the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Jun 2026
Systematic Observation-Based Estimate of Effective Radiative Forcing from Aerosol–Cloud Interactions
Abstract. The change in Earth's energy budget caused by anthropogenic aerosols interacting with clouds is the most uncertain contributor to the historical energy budget trend, with important implications for future climate projections. Recent studies estimating the effective radiative forcing from aerosol-cloud interactions (ERFaci) using satellite observations and a Cloud-Controlling Factor (CCF) analysis have produced a large spread of results, ranging from approximately -0.3 to -1.5 Wm-2. This spread is comparable to the full IPCC AR6 uncertainty range, reflecting the use of different datasets and methodological choices across studies, often without a systematic basis for selecting among them. Here we develop a unified framework to rigorously evaluate these methodological choices across multiple reanalysis datasets, using both climate model simulations and observed regional aerosol trends as independent validation tests. Applying model based bias-correction to the best configuration yields a best-estimate global ERFaci of -0.84 Wm-2 (66% confidence interval: -1.21 to -0.47 Wm-2) and an implied Equilibrium Climate Sensitivity of 3.33K (66% confidence interval: 2.65 to 4.22K), both consistent with IPCC AR6 and WCRP 2019 assessments but different from previous CCF-based estimates.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Chemistry and Physics.
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Status: open (until 31 Aug 2026)
- RC1: 'Comment on egusphere-2026-3075', Anonymous Referee #1, 10 Jul 2026 reply
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CC1: 'Comment on egusphere-2026-3075', Chanyoung Park, 23 Jul 2026
reply
Dear Omer Roi-Cohen and co-authors,
Thank you for this interesting and timely paper. I found the systematic comparison of CCF-based ERFaci methodologies very useful. I have a few comments on the perfect-model comparison and have attached here.
Best regards,
Chanyoung Park -
RC2: 'Comment on egusphere-2026-3075', Anonymous Referee #2, 06 Aug 2026
reply
General Comments
This manuscript presents a systematic framework for evaluating methodological choices in CCF-based estimates of ERFaci. The authors examine the sensitivity of ERFaci estimates to the choice of aerosol proxy, spatial domain, regression framework, reanalysis dataset, and treatment of aerosol activation. This systematic comparison is highly valuable and timely, particularly given the substantial spread among recent observation-based estimates of ERFaci. With revisions that fully address the points below, I believe this work could make a valuable contribution to the literature on observational constraints of aerosol–cloud radiative forcing.
Major Comments
- One of my main concerns is the use of a very limited number of models to derive the model-based bias correction. In the analysis, the key relationship appears to be based on only six models. While the Monte Carlo procedure propagates uncertainty in the fitted relationship, it does not overcome the fundamental limitation introduced by the small sample size and the struc. With these few models, a single model can exert substantial leverage on the regression slope and can strongly inflate or reduce the estimated correlation. The resulting relationship may therefore be highly sensitive to individual models and may not represent a robust emergent relationship across the models. Particularly, a Pearson correlation of r=0.51 based on six models is not statistically distinguishable from zero at conventional significance levels. An emergent-constraint-style model-based bias correction requires a statistically robust relationship between the CCF-predicted and ground-truth ERFaci estimates. In the absence of such evidence, I do not think this relationship provides a sufficiently strong basis for quantitatively adjusting the primary observation-based ERFaci estimate. A public comment by Chanyoung Park supports this concern. There it is shown that one of the major conclusions of the paper is changed dramatically if a larger set of models is sampled. Specifically, when a larger set of models is considered, the explicit inclusion of activation rates improves the perfect-model cross-validation, rather than degrades it as the manuscript currently asserts. This is a serious limitation of the current manuscript and one that must be addressed prior to publication.
- The manuscript adopts the combined ocean-and-land domain as the primary analysis domain, mainly because including land reduces the uncertainty in the domain-to-global scaling derived from the aerosol-only experiments. However, it is not clear that this statistical advantage in the model-derived scaling is directly transferable to the CCF-based analysis. The CCF framework has primarily been developed and applied to marine low clouds, for which the selected predictors have well-established physical relationships with cloud variability over ocean. Over land, boundary-layer structure and surface heterogeneity can differ substantially from those over the ocean. The authors should therefore provide a clearer physical justification for extending the CCF framework over land. Moreover, Figure S5 appears to show better predictive skill for the ocean-only domain, which is more physically consistent with the original CCF framework.
- As also noted by the first reviewer, the CCF-based estimate in this study is restricted to low clouds. I understand that this choice follows the original development and primary application of the CCF framework, which focuses on low-cloud radiative variability. Nevertheless, aerosol interactions with non-low clouds also contribute to the total ERFaci. More importantly, I’m also not sure about the consistency of the perfect-model evaluation. My understanding is that the RFMIP aerosol-only ground-truth ERFaci includes the radiative response of all cloud types, whereas the CCF-based prediction is derived only from low-cloud radiative anomalies. If so, the comparison is not strictly like-for-like?
- The perfect-model comparison appears to lead to the opposite conclusion from Park et al. (2025), with the activation pathway performing worse and therefore being excluded from the final estimate. Park et al. (2025) includes a larger model sample in its comparison, which may provide a more statistically robust assessment of the activation pathway. Because this comparison determines whether the activation step is retained, the discrepancy should be discussed further.
Minor Comments
- Figure 1a: I’m concerned about including land regions in the activation-based ERFaci estimates. Satellite retrievals of Nd are generally much less reliable over land because of heterogeneous and often highly reflective surface backgrounds (Grosvenor et al., 2018). Please justify this choice and clarify how retrieval uncertainty over land is treated.
- Figure 1b: The relatively high RMSE of the activation-based estimates may partly reflect an inconsistency in the data sources used along the causal pathway? Nd is obtained from satellite observations, whereas the aerosol proxies and meteorological predictors are taken from reanalysis products. This may favor the standard route and make the activation route appear less skillful for reasons that are not solely related to the physical validity of the activation framework. Why is MODIS-derived AI not used for the analysis? Because MODIS AI is a more directly observation-based product than reanalysis-derived AI, including it could help assess whether data-source consistency affects the comparison.
- L120: Please clarify which Nd retrieval is used in the activation analysis following Gryspeerdt et al. (2022). Specifically, is the dataset based on Aqua, Terra, or a combined Aqua and Terra product? Please also state which retrieval and filtering approach is applied for the analysis.
- L303: It would strengthen the validation if the authors also considered episodic aerosol perturbations, as in Wall et al. (2022), in addition to the regional decadal changes examined here.
- L364: It would be helpful to clarify for readers which reanalysis dataset, or combination of reanalysis datasets, is used to derive the final observational ERFaci estimate.
- Figure S7 caption: I don’t think the results are sufficient to support the statement that the raw CCF method systematically underestimates the magnitude of aerosol cooling. This conclusion is based on a limited number of models.
- Please report the corresponding p-value alongside each Pearson correlation coefficient (r) throughout the text and figures.
Technical corrections
- Eq (3): Because the Zelinka et al. (2012) kernel has units of W m-2 %-1, a factor of 100 % may be required in the equation. This differs from the CERES FBCT formulation in Eq. (1), where has units of W m-2.
References
Grosvenor, D. P., Sourdeval, O., Zuidema, P., Ackerman, A., Alexandrov, M. D., Bennartz, R., Boers, R., Cairns, B., Chiu, J. C., Christensen, M., Deneke, H., Diamond, M., Feingold, G., Fridlind, A., Hünerbein, A., Knist, C., Kollias, P., Marshak, A., McCoy, D., Merk, D., Painemal, D., Rausch, J., Rosenfeld, D., Russchenberg, H., Seifert, P., Sinclair, K., Stier, P., van Diedenhoven, B., Wendisch, M., Werner, F., Wood, R., Zhang, Z., and Quaas, J.: Remote Sensing of Droplet Number Concentration in Warm Clouds: A Review of the Current State of Knowledge and Perspectives, Reviews of Geophysics, 56, 409–453, https://doi.org/10.1029/2017RG000593, 2018.
Gryspeerdt, E., McCoy, D. T., Crosbie, E., Moore, R. H., Nott, G. J., Painemal, D., Small-Griswold, J., Sorooshian, A., and Ziemba, L.: The impact of sampling strategy on the cloud droplet number concentration estimated from satellite data, Atmospheric Measurement Techniques, 15, 3875–3892, https://doi.org/10.5194/amt-15-3875-2022, 2022.
Park, C., Soden, B. J., Kramer, R. J., L’Ecuyer, T. S., and He, H.: Observational constraints suggest a smaller effective radiative forcing from aerosol–cloud interactions, Atmospheric Chemistry and Physics, 25, 7299–7313, https://doi.org/10.5194/acp-25-7299-2025, 2025.
Wall, C. J., Norris, J. R., Possner, A., McCoy, D. T., McCoy, I. L., and Lutsko, N. J.: Assessing effective radiative forcing from aerosol–cloud interactions over the global ocean, Proc. Natl. Acad. Sci. U.S.A., 119, e2210481119, https://doi.org/10.1073/pnas.2210481119, 2022.
Zelinka, M. D., Klein, S. A., and Hartmann, D. L.: Computing and Partitioning Cloud Feedbacks Using Cloud Property Histograms. Part I: Cloud Radiative Kernels, https://doi.org/10.1175/JCLI-D-11-00248.1, 2012.
Citation: https://doi.org/10.5194/egusphere-2026-3075-RC2
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- 1
Omer Roi-Cohen
Gaea Hadary
Casey J. Wall
Paulo Ceppi
Overall, this is an important contribution to the literature on this topic of ERFaci which is still hotly debated. I appreciate the effort to reconcile various recent estimates of ERFaci, or at least document which analytic decisions lead to the major differences. While it is unsatisfying that the uncertainty range of the final report estimate is still just as large as in AR6, it is useful to know how smaller or larger estimates of the forcing have emerged. I have two major comments.
1. Regarding the use or not of the activation function (dNd/dA): Is this not more physical? You show that it performs worse against the RFMIP “ground truth”. But do you have a physical interpretation for why?
A very relevant reference for your discussion on aerosol proxy:
Hailing Jia et al., Optimal choice of proxy for cloud condensation nuclei reduces uncertainty in aerosol-cloud-climate forcing. Sci. Adv. 12, eaea4828(2026)..DOI:10.1126/sciadv.aea4828
2. Does ERFaci_low dominante? Is the ERFaci from non-low clouds really negligible? A lot rests on this one sentence caveat in L401.
These references all suggest that ACI in cold clouds can be substantial.
Zelinka, M. D., T. Andrews, P. M. Forster, and K. E. Taylor (2014), Quantifying components of aerosol-cloud-radiation interactions in climate models, J. Geophys. Res. Atmos., 119, 7599–7615, doi:10.1002/2014JD021710.
Alexandri, F., Müller, F., Choudhury, G., Achtert, P., Seelig, T., and Tesche, M.: A cloud-by-cloud approach for studying aerosol–cloud interaction in satellite observations, Atmos. Meas. Tech., 17, 1739–1757, https://doi.org/10.5194/amt-17-1739-2024, 2024.
Duran, B. M., N. J. Lutsko, and C. J. Wall, 2026: Aerosol–Ice–Cloud Interactions in a Perturbed Parameter Ensemble. J. Climate, 39, 4183–4203, https://doi.org/10.1175/JCLI-D-25-0724.1.
In particular, Duran et al. 2026 quantifies this ERFaci_ice = -0.43 W/m2. This is about 50% of the ERFaci_low you quantify. If you add these together it substantially increases the ERFaci (more negative) and the ECS (more positive). Your results currently do not really deviate from AR6 at all, but if there is a nonnegligible ERFaci_cold that may not be true at all.
The authors should at the very least substantially expand this one-sentence caveat. Preferably you would provide a more detailed quantification of either why you now believe this to be small or what the total low+non-low ERFaci actually is.
Minor comments:
L66: There is also considerable uncertainty on the total pre-industrial to present-day aerosol changes. This is worth emphasizing.
L149: Is the surface albedo calculated with clear-sky surface fluxes or TOA fluxes? This was unclear.
L309: Over Eastern North America, I would argue that MERRA and CAMS capture these trends at significantly different magnitudes. Why?
Fig 4b: Why is the largest ∆AI over the Arabian Peninsula?