The aerosol pathway is crucial for observationally constrained climate sensitivity and anthropogenic forcing

Skeie et al.

This paper is interesting and useful for comparing different aerosol modeling frameworks, especially for analyzing the impact of the structure of the time history of aerosol forcing. The authors replace aerosol ERF from AR6 with various idealized alternative pathways and also extend temperature, ocean heat content, and ERF time series using the most up-to-date versions of these data. I have a few major and minor comments. 

Major comments

Idealized pathways: I wonder if the authors could more clearly describe the advantages  and disadvantages of these various idealized pathways, vs. using a simple aerosol forcing model whose free parameters can vary in the Bayesian inversion and therefore yield different time histories of aerosol forcing. I am thinking of the simple aerosol forcing model in Stevens et al., 2015, and employed in Smith et al., 2021b and Albright et al., 2021, which are cited in this paper. How does the present approach change the results and allow for more flexibility? What would the results look like if using a simple aerosol forcing model (using SO2, and/or also including BC and OC)? 

Co-variance among parameters: One of the advantages of the Bayesian framework is that it yields a joint distribution of uncertain parameters. Aerosol forcing and ECS_inf are presented independently. Could these values be shown in a joint pdf? 

Other interesting parameters regarding how heat is mixed into the ocean (“e.g. mixed layer depth, air-sea heat exchange coefficient, vertical diffusivity in the ocean and upwelling velocity”, line 517) are presented. I was interested in how these parameters traded off in the various scenarios, and whether strongly differing scenarios of idealized pathways showed different parameter covariance? Could that parameter covariance provide physical insights?

NH vs. SH temperatures: It could be useful, I think, to provide physical insights why modifying the aerosol pathway over certain time periods changes the ECS_inf and other parameters more than changing it over other periods. For example: “The observed temperature and OHC used in the estimation do not allow for a weakening in the anthropogenic ERF in the second half of the century.” Is this result dependent on using hemispheric temperatures, or are similar results obtained when using global temperatures? Is there a particular decade in the second half of the century that emerges as most important for not allowing for more negative aerosol radiative forcing? Is it before / during / after peak emissions of SO2? 

Role of ocean heat uptake observations in the model: I was also interested to know how much ocean heat content constrained the model and added additional information, compared to surface temperatures, but, if I am understanding correctly, I did not see this discussed in much detail in the paper. Could the authors comment on it, or refer to a previous discussion of the role of surface temperatures vs. ocean heat content in a previous work by this team? Thank you! 

Minor comments

Line 78, for known reasonS. Small typo. 

In Figs. 2 and 3, panel c, I found the different lines / cases difficult to distinguish. 

Fig. 2a. Why is the posterior Skeie2018 so close / strongly constrained by the AR5 prior, whereas Base is less constrained by the AR6 prior? I see a description around line 175 but no reason given (is it elsewhere?)

Line 496-7, could “strong” be more clearly defined with a number value/range? Around -2 W/m2? 

Review of “The aerosol pathway is crucial for observationally constrained climate sensitivity and anthropogenic forcing” by Skie et al.

The paper investigates the important ways aerosols impact the constraining of climate sensitivity. The sensitivity tests and calculations are a welcome addition to the literature. I only have a few minor comments listed below that need to be addressed prior to publication.

Minor Comments

1. Grammar: I think the title should be "observationally constraining”?
2. General: Need to leave space between paragraphs, it was hard to read blocks of text
3. Line 41: Earth Energy Balance -> Earth energy balance
4. Line 106: Why not use the Oceanic Niño Index/Niño3.4, the most widely used index of ENSO?
5. Figures 2-3: Please provide more frequent x-axis labels, perhaps every 10 years. It is difficult to judge the years discussed in the text with 50 years spacing on the graph.
6. Line 250: Please elaborate on what exactly saturation means here as it's not fully clear from the sentences that follow. Saturation to a reader may sound like a huge perturbation like a 10xBC type experiment.
7. Line 282: Perhaps worth noting that even multi-millennial simulations don't equilibrate sometimes, i.e., T_s still keeps increasing.
8. Figure 4 and surrounding discussion on pattern effect: Perhaps Dessler (2020) (https://doi.org/10.1175/JCLI-D-19-0476.1) should be mentioned in this discussion as it relates quite closely to the discussion here. Furthermore, how should one reconcile these results with his results where \Delta \lambda = 0.2 Wm^-2K^-1 on average?
9. Line 343: At line 68 it's mentioned the lifetime of aerosols is days yet here it's mentioned that these aerosols can have an impact for decades. Could you please reconcile this for the reader?
10. Line 352: Sherwood et al. (2020) (https://doi.org/10.1029/2019RG000678) showed that paleoclimate has a strong constraint. Could that be relevant here? If so, please discuss it.
11. Line 439: Perhaps worth mentioning updated literature here: Raghuraman et al. (2023) (https://doi.org/10.1175/JCLI-D-22-0555.1) has separated this. They find that the observed SW trend is due to 40% ERF, 30% SW cloud feedback, and 30% surface albedo + SW water vapor feedbacks.
12. Line 514: What does m_t stand for/mean exactly?
13. Line 516: Why is climate sensitivity an input? Shouldn't it be an output? Please clarify/explain further.