Matthew Armstrong, Andrew J Dowdy,Jason Sharples, and Rick McRae. Climate change increases the potential for extreme wildfires. Geophysical Research Letters, 46(14):8517–8526, 2019.
  
  Citation: https://doi.org/10.5194/egusphere-2024-748-AC2
AC1: 'Comment on egusphere-2024-748', Stephen E. Schwartz, 20 Jun 2024

I thank Dr. MacDougall for his overall positive review and for his thoughtful suggestions for the revision. These will be taken into account in the revision.

Citation: https://doi.org/10.5194/egusphere-2024-748-AC1
RC2:
'Comment on egusphere-2024-748', Anonymous Referee #2, 22 Aug 2024

Per se interesting study. Not so easy to read. I have focussed on the part presenting the first model inter comparison study only. The results seem similar though.
Main point of manuscript that there is a trade-off in carbon cycle / earth system model simulations (results from two model inter comparison experiments are being analysed) between uptake of the anthropogenic perturbation of atmospheric carbon by oceans versus land pools is convincing (primarily figures 1 a-c and figure 2a).

Author suggests this is due to
‘… compensating treatments in the several models of the processes that govern uptake of excess CO2’ (excess CO2 defined as ‘atmospheric CO2 above pre-industrial amount’)
and not to ‘competition’ between the two sinks defined as

‘competition between the two sinks for the excess atmospheric CO2 remaining from the pulse at a given time subsequent to
the pulse; if, at a given time, more of this excess CO2 has previously been drawn down into one compartment, there would be
less CO2 available to be drawn down into other compartment’
To disentangle this question the author states / uses
‘As these net transfer coefficients are not dependent on prior uptake, they are not subject to what is denoted here as the competition effect, such that if more CO2 has previously been taken up by one sink compartment there is inevitably less available to be taken up by the other’

I am not sure / convinced this statement is correct (e.g. Revelle effect, land vegetation carrying capacity, land vegetation CO2 fertilization). While I may well be missing something (if so apologies) I do think the author needs to explain convincingly this claim in a revised version.

Author states ‘compensating treatments’ … more concerning ….

While the detected anti-correlation may be of some concern (some implicit constraint on the sum of ocean and land uptake) in my view (looking e.g. at Figure 1) at the 2013 stage off earth system modelling (and probably still in 2024) a much larger concern is that the spread across models of the predicted land carbon uptake of ‘excess atmospheric carbon’ is very large - ranging from nearly zero to very susbtantial uptake. Essentially we are not really in a position to predict how much / whether land carbon pools will have increased or decreased by the year 2100. Thus probably at the current stage of knowledge the issue highlighted by the author of the study is probably a second order problem only.

Minor comments
Figure 1

sometimes the same symbol is used for two different models (e.g. red dots, blue diamonds). Please use different symbols for different models- such that anti-correlation can be spotted / checked visually. Where are the black triangles in figure a ?
please describe in more detail how figures d and e have been calculated
is the regression made on ensemble mean ?
is the regression repeated on
{IRF(1},..., IRF(n)} for n=1, 2, .. 99 ?

why notation dIRF - i.e. why 'd' ? is it not just the the regression slope (i.e. not small increments)
please give more detail
it would be helpful to see all correlation time-series [i.e. for each model in the model suite]
Good to correct a few typos (e.g. ‘that that..’)

Citation: https://doi.org/10.5194/egusphere-2024-748-RC2
- AC3:
  'Reply on RC2', Stephen E. Schwartz, 27 Aug 2024
  Response (2024-0827) to RC2 Anonymous Referee #2, 22 Aug 2024
  Per se interesting study. Not so easy to read. I have focussed on the part presenting the first model inter comparison study only. The results seem similar though.
  Main point of manuscript that there is a trade-off in carbon cycle / earth system model simulations (results from two model inter comparison experiments are being analysed) between uptake of the anthropogenic perturbation of atmospheric carbon by oceans versus land pools is convincing (primarily figures 1 a-c and figure 2a).
  I appreciate the Reviewer's attention to the manuscript. I am especially pleased that the Reviewer finds the argument convincing.
  Author suggests this is due to
  ‘… compensating treatments in the several models of the processes that govern uptake of excess CO2’ (excess CO2 defined as ‘atmospheric CO2 above pre-industrial amount’) and not to ‘competition’ between the two sinks defined as
  ‘competition between the two sinks for the excess atmospheric CO2 remaining from the pulse at a given time subsequent to the pulse; if, at a given time, more of this excess CO2 has previously been drawn down into one compartment, there would be less CO2 available to be drawn down into other compartment’
  To disentangle this question the author states / uses
  ‘As these net transfer coefficients are not dependent on prior uptake, they are not subject to what is denoted here as the competition effect, such that if more CO2 has previously been taken up by one sink compartment there is inevitably less available to be taken up by the other’
  In the above text and quotations from the manuscript the reviewer accurately summarizes the line of reasoning.
  I am not sure / convinced this statement is correct (e.g. Revelle effect, land vegetation carrying capacity, land vegetation CO2 fertilization). While I may well be missing something (if so apologies) I do think the author needs to explain convincingly this claim in a revised version.
  The instantaneous (temporally local) net uptake coefficients (net uptake per excess atmospheric CO2, above preindustrial, depends only on instantaneous rates of uptake into the two compartments. The several processes noted by the Referee affect uptake by the respective compartments but not the "other" compartment. The Revelle effect affects the rate of uptake into the ocean but not the rate of uptake into the TB; the land carrying capacity and fertilization affect the rate of uptake into the TB but not the rate of uptake into the ocean. There is no "cross talk" whereby Revelle effect might affect the rate of uptake into the TB, or where carrying capacity or fertilization could affect the rate of uptake into the ocean. These processes would be expected to have affected the amount of excess atmospheric CO2 present at a given time, resulting in what I have denoted the compensation effect leading to autocorrelation in the amount of CO2 taken up in the two compartments (and indeed this compensation effect is quantified in the manuscript). However examination of the temporally local rates upon temporally local amount of excess CO2 obviates this concern.
  Author states ‘compensating treatments’ … more concerning ….
  While the detected anti-correlation may be of some concern (some implicit constraint on the sum of ocean and land uptake) in my view (looking e.g. at Figure 1) at the 2013 stage off earth system modelling (and probably still in 2024) a much larger concern is that the spread across models of the predicted land carbon uptake of ‘excess atmospheric carbon’ is very large - ranging from nearly zero to very susbtantial uptake. Essentially we are not really in a position to predict how much / whether land carbon pools will have increased or decreased by the year 2100. Thus probably at the current stage of knowledge the issue highlighted by the author of the study is probably a second order problem only.
  The reviewer hits the nail on the head. Looking at Figure 1c (for the Joos intercomparison), the spread in atmospheric IRF at 100 years is about a factor of 2, 0.3 to 0.6 or maybe a factor of about 1.5 about the average. But looking at Figure 1b for the terrestrial IRF, ignoring the one outlier, the range is a factor 4, 0.1 to 0.4 or a factor of 2 about the average. Part of the motivation for the present manuscript is to call attention to this and to try to identify the reason(s) for this. A major contributor is the anticorrelation under examination here.
  There are of course other intrinsic reasons for the spread in IRFs of the Ocean and TB uptake that are rooted in the treatments of the uptake processes in the several models. The point of an intercomparison is to accurately assess the spread, not necessarily to identify the reasons for the spread, but importantly to give some measure of the confidence that can be placed in model results based on spread. This study shows that the spread in the atmospheric IRF, the key quantity that is a measure of that spread, is artificially reduced because of the anticorrelation identified and quantified here.
  Minor comments
  Figure 1
  sometimes the same symbol is used for two different models (e.g. red dots, blue diamonds). Please use different symbols for different models- such that anti-correlation can be spotted / checked visually. Where are the black triangles in figure a ?
  
  I struggled with the line and symbol codes. In the analysis of the J13 results I used the same codes as in the original paper, which used these codes to distinguish model type (comprehensive Earth system models, Earth system models of intermediate complexity, and box models). To distinguish the symbols it seems that I made the symbols too large so that they obscure the underlying symbols. I have reduced the symbol size in Figures 1 and 3 to help better identify the models across the panels. I don't think any approach is "perfect". I do use vector graphics so that the interested reader can zoom in on the screen.
  The black triangles in figure 1a are partly hidden by the green circles and the red diamonds; in the revision they are more discernible toward the left and the right.
  please describe in more detail how figures d and e have been calculated
  
  The quantities shown in Figure 1d are the slopes of the regression fits of IRF_O vs IRF_T as shown in a single example in Figure 2a, all as a function of time t, as stated at lines 100-101. Similarly Figure 3d for k.
  3a. is the regression made on ensemble mean ?
  No. The regression is made in the usual way (see citation to Press et al., 1997), minimizing the sum of squares of the departure of the y distances from the regression line, where the sum is taken over the several models.
  3b. is the regression repeated on IRF(1},..., IRF(n)} for n=1, 2, .. 99 ?
  The quantity plotted in Fig. 1d is {dIRF_O(n)/dIRF_T(n)} for n (year since pulse) =1, 2, .. 99, where the notation dIRF_O(n)/dIRF_T(n) denotes the slope of the regression line obtained by least squares fit of the points IRF_O(i) vs IRF_T(i) for all models i = 1...14. The text refers frequently to "regression slope"; the axis label e.g. Figure 1d, dIRF_O(n)/dIRF_T(n) denotes that slope.
  why notation dIRF - i.e. why 'd' ? is it not just the the regression slope (i.e. not small increments)
  
  Yes, it is slope, as in the slope of a line, dy/dx. dIRF_O/ dIRF_T is a very different quantity from the quantity without the d, IRF_O/ IRF_T.
  please give more detail.
  
  The procedure is presented in detail at lines 138-145 for the IRFs and 156-180 for the net transfer coefficients. The procedure for the randomized pairs is presented in detail at lines 199-208 and 224-258.
  it would be helpful to see all correlation time-series [i.e. for each model in the model suite]
  
  If I correctly understand the referee's query, I would respond that a single model is not correlated. What is shown is time series of the correlation slope (for the set of models) e.g. fig 1d and correlation coefficient (for the set of models) r, e.g., fig 1.
  Good to correct a few typos (e.g. ‘that that..’)
  
  Good catch. I tried to catch them all and had others read the manuscript for that purpose as well as substance; inevitably some still typos seem to have persisted. I have looked the manuscript over again
  
  Citation: https://doi.org/10.5194/egusphere-2024-748-AC3

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-748', Andrew MacDougall, 30 May 2024

Review: Anticorrelation of Net Uptake of Atmospheric CO2 by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models
Overall Evaluation:

The manuscript used results from two prominent model intercomparison projects of Earth system models to show that uptake of carbon by the terrestrial biosphere and ocean are anti-correlated, beyond the degree one would expect from conservation of mass. The analysis is convincing and the the paper is well written. I believe that the paper can be published pending minor revisions.
General Comments:

(1) It would be helpful in the Introduction to briefly describe the principle underlying processes that drive ocean (air-sea gas exchange) and land (photosynthesis and respiration) carbon uptake .
Specific Comments:

Line 82: Please re-write sentence for clarity.
Line 87: J13 has also been used to tune the FAIR climate emulator (e.g. Smith et al. 2018), a very commonly used climate emulator.
Figure 1 (and other in the same format): The extra lines on panel d and e are visually distracting. Though they do add scientific value, the lines obscure the main point of these panels.
Line 231 to 232: Did you intend to refer to Figure 3 here?
Line 269: Note quite correct. Simulations stopped when 1000PgC of cumulative emissions was diagnosed. By coincidence this is almost the same point in time that most models reach 2X CO₂.
Figure 4: Metadata for this figure is visible.
Line 429: Fire is also a major contributing factor to inter-annual variability in the land carbon uptake (e.g. Di Virgilio et al. 2019).
Line 454 to 475: Far too main abbreviations in these two paragraphs. I recommend writing all of them out except 'GWP', which is a common abbreviation.
Line 486 to 496: I suspect tuning models to match the Keeling curves may be the source of the anti-correlation. Virtually all ESM try to replicate the curve as a test of their carbon-cycles.

References:

Smith CJ, Forster PM, Allen M, Leach N, Millar RJ, Passerello GA, Regayre LA. FAIR v1. 3: a simple emissions-based impulse response and carbon cycle model. Geoscientific Model Development. 2018 Jun 18;11(6):2273-97.
Giovanni Di Virgilio, Jason P Evans, Stephanie AP Blake, Matthew Armstrong, Andrew J Dowdy,Jason Sharples, and Rick McRae. Climate change increases the potential for extreme wildfires. Geophysical Research Letters, 46(14):8517–8526, 2019.

Citation: https://doi.org/10.5194/egusphere-2024-748-RC1
- AC2: 'Reply on RC1', Stephen E. Schwartz, 27 Aug 2024
  
  Response (2024-0827) to RC1: 'Comment on egusphere-2024-748', Andrew MacDougall, 30 May 2024
  I appreciate the Reviewer's attention to the manuscript and generally positive and helpful comments. I am especially pleased that the Reviewer finds the analysis convincing and the paper well written.
  Review: Anticorrelation of Net Uptake of Atmospheric CO2 by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models
  
  Overall Evaluation:
  
  The manuscript used results from two prominent model intercomparison projects of Earth system models to show that uptake of carbon by the terrestrial biosphere and ocean are anti-correlated, beyond the degree one would expect from conservation of mass. The analysis is convincing and the the paper is well written. I believe that the paper can be published pending minor revisions.
  
  General Comments:
  
  (1) It would be helpful in the Introduction to briefly describe the principle underlying processes that drive ocean (air-sea gas exchange) and land (photosynthesis and respiration) carbon uptake .
  
  A short para is added describing the underlying processes. I thank the reviewer for the suggestion
  
  Specific Comments:
  
  Line 82: Please re-write sentence for clarity.
  
  The sentence is divided into two.
  
  Line 87: J13 has also been used to tune the FAIR climate emulator (e.g. Smith et al. 2018), a very commonly used climate emulator.
  
  I thank the Reviewer for calling attention to this. A sentence to this effect has been added.
  
  Figure 1 (and other in the same format): The extra lines on panel d and e are visually distracting. Though they do add scientific value, the lines obscure the main point of these panels.
  
  The reviewer notes that the curves (thin curves, green, cyan, brown) that show indivdual instances add scientific value, but he finds them distracting. I would prefer to leave them in the figure as they give a sense of the extent of fluctuations of individual pairings of sets of (k_O, k_T) pairs. I think the reader will figure it out.
  
  Line 231 to 232: Did you intend to refer to Figure 3 here?
  
  Yes. Thank you. Corrected.
  
  Line 269: Note quite correct. Simulations stopped when 1000PgC of cumulative emissions was diagnosed. By coincidence this is almost the same point in time that most models reach 2X CO2.
  
  Corrected
  
  Figure 4: Metadata for this figure is visible.
  
  Will be deleted in the final.
  
  Line 429: Fire is also a major contributing factor to inter-annual variability in the land carbon uptake (e.g. Di Virgilio et al. 2019).
  
  Added (but without citation)
  
  Line 454 to 475: Far too many abbreviations in these two paragraphs. I recommend writing all of them out except 'GWP', which is a common abbreviation.
  
  I have looked over these two paras. The first para (beginning line 545 in the original, 471 in the revision) introduces (and defines) only the abbreviation AGWP, in addition to well known abbreviations IRF and IPCC.
  
  The second para (beginning line 464 in the original, 481 in the revision) introduces (and defines) only ncghg and introduces ghg, in addition to the AGWP, and IPCC previously introduced and GWP, which it specifically defines.
  
  On re-reading these paras, I feel that they do not overly tax the reader and suggest leaving as is.
  
  Line 486 to 496: I suspect tuning models to match the Keeling curves may be the source of the anti-correlation. Virtually all ESM try to replicate the curve as a test of their carbon-cycles.
  
  This comment caused me to think more about the pertinent paragraph. In the revision I avoid the use of the word "tuning" and the phrase "Keeling curve" suggested by the Reviewer. But I note explicitly that in historical runs satisfying the observational requirement of growth in atmospheric CO2 being equal to the difference between emissions and the sum of uptake into the ocean and the TB sets up a potential for anticorrelation in models. I thank the Reviewer for the comment.
  
  I also tightened that paragraph and re-arranged and removed some materials in the section.
  
  References:
  
  Smith CJ, Forster PM, Allen M, Leach N, Millar RJ, Passerello GA, Regayre LA. FAIR v1. 3: a simple emissions-based impulse response and carbon cycle model. Geoscientific Model Development. 2018 Jun 18;11(6):2273-97.
  
  Giovanni Di Virgilio, Jason P Evans, Stephanie AP Blake, Matthew Armstrong, Andrew J Dowdy,Jason Sharples, and Rick McRae. Climate change increases the potential for extreme wildfires. Geophysical Research Letters, 46(14):8517–8526, 2019.
  
  Citation: https://doi.org/10.5194/egusphere-2024-748-AC2
AC1: 'Comment on egusphere-2024-748', Stephen E. Schwartz, 20 Jun 2024

I thank Dr. MacDougall for his overall positive review and for his thoughtful suggestions for the revision. These will be taken into account in the revision.

Citation: https://doi.org/10.5194/egusphere-2024-748-AC1
RC2:
'Comment on egusphere-2024-748', Anonymous Referee #2, 22 Aug 2024

Per se interesting study. Not so easy to read. I have focussed on the part presenting the first model inter comparison study only. The results seem similar though.
Main point of manuscript that there is a trade-off in carbon cycle / earth system model simulations (results from two model inter comparison experiments are being analysed) between uptake of the anthropogenic perturbation of atmospheric carbon by oceans versus land pools is convincing (primarily figures 1 a-c and figure 2a).

Author suggests this is due to
‘… compensating treatments in the several models of the processes that govern uptake of excess CO2’ (excess CO2 defined as ‘atmospheric CO2 above pre-industrial amount’)
and not to ‘competition’ between the two sinks defined as

‘competition between the two sinks for the excess atmospheric CO2 remaining from the pulse at a given time subsequent to
the pulse; if, at a given time, more of this excess CO2 has previously been drawn down into one compartment, there would be
less CO2 available to be drawn down into other compartment’
To disentangle this question the author states / uses
‘As these net transfer coefficients are not dependent on prior uptake, they are not subject to what is denoted here as the competition effect, such that if more CO2 has previously been taken up by one sink compartment there is inevitably less available to be taken up by the other’

I am not sure / convinced this statement is correct (e.g. Revelle effect, land vegetation carrying capacity, land vegetation CO2 fertilization). While I may well be missing something (if so apologies) I do think the author needs to explain convincingly this claim in a revised version.

Author states ‘compensating treatments’ … more concerning ….

While the detected anti-correlation may be of some concern (some implicit constraint on the sum of ocean and land uptake) in my view (looking e.g. at Figure 1) at the 2013 stage off earth system modelling (and probably still in 2024) a much larger concern is that the spread across models of the predicted land carbon uptake of ‘excess atmospheric carbon’ is very large - ranging from nearly zero to very susbtantial uptake. Essentially we are not really in a position to predict how much / whether land carbon pools will have increased or decreased by the year 2100. Thus probably at the current stage of knowledge the issue highlighted by the author of the study is probably a second order problem only.

Minor comments
Figure 1

sometimes the same symbol is used for two different models (e.g. red dots, blue diamonds). Please use different symbols for different models- such that anti-correlation can be spotted / checked visually. Where are the black triangles in figure a ?
please describe in more detail how figures d and e have been calculated
is the regression made on ensemble mean ?
is the regression repeated on
{IRF(1},..., IRF(n)} for n=1, 2, .. 99 ?

why notation dIRF - i.e. why 'd' ? is it not just the the regression slope (i.e. not small increments)
please give more detail
it would be helpful to see all correlation time-series [i.e. for each model in the model suite]
Good to correct a few typos (e.g. ‘that that..’)

Citation: https://doi.org/10.5194/egusphere-2024-748-RC2
- AC3:
  'Reply on RC2', Stephen E. Schwartz, 27 Aug 2024
  Response (2024-0827) to RC2 Anonymous Referee #2, 22 Aug 2024
  Per se interesting study. Not so easy to read. I have focussed on the part presenting the first model inter comparison study only. The results seem similar though.
  Main point of manuscript that there is a trade-off in carbon cycle / earth system model simulations (results from two model inter comparison experiments are being analysed) between uptake of the anthropogenic perturbation of atmospheric carbon by oceans versus land pools is convincing (primarily figures 1 a-c and figure 2a).
  I appreciate the Reviewer's attention to the manuscript. I am especially pleased that the Reviewer finds the argument convincing.
  Author suggests this is due to
  ‘… compensating treatments in the several models of the processes that govern uptake of excess CO2’ (excess CO2 defined as ‘atmospheric CO2 above pre-industrial amount’) and not to ‘competition’ between the two sinks defined as
  ‘competition between the two sinks for the excess atmospheric CO2 remaining from the pulse at a given time subsequent to the pulse; if, at a given time, more of this excess CO2 has previously been drawn down into one compartment, there would be less CO2 available to be drawn down into other compartment’
  To disentangle this question the author states / uses
  ‘As these net transfer coefficients are not dependent on prior uptake, they are not subject to what is denoted here as the competition effect, such that if more CO2 has previously been taken up by one sink compartment there is inevitably less available to be taken up by the other’
  In the above text and quotations from the manuscript the reviewer accurately summarizes the line of reasoning.
  I am not sure / convinced this statement is correct (e.g. Revelle effect, land vegetation carrying capacity, land vegetation CO2 fertilization). While I may well be missing something (if so apologies) I do think the author needs to explain convincingly this claim in a revised version.
  The instantaneous (temporally local) net uptake coefficients (net uptake per excess atmospheric CO2, above preindustrial, depends only on instantaneous rates of uptake into the two compartments. The several processes noted by the Referee affect uptake by the respective compartments but not the "other" compartment. The Revelle effect affects the rate of uptake into the ocean but not the rate of uptake into the TB; the land carrying capacity and fertilization affect the rate of uptake into the TB but not the rate of uptake into the ocean. There is no "cross talk" whereby Revelle effect might affect the rate of uptake into the TB, or where carrying capacity or fertilization could affect the rate of uptake into the ocean. These processes would be expected to have affected the amount of excess atmospheric CO2 present at a given time, resulting in what I have denoted the compensation effect leading to autocorrelation in the amount of CO2 taken up in the two compartments (and indeed this compensation effect is quantified in the manuscript). However examination of the temporally local rates upon temporally local amount of excess CO2 obviates this concern.
  Author states ‘compensating treatments’ … more concerning ….
  While the detected anti-correlation may be of some concern (some implicit constraint on the sum of ocean and land uptake) in my view (looking e.g. at Figure 1) at the 2013 stage off earth system modelling (and probably still in 2024) a much larger concern is that the spread across models of the predicted land carbon uptake of ‘excess atmospheric carbon’ is very large - ranging from nearly zero to very susbtantial uptake. Essentially we are not really in a position to predict how much / whether land carbon pools will have increased or decreased by the year 2100. Thus probably at the current stage of knowledge the issue highlighted by the author of the study is probably a second order problem only.
  The reviewer hits the nail on the head. Looking at Figure 1c (for the Joos intercomparison), the spread in atmospheric IRF at 100 years is about a factor of 2, 0.3 to 0.6 or maybe a factor of about 1.5 about the average. But looking at Figure 1b for the terrestrial IRF, ignoring the one outlier, the range is a factor 4, 0.1 to 0.4 or a factor of 2 about the average. Part of the motivation for the present manuscript is to call attention to this and to try to identify the reason(s) for this. A major contributor is the anticorrelation under examination here.
  There are of course other intrinsic reasons for the spread in IRFs of the Ocean and TB uptake that are rooted in the treatments of the uptake processes in the several models. The point of an intercomparison is to accurately assess the spread, not necessarily to identify the reasons for the spread, but importantly to give some measure of the confidence that can be placed in model results based on spread. This study shows that the spread in the atmospheric IRF, the key quantity that is a measure of that spread, is artificially reduced because of the anticorrelation identified and quantified here.
  Minor comments
  Figure 1
  sometimes the same symbol is used for two different models (e.g. red dots, blue diamonds). Please use different symbols for different models- such that anti-correlation can be spotted / checked visually. Where are the black triangles in figure a ?
  
  I struggled with the line and symbol codes. In the analysis of the J13 results I used the same codes as in the original paper, which used these codes to distinguish model type (comprehensive Earth system models, Earth system models of intermediate complexity, and box models). To distinguish the symbols it seems that I made the symbols too large so that they obscure the underlying symbols. I have reduced the symbol size in Figures 1 and 3 to help better identify the models across the panels. I don't think any approach is "perfect". I do use vector graphics so that the interested reader can zoom in on the screen.
  The black triangles in figure 1a are partly hidden by the green circles and the red diamonds; in the revision they are more discernible toward the left and the right.
  please describe in more detail how figures d and e have been calculated
  
  The quantities shown in Figure 1d are the slopes of the regression fits of IRF_O vs IRF_T as shown in a single example in Figure 2a, all as a function of time t, as stated at lines 100-101. Similarly Figure 3d for k.
  3a. is the regression made on ensemble mean ?
  No. The regression is made in the usual way (see citation to Press et al., 1997), minimizing the sum of squares of the departure of the y distances from the regression line, where the sum is taken over the several models.
  3b. is the regression repeated on IRF(1},..., IRF(n)} for n=1, 2, .. 99 ?
  The quantity plotted in Fig. 1d is {dIRF_O(n)/dIRF_T(n)} for n (year since pulse) =1, 2, .. 99, where the notation dIRF_O(n)/dIRF_T(n) denotes the slope of the regression line obtained by least squares fit of the points IRF_O(i) vs IRF_T(i) for all models i = 1...14. The text refers frequently to "regression slope"; the axis label e.g. Figure 1d, dIRF_O(n)/dIRF_T(n) denotes that slope.
  why notation dIRF - i.e. why 'd' ? is it not just the the regression slope (i.e. not small increments)
  
  Yes, it is slope, as in the slope of a line, dy/dx. dIRF_O/ dIRF_T is a very different quantity from the quantity without the d, IRF_O/ IRF_T.
  please give more detail.
  
  The procedure is presented in detail at lines 138-145 for the IRFs and 156-180 for the net transfer coefficients. The procedure for the randomized pairs is presented in detail at lines 199-208 and 224-258.
  it would be helpful to see all correlation time-series [i.e. for each model in the model suite]
  
  If I correctly understand the referee's query, I would respond that a single model is not correlated. What is shown is time series of the correlation slope (for the set of models) e.g. fig 1d and correlation coefficient (for the set of models) r, e.g., fig 1.
  Good to correct a few typos (e.g. ‘that that..’)
  
  Good catch. I tried to catch them all and had others read the manuscript for that purpose as well as substance; inevitably some still typos seem to have persisted. I have looked the manuscript over again
  
  Citation: https://doi.org/10.5194/egusphere-2024-748-AC3

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Publish subject to minor revisions (review by editor) (07 Sep 2024) by Paul Stoy

AR by Stephen E. Schwartz on behalf of the Authors (09 Sep 2024) Author's response Author's tracked changes

EF by Lorena Grabowski (11 Sep 2024) Supplement

EF by Lorena Grabowski (12 Sep 2024) Manuscript

ED: Publish as is (13 Sep 2024) by Paul Stoy

AR by Stephen E. Schwartz on behalf of the Authors (17 Sep 2024) Author's response Manuscript

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15 Nov 2024

Anticorrelation of net uptake of atmospheric CO₂ by the world ocean and terrestrial biosphere in current carbon cycle models

Stephen E. Schwartz

Biogeosciences, 21, 5045–5057, https://doi.org/10.5194/bg-21-5045-2024,https://doi.org/10.5194/bg-21-5045-2024, 2024

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Anticorrelation in uptake of atmospheric CO₂ following pulse emission or abrupt cessation of emissions is examined in two key model intercomparison studies. In both studies net transfer coefficients from the atmosphere to the world ocean and the terrestrial biosphere are anticorrelated across models, reducing inter-model diversity in decrease of atmospheric CO₂ following the perturbation, increasing uncertainties of global warming potentials and consequences of prospective emissions reductions.


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Anticorrelation of Net Uptake of Atmospheric CO2 by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models

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Anticorrelation of Net Uptake of Atmospheric CO₂ by the World Ocean and Terrestrial Biosphere in Current Carbon Cycle Models