Review for ACP of Regayre et al. manuscript entitled “Remaining aerosol forcing uncertainty after observational constraint and the processes that cause it.”

Summary and General Comments:

This analysis uses an existing climate model perturbed parameter ensemble (PPE) and after first discussing how the progressive/sequential addition of observations yields constraints (with decreasing return) on aerosol forcing, they analyze the role of parameters on the remaining aerosol forcing uncertainty.  Interestingly, they find that parameters that initially seem unimportant contribute a larger role after the optimal constraint. They then take a different approach and use a K-means clustering algorithm to find the dominant clusters of parameters that contribute to the uncertainty, and they plot these clusters onto a latitude-longitude map, enabling visualization of spatial extent of clusters relative to the latitude-longitude resolved aerosol forcing uncertainty map. The paper has numerous quantitative details of parameter/cluster contributions to the uncertainty, and one has to pay close attention so as to not get lost in details, but the analysis is interesting, and the clustering approach toward understanding uncertainty contributions is an interesting approach that warrants publication.  I do not have major comments, but I do have a few questions (below), mostly about the chosen clustering approach, that the authors may wish to consider in their revision. 

Specific Comments/Questions: 

I see that in the PPE being analyzed, less than 10 non-aerosol parameters were perturbed, which is small.  But climate models have far more than 10 physics parameters that impact surface wind, surface-atmosphere fluxes, turbulence, convective mass flux, clouds, and by extension, aerosol-convection-cloud interactions.  One cannot at this point go back to re-do this particular PPE, and I applaud that there are many aerosol parameters (the other 27 parameters), but is it overall possible that the non-aerosol portion of the parameter space really was not explored much and results are muddled by a lack of effort to explore the many other parameters that impact environments and clouds?  Thus, when speaking of “remaining” uncertainty, would not the full parametric uncertainty be much larger and we’re really not at the level of looking at remaining parametric uncertainty?

Aside from the land domain of eastern Asia/China, it is obvious that the other geographic regions of large uncertainty in Fig. 2c – namely, the stratocumulus regimes off the west coasts of the continents – are covered by a diverse range of clusters (Fig. 4, with light/dark blues, oranges, reds, greens, purples, etc.).  I did not anticipate this; in general, I would have thought that there would be a mixing of clusters in geographic domains where the uncertainty was smaller in absolute W/m2.  Intuitively, for example, I would think that the oceanic stratocumulus regimes would have emerged as a consistent color that then transitioned to another color to the west as those cloud types transitioned into cumulus. 

With the above paragraph in mind, how does one interpret this spatial mixing of clusters in Fig 4 coincident with the bullseyes of larger absolute W/m2 uncertainties in Fig. 2c?  Might this imply that these clusters as defined are not as useful and could this have arisen due to arbitrary partitioning of a continuous distribution into 10-ish clusters? K-means clustering is most appropriate for data that does exhibit unique modes or clusters, but of course, one can impose k-means clustering on any continuous dataset, even a continuous one not suitable for clustering.  Which brings up my second question – how were the number of clusters determined?  Finally, instead of clusters connected to geographic domains, would it make more sense to define clusters according to cloud controlling factors (i.e., diagnostics related to stability, moisture, dynamic indices) and then check to see if similar clusters emerge no matter where you are on Earth, so long as you have a similar thermodynamic and/or dynamic environment? 

The manuscript “Remaining aerosol forcing uncertainty after observational constraint and the processes that cause it” use Gaussian Process Emulator technique along with observational constraints of aerosol and cloud properties to analyze and decrease the uncertainty in aerosol forcing determined using UKESM climate model. The manuscript makes a substantial contribution to scientific progress within the scope of Atmospheric Chemistry and Physics, mainly through its innovative approach to diagnosing remaining uncertainties and its ability to provide guidance for future model development and what kind of observations are needed to decrease model uncertainty. The manuscript addresses highly relevant questions within Atmospheric Chemistry and Physics by diagnosing the causes of aerosol cloud forcing uncertainty. It introduces novel concepts and methods. The study reaches substantial and actionable conclusions, recommending targeted existing and new observations to constrain the parameters causing uncertainty in the aerosol forcing. The scientific approach is sound and clearly described, and the results adequately support the conclusions regarding shifting uncertainty drivers. Result traceability is high, with both the analysis code and underlying ensemble data made available, and appropriate credit is given to the foundational work (R23) on which the study builds. The title and abstract accurately reflect the content, the manuscript is well structured, and the number and quality of references and appendices are appropriate. I can recommend publishing the manuscript after the following minor comments have been addressed.

- The manuscript relies very much on the Regayre et al., (2023) paper. It would be good to repeat what observational constraints for certain months, such as August Hd means although it has already been explained in Regayre et al.

- Line 197: why only OH and O3 are mentioned?

- Line 254: in R23 it says 225 observations

- Line 285: Why does high number concentrations of 10 nm particles suppress cloud formation? They are unlikely to activate being so small. I would expect that their size rather than number suppresses activation.

- Line 356: Can you be more specific, what kind of in-depth analysis would reveal good observational constraints?

- Figure 2: Why is the uncertainty so high over the southern oceans? I would expect that anthropogenic aerosol does not have a significant effect on clouds there, still the uncertainty looks to be similar to what it is over Europe. In Figure 3. the size of primary sulfate seems to be a significant source of uncertainty over that area. How does primary sulfate affect those regions?

- Line 607: Alternatively: cloud droplet activation → updraft velocity in cloud droplet activation

- I expect that all simulations are done using the model tuning setup of the default setup. Can different parameter combinations cause the model to go out-of-tune (for example with respect to radiative balance) and thus causing problems in PPE analysis?

- Table A1: For kappa_oc “affects wet diameter and clear-sky radiative flux” can be removed.

Technical comments:

School of Earth and Environment is twice in School of Earth and Environment, School of Earth and Environment, University of Leeds, Leeds, LS2 9JT, UK

Please fix journal abbreviations, fix typos (for example, Regayre 2014, 2015, 2024)