Review response to Jia et al.: “Process-level contributions to uncertainty in aerosol effective radiative forcing: a perturbed parameter ensemble with aerosol-climate model ICON-HAM”

In their manuscript, Jia et al. describe a novel PPE developed with the ICON-HAM model framework designed to analyze both aerosol-cloud interactions as well as aerosol direct effects. Through Gaussian Process emulation, they expand their sample space allowing for robust parametric uncertainty analysis compared against both PPEs and model intercomparison projects, as well as select observational datasets. While not directly constraining the PPE with observations, their comparisons highlight parameters that may benefit from constraint, and the authors describe a natural next step in their work as constraining their ensemble to observations. In addition to the parametric uncertainty analysis, they present a novel experimental design to determine an optimal ensemble member-to-parameter ratio for the design of PPEs. This is a highly beneficial addition to the PPE community and provides much needed guidance in terms of PPE experimental design.

This manuscript reads very well and presents impactful and novel analyses to benefit the PPE community. Some minor clarifications are needed, but overall the analysis is thorough and clear. The scientific significance, quality, and presentation of the material are all excellent. Below are minor comments and suggestions. Overall, I recommend acceptance after minor revisions.

Major comments/questions:

Regarding the rsp analysis: (line 276) This is a very exciting finding and makes the prospect of generating PPEs easier to accomplish when limited by computational resources. Do the authors think that using a single model to sample across this rsp range introduces biases inherent in ICON-HAM? Would they expect these results to be consistent no matter the PPE/base-model?

Fig. 11 and Fig. 12: With your emulator output, would it be possible to extract the fractional parametric uncertainty within the green isolines and include as additional bar plots following these figures? I think this would make the message much clearer for the reader than having to reference patterns in the supplementary figures that are quite numerous and somewhat challenging to track. This may complicate the regional estimates, but potentially your regional sectors in Fig. A1 could be applied and masked by the green sectors which may result in some empty slots due to sparse green isolines. This visually could be important information for understanding what observational products might be regionally important for constraint. I'd think these bar plots could be interpreted as an observationally informed parameter set that is most in need of observational constraint.

Specific in-line comments:

Line 110-111: Consider changing to "...from those obtained using a satellite simulator...". I was a little confused as ‘the simulator’ makes it sound like the simulator had already been mentioned, but this is the first mention of it in the text. Reading on made it clear you were referencing the COSP simulator for comparisons.

Line 199-200: I very much like this idea for testing the rsp. I see that you show the number of members per subset in Fig. 1. Can you please also reference the number of members corresponding to the different rsp in the text for consistency? Something like, "...corresponding to rsp ranging from 2 (n=84 members) to 8 (n=363 members)."

Line 286-287: It is unclear to me how you fix the other parameter group from what I have read so far. I assume this is derived from your emulator output whereby you have control over the parameter sets and their ranges over which to emulate, but I'm not sure. Can you add a sentence elaborating on how you isolated the different parameter groups? A reference to this in the methods or clarification in the methods would also be helpful.

Line 350-351: Can you support this claim with a figure from the PPE/emulator or with a previous literature reference?

Line 384-386: Can you clarify where you are getting this these percent values? I would assume that holding emissions fixed means ERFaci (Fig. 7b), but I don't see as strong a contribution from the referenced variables as mentioned here. Please reference the table or figure used to retrieve these values and elaborate in the explanation.

Line 434: I wonder if the contributions of biomass burning and anthropogenic emissions (along with their radiative properties) to ARC, NAM, EUR, and ASI may be related to the ERF sensitivity to higher pre-industrial emissions over these regions. Given that these uncertainties are not reflected in the present day (Figs. 8,9) it may be worth mentioning the sensitivities of these results on PI emissions and choice of PI period (e.g., 10.1038/s41467-018-05592-9; 10.1029/2025GL121443). Namely, the role that a higher carbonaceous aerosol influenced PI may have on a PI to PD radiative forcing change. It may also be possible that if your PI emissions are incorrect, constraining to PD observations may not actually improve your ERFaci.

Line 450: In the bar plots this is referenced as ASI but in Figure A1 it is referenced as ASIA. Please change within text or plots to be consistent throughout.

Line 578: This seems to be the first time mentioning ‘AI’, please define the acronym.

Line 599: This was briefly mentioned above in the context of past work conducting observational constraints. Could you please define in more detail here? Based on Regayre et al. 2023, something like: "(AI;  the total MODIS aerosol optical depth at 550 nm multiplied by the Ångström exponent)". Also, why is this diagnostic important in addition to the AE?

Line 678-679: Please elaborate on this. Is this in reference to supplementary figures? If so, please reference those figures.

Line 689-690: It is unclear to me what you are trying to say here. Are you saying that rad_oc_ni reflects wavelength dependence of OC, or are you saying that AE reflects wavelength dependence of OC? I'm also not sure how this relates to the previous sentence. Please reword or expand into two sentences to walk the reader through your reasoning.

Line 772-775: Please check the bullets in this sentence as they are inconsistent.

In this manuscript, the authors run and emulate a large PPE for ICON-HAM, finding that aerosol-related parameters, rather than cloud parameters, dominate uncertainty in both ERFaci and ERFari. For global ERFaer, about a quarter of parametric uncertainty comes from DMS emissions, another quarter from anthropogenic sulfur dioxide emissions (excluding shipping), a third quarter from the size of emitted fossil fuel and biomass burning primary aerosol particles, and the remainder split amongst smaller contributions from the other 38 parameters. Useful results are obtained for future PPE development as well, with a recommended simulations-to-parameters ratio of around 5 nicely balancing accuracy with computational efficiency. The analysis appears overall sound and the paper is very well written — the manuscript is almost ready for publication as-is, although the authors may wish to consider the comments below in minor revisions.

General comment: Are there any parameters accounting for uncertain VOC emissions and processing, etc., over land? This seems potentially relevant given the importance of DMS via the PI background.

Specific comments:

1. Line 2: It would be helpful to spell out ARI and ACI when they’re first introduced here.
2. Line 6: The parametric uncertainties lead to the credible range but not the mean, right?
3. Line 56: Repeated phrase.
4. Line 125: Horizontal wind nudging eliminates the possibility of ERFaer due to large-scale circulation changes… how much this may affect your results, particularly for biomass burning emissions/black carbon, should be discussed.
5. Line 200: I’m struggling to understand here how the n = 84, 126, … 336 is determined for the r_sp = 2, 3, … 8 cases, as illustrated in Fig. 1.
6. Line 285: It seems like the emulator has a strong positive bias, which is an important caveat for the “uncertain magnitude and sign” for ERFari. It’d be useful to show ERFari and ERFaci separately in Figure 2, or perhaps in the SI if you don’t want to add more panels there.
7. Lines 325-326: Do observational estimates necessarily increase the total uncertainty in the IPCC compared to MMEs?
8. Tables 1 and 2: Double-check units and (Abs) versus (Rel)… For example, coating_so4 seems like it should be (Rel) instead of (Abs) and if activ_w were (Rel), shouldn’t the default be 1?
9. Figure 11: I don’t understand what the criterion for the green contours means, is it possible to rephrase? I’m specifically confused about what it means to compare a regional parametric 2-sigma uncertainty to the “90th percentile of the global distribution”.
10. Figure 12: There’s a suspicious linear-looking feature in ICON-HAM at ~130 W, especially in liquid cloud fraction but also seemingly in LWP and CDNC…
11. Lines 741-750: The sizeable positive bias in ERF in the emulator seems worth mentioning here.
12. Data/code availability: Can’t the emulator be shared publicly?
13. Figures S5,6,11: Ship emissions contributing zero uncertainty everywhere, including the northern Atlantic and Pacific, seems implausible. This should be discussed somewhere in the paper.