In this paper, Morgenstern uses 15 CMIP6 models contributing to the Detection and Attribution Model Intercomparison Project (DAMIP) to estimate the relative contributions to greenhouse gas and aerosol forcing in the present day, and uses the analysis to provide an emergent constraint on the equilibrium climate sensitivity (ECS). The two main findings of the paper are that (1) the ECS is in line with the IPCC headline assessment (likely range 2.5-4.0°C), a little lower than the models’ unadjusted values, and (2) the aerosol warming contribution is only one-third as large as the models' unadjusted values and substantially less negative than the IPCC headline assessment of -0.5°C (-1.0°C to -0.2°C very likely range). If the second point is correct, the implications for future climate change are huge, in the sense that the masked warming by aerosols is small and climate would not be expected to warm by a large amount in any future emissions mitigation scenario.

The analysis hinges solely on CMIP6 models. Therefore, there is a risk that the conclusions are over-confident. One weakness of a purely CMIP6 historical approach is that the models are all forced with the same (largely uncertain) spatial and temporal aerosol emissions data set. It’s possible that the era of strong aerosol cooling in many CMIP6 models (the whole 20^th Century in some models, but we see that many see a bit of a step change around 1950) could be an artefact of the forcing dataset. It could also be because the models are producing overly sensitive responses to aerosols during these time periods, which may also be a factor of some models having high climate sensitivity. I don’t believe anybody has put forward a convincing argument one way or the other yet, though Smith & Forster (2021) and Flynn et al. (2023) have both tried to answer this question.

The point I’m trying to make is that if the “shape” of the aerosol cooling time series differs between the models and reality, then an optimal fingerprinting approach may try to mitigate the effect by selecting regression coefficients \beta_1 that are less than one. This will reduce any error in the total warming time series when the individual components are summed up, and also implies that \alpha_1 < 1 to balance out the positive effect of the GHG warming. We indeed observe that \beta_1 < 1 in all models and \alpha_1 < 1 in all but two models. The author “normalizes” this approach by also determining the regression coefficients compared to each model’s historical run, which is a good idea. However, interestingly again, the regression coefficients \alpha_2 and \beta_2 are also usually less than one (described in lines 150-151 as a lack of additivity). This could be suggestive of the regression approach attempting to minimize residual errors caused by natural variability rather than a genuine lack of additivity, though it should be noted that the omission of ozone and land use forcings may not be insignificant. To investigate this, perhaps a rolling mean filter applied to the T_h* terms in eqs. (1) and (2) could be investigated. CanESM5 hints at this effect: at 25 ensemble members, its model-derived internal variability is small, and it is the only model where \alpha_2 and \beta_2 are both greater than (and are also quite close to) 1, and the noted HadGEM3’s approximate linear behavior has a 60-member hist-aer ensemble to draw upon.

The shape of the historical aerosol cooling is something that we investigated in Smith et al. (2021). If we allow this to vary more (taking CMIP6 as an ensemble of opportunity, fitting a non-linear functional form and sampling the parameters) then we can construct aerosol forcing histories that do permit strong cooling and are still consistent with observations.

Therefore, it is my working hypothesis that the author finds a weak contribution to historical aerosol cooling because the historical shape of aerosol cooling (and forcing) is a poor fit to that implied by global temperatures and not easily resolved using a linear combination of GHG and aerosol attributed warming, and not necessarily because the present-day level of cooling is incorrect in the models (though historically, it likely was in some).

I’m also curious about the slightly different estimate for the present-day aerosol cooling to Gillett et al. (2021), who also did an optimal fingerprinting approach with CMIP6 DAMIP models and found aerosol cooling to be -0.7 to -0.1 °C. In their fig. 2b, it can be seen that aerosol regression coefficients > 1 for some models, though typically they also are in the 0 to 1 range. It would be useful to compare the differences and methods between the two papers.

I do not want to come over as overly critical. It is a thorough yet concise paper, mathematically rigorous but not over-complicated, and the figures, equations and structure are clear and logically organized. Given the sensitivity and importance of the topic, the results should be contextualized relative to the IPCC assessment, which used more lines of evidence than solely CMIP6 (analogous to the ECS).

Minor comments:

Abstract line 2: suggest replacing “anomalously large” with simply “larger”. I don’t think ECS of 5.6 or 5.7 K can be categorically ruled out.

Line 35: “heuristic regression”. I might be showing my ignorance here but I don’t know what this is. It seems to be defined as a machine learning concept (https://dl.acm.org/doi/abs/10.1145/503810.503823). Was this the method used? Eqs. (1) and (2) look more like regular least-squares.

Line 60: I wonder why 1920-2020 and not the whole time period. Are results sensitive to the start date? I imagine they’d be very different if you used 1970.

Line 72: “single variable uncertainties”: would this be standard error?

Line 219-220: This statement of models exceeding 0.5K cooling being unrealistic is too strong.

Line 246: “global warming”: since we’re also talking about aerosol cooling, I suggest being more general: “anthropogenic climate change”.

Sign convention for any time you talk about a cooling, e.g. lines 9, 218, 219: a minus cooling is a double negative.

References:

Flynn et al. (2023): https://acp.copernicus.org/articles/23/15121/2023/acp-23-15121-2023.html

Gillett et al. (2021): https://www.nature.com/articles/s41558-020-00965-9

Smith et al. (2020): https://acp.copernicus.org/articles/20/9591/2020/acp-20-9591-2020.html

Smith et al. (2021): https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020JD033622

The author aims to constrain both the climate sensitivity and the aerosol-induced cooling (between pre-industrial to present-day) from the time evolution of the global mean surface temperature. The constraint comes from the decoupling between the greenhouse gas and aerosol forcings that occurred between 1980 and 2000 and its impact on the historical temperature record. The author finds a smaller aerosol cooling effect than predicted in the models but also a smaller aerosol cooling effect than generally found in other detection and attribution studies. While this manuscript is complementary to previous studies and it represents an interesting contribution to the literature, I doubt it is the end of the story. Furthermore I have a number of major comments that would require clarifications and most likely further analysis. Overall I recommend major revisions to the manuscript before it can be considered for publication in Atmospheric Chemistry and Physics.

Major comments

1/ The author should do a much better job at citing and describing previous work on the topic (e.g. doi: 10.1038/s41558-020-00965-9, 10.1175/JCLI-D-19-0091.1, 10.1038/ngeo2670 but I am sure there are other references as well). There is a large variety in approaches. Storelvmo et al. used a multi-variate fingerprint of the aerosol impact on the climate system. Charles et al. relied on time variations of the ocean heat content. Gillet et al. used not only the magnitude but also the pattern of the aerosol cooling to constrain the climate sensitivity and forcing. The uncertainties remain large but available studies generally find a larger contribution of the aerosols (relative to greenhouse gases) than found in this manuscript. For instance Gillett et al. (2021) concluded that “Greenhouse gases and aerosols contributed changes of 1.2 to 1.9 °C and −0.7 to −0.1 °C, respectively, and natural forcings contributed negligibly.” The author should discuss or at least speculate why his conclusions are somewhat different from those of past studies.

2/ The author compares the global surface air temperature (variable tas) from the models to the global-mean surface temperature from HadCRUT5 but fails to recognize that these are two different things. HadCRUT5 is actually a mix of SST over the ocean and surface air temperature over land. It should be noted that the trends in GMST and GSAT are somewhat different because of the contributions from regions of melting sea ice. Indeed GSAT increases a lot in places where sea ice melts while SST is hardly affected. Furthermore the kink in GMST and GSAT due to aerosols may not be synchronous. Both IPCC and Gillett et al (2021) moved away from GMST to embrace GSAT. I strongly recommend that the author repeats his analysis with GSAT observations (such as provided by the Berkeley Earth project) to avoid the inconsistency in the way temperature trends are estimated between models and observations.

3/ It is annoying and worrying that the total warming (from the sum of the three experiments) differs so much from the historical warming given that climate models are generally thought to be largely additive for small perturbations. Is the plot in Fig 1b for the ensemble mean? How large is the ensemble?  How significant is the non-additivity? Can it be explained by natural variability or missing terms in the total warming? And if so what is the impact on the author’s analysis? If the departure of alpha2 and beta2 from unity is due to natural climate variability (which I suspect), then I do not see the rationale for normalizing alpha1 and beta1 with alpha2 and beta2 as done in Eq. 3. If the departure of alpha2 and beta2 from unity is instead due to missing forcing terms, then should the missing term not be inserted in Eq 1? Fig 4 shows that the departure of the black ellipses from the (1,1) point is quite generalized. If it was due to climatological noise, then should we not expect values that are both smaller and larger than 1? Here we have mostly values smaller than 1 (especially for beta2). Such low values question the validity of the framework. I note that the author discusses this issue in the conclusion section (line 227ff), however this comes far too late in the manuscript. The fact that beta2 < 0.5 for several model does not only “question the suitability of these models for attribution”, it questions the suitability of the method. I would strongly recommend the author to investigate further the reason for non-unity values of alpha2 and beta2 and its impact on the analysis. This is a show-stopper in my opinion.

4/ How do uncertainties in Tobs, not accounted for in the current analysis, affect the results?

5/ ECS computed from abrupt 4xCO2 simulations is generally larger than when computed from abrupt 2xCO2 simulations. It is also an imperfect predictor of the warming predicted in transient simulations. It is not clear to me why the author considers ECS rather than TCR as a predictor of GHG or total historical warming.

6/ The author argues that his estimate of ECS is “very consistent with the AR6 estimate”. Yet his estimate of the aerosol cooling (-0.19°C ± 0.14 °C) isn’t consistent with the IPCC estimate (see bullet A.1.3 of the AR6 SPM that says “The likely range of total human-caused global surface temperature increase from 1850–1900 to 2010–2019 is 0.8°C to 1.3°C, with a best estimate of 1.07°C. It is likely that well-mixed GHGs contributed a warming of 1.0°C to 2.0°C, other human drivers (principally aerosols) contributed a cooling of 0.0°C to 0.8°C, natural drivers changed global surface temperature by –0.1°C to +0.1°C, and internal variability changed it by –0.2°C to +0.2°C”). Thus IPCC estimate is centered on -0.4°C rather than -0.2°C. It would be good to mention and discuss this apparent disagreement, otherwise there is little value in flagging the agreement on the ECS.

7/ Bottom-up estimates of the aerosol radiative forcing (e.g. Bellouin et al., doi: 10.1029/2019RG000660, 2019) are also larger (i.e. more negative) than implied by the aerosol cooling inferred from this study. This does not invalidate the current analysis. Yet the fact that it is at odds with a number of other studies requires some discussion.

8/ Ocean diffusivity also affects the time evolution of the GSAT in models. How would biases in ocean diffusivity in the models affect the author’s analysis?

9/ Lines 70-71, equations 4 and 5: the author appears to assume that alpha1 and alpha2 (beta1 and beta2) are independent variables so that their error variances can be summed but is this really the case?

10/ The reader needs to understand how DAMIP ensemble members for a given model were treated in the analysis.

Minor comments

Lines 19-20 is a bit of a truism.

Line 28: the decreasing aerosol loading is not a “feedback” but a forcing.

Lines 33-34: sentence unclear, please reformulate.

Figs 1 and 5: Plotting b versus a generally implies that b is on the y-axis. Doing the opposite is confusing.

Line 116: why four models and not all models?

Fig 2: is the plot for the model ensemble mean or for a particular member of DAMIP?

References

Bellouin, N., J. Quaas, E. Gryspeerdt, S. Kinne, P. Stier, D. Watson-Parris, O. Boucher, K.S. Carslaw, M. Christensen, A.-L. Daniau, J.-L. Dufresne, G. Feingold, S. Fiedler, P. Forster, A. Gettelman, J. M. Haywood, F. Malavelle, U. Lohmann, T. Mauritsen, D.T. McCoy, G. Myhre, J. Mülmenstädt, D. Neubauer, A. Possner, M. Rugenstein, Y. Sato, M. Schulz, S. E. Schwartz, O. Sourdeval, T. Storelvmo, V. Toll, D. Winker, and B. Stevens, Bounding aerosol radiative forcing of climate change, Reviews of Geophysics, 58, e2019RG000660, doi: 10.1029/2019RG000660, 2019.

Charles, E., B. Meyssignac, and A. Ribes, 2020: Observational Constraint on Greenhouse Gas and Aerosol Contributions to Global Ocean Heat Content Changes. J. Climate, 33, 10579–10591, https://doi.org/10.1175/JCLI-D-19-0091.1.

Gillett, N.P., Kirchmeier-Young, M., Ribes, A. et al. Constraining human contributions to observed warming since the pre-industrial period. Nat. Clim. Chang. 11, 207–212 (2021). https://doi.org/10.1038/s41558-020-00965-9

Knutti, R. (2008), Why are climate models reproducing the observed global surface warming so well? Geophys. Res. Lett., 35, L18704, doi:10.1029/2008GL034932.

Storelvmo, T., Leirvik, T., Lohmann, U. et al. Disentangling greenhouse warming and aerosol cooling to reveal Earth’s climate sensitivity. Nature Geosci 9, 286–289 (2016). https://doi.org/10.1038/ngeo2670