Summary.

This study used novel causal machine learning techniques to statistically quantify the impact of aerosols on tracked isolated deep convection observed by the NEXRAD. The authors argue that the new machine-learning technique can separate the various meteorological parameters to isolate the relationship between aerosols and deep convection. The results indicate that increases in background aerosols are associated with a 1.4km deepening of the echo-top height of deep convection. Overall, this paper is well-written, and the approach seems appropriate. However, I suggest some modifications in writing and explanation, which can improve the readability. These are described in the major comments, but not so critical. Hence, my recommendation is a "minor revision".

Major Comments.

1) Readability: The new statistical approach is meticulously written, but it is often hard to read due to various statistical jargon that is unfamiliar to atmospheric scientists like me. Can you clearly define these terms at the beginning? For example, define like this in the table.

Confounder: a variable that affects both the dependent and independent variables in a study, causing an association that may not be accurate. (parameters include ….)

Exposures: Any factor that may be associated with an outcome of interest. (parameters include ….)

Probably these terms are common in epidemiology, but not in atmospheric science.

2) New and traditional approach: At the end of the manuscript, authors mentioned quite significant statements “Nevertheless, this study pioneers the use……….. scientistifc questions”. To be honest, I still wonder why this new method is so novel compared to the previous old approach because there’s no comparison between the new and traditional statistical approaches. For example, here is one of the earliest aerosol-deep convection manuscript.

Lin, J. C., Matsui, T., Pielke, R. A., & Kummerow, C. (2006). Effects of biomass-burning-derived aerosols on precipitation and clouds in the Amazon Basin: A satellite-based empirical study. Journal of Geophysical Research: Atmospheres, 111(D19). https://doi.org/10.1029/2005JD006884

In this paper, DCC properties (precipitation, cloud top height, and cloud fraction) are related to aerosol optical depth for a given meteorological parameter (cloud work function in that study). Can you compare your novel approach with this traditional approach (simple statistics stratified by meteorological parameters)? Do you think the old approach leads to significant biases in understanding the aerosol-DCC relationship? Can you prove or briefly explain?

3) Potential biases in radar-based approach: Authors use threshold NEXRAD radar parameters to define DCC. However, if DCC has a much smaller amount of raindrops due to a large number of background aerosols, this cell may not be counted as DCC due to larger concentrations of small-size droplets, which won’t increase S-band reflectivity. Alternatively, if you use cloud optical depths and top height, the DCC sampling can include such cells. This is a NEXRAD-based cell tracking approach, so you cannot change your approach. However, it is important to discuss potential sampling biases using the NEXRAD radar.

Minor Comments.

Line 87: Please remove parenthesis “(either invi….. )”.

Line 120-121: “exclude the presence of shallow convection” sounds like removing the sampling during shallow stages. So I suggest just  re-write as “exclude the shallow convection cells”.

Line 179: Please define the threshold of diameters of “ultrafine aerosols”.

Line 274: “buoyancy-driven DCCs”. Well, all DCCs are driven by the buoyancy over the flat terrain. So you may re-write this as “locally driven DCCs”.

Line 294: “30-dBZ ETH/15-dBZ ETH” should be “30-dBZ ETH and15-dBZ ETH”.

Line 303-306: We won’t be able to measure supersaturation directly within the convective storms. however, you can infer the required supersaturation in order to active all aerosols (including ultrafine). For this case, can you describe roughly how much supersaturation is required to support your argument?

Fig. 4: Why is there no correlation between thermodynamics and Nccn? It seems to be more important?

Line 547: “30-dBZ ETH/15-dBZ ETH is 1.1 km/1.0 km,” should be “30-dBZ ETH and15-dBZ ETH is 1.1 km and 1.0 km, respectively.”

Overview

This study tracks isolated convective cells during conditions of large-scale subsidence using NEXRAD radar reflectivity within different distances of 20 to 50 km of the TRACER primary observing site. Per 4 to 6-hourly sounding, the average of cell maximum radar echo top heights (ETHs) are used to derive a multiple linear regression where predictors consist of an aerosol concentration variable and 2 sounding-derived meteorological variables, with different variables tested and chosen based on their correlation with ETHs. This regression is then used to keep confounding meteorological predictors constant and define aerosol concentration predictors as separately polluted and clean to compute a change in ETH, which is then called the causal effect from aerosol concentration. The increase in ETH between high and low ultrafine aerosol concentrations is approximately 1 km. In sea breeze conditions, this increases to 1.4 km. CCN variables with supersaturation up to 1% do not have any robust relationships with ETHs, but CN concentrations do, which is attributed to ultrafine aerosols activating in updraft regions and creating condensational invigoration. Convective core maximum reflectivity also increases by about 2 dBZ moving from low to high aerosol concentrations but this result may not be robust given radar reflectivity uncertainty.

There are some nice analyses and discussion in this study including sensitivity tests and some caveats that provide important context. However, I have several major concerns with how the analyses are interpreted and some of the conclusions that are drawn.

Major Comments

1. Non-invigoration aerosol-DCC interactions that could affect aerosol-ETH relationships are ignored. Aerosol-DCC interactions include direct effects on microphysics in addition to indirect effects on updraft strength. The paragraph starting on line 43 starts by referencing aerosol-DCC interactions in general but then the discussion that follows in the introduction focuses purely on updraft invigoration. This is problematic because aerosols can also directly affect microphysical properties (e.g., collision-coalescence, riming), which affects radar reflectivity and thus reflectivity echo top height. These direct effects may or may not be further associated with a change in updraft strength. To assume that updraft strength alone is the cause for changed in ETH assumes that changes in aerosols do not alter the reflectivity profile for a given cloud top. Furthermore, there is an assumption that the relationship between ETH and the true cloud top (the vertical gradient of reflectivity between the ETH and cloud top) does not change with changes in aerosols. It is not clear how valid those assumptions are. What evidence is there to suggest that ETH changes are primarily corresponding to changes in updraft strength?
2. The g-computation model does not provide the causal direction, which still needs to be assumed, even if it is called a causal inference model. This assumption is made in the multiple linear regression model where the predicted convective property is assumed to follow from the predictors. The reasoning for this is that the meteorological and aerosol properties are defined prior to the convective cell properties, which makes sense, but this is similar to what has been done in some prior studies. Furthermore, this time offset still doesn’t ensure the assumed causal direction because there is a lot of atmospheric complexity that isn’t being quantified that can affect the properties of the cells and atmosphere offset in space and time. Thus, describing this research as the first to show cause-effect is misleading. The methods do have unique aspects relative to past studies that can be highlighted but there is no reason to believe that the causal direction has been more discerned than in past studies.
3. It is not clear what value the g-computation model provides over the multiple linear regression. If the underlying model where a more complex nonlinear model, there would be some justification for it, but multiple linear regression is used. The multiple linear regression coefficients can be used to describe convective sensitivity to aerosols, giving the same results. Even with using the g-computation model, describing an aerosol effect as just the change in ETH without the corresponding change in aerosols, as is done throughout the paper, doesn’t make much sense. It is the sensitivity, i.e., the change in ETH per change in aerosol concentration, that is most relevant with the underlying assumption that this is approximately linear, and this is simply the slope for the aerosol concentration predictor from the multiple linear regression model. What does the g-computation model provide that the regression cannot other than calling the model “causal machine learning”?
4. Tests for multiple linear regression model accuracy and robustness are missing. For example, the predictor coefficients should have 95% confidence intervals computed. In addition, how well does the MLR predict the observed ETHs? What is its r² value? The r² is important as it shows how much of the ETH variance remains unexplained by the model, which is relevant for missing information that could still confound the relationships of ETH with the current predictors.
5. The argument for activation of ultrafine aerosols in updrafts leading to increases in ETHs lacks evidence. Activation of ultrafine particles seems highly unlikely given the high concentrations of larger aerosols for most of the samples assessed (Figure 7). Activation of the ultrafine particles would result in cloud droplet concentrations of a few thousand per cm³. Are there aircraft measurements (e.g., during ESCAPE) to support such high drop concentrations? Assuming a favorable composition for nucleation, what would the supersaturation need to be to activate particles at a certain size (e.g., 10 nm) given observed aerosol size distributions? This could be assessed in a parcel model to show if the argument being made is even physically possible.
6. The diurnal cycle needs to be ruled out as a cause of the CN-ETH and UFP-ETH relationships. Over land, ultrafine aerosols often have a strong diurnal cycle just as deep convection does, which can affect relationships between the two. Accumulation mode aerosols often have a much weaker diurnal cycle, which is potentially a hypothesis for why one wouldn’t get robust CCN relationships but robust CN relationships with ETHs. For example, Fast et al. (2024) shows this for the CACTI campaign. This occurs because new particle formation processes over land operate during the daytime. What are the typical changes in ETH and predictor variables including CN and CCN over the diurnal cycle? Do CN and ETH variables both peak in later afternoon? If hour of day is controlled for, does that affect the aerosol-ETH relationships? 
7. Relevance of sounding convective parameters at M1 for some situations needs further inquiry. Convective parameters like CAPE are not stable for 4-6 hours over land, and the study (Prein et al., 2022) used to support this claim on line 209 does not state that so far as I can tell. That study uses a limit of 4 hours difference between observed and simulated MCSs to match them, and MCSs are not the same as isolated convective clouds in atmospheric sensitivities. Other studies such as Nelson et al. (2021) show large changes in low level moisture on distances < 50 km and times of ~1 hour over some land convective regions. The statement after this on lines 209-211 that the M1 site is not heavily affected by maritime conditions is also confusing because the M1 site is close to Galveston Bay, and as noted in the study, a bay breeze often forms. Perhaps the bay air mass is similar to the continental air mass in terms of aerosol and thermodynamic properties, but I’m not sure that can be assumed. It may not be possible to easily assess these caveats, but they should at least be highlighted. Something that could be looked into though is whether the M1 surface measurements are relevant to air feeding cells at nighttime and/or after the bay/sea breezes have passed inland of the M1 site by examining stability at and through the boundary layer up to approximate cloud base to assess the likelihood of coupling to M1 site surface conditions.
8. More information on the spatiotemporal distribution of cells and cell properties is needed. Because of potentially substantial gradients in aerosol and thermodynamic properties given the coastal and large urban area, it would be ideal to plot the initiation locations and/or locations where the cell ETHs are maximized on maps for different ranges from the M1 site rather than the tracks in Figure 1 that don’t provide much information. In addition, it would be helpful to map out cell properties like those in Figure 6 to see if there are spatial gradients in the properties with respect to the M1 site location.
9. Are ETH retrievals from level 2 NEXRAD data unbiased with range from the radar? Related to the previous comment, ETHs should be mapped with range from the radar to see if there are biases related to beam filling and gaps between elevation angles with range.
10. ACP recommends making processed data and code openly available in a FAIR-aligned reliable public repository to support study reproducibility. It is likely not possible to reproduce the methodology with only links to TINT and raw datasets given the information provided in the study.

Minor Comments

1. Line 7: Only a single model predicts a significant relationship between an aerosol concentration and convective core area, which 0.8% CCN within 30 km of the M1 site (Figure 10). The other 31 models are not significant. That seems pretty random, particularly since some models switch sign with changes in range within M1, and not enough to support this statement in the abstract that greater aerosol levels correspond to increased convective core area.
2. Lines 31-33: This is an odd motivation since ERFaci uncertainty is currently mostly attributed to non-deep convective clouds that are not the focus of this study.
3. Discussion of leading invigoration mechanisms in introduction: Semi-direct effects by aerosols that alter atmospheric thermodynamic stability should also be included.
4. Lines 60-63: Some of the studies cited here are not simply questioning the importance of invigoration mechanisms relative to other forcings but showing that there is a spectrum of enervation to invigoration possible, thus suggesting that referring to the mechanisms only in terms of invigoration is misleading.
5. Lines 75-76: Though individual modeling studies have quantified aerosol effects, it is important to note that there is still disagreement between these studies, even in the sign of effects, because models and the methods for analyzing them (e.g., discussion in Varble et al., 2023).
6. It isn’t clear how updraft strength is being defined. Is this referring to updraft mass flux, average vertical wind speed, or maximum vertical wind speed?
7. Lines 124-128: Not tracking cells when max 2-km Z < 40 dBZ leaves out more than non-precipitating stages as suggested here. It also leaves out lightly precipitating periods.
8. For the meteorological variables, there is almost an unlimited number that could potentially be relevant and tested. Were different shear layers other than 0-5 km tested? Was mid-level RH tested (separate from the boundary layer)?
9. What assumptions are made for the lifted parcel calculations (LCL, LNB, CAPE)? Is liquid pseudoadiabatic or reversible ascent assumed?
10. Line 187: CCN at various supersaturations does not have a temporal resolution of 1 minute or less as stated here. The supersaturation is varied over the course of about an hour usually so there is 1 value at each supersaturation every ~hour or so.
11. Lines 194-195: A t-test may not be valid here if the aerosol distributions are skewed.
12. How are DCC tracking results averaged? Does each DCC have a single value for a variable like ETH and then all of the ETHs are averaged together?
13. Lines 234-235: I don’t follow the argument for why large-scale ascent needs to be avoided, though I can see why MCSs would want to be avoided. Is that the primary reason for avoiding certain large-scale meteorological conditions?
14. Lines 273-275: Mesoscale deep convective systems are still buoyancy driven, so I don’t understand what this sentence is trying to get across.
15. Figure 4: Why are values not filled in for the significant correlations less than 0.4? Also, I may have missed it, but are the aerosols in Figure 4 sampled around the same time as the soundings or are they sampled after the soundings?
16. In some places, LWS is used and in others, shear is used. It would be best to choose one or the other and be consistent throughout.
17. Line 342: Should “accuracy” be “robustness” here?
18. Lines 364-365: Including some critical meteorological quantities supports this assumption, but I wouldn’t say that it is necessarily sufficient. That is hard to know without an in-depth study of possible confounders.
19. Lines 388-389: I don’t follow the argument of multi-collinearity supporting standardization. Isn’t the reason for standardization stated on lines 390-392?
20. Lines 463-464: There is not enough evidence to make this statement that Ncn and Nupf are causing higher ETH via their activation.
21. Line 494: I disagree that a causal link was demonstrated. The only thing supporting cause is that the aerosols are sampled prior to cells in time, but there is no evidence to show the causal mechanisms, and there are potentially other confounders not accounted for (see major comments).
22. Lines 536-540: It’s true that uncertainty renders the max reflectivity results less robust, but the same argument can be made for how well 4-6 hourly soundings and aerosols at a single point represent conditions where cells are growing.
23. Lines 603-605: I think this sentence can be clarified. Aerosol is not robustly associated with DCC max ETH (not its evolution) given the sampling in this study. That does not mean that it couldn’t be if more samples we added.

References

Fast, J. D., Varble, A. C., Mei, F., Pekour, M., Tomlinson, J., Zelenyuk, A., Sedlacek III, A. J., Zawadowicz, M., and Emmons, L. K.:, 2024 Large Spatiotemporal Variability in Aerosol Properties over Central Argentina during the CACTI Field Campaign, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2024-1349.

Nelson, T. C., J. Marquis, A. Varble, and K. Friedrich, 2021: Radiosonde Observations of Environments Supporting Deep Moist Convection Initiation during RELAMPAGO-CACTI. Mon. Wea. Rev., 149, 289–309, https://doi.org/10.1175/MWR-D-20-0148.1