Major comment

Minor comments

• Title: the current title is very generic. Please at least refer to gravity waves in it.
• L. 1: "a decade" please state which years we are talking about here (2002-2012 ?)
• L. 18: "The surfaces of PSCs" I don't think we can say that clouds have surfaces. Maybe "the surface of PSC particles"
• L. 46-47: This paragraph begins by explaining the primary focus of the study is to investigate the occurrence of ice PSC observed by MIPAS and characterized by temperatures above the ice existence threshold. Please explain why, when interested in the relationship between ice PSC and gravity waves (as the beginning of the section suggests), it would be a good idea to do that (see major comment).
• L. 76-85: Here you explain your alternative to using the tangent point for identifying the location of a PSC that MIPAS has detected along its line of sight. Have you tried to investigate the spatial distribution of temperatures along the line of sight? Is it frequent for cold temperatures to be spatially spread along the line of sight far from the point identified as the coldest? Or can you have two locations along the line of sight with similar coldest temperatures? This would mean the PSC location is affected by strong uncertainties. In other words, how well defined spatially is the ΔTicemin?
• L. 101, 103: References to Hoffmann et al. 2017b and a are missing parentheses. Also please fix the citations (a should be cited before b).
• Section 2.2: Please explain why you use both ERA-Interim *and* ERA5. Spatial/temporal resolutions appear similar, so why isn't it possible to pick just one reanalysis dataset? If using two datasets is mandatory, could you talk about how potential disagreements in polar stratospheric temperatures from both datasets would affect your results?
• Section 2.2: I was under the impression that Hoffmann et al 2017 (the one about Concordiasi) suggested that ERA-Interim suffers from a zonally increasing warm bias in the south pole. Is that affecting your results in any way? Is this bias corrected in ERA5?
• L. 116: what does it mean for the Lagrangian transport to be significantly impacted? Is it better, worse, something else? Does this suggest that using ERA5 (instead of ERA-Interim) for locating and quantifying the ΔTicemin would lead to different results?
• L. 119: Here you state that your aim is to "conduct a statistical analysis of ice PSCs where the temperature at the MIPAS observation is above the frost point temperature". Again, in my opinion you have not made clear enough why you might want to do that (see main comment). Please make explicit the link with gravity wave activity.
• L. 135: After lines 76-85, this is the second time you explain your alternative to the tangent point for PSC detection. You explain it again on lines 240-242. Please try to limit these explanations.
• L. 139: "highest occurrence frequency": over which time scales? 2% is not a lot.
• L. 146: Here you describe that most ΔTicemin are found below the frost point. Reading this confused me at first, since on lines 119 you explain that your focus is on points that are above the frost point. I think you could limit reader confusion that making it clearer from the start that you expect ΔTicemin above the frost point to be rare, and that you take them as the sign of small-scale temperature perturbations from gravity waves, i.e. by clarifying why you are doing what you are doing (see main comment).
• L. 148-149: The discussion about ice PSC particles nucleating at temperatures colder than Tice mirrors the one found on lines 123-125, but with fewer details. Please find a way to combine both discussions. I think the discussion should happen in Section 3.1, but with the details found in lines 123-125.
• L. 151: "T-Tice-3K" I'm guessing here you mean Tice-3K
• L. 175: "Fig. 5 displays the fraction of ice PSCs above Tice". I did not understand this part. As I understand, MPTRAC calculates backward trajectories starting from the point where a PSC was located according to MIPAS observations + ΔTicemin from ERA5. MPTRAC provides the evolution of temperature and other parameters along the backtrajectory, but has no way to know when a PSC was present in the air mass that it is tracking, and does not provide that information. Are you assuming that the air mass where a PSC was detected at t=0 contains a PSC over the previous 24 h through the entire backtrajectory? Please clarify my misunderstanding. (also please fix related wording line 309)
• L. 176: "(t) t=-24 (h)" -- do you mean t=-24h ?
• L. 177-178: It appears strange to me to say the fraction decreases by going from t=0 to t=-6h, ie going backwards in time. It would appear more natural to say the fraction increases from t=-6h to t=0.
• L. 180: "6h before the observation, temperatures of most ice PSC... are below Tice". If I read Fig. 5 correctly, it looks to me like temperatures of most ice PSC are below Tice at all times.
• Section 3.4: If I understand correctly, your main hypothesis is that the influence of gravity waves on PSC can be inferred by ΔTicemin being positive, as it means that the reanalysis temperatures are failing to capture small-scale temperature variations due to GW. In this section, however, you look for short-scale temperature variations within the reanalysis as indicators for the influence of gravity waves. There seems to be a contradiction -- either GW influence is captured in reanalyses, or it isn't. Please clarify my misunderstanding. Are you expecting ERA5 (used by backtrajectories) to better capture the gravity wave influence on temperatures than ERA-Interim (used for ΔTicemin)? Why?
• L. 209-210: "This observation strongly suggests a correlation with orographic waves with ice PSCs above Tice". This reads strange to me. We *know* that orographic waves trigger the formation of ice PSCs. Unless I'm mistaken, this is actually the (unstated) reason why you look for positive ΔTicemin -- because they are the sign of short-scaled temperature perturbations, that are not well captured by ERA-Interim, and are generated by gravity waves. It looks like you are trying here to avoid stating that we already know that orographic waves trigger PSC formation. Please be explicit about your assumptions.
• L. 218-223: I am very confused by this paragraph. I understand your results find that the fraction of T > Tice related to mountain waves are higher in the Arctic than in the Antarctic (l. 220-223), no problem there. But, unless I'm mistaken, your main point is that the fraction of T > Tice related to mountain waves decreases as it gets closer to the observation point. This is what you open your paragraph with, and the main result from Table 1. And yet you make no attempt to explain this decrease. Why is this fraction decreasing as we get closer to observation point? I personally find this result perplexing.
• L. 230: double parentheses
• L. 226-238: This paragraph is the closest you get to state your assumption that PSCs observed at ΔTicemin > 0 are due to small-scale temperature fluctuations from gravity waves that brought temperatures below Tice in a way that is not captured by ERA-interim reanalyses. Still, you need to make this reasoning explicit. Also: if the main hypothesis is that ERA-Interim misses temperature fluctuations that generate PSCs, why should we trust the location of the ΔTicemin according to ERA-Interim? The PSC detected by MIPAS might be somewhere else along the line of sight, in a place more affected by gravity waves (which are not well captured by ERA-Interim). Please address this somehow.
• L. 317: "with temperature fluctuations at the observation point" -- as I understand it, the observation point is fixed in time and space. How can there be temperature fluctuations are the observation point then?
• L. 319: "... suggests a correlation with orographic waves with ice PSCs above Tice". That ice PSC are correlated with orographic waves is a given from the beginning -- you even explain the mechanism in the introduction. You could say that your results are a strong confirmation of these correlations.

Review of ‘A statistical analysis of the occurrence of polar stratospheric ice clouds based on MIPAS satellite   observations and the ERA5 reanalysis’ by Ling Zou et al.

Summary:

The manuscript uses a decade of MIPAS satellite observations of PSCs (polar stratospheric clouds) to investigate the water ice PSC occurrence with respect to frost point temperature, determines their spatial location, and examines back trajectories in order to understand the temperature history of the air parcels in which PSCs are observed. The authors consider the role which small-scale temperature fluctuations (i.e. gravity waves) play in PSC formation and quantify the fraction of PSCs associated with orographically-forced gravity waves. Because of the limb-viewing geometry of the MIPAS satellite, there are uncertainties in the position of the clouds along the line of sight observation path. The authors propose using the point where temperatures are closest to the frost point as the location of the ice PSCs.

The manuscript is well written and provides plenty of evidence to support the idea that orographic gravity waves can play an important part in driving ice PSC formation. I think that the manuscript should become acceptable for publication once the authors consider implementing the below comments.

Major comment:

Overall comment: Most of the manuscript builds up to the point that orographic gravity waves can explain a percentage of the ice PSC observations (33% in the Arctic, 9% in the Antarctic, as noted in the abstract). Yet it seems to me that this is already a well-established result in the literature (much of which is cited within the text already) and so these parts of the manuscript are really just supporting that which is known already. I feel that the novel parts of the manuscript, i.e. the use of MPTRAC back trajectories together with the proposition to use air parcel history (in particular, minimizing the temperature difference to the frost point) as the location of the PSCs, should be brought forward as the central point of the manuscript, and thus emphasized much more clearly in the abstract and conclusions, and indeed through the whole text. Your title could also be reworded in this context.

Line 76 onwards: Discussion about method of identifying most likely ice PSC location as minimizing relative to the frost point temperature. Does this method reduce the hundreds of kilometers of horizontal uncertainty (which you noted on line 80)? By how much? I should like to see some attempt to quantify the reduction in error as I think that is central to your manuscript. For instance, with the method here do you observe any gravity-wave connected ice PSCs upwind of mountain ranges? This may help indicate a bound on your accuracy. You would likely have better ideas on quantifying this uncertainty.

Minor Comments:

Line 1: ‘occurrence of ice clouds’. I think you mean PSC water ice clouds, rather than tropospheric cirrus clouds. Clarify.

Line 2: which decade?

Line 13: ‘correlation’: have you performed a correlation analysis? I couldn’t find one. Correlation doesn’t imply causation anyway.

Line 24 (or somewhere close by): Given that you spend much of manuscript discussing ‘small-scale temperature fluctuations’, I think you need to introduce the concept of gravity wave generation by mountains, explaining that these can cause small horizontal scale temperature perturbations in the stratosphere which are large enough to enable some PSC formation in the cold phase of these waves, even when the background (synoptic) scale temperature is too warm for their formation. And thus missing these waves in model (climate) simulations will effect the model PSC representation. Plenty of references abound for this discussion, many of which you already cite.

Line 38 (or somewhere close by): You haven’t discussed the CALIOP wave-ice PSC class, as defined by Pitts et al. 2013 doi:10.5194/acp-13-2975-2013. This class addresses a similar problem to what you are here, namely using satellites to attempt to quantify gravity wave influence on PSC formation, but in a different way to how you do it with MIPAS. Some mention of the CALIOP wave-ice would be beneficial in the introduction.

Line 51: ‘we explore the temperature variations’: There seems a bit of a reluctance in the paper to use the phrase ‘gravity waves’ or ‘orographic gravity waves’ when this is what you are doing. Maybe because you are building up to attributing the ice PSCs to gravity wave activity. Consider rephrasing. See also Major Comment above.

Line 85: You use ERA-Interim for this identification but use ERA5 elsewhere, so why use ERA-Interim anymore? There is no explanation given, so please provide a justification. But, line 116 says ERA5 is much better for Lagrangian transport, it is “significantly impacted” as you write. So I think that you should really use ERA5 for identifying the minimum difference to the frost point. It will capture the small-scale gravity waves more effectively than ERA-Interim, which is a major point of your study. Also given the finer resolution in ERA5, I would expect that it will improve your results and likely reduce the horizontal uncertainties. See also my Major Comment ‘Line 76 onwards’ above.

Line 88: ‘up to -6.1km below’ reads awkwardly. Reword and simplify.

Line 123: Add year to Koop reference

Line 129: ‘less than 10K above’ should be reworded for simplicity

Line 139: ‘frequency over 16%’ – but your scale is cut at 16% so you can’t comment on this!

Line 142: discussion of the Arctic vortex. I think you need some references and explanations about the off-pole position of the Arctic vortex here, noting the role of planetary waves in the NH in forming the vortex in this location.

Line 143: A sentence linking this climatology to previous PSC climatologies would be useful (e.g. see Tritscher et al. Rev Geophys 2021, their Fig 11 and Fig 21)

Line 148: sentence beginning ‘Since ice PSCs…’ this sentence on thresholds was discussed already. Consolidate or remove.

Line 150-151 : You should consider a cumulative frequency plot to illustrate the points you are making here (i.e. the 90% and 100% thresholds)

Line 151: ‘T-Tice-3K’ recheck this phrase

Line 162: Worth stating clearly that these are low fractions (a few %). But, they are similar to CALIOP results (e.g. Alexander et al. 2013).

Line 167: Years 2005 and especially 2011 were major SSWs with large ozone losses (See Manney et al. Nature, 2011, doi:10.1038/nature10556). Think about the larger context, and suggest you cite this Manney paper, or others which you may wish, to provide this larger overview of the interannual variability.

Figure 4: You should add some uncertainty bars on these panels. You have 10 years of data. These can describe the interannual variability

Figure 6: A really bad color choice of a red star! I suggest you use black

Section 3.5 title and wording ‘Correlation’. Are you actually performing a correlation analysis? Seems not. I think you need to remove this word ‘correlation’ throughout your text.

Line 222: Is gravity wave activity really more frequent in the NH (mountainous regions) than in the SH? You need to provide a reference here! Or, is it that the Arctic is synoptically warmer and generally hovers just above Tice, so any orographic waves are more likely to increase ice PSC fraction when compared with the synoptically colder Antarctic. Explanation is needed, either way.

Line 237: Can you quantify, or at least state/cite the underestimation of temperature fluctuations?

Line 238: ‘The analysis applied in this study provides important information on the frequency and significance of these discrepancies’: I’m afraid that I can’t find the text which supports this statement. Please refer back to the figure / section where this is true, or remove/reword.

Line 262: Uncertainty of approximately 0.2K. Is this about the figure for the polar regions? How bad is a 0.2K uncertainty? Your bins in Figure 10 are much larger so I suspect this uncertainty is not a big deal. Comments required.

Line 267: You write that you use water vapor data from ERA5. But you can obtain water vapor data from MLS satellite (e.g. see Tritscher et al. 2021, Rev. Geophys.). Have you considered doing so?

Line 291: How about also considering the actual generation mechanism of the waves? Dornbrack et al. (2001, doi: 10.1029/2000JD900194) provide a set of criteria for mountain wave activity. Essentially, at many times, near-surface winds are not conducive for the formation of orographic gravity waves. They only happen when surface winds are of the correct angle against the mountain range, and the background wind allows their propagation into the stratosphere. So while it may be the ’unresolved temperature fluctuations in ERA5’ which is the issue, or it could be something else.

Line 295: ‘are proposed to’ – what about ‘are shown to’?

Line 300: ‘which is about 2-4km higher above the tangent point’. This phrase needs explaining

Line 316: where has the ‘significant correlation’ been demonstrated?

Line 324: As suggested above, what about the point that the Arctic is synoptically warmer and thus orographic waves’ influence on PSC formation can have a larger fractional impact?

This manuscript looked at the relationship between temperatures and the formation of ice PSCs. Unfortunately, it was difficult to read, and also rather unconvincing.  For example, the importance of the science question being addressed was unconvincing (e.g., how does this work build on state-of-the-art understanding).  The methods were also unclear, and muddled. For example, it was never clear to me whether reanalysis was meant to represent fine-scale gravity waves or not meant to.  The writing was also poor / casual and the figures poorly explained, with many mistakes (I have only mentioned some of them below).  I suggest that the authors should take their time with thoroughly revising this paper and improving the motivation, methods, structure, grammar, explanation of results, etc.  To do this requires a fresh submission. 

Major comments

1 The justification for this work is weak. The manuscript states that the ‘primary focus is to investigate the occurrence of ice PSCs observed by Envisat MIPAS (Spang et al., 2004, 2018) and characterized by temperatures above the ice existence threshold (Tice), as derived from by ERA5 reanalysis (Hersbach et al., 2020)’.  But surely there has already been considerable research on this topic (e.g., Tritscher et al., 2021).  This needs to be properly explained in the Introduction (i.e., knowledge gaps), and the novelty/importance of the science question then properly justified.     

2 The Introduction explains the importance of fine-scale mountain waves for PSC formation.  It then states that such waves are poorly or under-represented in reanalysis. But it then proceeds to use reanalysis to resolve the temperature perturbations.  I think the idea is that the work then goes onto to show that ice PSCs are shown to occur at temperatures warmer than Tice based on reanalysis temperatures, which implies that fine-scale mountain waves are likely responsible for lowering the temperature to below Tice – but these perturbations are not captured in reanalysis.  This is not well explained, and together with my comment above that the justification for the work is weak, gives an overall impression of the paper being rather muddled.     

3 Some justification is necessary for using ERA5/ERA-Interim. For example how accurate is it at representing (environmental) temperatures in the stratosphere during the polar winter – which is crucial to the approach used here.  Maybe you could also give some detail of the observational products assimilated in this region, etc.  Also, how ERA-Interim and ERA5 are used is poorly explained and confusing.  Some justification is also necessary for why two separate reanalyses were used, and not simply one.  I would suggest that it would be clearer if the reanalysis has a separate sub-section in the methods, rather than being lumped together with the sections describing the models or satellite data. 

4 The Methods section needs to be clearer / more coherent, as it has perhaps been written by a number of authors. It is difficult to follow and weak.  Also, not sure that the title of the manuscript can solely mention ERA5, when ERA-Interim also used.    

5 The figures and captions need to be improved.  There are many mistakes, such as different font sizes, missing units.  The captions are not complete enough.  Especially, use either T-Tice in the text/figures or define \Delta Tice_min properly and use that – but don’t use both or flip between the two.

6 There are a lot of minor/casual/obvious mistakes in the manuscript, including grammar. All these mistakes must be found and corrected.  Also please check the headings.  For example, 3.1 is ‘Ice PSCs detected by MIPAS’, but surely 3.2 is also MIPAS observations. 

Minor comments

1 Line 1: The opening line on the importance of mountain waves as a PSC formation mechanism seems completed disconnected with most of the abstract – especially the earlier parts.  This needs to be much more coherent.

2 Line 3: The definition of \Delta Tice_min is poorly described and confusing.

3 Line 27: I would quantify what you mean by small-scale waves, i.e., explcitly give the scale in km.

4 Line 30: This sentence is not quite clear.  Are you saying that 63% of all ice PSCs during the period of interest were associated with mountain waves?  Please clarify.

5 Line 41: Grammar. Suggest ‘Carslaw et al. (1999) unveiled’.

6 Line 44: Maybe better to refer to ‘mountain waves’ throughout the text, rather than swop between gravity waves and mountain waves.

7 Line 43: I’m not quite sure what the sentence beginning ‘Temperature perturbations …’ is trying to say here.

8 Line 44: The waves are ‘fine-scale’ temperature fluctuations, not ‘subgrid-scale’. And its not ‘may not be fully resolved’, its ‘are underestimated / not fully resolved’.

9 Line 61-62: Slightly awkward sentence. Can it be revised.

10 Line 68: The CI needs to be defined first, before a statement can be made saying its sensitive to PSCs.  This paragraph maybe needs some reorganisation.  

11 Line 74: ICE_NAT, STS_NAT etc need to be properly explained/defined, ie state that class #4 is a mixture of ice and NAT PSCs.  

12 Line 86: Please see comment above about the CI not being properly defined. This needs to be done so that the reader understands what CI > 1.2 means. 

13 Line 47 and 85: Not sure whether its ERA-Interim or ERA5 being used.  Please clarify.  Title says ERA5.  Also, need some explanation of how reliable reanalysis is for this task.  

14 Line 95: MPTRAC already defined.

15 Line 98. Grammar. I think this should ‘e.g.’ and not ‘i.e.’.

16 Line 99: FLEXPART needs to be defined.

17 Line 107 to 111: This paragraph should be included when ERA-Interim is first used in the methods. The heading for section 2.2 should also be revised.

18 Line 120: Repetition.  It was only just mentioned earlier that ERA5 was used to calculate Tice. 

19 Line 134: This sub-heading does not seem appropriate.  Is only 3.1 focused on MIPAS?

20 Line 135: Repetition.  This has already been explained in the methods. And if wasn’t completely explained there, then absolutely should be.

21 Line 138: Please refer to latitude and longitude correctly. ‘south of 65deg’ means nothing, unless its written 65S. Also ‘longitude range of +-90deg’ is also wrong.  Please ensure that lat and lon are correctly described everywhere in the text.

22 Line 139: Grammar. Highest occurrence frequency over 16%.  Also ‘Over the seasons’ – not sure what that means.

23 Line 145: Sentence beginning ‘In both polar regions’ does not make sense.

24 Figure 1: Colour bars are not labelled.  The caption does not mention what the different panels are.   Why are different font sizes used for the labels in panels b and d?  Presumably panels b and d show mean values over the entire polar region?  - This is not clear from the caption.   In the figure, I don’t think that the labels for each panel are necessary or even helpful.

25 Figure 1: This is unclear: difference between Tice and T along the line of sight (∆Tice_min).  Why have such a convoluted way of explaining what Tice-T is?  Also, it should be written as \Delta Tice_min = T – Tice (ie as a formula).

26 Lines 144-145: Convoluted way of explaining what is in Fig. 2.  Either use T-Tice everywhere, or defined \Delta Tice = T – Tice and use this everywhere. 

27 Figure 2: Same comments as above.  Figure does not have units of temperature.  The label SH \Delta Tice_min is wrong as the axis is already labelled as T-Tice.  The panel labelling of ‘ICE’ is unnecessary.  Also, not sure what ‘Fraction to observations’ means.

28 Line 147: Grammar. Comma after 56% not required.

29 Line 148: ‘Derived from ERA5 reanalysis’ not required.

30 Line 149-150: Repetition.  T-3K and T-1.5K are already explained.

31 Line 150: Is T-Tice-3K correct?  Should it not be Tice-3K?  Why is a ‘)’ included here.

32 Line 154: Please revise sub-headings.  I’m not sure how the material in this sub-section differs from the previous section.

33 Figure 3 caption:  Grammar – please correct.  Also, normally captions say ‘Analogous’ rather than ‘Similar’ in this context.

34 Line 160: Not sure use of ‘trend’ is appropriate here.  Could simply say ‘decrease in altitude throughout winter’.

35 Line 161: This is a strange sentence, and does not make sense.  Also, why is the physically basis for this rather randomly explained here, but not for other results?

36 Line 165: Rather than writing just ‘comparable’, you also need to give the values.

37 Line 167-168: This sentence makes no sense.  ‘lower occurrence of ice PSCs … due to few ice PSCs’.

38 Line 169: Again, the explanation for this points is welcomed for its insight, but should be done consistently, or saved for the discussion.  Broad statements such as the stability of the Antarctic vortex v Arctic vortex should be introduced in the Introduction – also surely results such as this have been readily explained / shown elsewhere.

39 Line 172: Poor English.

40 Figure 4: Please improve formatting of plots, such as the values on the axis.  These are different for panels b and d, despite both panels being identical.

41 Line 175: What does ‘point of observation at \Delta Tice_min’ mean? 

42 Line 176: ‘(t) t’

43 Line 179: These are not a ‘trend’.  Please use a different word.

44 Figure 5: Not sure what label of vertical axis means. Caption is also far to brief and not enough information for the reader to understand the plot.

45 Lines 184-188: This text should be in the methods section.  Why is the methods being explained in the results section?

46 Line 191: What is ‘t=-0’?

47 Line 193: h^-2 is not a rate.  Rate is per hour.

48 Figure 6 caption:  This seems to be written by a different person as the previous captions were brief.  But surely no need to define T for temperature at this stage of the paper.

49 Line 202: Confused here, as introduction stated that ERA5 poorly resolves temperature fluctuations (fine-scale) but here says that it does.

50 Line 228: What does warm large spatial scales mean?

51 This claim that ERA5 misrepresents fine-scale waves has never been justified in the paper. What study are you referring to?