Dear Authors,

I have obtained comments from the original reviewers and one additional set of comments in form of an informal review as shown below. Please address the comments shown below and those made by reviewer #1 and submit a revised version of your manuscript.

Review of Wang, Cohen, Lin, and Deng,

Constraining the relationships between aerosol height, aerosol optical depth, and total column trace gas measurements using remote sensing and models

Overall, this paper includes a novel idea of incorporating CO and NO2 column-concentration measurements, as well as CO/NO2, in a statistical regression approach to modeling plume rise. They input MOPITT CO, and NO2 from the OMI instrument, and use MISR aerosol data for model validation. However, the paper needs work, in my opinion. There are a few overall considerations that might warrant further attention, and some smaller technical issues; key points are given below.

Top-Level Notes:

Greater care is needed in separating background aerosol, including aged smoke and pollution, from smoke emanating from specific fires. Note that “pollution” often indicates anthropogenic origin, whereas the term appears to be used here to include aged (and possibly also some fresh) fire emissions, as well as background emissions from other sources. It would be helpful to make clear what definition is being used, and to make a distinction between fresh emissions (the target of the modeling here) and background emissions, either from earlier fires or from other sources.

Contributing to the issue of distinguishing sources, burning conditions often produce many small fires, possibly in addition to a few large ones. These might be difficult to represent accurately in a model.

Also, there are limitations in the degree to which the remote sensing instruments can resolve structure in the boundary layer (MISR plume-height uncertainty is between 250 and 500 m), and models are notoriously poor in simulating boundary layer height and vertical mixing timescales. So there are plenty of possible reasons why discrepancies between the “observed” and “modeled” boundary layer results might occur.

Many 1-D plume rise models tend to overestimate injection heights for low plumes and underestimate them for higher plumes, thus diminishing the range of simulated height variation. With a closer analysis of the reasons CO and NO2 column concentrations improve the correlation with plume height in regression models, the current paper might shed some specific light on this issue.

Detailed Notes:

1. The references used in the introduction are a bit off. Although they are relevant to the subject of plume-height retrieval, many are cited in the wrong context. A few cases are listed here. The authors might go over all the cited references and assure they are listed in the appropriate context;

a. For example, on Line 27, Val Martin et al. 2012 is about testing a plume-rise model using MISR plume heights, and Nelson et al. 2013 is about the MISR plume height algorithm. Yet they are referenced regarding “the impacts that aerosols have on clouds, radiation, the atmospheric energy balance, and climate, human health, and ecosystems…” Although plume-rise does bear upon all these, the papers referenced do not cover those aspects.
b. Mims et al. 2010 (Line 29) is about plume-rise in Australia, not about the atmospheric energy budget. An aerosol transport model result would probably be a more appropriate reference than Winker et al. 2013 (Line 31) when talking about the atmospheric distribution of aerosols in general.
c. On Line 37, Vernon et al. (2018) should probably be Flower and Kahn (2017; doi: /10.1016/j.jvolgeores.2017.03.010). The Alaska plume-rise results (Lines 47-48) are in Kahn et al. 2008, not Kahn et al. 2007. Val Martin et al. 2018 (Line 48) is about the MISR plume-height climatology, and although it mentions CALIPSO, that is not the point of this particular paper. (Maybe the Winker et al. 2013 reference belongs there.)
d. On Lines 51-52, the climatology of plume heights in Val Martin et al. 2018 shows that smoke is injected above the boundary layer frequently at high latitudes in summer, and in a few other geographic locations, but in areas where agricultural burning is prevalent, high injection is rare.
e. On Line 58, Ichoku and Ellison 2014 actually derive emission factors to estimate smoke source strength; they do not assess plume-rise models – that might be Val Martin et al., 2012 and Paugam 2016.
f. And it continues… it is up to the authors to go through all the references.

2. Lines 74-75. “The vast majority of biomass burning is a man-made activity…” This is true only in certain regions, not in general, and not globally.

3. Lines 85-90. The primary reasons plume rise models have difficulty reproducing the actual aerosol vertical distribution in the atmosphere is difficulty in quantifying the heat flux and in modeling entrainment (Kahn et al., 2007, Val Martin et al., 2012). Removal mechanisms in general, and rainfall in particular, are relevant to longer distance transport and deposition, but not to plume rise in most cases. Aerosol processing in polluted conditions is important for aerosol chemical evolution but is likely to be a dominant factor in plume rise modeling only in very special cases. This entire paragraph discusses factors relevant to transport and deposition, without making clear that it is no longer discussing plume rise modeling.

4. Lines 94-95. Again, the references don’t seem to address the context. And it is not clear what type of simple models are being discussed (plume rise or transport and deposition).

5. Another paper that might be worth reviewing in the context of this study is Heald et al. 2004, doi:10.1029/2004JD005185. And the following might also be of help: Kahn 2020 doi.org/10.1029/2020EO138260.

6. Lines 129-133. Given the diversity of burning conditions in boreal forest, tropical forest, grassland, agricultural land, etc., it is not clear why one would look at global average variability rather than stratifying at least into these general categories.

7. Lines 134-137. Rather than something deeper, the distribution of burning reported here seems to just reflect that the subtropics are dominated by un-vegetated desert.

8. Line 147. The reason given for averaging MOPITT to 1x1 degree does not seem to be justified by the statement that the data are affected by clouds and orbital limitations. MISR data are also affected by clouds, MISR is in the same orbit as MOPITT, and MOPITT actually has a wider swath, yet the MISR data are averaged to 10 x 10 km in this study.

9. Line 158. Note that NO2 is produced by a range of anthropogenic activities, so as the focus here is on wildfires, one must be careful not to assign to wildfires NO2 produced by other sources.

10. Lines 162-163. There are many other differences between wildfire emissions and those from urban combustion sources.

11. Line 169-173. Note that the Freitas (2007) model was developed in part to address some of the limitations of the Briggs model. So was Sofiev et al. (2012, doi:10.5194/acp-12-1995-2012), which probably should be contrasted with the approach given in Section 2.7 of the current paper.

12. Line 177. You might say more about the MODIS data used; “MODIS hot-spot information” is not enough.

13. Lines 179-185. A key input to the plume rise model would be the dynamical heat flux, or some other measure of the buoyancy generated by the fire. As this would not come from the NCEP reanalysis, does this come in some way from the MODIS hot-spot information?

14. Lines 223-224. Figure 2 is very difficult to interpret. The axes should be labeled, and the number of counts in each region should be given, maybe in the legend or in Table S1 (or both). Also, some smoothing or an expanded vertical axis might help in eliciting the main patterns from the mass of lines in this figure.

15. Line 225. An injection height of 29 km seems very unlikely. The most extreme PyroCb on record reached no more than 3-5 km above the tropopause, to about 17 km in that case. The extreme height seems more likely to be an error, perhaps in co-registration of the multi-angle images.

16. Line 231. If ~8% of the plumes in this study are above 5 km, and they are likely to be concentrated in certain regions, wouldn’t that be important to include in the study, especially as these would have to be major events, possibly generating a disproportionate amount of smoke?

17. Line 240. The vertical resolution of the MISR plume height retrievals is between 250 and 500 m, so how does the data set report percentages of plumes below 200 m?

18. Lines 244-253. Two limitations of the MISR data should be noted. First, as the MISR swath is about 380 km wide, locations on Earth are sampled on average about once per week, which still captures many fires, but misses many others. Second, the MISR overpass is at about 10:30 AM local time, whereas biomass burning tends to peak in the late afternoon. These limitations do not invalidate the work, but they should be taken into consideration when presenting global statistical conclusions. For example, the burning season might appear truncated if much of the actual burning occurs only later in the day than the MISR overpass.

19. Lines 259-269. FRP is only loosely correlated with plume buoyancy, for specific physical reasons; the dominant ones are: (1) partly filled pixels; (2) non-zero smoke opacity above the fire front (which you mention), and (3) fire emissivity less than 1 (e.g., smoldering). This results in loose correlation between FRP and injection height. See, e.g., Kahn et al., 2007 or Val Martin et al. 2012, Figures 7 and 8 and associated text.

20. Lines 283-284. Gas emissions are related not solely on the buoyancy generated. In addition to the factors mentioned, different ratios of CO and NO2, depend, for example, on fuel type and surface moisture.

21. Lines 294-300. Note that fire fronts are typically on much smaller scales (10s of meters) than the CO and NO2 measurements. In Northern China, high background CO and NO2 is likely due to anthropogenic activity, whereas in Siberia, it is likely from other fires. Often multiple fires of different sizes burn in an area where fuel load and fire weather conditions are favorable. You probably need to carefully separate any background contributions from those generated by the fire of interest to obtain a meaningful relationship between the gas concentrations and plume rise. Simply identifying above-background pixels and assuming the background contributions are negligible might not be good enough.

22. Lines 323-328. Aerosol radiative effects, rainfall, etc., can be important for transported smoke, perhaps even a few hours after emission. But the buoyancy, ambient atmospheric structure, and entrainment are likely to dominate during plume injection.

23. Line 337. I’ve lost track of which plume rise model is being discussed here. I thought you were testing all seven regression models given in Equations 1-7.

24. Lines 352-355. Again, I’m unclear what model is being discussed. I do not recall discussion earlier of a plume rise model having a vertical resolution that would resolve better than 0.5 km in the boundary layer.

25. Lines 414-421. It is interesting that the column concentrations of CO and NO2 provide better correlation with plume height than FRP or wind. The CO and NO2 are not height-resolved, although in some cases these gases would be primarily generated by the fire in question, perhaps yielding an indication of fire intensity. It might be worthwhile to investigate this further, as it would offer a physical explanation for the observed correlations. Identifying the conditions when the relationship does not apply, perhaps cases where NO2 or CO from other sources dominates, for example, might also help in interpreting the data and improving the model.

26. Lines 435-437. Regarding the much smaller variance in the measured values, it might be worth remembering that the MISR plume heights are all acquired only around 10:30 AM local time.

27. Lines 451-458. I think the reasons behind the performance of the regression model might be among the most important results of a study such as this one.

28. Section 3.4. One way to assess regression model performance is by randomly selecting 10% or 20% of the data to leave out when the regression coefficients are calculated, and then comparing the model with against the withheld data.

29. Lines 508-514. Accounting for the complex distribution of flaming and smoldering in many fire situations, especially larger ones, and modeling entrainment accordingly, are probably important if not dominant factors.

Dear Authors,

I am pleased to let you know that I am happy to accept your manuscript subject to some additional minor revisions related to the Figures of your manuscript. You have done a good job addressing all reviewer comments but there are no axes labels on Figures 1, 2, and 6, and the font on a lot of your Figures appears too small in my pdf version of the manuscript to be legible. Please can you carefully check each figure, add labels and increase the font size etc and then upload a revised version of your manuscript? If you have any questions then please don't hesitate to get in touch with me.

Thank you for your submission to ACP.

Kind regards,
Anja Schmidt (as2737@cam.ac.uk)