Decomposition of the Zero Emissions Commitment into thermal warming pipeline and carbon buffering components

Sanderson, Benjamin M.; Sandstad, Marit; Romero-Prieto, Alejandro; Jenkins, Stuart; Koven, Charles; Peters, Glen; Séfèrian, Roland; MacDougall, Andrew H.; Seshadri, Ashwin; Brovkin, Victor; Dunne, John; Swann, Abigail L. S.; Koenigk, Torben; Fisher, Rosie A.; Hohn, David; Ilyina, Tatiana; Jones, Chris D.; Li, Hongmei; Lawrence, Peter; Liddicoat, Spencer; Mengis, Nadine; Romanou, Anastasia; Sentman, Lori T.; Smith, Chris; Steinert, Norman J.; Tjiputra, Jerry; Ziehn, Tilo

doi:10.5194/egusphere-2026-1875

Preprints

https://doi.org/10.5194/egusphere-2026-1875

Preprints

19 May 2026

| 19 May 2026

Decomposition of the Zero Emissions Commitment into thermal warming pipeline and carbon buffering components

Benjamin M. Sanderson, Marit Sandstad, Alejandro Romero-Prieto, Stuart Jenkins, Charles Koven, Glen Peters, Roland Séfèrian, Andrew H. MacDougall, Ashwin Seshadri, Victor Brovkin, John Dunne, Abigail L. S. Swann, Torben Koenigk, Rosie A. Fisher, David Hohn, Tatiana Ilyina, Chris D. Jones, Hongmei Li, Peter Lawrence, Spencer Liddicoat, Nadine Mengis, Anastasia Romanou, Lori T. Sentman, Chris Smith, Norman J. Steinert, Jerry Tjiputra, and Tilo Ziehn

Abstract. The Zero Emissions Commitment (ZEC), the residual warming after anthropogenic CO₂ emissions cease, remains poorly constrained and directly affects remaining carbon budget calculations. We fit a simple coupled carbon-climate model to ten Earth System Models (ESMs) in the flat10 Model Intercomparison Project. Near-zero multi-model mean ZEC can be decomposed into unrealised ocean warming contributing roughly +0.2 K at 50 years post-cessation, which is almost exactly offset by ~-0.2 K of cooling from atmospheric CO₂ drawdown into land and ocean carbon sinks. Yet the thermal term carries more than twice the inter-model spread of the carbon term; as such, in the context of current ESMs, reducing ZEC uncertainty depends more strongly on equilibrium climate sensitivity and the slow ocean heat uptake timescale than on carbon-cycle parameters. Individual models split into a carbon-dominated majority (eight of ten, negative ZEC) and a thermal-dominated minority (positive ZEC), distinguished primarily by their realised warming fraction and equilibrium climate sensitivity. The simple model yields a compact analytical formula for ZEC in terms of component climate and carbon-cycle parameters, reproducing ESM-simulated values to within ~0.03 K (less than 5% of the ~0.6 K inter-model spread). The decomposition also reveals that the carbon cycle buffers ZEC against uncertainty in committed warming to an existing energetic imbalance: recent downward revisions of the realised warming fraction (the ratio of transient to equilibrium warming) imply substantially more committed warming at fixed atmospheric composition, yet this additional heat is strongly attenuated before it appears in ZEC. A reduction of 10 per cent in the realised warming fraction would increase the radiatively committed warming by ~0.5 K at cessation, but this shifts the 50-year ZEC by only ~0.05 K. This allows potential for process-level constraints on climate and carbon-cycle components on ZEC to narrow carbon budgets. Out-of-sample testing on the flat10-cdr experiment shows that CO₂ predictions diverge from ESMs within ~50 years of the emission trajectory departing from the training rate, so the framework does not extend to full climate reversibility under sustained negative emissions. Structural limitations, including under-sampled land biosphere diversity across ESMs, may further emerge at higher warming levels or on multi-centennial timescales.

How to cite. Sanderson, B. M., Sandstad, M., Romero-Prieto, A., Jenkins, S., Koven, C., Peters, G., Séfèrian, R., MacDougall, A. H., Seshadri, A., Brovkin, V., Dunne, J., Swann, A. L. S., Koenigk, T., Fisher, R. A., Hohn, D., Ilyina, T., Jones, C. D., Li, H., Lawrence, P., Liddicoat, S., Mengis, N., Romanou, A., Sentman, L. T., Smith, C., Steinert, N. J., Tjiputra, J., and Ziehn, T.: Decomposition of the Zero Emissions Commitment into thermal warming pipeline and carbon buffering components, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2026-1875, 2026.

Received: 01 Apr 2026 – Discussion started: 19 May 2026

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Preprint (PDF, 6717 KB)

Supplement (2032 KB)

Download & links

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-1875', Anonymous Referee #1, 10 Jul 2026
This manuscript presents an elegant analytical framework that decomposes the ZEC into thermal warming pipeline and carbon buffering components using a coupled impulse response carbon cycle model and two-layer energy balance model. The framework is fitted to flat10MIP simulations from multiple Earth system models, reproduces the simulated CO2 and temperature evolution well, and provides a physically intuitive interpretation of the processes governing ZEC and inter-model differences. I found the manuscript interesting and believe it makes a valuable contribution. The manuscript is well written, the analytical derivations appear mathematically sound, and the figures support the main conclusions.
Main comments:
I found the treatment of the efficacy parameter ε to be the most confusing aspect of the methodology. Section 2 introduces ε as part of the model formulation, while Section 3 describes an 11-parameter fitting workflow in which stage 2 fits only C_f, C_s, λ_f, and γ. Later, Figures 2 and 6 discuss ε alongside the other parameters. The supplement makes clear how ε is handled separately from the principal optimisation, including its estimation from TOA radiation data for only a subset of models. I would therefore recommend adding a short paragraph in the main text that explicitly states which parameters are fitted in the principal calibration, how ε is treated and which figures draw on the separately diagnosed efficacy values.

Equation (4) is a reasonable first-order carbon-climate feedback parameterisation, but it is also an important simplifying assumption in the framework. Because the same temperature-dependent scaling is applied to all finite uptake pools, with the remainder assigned to the effective permanent airborne fraction, I think the manuscript would benefit from one or two additional sentences clarifying that this is intended as a simple effective description of the overall carbon sink response rather than implying that each physical carbon reservoir responds in the same way to warming. I also found the reported ranges of ζ difficult to reconcile: Table 1 gives a range of 0.01–0.06 K-1, supplement S1 refers to fitted values around 0.03-0.06 K-1, whereas Figure 2 and Tables S2 and S3 indicate values clustered much closer to 0.11-0.20 K-1. I would appreciate it if the authors could clarify the apparent discrepancy between these values.

Minor comments:
Line 380: Just before Equation (18), the eigenmodes are labelled using j∈{f,s}, whereas earlier the manuscript distinguishes the physical boxes (f,s) from the eigenmodes (j=1,2). Please use consistent notation to avoid confusion.

Figure 2 should state in the caption or main text where the green-star “published ECS values” come from.

Figures 6 and 10 refer to analyses over nine ESMs, while the main calibration framework is described for ten models. It would be helpful to state which model is omitted from these analyses and why.

Figure 6 appears to label the carbon-climate feedback as something like γ_c in the axis labelling, whereas the text elsewhere consistently uses ζ. Please harmonise this notation.

Line 265: The sentence “Equal weighting between the two experiments is somewhat arbitary” contains a typo: should be “arbitrary”.

Line 617: The sentence “In a another model…” should be “In another model”.

Please check the supplementary-section cross-references. The eigendecomposition and eigenvector discussions in Section 2 point to S4 but appear to belong to S3 (e.g. line 183); the efficacy extension in Section 4.4 points to S3 but should be S4 (line 445); and the longer-timescale extension points to S4 but should be S5 (line 446).

Overall, I found this to be a strong and novel manuscript that provides a clear and useful analytical framework for interpreting the ZEC. My comments are largely aimed at improving the clarity of the methodology, parameter interpretation and presentation rather than questioning the underlying scientific conclusions.
The data used in the study are publicly available through the archive cited in the manuscript. I did not install or execute the analysis code, but I inspected the jupyter notebooks provided to reviewers and based on this inspection, the figures appear to be reproducible from the provided code.
Citation: https://doi.org/10.5194/egusphere-2026-1875-RC1
- AC1:
  'Response to Reviewer 1', Benjamin Sanderson, 31 Aug 2026
  Many thanks for a careful and constructive report, including the close reading of the parameter tables. The comment on the carbon-climate feedback parameter ζ (M2) pointed to a bug relating to the prior bound, and in considering this we widened our C4MIP-informed prior range (justification below). As such, we think the current version is more defensible on both counts – many thanks for this and for the overall assessment:
  “Overall, I found this to be a strong and novel manuscript that provides a clear and useful analytical framework for interpreting the ZEC. My comments are largely aimed at improving the clarity of the methodology, parameter interpretation and presentation rather than questioning the underlying scientific conclusions.”
  Widening the ζ prior required refitting the full ensemble including numbers, figures and parameter tables. The central near-cancellation result is unchanged, and slightly cleaner. Our point-by-point replies follow.
  Main comments
  M1. Treatment of the efficacy parameter ε
  “I found the treatment of the efficacy parameter ε to be the most confusing aspect of the methodology. Section 2 introduces ε as part of the model formulation, while Section 3 describes an 11-parameter fitting workflow in which stage 2 fits only C_f, C_s, λ_f, and γ. […] I would therefore recommend adding a short paragraph in the main text that explicitly states which parameters are fitted in the principal calibration, how ε is treated and which figures draw on the separately diagnosed efficacy values.”
  Thanks – we agree that this was under-explained. R2 raised the same issue. We have added a paragraph to the fitting section that states the eleven fitted parameters directly, with efficacy held at ε = 1 in the main fit. The text then explains why efficacy is kept out of that fit:
  “Stages 1 and 2 fit 11 (of the total 12) parameters: seven describing the carbon cycle […] and four the two-box climate model […]. These are fitted to the CO₂ and temperature trajectories of both experiments, with the efficacy held at ε = 1. The 12th parameter, ε, is degenerate with γ when only surface temperature is constrained (Sect. 2.2) and so is not identifiable from the flat10 temperature record alone. We instead diagnose ε separately from the top-of-atmosphere radiative imbalance, which is available for eight of the ten ESMs (MPI-ESM1-2-LR and UVic-ESCM-2.10 lack the required fields).”
  We now clarify which analyses use the diagnosed efficacy values (the efficacy panel of the parameter figure, the pattern-effect discussion, the Supplementary efficacy extension) and which rest on the eleven-parameter fits (the ZEC decomposition itself).
  M2. Equation (4) as an effective description, and the ζ range discrepancy
  “I also found the reported ranges of ζ difficult to reconcile: Table 1 gives a range of 0.01–0.06 K^-1, supplement S1 refers to fitted values around 0.03–0.06 K^-1, whereas Figure 2 and Tables S2 and S3 indicate values clustered much closer to 0.11–0.20 K^-1.”
  Many thanks for catching this. The error was in Table 1 and the supplement text, not in the fits. Figure 2 and Tables S2 and S3 showed the correct fitted values; Table 1 and the supplement sentence instead carried an old placeholder that was never a fitted result. We have since done a complete audit, and the figures, Table 1 and the supplement now all report the same fitted range.
  In the process, we re-assessed our prior assumptions for ζ. The upper bound on ζ was 0.2 K^-1 in the preprint, informed by the C4MIP carbon-climate feedback CMIP6 multi-model mean plus one standard deviation. However, four of the ten models were fitted against that bound in the posterior, with several more whose ensemble 5–95% intervals reached it, so the reported ζ range was truncated by the prior. Given this, we widened the bound to 0.4 K^-1, beyond the strongest documented C4MIP feedback, and refitted the whole ensemble.
  The preprint ζ 5–95% interval was [0.11, 0.20], now [0.12, 0.32] with a median of 0.20 K^-1. As such, all models’ optimum result now falls within the prior range (but the tail is still truncated in some cases):
  “a small tail (6 of the 500 pooled members, confined to ACCESS-ESM1-5 and GFDL-ESM4) reaches the 0.4 K^-1 prior ceiling, so the upper end of the ζ range is likewise partly prior-limited.”
  This adjustment improved the fit at every approximation level, and does not change the headline results about thermal/carbon near-cancellation.
  “Equation (4) […] I think the manuscript would benefit from one or two additional sentences clarifying that this is intended as a simple effective description of the overall carbon sink response rather than implying that each physical carbon reservoir responds in the same way to warming.”
  Added, following the reviewer’s suggestion:
  “ζ scales carbon uptake, allowing a lever on sink weakening under warming, but does not distinguish between processes (ocean solubility, land productivity, respiration). It is not directly comparable to the purely diagnostic C4MIP carbon-climate feedback parameter γ, which is derived from counterfactual experiments.”
  We tried to quantify this caveat: converting ζ to the C4MIP parameter (γ = −ζ × U₀, with U₀ the no-feedback cumulative uptake at cessation) and comparing against Arora et al. (2020) for the overlapping models suggests the following:
  ζ implies a feedback several times stronger than the 1pctCO2 value at a comparable CO₂ level.
  
  Across the seven overlapping models, we find the implied fitted γ correlates well with the ocean part of the C4MIP feedback but not with the land part or the total, suggesting that ζ is primarily representing ocean uptake (perhaps due to a structural constraint, given that the three-pool IRF is structurally an ocean-carbon model, so ζ reflects ocean processes), but the land feedback dominates the inter-model spread (Arora et al., 2020). As a result, the ζ calibrated on net CO₂ largely represents the ocean feedback and the signal from land-dominated γ cannot be reliably fitted.
  
  We state both points in the manuscript, with the appropriate caveats (seven overlapping models; a significant ocean correlation but only an absent land correlation rather than demonstrated independence; non-identical model configurations; and the dependence of the extensive γ on the evaluation point). A third diagnostic we ran but do not report is that ζ, atmospheric CO₂ and temperature are near-collinear during the flat10 emission phase (r about 0.99), so a ζ calibrated on this experiment cannot cleanly separate concentration-driven from temperature-driven uptake – which reinforces the same conclusion. We agree that the reviewer’s point “not every reservoir responds identically” is correct, and that ζ should be seen as an effective total sink-weakening parameter, not related directly to γ.
  We have added a short Discussion subsection on this (“Carbon-climate land feedbacks have less impact at low warming levels”), given that it applies to any reduced-complexity model that applies a single temperature feedback to an impulse-response carbon cycle (such as FaIR): an aggregate feedback constrained by net CO₂, calibrated in a relatively cool regime, tracks the ocean feedback and is likely to under-represent the land feedback that dominates carbon-cycle spread across ESMs.
  One consequence for our own results is that the small inter-model spread we find in the carbon component is partly a feature of the (relatively) cool flat10 regime rather than evidence that carbon-cycle uncertainty is intrinsically small, and we see this in the out-of-sample results.
  In the process, we did a wider assessment of priors to ensure that fits were not bumping against our prior range. The lower prior bound on λ_f (0.30 W m^-2 K^-1) imposes a hard ECS ceiling of about 12.3 K, and 13% of ensemble members sit on it, so the submitted “5th–95th: 2.1–12.4 K” was reporting a prior bound as an inferred limit. We have not widened λ_f – as it is an effective indication that the flat10 experiment does not provide a clean upper bound on ECS. We state now that the upper tail is prior-limited: “Its upper 5th–95th bound of 12.4 K is not an inferred limit but the λ_f prior floor […]: 13% of members sit at this ceiling. The flat10 protocol constrains ECS from below but not from above.”
  Second, per-model ZEC skill is limited, which we explain (ZEC50 with an RMSE of about 0.10 K, comparable to the roughly 0.12 K inter-model spread), so individual-model values are weakly constrained. CNRM-ESM2-1 (climate R² = 0.90) is the clearest case: the emulator assigns it +0.19 K, whereas the ESM’s own ZEC50 is near zero (−0.06 K). We now add these caveats for individual models, while noting that the multi-model distribution is more robust because these errors are not systematic. We also note that two models somewhat trade off CO₂ and temperature fit skill.
  Minor comments
  m1. Eigenmode notation
  “Line 380: Just before Equation (18), the eigenmodes are labelled using j in {f,s}, whereas earlier the manuscript distinguishes the physical boxes (f,s) from the eigenmodes (j=1,2). Please use consistent notation to avoid confusion.”
  Corrected: the eigenmode sum now reads j ∈ {1,2}. Reviewer 2 notes the same confusion, which we now address generally: (f,s) is used only for the physical boxes and (1,2) only for the eigenmodes throughout the paper and supplement. We also added a statement at first mention that the eigenmodes are not the boxes (“each is a fixed linear combination of the two box temperatures that relaxes on its own single timescale”), and a note that the carbon-pool timescales τ_i and the climate eigenmode timescales are different (noted by R2).
  m2. Provenance of the green stars in Figure 2
  “Figure 2 should state in the caption or main text where the green-star ‘published ECS values’ come from.”
  The caption now clarifies that CMIP6 values are from Zelinka et al. (2020), and the two non-CMIP6 models (HadCM3LC-Bris and UVic-ESCM-2.10) come from their model descriptions.
  m3. Nine versus ten ESMs in Figures 6 and 10
  “Figures 6 and 10 refer to analyses over nine ESMs, while the main calibration framework is described for ten models. It would be helpful to state which model is omitted from these analyses and why.”
  Apologies for this – the reference to nine models came from an earlier version of the analysis and the caption was a typo. Now fixed: 10 models throughout, apart from the efficacy plots (only eight models have the top-of-atmosphere radiation diagnostics).
  m4. γ_c versus ζ in Figure 6
  “Figure 6 appears to label the carbon-climate feedback as something like γ_c in the axis labelling, whereas the text elsewhere consistently uses ζ. Please harmonise this notation.”
  Fixed: now using ζ throughout.
  m5. Typos
  “Line 265: […] ‘somewhat arbitary’ […] should be ‘arbitrary’.” / “Line 617: ‘In a another model…’ should be ‘In another model’.”
  Both corrected.
  m6. Supplementary cross-references
  “Please check the supplementary-section cross-references. The eigendecomposition and eigenvector discussions in Section 2 point to S4 but appear to belong to S3 […]; the efficacy extension […] points to S3 but should be S4 […]; and the longer-timescale extension points to S4 but should be S5.”
  Apologies for this – we had hard-coded cross-references which became misaligned. Now switched to automatically resolved cross-section and equation references.
  Code and data availability
  “[…] based on this inspection, the figures appear to be reproducible from the provided code.”
  Thanks. The code has been updated to use the updated priors and subsequent analysis from this revision.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1875-AC1
RC2:
'Comment on egusphere-2026-1875', Anonymous Referee #2, 04 Aug 2026

The manuscript by Sanderson et al. attempts to use an analytical framework to distinguish between and quantify the contributions to ZEC from 1) thermal warming in the pipeline, and 2) cooling from CO2 drawn down associated with carbon uptake by land and ocean, after cessation of emissions. The analytical model used is sound and based on published studies. The manuscript does a good overall job of illustrating how the analytical model can be used to disentangle the above-mentioned two effects when emissions cease. Overall, this is a very good effort, and this manuscript should be published.

My only critiques are related to clarity, length of the paper, repetitions, and some typos/clarifications for figures. I also attach with this review an annotated PDF with my handwritten comments which contain in more detail all the minor comments. Hopefully, the authors will find my handwriting legible.

1) I found the abstract unclear based on its first read. It’s only after reading the entire manuscript that the abstract became more meaningful to me. Please consider rewriting the entire abstract from a high-level point of view assuming that a reader hasn’t read your paper yet.

2) While thorough, the manuscript is long, and there is a fair bit of repetition. Long manuscripts can hide the overall big message as a reader gets swamped with too much information. Please consider if the manuscript may be shortened.

3) Simplify – as it is written the manuscript assumes that a reader has a good understanding of all aspects of the Earth system. As a carbon cycle person, I found myself looking up on the web the aspects of the 2-box physical climate model described by equations (5) and (6). The same may be true for folks who are more experienced with physical climate system but not so much the carbon cycle. Please consider making the manuscript somewhat easier by simplifying the language and concepts. As an example, as a carbon cycle person, I wasn’t familiar with efficacy (epsilon) and to my simple mind this term was leading to non-conservation of energy in eqns (5) and (6). I had to resort to AI to help explain this. Another example is Section 3.3 where the ensemble generation approach is described. I found this section hard to follow. For example, “wave” in this context is an iteration. Correct? I also found some of the figures very hard to follow/interpret. I have provided a lot of comments in the annotated PDF.

4) Even the relatively simple 2-box model has 12 parameters and complex modes. It’s remarkable that the dynamics of two sets of differential equations can be so complex. I found it hard to keep up with model parameters and symbols. Please consider using text to describe the model parameters throughout the paper even if the parameters have been described earlier on. This is already done at a few places to remind readers what a given parameter is. I suggest doing this throughout the manuscript and more consistently.

Other comments

1) Is deterministic case a special case of ensemble? How?

2) On Line 548 you will see that I confused the range with std. dev. Please use parentheses around 0.145K (the std. dev.) and report the 5-95% range separately.

3) Please consider labelling the subpanels of the figures as a), b), etc. and refer to them in the text as needed.

Citation: https://doi.org/10.5194/egusphere-2026-1875-RC2
- AC2: 'Response to Reviewer 2', Benjamin Sanderson, 31 Aug 2026
  
  We thank the reviewer for the thorough report, and for the annotated manuscript, which helped us clarify the carbon and physical-climate arguments; we have rewritten a good deal of the manuscript to improve this. Thanks also for the overall assessment:
  “The analytical model used is sound and based on published studies. The manuscript does a good overall job of illustrating how the analytical model can be used to disentangle the above-mentioned two effects when emissions cease. Overall, this is a very good effort, and this manuscript should be published.”
  The annotated manuscript was used as a reference – many thanks for the detailed markup. We have processed (but do not explicitly respond to) all annotations. Below we reply to the headline and review comments, grouping the annotated-PDF points by theme. We thank the reviewer for noting the issue of the relative size of the thermal and carbon terms in the pipeline figure, which was an error we address in T6.
  Headline comments
  H1. The abstract needs a rewrite
  “I found the abstract unclear based on its first read. It’s only after reading the entire manuscript that the abstract became more meaningful to me. Please consider rewriting the entire abstract from a high-level point of view assuming that a reader hasn’t read your paper yet.”
  Well taken – the abstract has been rewritten from the top down, so that the mechanism is stated before any detail, and the near-zero mean is framed as a compensation rather than as an absence of change:
  “we show mean compensation between unrealised ocean warming and cooling from CO₂ drawdown into land and ocean sinks at 50 years post-cessation of emissions”
  The abstract then explains that the two terms compensate in the mean but not in their spread, that the thermal term varies about twice as much as the carbon term, and what this implies for which parameters govern ZEC uncertainty. The component magnitudes themselves are now given in the Results and Conclusions rather than the abstract to keep focus on the mechanism.
  H2. Length and repetition
  “While thorough, the manuscript is long, and there is a fair bit of repetition. […] Please consider if the manuscript may be shortened.”
  Thanks for this – we have worked on length throughout the revision. The decomposition now receives a single treatment, the Discussion is tightened, and repeated statements of the mechanism have been consolidated. The revision does also gain material in direct response to comments from both reviewers, including the discussion of the ζ and ECS priors, the efficacy explanation (H3 below), the Section 3.3 rewrite, and a new Discussion subsection on the calibration dependence of the carbon-climate feedback.
  Even so, the main text is now about 10% shorter than the preprint (approximately 15,800 to 14,300 words, excluding equations and references), and carries one fewer figure. The largest reductions are in the Introduction, the physical interpretation of the analytical framework, the Discussion and the Conclusions. The Supplement grows by about 6%.
  H3. Simplify for readers from one side or the other
  “as it is written the manuscript assumes that a reader has a good understanding of all aspects of the Earth system. […] as a carbon cycle person, I wasn’t familiar with efficacy (ε) and to my simple mind this term was leading to non-conservation of energy in eqns (5) and (6). I had to resort to AI to help explain this. Another example is Section 3.3 […] I found this section hard to follow. For example, ‘wave’ in this context is an iteration. Correct?”
  Thanks for this – R1 also raised the efficacy half of it independently.
  For efficacy: the apparent problem is that ε multiplies the heat-exchange term in the fast equation but not in the slow equation – apparently violating conservation. We now explain that only γ(T_f − T_s) is transferred to the deep ocean; the extra (ε − 1)γ(T_f − T_s) is an enhanced radiative loss to space under the ocean-uptake warming pattern, represented by the top-of-atmosphere flux N. We give the fast-box energy balance in full with all four terms (radiative response, pattern-enhanced radiative loss to space, deep-ocean uptake and fast-box internal storage).
  On Section 3.3: “wave” does mean an iteration. We add the reviewer’s requested references (adaptive Latin Hypercube Sampling after McKay et al., 1979, with history matching, Williamson et al., 2013), to justify the 3× RMSE threshold, and the relationship of the deterministic fit to the ensemble. We now define the realised warming fraction, out-of-sample, and q_eff when they first appear.
  H4. Restate parameter meanings throughout
  “I found it hard to keep up with model parameters and symbols. Please consider using text to describe the model parameters throughout the paper even if the parameters have been described earlier on. This is already done at a few places […]”
  Thanks for the annotations to this point, which helped us improve the notation. Key parameters are now briefly re-explained when raised in Results and Discussion, so γ reads as “the ocean heat exchange coupling”, τ₂ as the slow climate timescale, and so on.
  Other comments
  O1. Is the deterministic case a special case of the ensemble, and isn’t this over-fitting?
  “Sorry is deterministic fit a special case of the ensemble. How?” / “Isn’t this the definition of over-fitting?”
  Thanks for this point. We now address over-fitting in the rewritten Section 3.3. The deterministic fit is the single least-squares optimum – but it is not used directly, and the ensemble is the set of parameter vectors that reproduce the same ESM almost as well: a candidate is retained when both its CO₂ and its temperature RMSE fall below three times the deterministic-fit RMSE (subject to small floors). The deterministic fit therefore has two roles: seeding the search and fixing the retention threshold (each member is judged relative to the deterministic error rather than an absolute one). The ensemble is then the region of parameter space around it that the data do not rule out at that tolerance, so its 5–95% range is a not-ruled-out plausibility range and is framed as such.
  On over-fitting, we address this concern by changing our downsampling strategy and increasing our sample size. Our previous downsampling kept the ten best-scoring members per model, which narrowed every reported range; selection is now random and the target is raised from 10 to 50 per model, so the spreads are wider and a better representation of the uncertainty associated with random model fits which are consistent with the not-ruled-out space. Because the retention threshold is a fixed multiple of each model’s own deterministic RMSE, a poorly fitted model gets a looser threshold and a wider ensemble. We would argue this is somewhat desirable, given that models which cannot be well fitted deterministically because of the structural response of the emulator should have less well defined parameter values than a case where the emulator cleanly captures the global mean evolution – but we accept this is a design choice, and we state this.
  O2. Standard deviation reported as a range
  “Please use parentheses around 0.145 K (the std. dev.) and report the 5–95% range separately.”
  Adopted throughout – parenthesising the standard deviation and reporting the 5–95% range in a separate clause.
  O3. Label subpanels
  “Please consider labelling the subpanels of the figures as a), b), etc. and refer to them in the text as needed.”
  Done. The figures with discrete panels (Figs. 4, 5, 8, 10 and 11) now carry (a), (b), … labels, and the captions and text refer to them. The remaining multi-panel figures (Figs. 1, 2, 7 and 9) are regular grids in which each panel is identified by the ESM or parameter it shows, so we have kept the row/column labelling there rather than adding letters.
  Points from the annotated PDF, by theme
  The margin comments cluster into a small number of themes. We address them here rather than one at a time.
  T1. RAZE is under-introduced
  First use now defines RAZE as the fractional rate, in units of “per year”, at which CO₂-induced warming changes once emissions cease. Both the thermal adjustment and the effective carbon-uptake rates are “per-year” fractional changes in post-cessation warming; sharing units, the terms subtract to give the net rate.
  T2. Modes versus boxes
  Also raised by R1. We did a global notation sweep so that (f,s) is used only for the physical boxes and (1,2) only for the eigenmodes. On introduction, we note that the eigenmodes are not the boxes but fixed linear combinations of them defined by timescale. Further, we note that the carbon-pool timescales and the climate eigenmode timescales are different objects and not directly comparable.
  T3. Derivation steps that lose the reader
  Several inline equations are now written in full, and we have made an effort to clarify the role and source of each equation and solution. The eigendecomposition step is now properly introduced.
  T4. “Thermal pipeline”
  The reviewer objected to “thermal pipeline”, suggesting instead “warming in the pipeline”. We considered this – however, “thermal pipeline” is used specifically for the thermal-only quantity (associated with holding CO₂ fixed), to keep it distinct from the net post-cessation change, which is what MacDougall’s “warming in the pipeline” considers as a stand-in for ZEC itself. As such, we rewrote its definition to make the distinction explicit on introduction and throughout.
  T5. Figure legibility
  The figures have been regenerated with these comments in hand: subplot letters added, legends and labels enlarged and relabelled, shorthand spelled out.
  T6. Figure updates
  Figure 9: for the three-row sensitivity figure, there was some confusion about the purpose of the figure (“Does this mean A not equal B + C?”). We now clarify that the three rows are three representative ESMs representing different ZEC regimes, not three additive components of one decomposition, and the caption clarifies this.
  Figure 10: the reviewer noted “the red lines have a much smaller magnitude than blue lines. what am I missing?”. Apologies – this was a (diagnostic) plotting error which impacted this figure only. We corrected it to the correct expression from the forward model: the thermal and carbon curves are now near-equal and opposite, as should be expected, at least near the ensemble-average realised warming fraction. The thermal curve tracks the committed pipeline and grows as RWF falls, while the carbon offset is nearly independent of RWF. Many thanks for catching this.
  T7. “Out-of-sample” is unclear
  “You have results from 10 ESMs, what’s sample and what’s out of sample.”
  Clarified. The text now states that the model is calibrated on flat10 and flat10-zec, and validated on flat10-cdr.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1875-AC2

Supplement

https://doi.org/10.5194/egusphere-2026-1875-supplement

Data sets

Global Mean flat10 data Ben Sanderson et al. https://doi.org/10.5281/zenodo.15267556

Viewed

Total article views: 669 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	Supplement	BibTeX	EndNote
468	152	49	669	69	36	43

HTML: 468
PDF: 152
XML: 49
Total: 669
Supplement: 69
BibTeX: 36
EndNote: 43

Views and downloads (calculated since 19 May 2026)

Month	HTML	PDF	XML	Total
May 2026	189	58	12	259
Jun 2026	29	14	4	47
Jul 2026	131	32	5	168
Aug 2026	52	20	16	88
Sep 2026	67	28	12	107

Cumulative views and downloads (calculated since 19 May 2026)

Month	HTML	PDF	XML	Total
May 2026	189	58	12	259
Jun 2026	29	14	4	47
Jul 2026	131	32	5	168
Aug 2026	52	20	16	88
Sep 2026	67	28	12	107

Viewed (geographical distribution)

Total article views: 552 (including HTML, PDF, and XML) Thereof 552 with geography defined and 0 with unknown origin.

Country	#	Views	%

Cited

Latest update: 18 Sep 2026

Short summary

When humanity stops emitting carbon dioxide, will temperatures keep rising, stabilize, or fall? Our study reveals in most models, temperatures remain nearly stable, but this hides a balance between the warming in response to radiation imbalance, and the cooling due to uptake of carbon in the land and ocean. Understanding this balance helps refine how much more CO₂ we can safely emit.


Total:	0
HTML:	0
PDF:	0
XML:	0

Decomposition of the Zero Emissions Commitment into thermal warming pipeline and carbon buffering components

Supplement

Data sets

Viewed

Viewed (geographical distribution)

Cited

1 citations as recorded by crossref.