Tropical circulation and so-called “tropical width” changes are important phenomena to better understand in the context of climate variability and change. The paper “Variability and trends in the PV-gradient dynamical tropopause” by Turhal et al. examines a new definition for tropical width based on a potential vorticity-based definition that is applied to several reanalyses. This paper is very well written and thorough, and I have no doubt it will be of great interest to ACP readers. I have mostly minor suggestions to clarify a few points in the manuscript.

The only “major” point I would like to suggest is that the authors consider whether their rather more involved methodology (which involves computing PV, etc. from the reanalysis model level fields at high temporal frequency and complicated peak finding rules) is really necessary in order to accurately quantify the seasonal to multidecadal variability in the PVG tropopause latitudes? I have no objection to applying this more “expensive” approach to analyzing the data if it is truly necessary, but it would be helpful for future users to know whether it really is necessary, or whether more simplified approaches with averaged fields could be used without a loss of fidelity (e.g., monthly mean PV/wind fields on pre-determined isentropic levels, as is commonly provided by reanalysis centers)? The answer to this question has implications for how easily this type of analysis might be extended in time or to other reanalyses, as well as how straightforwardly it might be applied to model output fields from multi model experiments (where high temporal / vertical resolution fields are often not made available). If the authors could provide some insight on this issue, I think it would be a valuable contribution to the community.

Other than the one more major comment, below is a list of a few minor comments/revision suggestions:

Line 53: I suggest defining PVU at its first use (i.e., the SI unit equivalent)

Line 84: Suggest citing Waugh et al 2018 here.

Line 97: Suggest citing Santer et al 2003 here: Santer, B. D.: Contributions of Anthropogenic and Natural Forcing to Recent Tropopause Height Changes, Science, 301, 479–483, https://doi.org/10.1126/science.1084123, 2003.

Line 114: I think “contracted” might be a more appropriate word here than “converged”

Line 119: “to which extent” -> “to what extent”

Line 140 – 145: This intro section confused me at first because it seemed to not be a detailed enough description, but then I eventually figured out that the material was discussed in further detail in the following subsections. You might consider referencing the subsections here to make it clear that further details are provided there.

Line 140 – 141 (and elsewhere): I found myself confused a few times in the manuscript regarding some of the uses of words like “gradient” where the direction of the gradient was not really specified. In this sentence (and throughout the paper) the gradients being referenced are meridional gradients on isentropes. Similarly, there’s a bit of potential confusion around the discussion of the PVG dynamical tropopause being something that is defined based on a meridional gradient, versus what most people think of which is the tropopause being defined based on a vertical gradient/threshold. It might be worth considering the language in the paper and whether it would be more appropriate to use the term PVG dynamical tropopause *width* when referring to the latitude, rather than just calling it the PVG dynamical tropopause.

Line 147: Why does the analysis only go through 2017?

Line 175: I don’t see the Bosilovich refence in the bibliography, but I think a more appropriate reference is Gelaro et al.

Gelaro, R., Suarez, M. J., Molod, A., Takacs, L., Randles, C., Darmenov, A., Bosilovich, M. G., Reichle, R., Cullather, R., Draper, C., Akella, S., Buchard, V., Gu, W., Koster, R., Merkova, D., Nielsen, J. E., Partyka, G., Putman, W., Rienecker, M., Bin Zhao, McCarty, W., Todling, R., Randles, C., Darmenov, A., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A., Kim, G.-K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J. E., Pawson, S., Rienecker, M., Schubert, S. D., Sienkiewicz, M., and Bin Zhao: The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2), http://dx.doi.org/10.1175/JCLI-D-16-0758.1, JCLI-D-16-0758.1, https://doi.org/10.1175/JCLI-D-16-0758.1, 2017.

Line 180: What is the temporal resolution of the reanalysis data sets used here? The issues regarding the use of full resolution reanalysis data versus isentropic-interpolated monthly mean data could be at least partially addressed in this paragraph.

Line 197: I think the lapse rate should be -dT/dz here?

Line 200 and 204: Would it be helpful to be more specific about the dimension (vertical or horizontal) which is being referred to here in the context of gradients?

Line 215: One thing that I was curious about in the PVG tropopause definition here is why both windspeed and PVG are used rather than just simply PVG. Perhaps this is addressed in the Kunz paper but could the authors mention somewhere in the paper why both are necessary? This relates to my comments around whether or not one really needs to implement the most maximalist analysis of the data in order to capture the important variability, or whether a more simplified definition (e.g., based on monthly mean PV data alone) would suffice?

Line 228: Again, going to the simplicity of the definition, is it really necessary to compute the break on equivalent latitude rather than geographical latitude?

Line 235 – 248: These seem like a complicated set of rules and bring up several questions to me. First, do the authors really need to identify the PVG tropopause width at each reanalysis time step? If the goal is to create monthly means, why not average fields first? I suspect that doing something like this could allow the peak finding to be more straightforward and not require so many ad hoc rules. Also, related to peak finding, there are several methods outlined in the TropD software package (Adam et al., 2018). Is there a reason the authors chose a different approach rather than adopting one of the well documented methods outlined there?

Adam, O., Grise, K. M., Staten, P., Simpson, I. R., Davis, S. M., Davis, N. A., Waugh, D. W., and Birner, T.: The TropD software package: Standardized methods for calculating Tropical Width Diagnostics, Geosci. Model Dev., 1–35, https://doi.org/10.5194/gmd-2018-124, 2018.

Line 265-267: I find the discussion around the seasonal cycle term confusing here. It seems as though it is something that is fit from the fact that it is included in the equation, but then it sounds like it is not included in the fit and that what is fit to is actually the de-seasonalized data.

Line 276: The QBO winds at 30 and 50 hPa are not truly orthogonal to one another, and I think that a better practice is to fit to QBO EOFs. That said, my guess it doesn’t significantly impact the results that much.

Figure 1: I appreciate that it is easier to look at 2 plots than 4, but I always feel like I am missing something when people only show 2 seasons rather than 4. Given that the authors are trying to document a new method, I think it is important to show results for all 4 seasons. This could easily be done with the use of supplemental figures if the authors feel like it would significantly detract from the manuscript.

Line 322: It looks to me like PVG and WMO tropopauses agree well up to 360K, but not 370K in all seasons/hemispheres.

Line 376-378: Is this due to STJ/EDJ separation?

Line 426-435: Is this due to horizontal resolution differences?

Line 439: The word “Conclusively” doesn’t seem right here

Line 460-461: Do you have an idea of why ERA5 is different. Horizontal resolution?

Line 585: “Hereof” doesn’t seem like the correct word to use.

Review of Variability and trends in the PV-gradient dynamical tropopause by Katharina Turhal et al. 

This paper uses a PV-gradient tropopause definition to assess the climatology, variability, and long term trends of the tropopause in potential temperature space, with applicability to assessing tropical width. The authors’ method is novel in allowing for vertical variation of tropical width and their results fit in well with the current state of the research. The paper is thorough and compelling and will be of substantial interest to the readers of ACP. 

There are some places where I feel the manuscript could be more clear and concise to improve the readability of the paper, for which I have provided some suggestions below. Additionally, I find the global-zonal mean aspect of the analysis to be a limitation of the work which should either be addressed by additional analysis or further discussion. My detailed comments are below.

General Comments:

1. The use of a global zonal mean in all the analysis seems limiting for the work, especially given some of the citations provided that emphasized that there were strong regional (longitudinal) differences in assessing STJ/tropical width changes. Specifically, the asian monsoon anticyclone has such a profound impact on the tropopause height and the lower stratosphere in general in the northern hemisphere that is lost in this analysis because of global zonal means. Additionally, some of the tropopause characteristics of the northern hemisphere might be skewed because of the influence of the asian monsoon. I think some supplementary regional analysis would greatly improve the paper. Otherwise, there should be some discussion about these limitations.
1. Current figure captions should probably all include that they are zonal means for clarity
2. I suggest eliminating the uses of "cf." throughout the manuscript in references to figures/equations, as this suggests that you are wanting readers to “compare” with your own works. In many of these situations just deleting the cf. and using (Fig. X) or (Eq. Y) is appropriate. In other cases, I suggest replacing (cf. Fig. X) with (see Fig. X)  
3. There are several uses of the word “significant” throughout the manuscript that may be more suitably expressed as “substantial” or a similar word, since “significant” implies the existence of statistical significance testing.
4. There are several uses of the word “resolution” throughout the manuscript that I believe is intended to describe horizontal or vertical grid spacing and therefore should be replaced with “grid spacing”
5. What time steps are used in your analysis? Are they all at the reanalysis native time steps (6 hourly except for ERA 5 at 1 hourly)? Or are they all 6 hourly? Or daily? If you are working at every timestep, does the increased temporal frequency make a difference? 
6. With the value of PV being important and frequently discussed throughout the paper, it makes me wonder if the strength of the gradient is important? And how would that vary seasonally and over time? This may be outside of the scope of this work but seems just as important as PV magnitude when thinking about relevance to dynamic transport.
7. I found some of the differences between reanalyses surprising. Some discussion into possible reasonings could be helpful. Especially when ERA-5 is quite a bit different from the others… is it because of resolution? 

Specific Comments:

1. Lines 1-2: This opening sentence was a little confusing to read at first. I suggest rewording to “The dynamical tropopause acts as a transport… lowermost stratosphere and is characterized by…” or something similar
2. Line 34: suggest adding “at altitudes” before “slightly below the subtropical jets”
3. Lines 35-36: Do these citations present estimated frequencies of these occurrences that could be included here?
4. Line 38-41: I wouldn’t say the lowermost stratosphere plays a role in STE as much as it is an important location with regards to STE. Suggest rewording.
5. Line 46: Suggest rewording to “At the tropopause, there is a transition from lower PV values…”
6. Line 55: ‘Applicability’ might be a better word than ‘accuracy’ here?
7. Lines 87-91: This sentence is a bit long and hard to understand. Specifically, I’m not sure exactly if the statement “and coupling with sea surface temperatures” is supposed to be related to the Hadley cell or jet locations or ENSO or the PDO or all of the above.
8. Line 91: Suggest rewording “It is even under discussion”
9. Paragraph starting at Line 94: Discussion of double tropopauses and their relationship to a changing climate/tropical width could be a nice addition here
10. Section 2.1: The approximate vertical resolution of each reanalysis in the region of interest (UTLS) would be a helpful addition here 
11. Line 175: I think Gelaro et al. 2017 is the appropriate reference here (https://doi.org/10.1175/JCLI-D-16-0758.1)
12. Line 183: I don’t think “down-scaled” is the right word here. Also, is the vertical resolution changed at all in this run?
13. Section 2.2: This section is where I felt the manuscript most lacked clarity and conciseness. I understand and sympathize with the fact that there are many important details that should be included here, but there were some places where it felt some of these details overshadowed the main goal of what you were trying to show and emphasize here. One potential suggestion would be to carefully consider which equations actually need to be shown here and described in detail. And/or, I think it would be possible to shorten some of the discussion on page 7 without taking away from the important points you are wanting to get across.
1. Some of the details in this section also confused me a bit about the inclusion of the importance of wind shear in calculating PV. Its emphasized in line 203-207 that relative vorticity is strongly impacted by horizontal wind shear and therefore the STJs. This led me to question whether the inclusion of horizontal wind in calculating Q sort of ‘double counts’ the STJ in a way? I think clearer discussion on this would be helpful.
14. Line 197: lapse rate should be negative dT/dZ
15. Figure 1: Specify that this is a global zonal mean. 
16. Lines 298 - 300: This sentence is a bit wordy, suggest revising to something along the lines of “Hence, the common practice of defining the dynamical tropopause as a PV isosurface (e.g., 2 PVU) for studies of stratosphere-troposphere exchange…”
17. Lines 300-301: I would be careful saying that they agree well throughout different seasons when MAM and SON are both not shown here
18. Line 350: Please provide reasoning for only including DJF and JJA. Is it just that the results from other seasons just not that interesting? 
19. Figure 2: The organizing of the panels on this figure (going a,b,e,f across the top row and c,d,g,h across the bottom row) feels a bit weird 
20. Line 387: Please include a citation here 
21. Line 417: I think “consistent” might be more appropriate than “robust” here
22. Line 420: Suggest rewording “could probably be related to”
23. Line 432: Maybe go with “qualitatively similar” or “qualitatively consistent” instead of robust
24. Line 439: Conclusively doesn’t feel like the right word here.
25. Lines 439-442: While I agree with the sentiment of this statement about avoiding errors by using one consistent reanalysis, I think it's also important to emphasize that use of multiple models could be important to represent the range of possibilities of the actual atmosphere due to some of the larger inconsistencies between the reanalyses.
26. Line 474: “PV variability appears smaller than expected…” compared to what? What was expected and why? 
27. Lines 474-478: suggest rewording this for clarity, maybe by breaking into two separate sentences?
28. Figure 5: It could be useful here to plot the absolute value of pv on the ordinate to make it easier for the reader to see the direct comparison of the NH and SH? But this may just be a personal preference 
29. Figures 6,7,8: I suggest changing the order in which the reanalysis markers are plotted, such that the ERA-Interim “x” and the MERRA-2 “+” are plotted last and are therefore not covered up by the diamonds/circles. 
30. Figure 7: What does the "d.” in "d. El Nino" mean in the panels on the top row? I’m not sure if this is commonplace and I just haven’t seen it before, or if other readers would maybe be confused by this as well.
31. Line 491: Suggest changing “vertical structure in the different reanalyses” to “vertical structure consistent between the different reanalyses”
32. Line 512: Do you include amplitudes of 0 - 1.5 degrees just because of the ERA-Interim outlier at the 320 K? I would maybe suggest changing this to say that amplitudes are primarily confined to 0-1 degree (or even smaller), since that is what is shown basically everywhere else. Do you have any thoughts as to why ERA-Interim is such an outlier at this level in both Figs. 7 and 8?  
33. Lines 515-518: This is a really interesting result and is surprising to me. Is this something you expected or is consistent with previous work? Some discussion of this here or in the conclusion could be nice
34. Lines 554-555: This concluding sentence feels a bit strong considering the large differences between the reanalyses.
35. Line 578: This first sentence feels repetitive with the following sentence. Suggest deleting or reworking
36. Line 583: I think “largely robust variability” is a bit strong here
37. Line 585: suggest deleting or changing “hereof”
38. Lines 607-608: This seems very important and potentially deserving of a few more sentences

Technical Corrections:

1. Line 8: inter-annual → interannual 
2. Line 29: concurs → coincides
3. Line 51: The PV-based → A PV-based
4. Line 53: Define/include metric equivalent of PVU
5. Line 61: Don’t capitalize upper troposphere lower stratosphere 
6. Line 63: Furthermore → Hereafter
7. Line 68: metrics are → metrics have been
8. Line 125: As of now → To the authors knowledge
9. Line 133: Remove dash in “time-scales”
10. Line 156: ERA5 is extended from → ERA5 extends from
11. Line 190: levels of potential temperature → surfaces of constant potential temperature
12. Line 250: World Meteorological Organization WMO (1957) → World Meteorological Organization (WMO; World Meteorological Organization 1957)
13. Line 275: normed → normalized
14. Line 301: remove “ca.” 
15. Line 353 and nearby: resolution → bin size
16. Line 362: span → reach 
17. Line 483: Inter-annual → Interannual 
18. Line 498: similarly → similar
19. Line 512: magnitudes → magnitude
20. Line 567: fix the single quotation mark direction