the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Jun 2026
Process-based constraints are not sufficient: evaluating their role in combination with state variable-based constraints on aerosol–cloud radiative forcing
Abstract. Atmospheric aerosols and their interactions with clouds remain one of the largest sources of uncertainty in estimates of effective radiative forcing from aerosol–cloud interactions (ΔFaci). While perturbed parameter ensembles (PPEs) have been used to explore and constrain this uncertainty using observed state variables, recent work has proposed process-based constraints, such as the slope of the relationship between cloud droplet number concentration (Nd) and liquid water path (L), as potentially more informative indicators. Here we evaluate the effectiveness of the Nd–L slope as a process-based constraint using the UKESM1 model across three climatically distinct marine regions, and compare it with a previously established state variable-based constraint. The slope primarily constrains uncertainty associated with physical atmosphere parameters, while state-based observations constrain aerosol emissions and processes. However, the slope constraint alone produces only small reductions in Nd, L, and ΔFaci uncertainty. Combining the slope and state-based observations further constrains ΔFaci beyond the state-based constraint alone (up to an additional 36 % reduction in uncertainty). However, the combined constraint appears to rely on compensating parameter effects, highlighting structural limitations in the model representation of aerosol–cloud interactions. Our results show that process-based constraints provide complementary information to state-variable constraints, but cannot be used in isolation to meaningfully constrain ΔFaci. Specifically, combining process-based and state-variable constraints reveals structural deficiencies in current climate models, indicating that reducing uncertainty in ΔFaci ultimately requires improved representation of aerosol–cloud coupling.
Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2990', Anonymous Referee #1, 16 Aug 2026
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RC2: 'Comment on egusphere-2026-2990', Anonymous Referee #2, 03 Oct 2026
In this manuscript, the authors analyse an existing PPE of UKESM1 and apply different observational constraints to reduce the uncertainty in ERFaci. In addition to a previously established state-variable-based constraint, they propose a process-based constraint using the lnNd-lnL slope. They evaluate both constraints individually and in combination, finding that the process-based constraint alone does not substantially reduce ERFaci uncertainty but provides complementary information to the state-variable-based constraint. Combining the two leads to a stronger constraint on ERFaci. The authors also attempt to identify non-physical confounding processes linking Nd and L, offering a way to expose potential structural deficiencies in the model.
The study presents interesting and useful results that could inform future observational constraint strategies. Overall, the analysis is sound, and the manuscript is very well written. I have only a few minor comments and suggestions for the authors to consider.
Specific comments:
Line 42: Before moving on to observational constraints, it might be worth mentioning another application of PPEs: assessing the sensitivity of model outputs to parameters (e.g., https://doi.org/10.5194/gmd-17-7835-2024), and how such analyses have been used to identify which observations should be prioritized for constraining model uncertainty (e.g., https://doi.org/10.5194/egusphere-2026-3275).
Lines 54-55: The lnNd-lnL slope indicates the strength of the liquid water path response to changes in Nd, rather than the role of aerosols. The aerosol influence on Nd is instead reflected by the lnNd-ln(aerosol) relationship. It would be more accurate to phrase this as ‘…how instantaneous changes in Nd alter cloud properties.’
Lines 55-58: The inverted V-shape should be associated with changes in precipitation intensity rather than changes in aerosol concentration.
Line 59: ‘also apparent in satellite observations’: the word ‘also’ is a bit confusing here, as the findings described in the previous sentence are already based on satellite observations.
Lines 94-95: Could the authors elaborate a little on how “structural development” can inform the choice of parameters?
Lines 95-99: Why are the years used for emissions and SST/SIC different from those used for atmospheric circulation? Given that the model is later constrained using actual observations, could this mismatch have any unexpected consequences?
Line 112: It would be helpful to briefly explain how you determine whether a constraint is optimal.
Line 137: It would be better to include a reference for the calculation of Nd based on the adiabatic assumption. I think this method was originally introduced by https://doi.org/10.5194/acp-6-947-2006.
Section 2.2: Using the original MODIS product is fine here, but in case the authors are not aware, there is also a COSP-based MODIS product (https://www.earthdata.nasa.gov/data/catalog/laads-mcd06cosp-d3-modis-6.2) that could facilitate a more consistent model-observation comparison.
Line 146: ‘a’ → ‘an’. It would also be interesting to see how the slopes differ when calculated using monthly versus daily or hourly data, perhaps in the Supplement. There has been some debate about whether monthly or daily data should be used to calculate Nd–AOD relationships, as monthly averaging may mask some important variability.
Line 164: ‘following the terminology of ?’: Is there a missing reference here?
Figure 2: Such relationships are commonly shown on a logarithmic scale, as we are more interested in relative rather than absolute changes. Also, perhaps I missed something, but what does the red PDF curve represent? Is it derived from the emulators?
Figure 3: It is quite interesting that the PPE shows little seasonal variation in the slope, whereas the observations show a clear seasonal cycle. Do the authors have any explanation for this? Could it be related to model biases in precipitation?
Lines 203-206: Have the authors directly compared the emulated slopes with those calculated from emulated Nd and L? Previous validation studies have shown that GP emulators perform well in reproducing state variables, but I wonder whether they can also directly predict the relationship between these variables.
Lines 228-238: I did not quite follow how the GAM was applied and what its advantages are in this analysis. Even without GAM, one could still estimate the variance in ERFaci associated with an individual parameter by varying that parameter while holding the others fixed using the trained GP emulator, right? Could the authors elaborate a little on this?
Figures 4 and 5: It is somewhat counterintuitive that the slope constraint results in an even broader uncertainty range in ETA. Since the constraint effectively removes PPE members, I find it difficult to understand why the resulting uncertainty would increase. Could the authors explain this?
Line 328: Primary sulfate is expected to contribute relatively little compared with secondary sulfate, so it is somewhat surprising that the parameter ‘primary sulfate mode diameter’ dominates the uncertainty. Could the authors clarify why this parameter is so important and briefly explain how primary sulfate emissions are treated in the model?
Figure 7: It would be helpful to specify the vertical level at which q is evaluated. The authors might also consider focusing on the levels where liquid clouds are present.
Citation: https://doi.org/10.5194/egusphere-2026-2990-RC2
Data sets
Dataset for manuscript "Process-based constraints are not sufficient: evaluating their role in combination with state variable-based constraints on aerosol–cloud radiative forcing" Kunal Ghosh https://doi.org/10.5281/zenodo.19923874
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- 1
Review of Ghosh et al. “Process-based constraints are not sufficient: evaluating their role in combination with state variable-based constraints on aerosol-cloud radiative forcing” submitted to ACP.
Summary:
Leveraging perturbed parameter ensembles (PPEs) that yield information on parametric uncertainty in climate models, the authors aim to determine how new process-based constraints can reduce the parametric uncertainty space. Their efforts build on those that use typical mean-state (i.e., average radiation, average precipitation, average water vapor, etc.) constraints to isolate the plausible sets of parameters that can be used in models. The effort to use process-based constraints alongside mean-state ones is conceptually quite appealing, and thus this paper is welcomed. The paper is quite dense and there is a lot of material to go through in terms of sensitivities that are quantified, etc. It was hard to keep track and collectively aggregate and assess all of these details, so my review largely focuses on the implementation of the new process-based constraint -- specifically, computation of and use of the observed/simulated relationship between liquid water path (L) and droplet number concentration (Nd) -- and questions that arise related to the computation of this relationship, and quantitative implementation of this constraint on a regime by regime basis. Addressing my general questions below might result in manuscript modifications that fall between minor and major revisions.
General Comments:
1.The approach to use the observed relationships between L and Nd in a few K-means clusters (where clusters are defined as those that have emergent uncertainty likely impacted by similar sets of parameters) as constraints was novel. But, spatially, the clusters have quite odd geometric shapes (in terms of where they span geographically and how amorphous they are; see Figure 1). In my own modeling work, for example, I am aware that simulated stratocumulus fields occur to the east (by a few hundred km, or a few ESM grid boxes) of where they occur in nature. When I am doing my regime-by-regime comparison, I try to eyeball and correct for this spatial misalignment so that I can then focus on the thermodynamics-cloud relationships in the regimes without enforcing that they *must* occur within the same amorphous spatial bounds. Of course, at the end of the day, we would want there to be spatial alignment of simulated-observed cloud regimes on Earth, but there are myriad reasons why this might not occur even in AMIP-style mode (circulation, large scale modes of variability, topography representation). And I am not even 100% sure that nudging would force the regimes to be exactly spatially coincident. Have you determined if your “hotspots” of marine cloud locations within the spatial clusters you identify are at least spatially co-aligned across the models and observations? Can you ensure this? In effect, you are forcing a restricted amorphous geographic domain to be used for constraint, and nudging will help this, but your regimes (clusters) are quite oddly shaped (especially the SE Pacific one). Commentary and a possible supplementary set of images showing that at least the cloud-aerosol processes we are aiming to constrain with observations are (in the spatial sense) simultaneously occurring in these amorphous geographic domains in the observations would be very beneficial. It would be a shame to misunderstand the constraint simply because in nature, these regimes are spatially shifted or have their own different amorphous shapes, and I’ve suffered from this in my own past work when trying to compare regional observations to the same region in models. You could start with the clusters as you’ve identified them, and then shrink them down to smaller domains in some way (perhaps by looking at where hotspots/peaks or storm-track enhancements in LWP occur?). If they are suitable as derived and spatial alignment not an issue, this reviewer would appreciate being convinced of that.
2.The observed Nd-L relationship (from MODIS) for the 3 different regimes, in the supplementary section, shows a negative (or near zero) relationship always, and I realize this is because of sampling that has to do with a min Nd threshold for observational sensitivity, but this makes me very concerned because the min Nd for which the linear fit is performed is really quite low, and the turn-over point (from positive to negative slope) in the PPE members are really quite variable. And, taking a step back even further, sometimes, the inclination to even fit a line to a number of these scatterplots is, well, questionable (e.g., in the observations, Fig. S4a, d or Fig. S6a) – I guess I’d not advise my students in class that a good analysis would start with fitting lines to some of these scatterplots. But, if it must be done this way and lines must be fit, why not just eyeball the approximate min Nd threshold from MODIS and use the same min for the model PPE members, and compute the slopes for the model PPE from that same min Nd onward? I see some PPE members actually have that negative slope beginning at lower Nd, so could they perhaps be better performing if we quantified the starting Nd for slopes differently? I realize that the authors didn’t want to force a specific Nd and L magnitude agreement, but that is a subjective decision, and it is not clear to me that having or not having the same slope from a really noisy set of points *and* one that is defined from differing Nd minmax intervals is the best. Why, conceptually, would it be so much worse to enforce the same Nd interval across all PPE members and observations? At least you wouldn’t be enforcing the same LWP magnitude. I am going to hypothesize that the slope of the Nd-L line for the high Nd part of the spectrum is quite sensitive to where that cross over point in Nd space is, and this makes me quite uncomfortable that the observations are being used in the optimal way. I even see some PPE members that have negative slopes for both the low and high Nd portions or at least starting at much lower Nd (somewhat like the observations; e.g., p=73 and p=161). Overall worried that slopes could be quite sensitive to turn over points in conjunction with the nature of fitting lines to these data that are, to my eyeball, not data I’d fit lines to across the board.
Specific Comments:
--I see the model has 85 levels, but what is the approximate vertical resolution in the PBL/lower trop? Parameterization structure aside, is the vertical resolution suitable for these marine cloud regimes? Can we rule that out at least in terms of “structural” error?
--Toward the end of the paper, uncertainty in observations is mentioned – obviously not real “observations” (no one is out there counting Nd or mass), they are remote sensing retrievals, or simpler (than ESM) retrieval algorithm models in themselves. The possibility that systematic errors exist even for these warm marine clouds particularly for LWP should be expected (see for example Fig. 15 here: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014JD021568), where microwave and optical estimates differ even at times when the clouds are filtered to be low/warm, and who knows how it would impact the slope of the lines particularly if bias is regime-dependent and/or varying as Nd itself might vary.
Line 164: “following the terminology of ?” – the question mark is denoting text that was not added.