the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Aug 2026
Inferred effective climate sensitivity from a selection of CMIP6 models
Abstract. Climate sensitivity is a key metric in climate science, defined as the equilibrium global mean surface temperature response following a doubling of the atmospheric CO2 concentration. Climate sensitivity, which is an idealized concept, can be quantified using different approaches, all with their own limitations. In this study, we employ a method previously used to infer climate sensitivity based on Earth system observations and radiative forcing estimates over the industrialized period, on historical climate model simulations. We estimate climate sensitivity using the transient response in historical simulations from four models contributing to the sixth phase of the Coupled Model Intercomparison Project (CMIP6), with a total of 40 ensemble members. The surface temperature and ocean heat content evolution from each ensemble member is known, effective radiative forcing time series for each model are diagnosed from targeted simulations within CMIP6 and the effective climate sensitivity (ECSeff) for each model is calculated from the abrupt four times CO2 experiment. The inferred effective climate sensitivity (ECSinf) from the transient model response is generally lower than the models’ ECSeff, as expected due to time and state dependencies of climate sensitivity. For different ensemble members, the ECSinf can be quite different. For CNRM-CM6-1, the posterior mean ECSinf varies by 2.2 K among its 30 ensemble members, but the 90 % confidence intervals all contain the model’s ECSeff. The posterior mean ECSinf for HadGEM3 GC3.1-LL varies by as much as 4 K. For NorESM2-LM and NorESM2-MM where the ECSeff is 2.5 K for both models, the posterior mean ECSinf varies by 0.62 K and 1.2 K respectively, and only one of the in total six ensemble members has posterior mean ECSinf larger than ECSeff. Because the observed historical climate represents only one realization of the Earth’s climate, these results highlight the importance of natural variability when estimating climate sensitivity using observations over the historical period and not only the uncertainty in the historical forcing due to aerosols.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-4634', Anonymous Referee #1, 28 Oct 2026
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RC2: 'Comment on egusphere-2026-4634', Kyle Armour, 28 Oct 2026
This paper compares the inferred climate sensitivity (ECSinf), as estimated from historical simulations of GCMs, with the effective climates sensitivity (ECSeff), as estimated from the GCMs’ abrupt4xCO2 simulations. Consistent with previous studies, the main findings are that ECSinf is smaller than ECSeff owing to pattern effects and there is a large spread in ECSinf across ensemble members owing to internal variability.
One key difference from previous studies is that an idealized energy balance model is used which, when constrained by temperature T and OHC changes, allows an estimate of the climate sensitivity parameter (lambda) which directly sets ECSinf. The authors also consider whether this energy balance model can replicate GCM timeseries of T and OHC given the timeseries of ERF, and find that it produces errors, which they attribute in part to the fact that the energy balance model assumes constant ocean heat uptake efficiency when in fact it changes over time in the GCMs.
In general, I like the approach of using GCM output to perform perfect model tests (i.e., to evaluate methods on model otuput where the answer is known, prior to applying those methods to observations). Figure 3, Figures S1-S15, and Section 4 (Discussion) focused on comparing the energy balance model against GCM output seem like a valuable contribution worth writing a paper around; it would help to clarify limitations of this method when applied to observations, for instance.
However, the focus of the paper on ECSinf seems misplaced. Firstly, the main points (that ECSinf from historical simulations is smaller than ECSeff, and that ECSinf has a large spread owing to internal variability) have already been made in previous studies (Dessler et al. 2018; Dong et al. 2021). Secondly, the values of ECSinf found here depend directly on the use of the energy balance model, which as the authors note produces a mismatch with GCM output of T and OHC.
My recommendation is that the authors reconsider the scope of this paper. If they wish to use the energy balance model (as in their previous work), then a paper comparing it directly to the T/OHC output of GCMs after being constrained would be a valuable contribution. Even better would be to compare its 21st century projections against GCM output (e.g., as we’ve done in Nayak et al. 2025).
If they wish to write a paper about ECSinf in GCM historical simulations, then they should use the same methodology as in AR6, Sherwood et al. (2020), Dong et al. (2021), and many other papers to calculate ECSinf without the use of the energy balance model; and they should highlight what new knowledge they’ve contributed. I think a valuable contribution could be the quantification of the ECSinf spread across a broader range of models than were considered previously, and the evaluation of SST patterns in the ensemble members for which ECSinf is most similar or most different from ECSeff (as discussed on L340-360).
Specific comments:
- L46: Proistosescu et al. (2017), Andrews et al. (2018), and Andrews et al. (2022) are key references here.
- L90-105: No justification is given for why this model is used, rather than using the much more standard approach of estimating ECSinf using global energy budget constraints (Otto et al. 2013, Andrews et al. 2018, 2022, Dong et al. 2021, Forster et al. 2021, Sherwood et al. 2020, etc). This would also avoid the issue that your ECSinf values depend on your energy balance model, which does not match GCM output (see above).
- Table 1: Why is the analysis limited to these four GCMs? All data (including historical ERF) are available for MIROC6, CanESM5, and IPSL-CM6A-LR large ensemble as well.
- L132-133: I don’t understand this justification to add uncertainty to the T and OHC values from model output. If the aim is to study how model values of ECSinf compare to ECSeff, then you should use the exact output. If the aim is to study how uncertainties in observed quantities contributes to uncertainty in ECSinf from observations, then you should also add uncertainty to ERF that accounts for aerosol forcing uncertainty. Perhaps both are worth doing, separately.
- L139-159: How is the radiative response to land warming adjusted for in ERF estimates?
- L166-168: Why not use a consistent definition for global T in the ECSinf and ECSeff calculations, given that it’s a perfect model test where the same fields could be used for both?
- L210-213: I don’t agree that estimated TCR is expected to be less influenced by climate state and time. TCR calculated from historical simulations can be substantially different from the true TCR calculated from 1%/yrCO2 simulations (it tends to be lower), for multiple reasons (Dong et al. 2021. First, non-CO2 forcings can produce different SST patterns, which affects the feedbacks. Second, ocean heat uptake efficiency can be substantially different between the two scenarios.
- L212-217: As above, it would be useful to calculate TCR directly from the GCM output from historical simulations as TCR = T/F*F2x for consistency with previous studies (e.g., Otto et al. 2013, Forster et al. 2021, etc), rather than relying on energy balance model parameters.
- L314-315: Assuming constant ocean heat uptake efficiency seems like a major limitation of the energy balance model, particularly given how much the efficiency changes over historical simulations of GCMs (Nayak et al. 2025). Is there no way to modify the model to allow for such changes?
- L361-375: As above, the pattern effect could be calculated directly from GCM output, rather than needing the energy balance model.
- L392-394: The role of internal variability (and other factors influencing SST patterns) is at this point widely acknowledged when estimating climate sensitivity from historical observations (see Forster et al. 2021, Sherwood et al. 2020).
References not already cited in the paper:
Nayak et al. (2025) Evaluating physical climate model emulators for global warming projections. Geophysical Research Letters, 52, e2025GL118591
Proistosescu et al. (2017) Slow climate mode reconciles historical and model-based estimates of climate sensitivity. Science Advances, 3 (7) e1602821
Andrews et al. (2018) Accounting for changing temperature patterns increases historical estimates of climate sensitivity. Geophysical Research Letters, 45. https://doi.org/10.1029/ 2018GL078887
Andrews et al. (2022) On the effect of historical SST patterns on radiative feedback. Journal of Geophysical Research: Atmospheres, 127, e2022JD036675
Otto et al. (2013) Energy budget constraints on climate response. Nature Geoscience, 6, 415–416
Kyle Armour
Citation: https://doi.org/10.5194/egusphere-2026-4634-RC2
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- 1
A perfect-model test is used to compare effective climate sensitivity as predicted from models' abrupt-4xCO2 simulations with an inferred effective climate sensitivity as predicted by a Bayesian estimation model. The Bayesian estimation model was previously used on observations and now applied to climate models to investigate the spread in the inferred ECS estimate.
The questions that the paper intends to answer are clearly laid out, but I found it harder to find the overarching conclusions of the results, as it doesn't seem like the authors answer their own questions, or the answers are somewhat hidden in methodologies and uncertainties (at least to me). That said, I think the results presented here are interesting and worthy of publication. In my opinion, the paper would benefit from overall clarification of the main claims and conclusions, and would be suitable for publication after major revisions.
The difference between equilibrium and effective climate sensitivity could be clarified. Currently, the two concepts seem to be used somewhat interchangeably. The authors correctly use effective climate sensitivity for their results, as equilibrium has not yet been reached, but this is sometimes compared to equilibrium climate sensitivity, which is not exactly the same concept (e.g., Rugenstein & Armour, 2021, doi:10.1029/2021GL092983).
It is not entirely clear to me why the authors expect ECS_inf to be lower than ECS_eff. In observations, I agree that prior results have shown that ECS_inf < ECS_eff, but in coupled model runs, internally generated temperature patterns could, in principle, create both lower and higher ECS in the historical period. Especially since coupled climate models don't reproduce the observed temperature patterns, there is no a priori reason to expect ECS_inf to be lower than ECS_eff, or at least it is not immediately clear to me. Could the authors comment on this? I wonder if we can actually learn something from this finding: does it mean that the "observed" (either in actual observations or in models) ECS_inf in the historical period is forced? That is, if, without any prior knowledge, ECS_inf could be any value around ECS_eff in internal variability, does the bias tell us something about a forced signal? Or is the abrupt-4xCO2 pattern "maximising" the climate sensitivity? Alternatively, I suppose the overall bias could also be related to the method itself, maybe it always underestimates the actual ECS_eff?
Why are only these four models used? Is it because only these models have the necessary simulations/data? Since there seems to be a very large model spread, it would be useful to compare these results to a broader set of CMIP6 climate models. At the very least, it should be mentioned why these models are chosen. Using a larger ensemble would strengthen the results.
The methods could be clarified/expanded a bit. The authors refer to prior work for more details, but since the method is central to the current analysis, there should be enough information to understand the method without having to read the prior work. For example, it was unclear to me what exactly goes into the Bayesian model and what approximations are made. Later in the text, it is mentioned that the model does not take into account the separate forcing components, so where are those single-forcing simulations used? Also, it would be useful to briefly summarize the results of Skeie et al (2024) in L166-168.
The overarching take-aways from Fig. 3 and its discussion are unclear to me. It would be useful to clarify what these results mean for the ECS estimates, instead of only explaining in words what the figures show. For example, reading L245-251, it sounds to me that the fact that ECS_inf < ECS_eff could just be because the Bayesian model has some biases. If this is the conclusion, that should be clearly stated. But I'm probably missing something, in which case it should be clarified what the implications of this analysis are.
The pattern effect discussion could be clarified. Since ECS_inf could also have biases due to the method used, the difference with ECS_eff cannot be entirely attributed to the temperature pattern.