This manuscript analyzes the wave geometry of Final Stratospheric Warming (FSWs) for both northern and Southern Hemispheres. It presents some interesting results that warrant publication.  However, it is not clear to me that the  differences between wave geometry are important (point 1 below).  Also, the analysis of the Elliptical Diagnostics needs to be greatly improved or removed (major point 2).  So, I think major revisions are required before the manuscript is suitable for publication.

MAJOR

1. Key results

The presented analysis does find some differences between wave 1 and 2, but overall I find these differences to be small and even when there is a statistically significant difference it is not clear to me that these differences are important.    Even the abstract doesn't present the results as having important implications.  I actually came away with conclusion that probably not important /necessary to consider wave 1 vrs wave 2. This is an OK conclusion from a study, but I suspect authors disagree with this and if so they need to more clearly present results that will have implications.  

I actually was more interested in some of the other results presented and only briefly discussed. In particular I think that there needs to be more discussion of trends, connection of SH FSW date with ozone, and late versus early. Even if some previously discussed you are presenting a longer time series. Also you could making comparisons with wave geometry. 

For example:

(a) The existence and lack of trends in Fig 1 is not discussed. Fig 1a appears to show a trend between 1979 and 2010 but I guess an insignificant trend over 1979-2019 or whole record. At least some comment on this is needed. Also possible trends / pause in SH needs to be mentioned (see more below).

(b) The connection between ozone and FSW needs to be expanded. The analysis here focuses on the impact of the FSW on ozone, but for SH (as stated in manuscript) a key point is timing of FSW is linked to ozone depletion. This connection is not actually shown here.  Line 155 says SH final warming date tends to occur later during years of strong ozone depletion but no references are given ("As noted previously" is very vague). Even if noted before should be some analysis here. Also, on Line 232 it is stated that "These differences reflect a key point, which is that late events in the SH tend to occur in years with strong ozone depletion that further strengthen the vortex winds and allow the vortex to persist longer." Where is this shown in this paper? If this is a key point then show it.

Returning to trends, does Fig 1b support a trend before 2000 and then a pause since (consistent with ozone recovery)? Banerjee et al reports such a pause in tropospheric circulation, is there also a pause in the FSW date trends?

(c) I am not convinced that a wave separation provides any more (or even as much) insight as separation by timing.  Fig 4 shows only small differences between wave 1 and 2, but on line 190 is states that "Early FSW events are associated with a stronger deceleration of the winds as compared to late FSW events due to the seasonally stronger winds earlier in the season". This needs to be shown and contrasted with the wave differences.  Note Figure 5 also shows that the difference between late hrs early is more important than difference in wave geometry. Again, I don't think this means not valuable to show wave geometry differences but it just needs to be put in better context.

2. Elliptical Diagnostics 

The fact that Elliptical Diagnostics (EDs) are considered is only mentioned in Section 2, and the fact they are used needs to be started earlier (and in conclusions).  However, having said this, it is not clear to me that EDs are actually being used correctly or influencing the analysis. I think that additional analysis is needed or they should  be removed.

Looking at table A2 it appears that for over half the NH cases and many of the SH cases the ED classification does not agree with the final classification. In other words for many/most years the classification is due to agreement between the two wave number analyses but the ED are saying something else.  This needs to be much more clearly presented (if EDs are kept). 

The assumption of split = wave 2 and displacement = wave 1 is not valid, and you should not call a split a wave 2 or a displacement a wave 1. The fact this is not a good assumption is exactly the reason EDs were introduced. Further the disagreement between ED and wave numbers appears to support this.

If you keep the EDs then I think you should do an analysis based on S vrs D. Does this show any significance difference (is it similar / different to wave 1 vrs wave 2 difference). 

MINOR

Line 102-105:  Quote the standard deviation in date?  Also, add a statement comparing April 12 and November 19 in terms of respective seasons (i.e. days after winter solstice / before summer solstice).

Line 109-110: Why not just use JRA for the complete record?  It seems strange to add two reanlyses together and further complicates interpretation of the 1958-present day record.

Table 1 and 2: How about Table 1 = NH and table 2 = SH? I don't think any of the analysis compares the FSW in SH with that in NH for same year, and I think better to list all years for one hemisphere in a single table.

Line "133" "Another disadvantage" What was the first disadvantage?

Review for 'The wave geometry of final stratospheric warming events' 

by Butler and Domeisen (2021)

This paper investigates whether final stratospheric warming events (FSWs)

have a wave geometry associated with them, as found in midwinter sudden

stratospheric warmings. They find that FSWs can be classified as wave-1 or

wave-2 events fairly robustly using 3 different methodologies. They also 

find that such differences may be useful for improving tropospheric 

predictability, given that each type can be associated with different 

near-surface signatures. 

I found the paper to be interesting as it examines a topic that has mostly 

been overlooked in the literature and it is well-written. Although I would like to

see more of a mechanistic explanation of some of the differences, particularly in the

tropospheric response, which in the SH is quite startling (figure 6d,f), I feel 

that the paper is mostly good to go and worthy of publication. Hence, my 

suggestion is of minor corrections.  

Comments:

Line 31; Maybe add about the latest SH warming in 2019? 

Lines 109-110; It seems strange to stitch together the two

reanalysis datasets, especially when JRA-55 could be used for both

before and after 1979. Can you better explain why this is done? Why

not just use JRA-55 for both periods (from 1979-2009, you say that

dates vary only by 1-2 days, so surely it should not matter)?

Lines 100-110; I think something should be said about how your 

definition compares to other definitions. I understand that FSWs 

are usually defined using the 50hPa winds, which you mention 

is not possible in the SH as the winds do not clearly reverse from 

westerly to easterly at this level. But in the NH for instance, I 

wonder how the FSW classification at 10hPa and 50hPa may impact your

results. I am not entirely sure, but I guess that the vortex breaks up

at one level earlier than the other? This may affect your composites as 

you may be either capturing (or not) the actual wave pattern in the 

build up to the FSW. So in conclusion, I think that more should be said

about the sensitivity to FSW definition; what if you define an FSW in 

NH using 50hPa winds, as I think is more traditional. 

Line 128; Is it the total number of days in [-10:10] spent with an aspect

ratio or centroid latitude satisfying the threshold, or the longest continuous

chain of days satisfied, that determines whether it is a wave-2 or wave-1? For

instance, an event may overcome the aspect ratio threshold on day -10 but not

again until days +7:+10, whereas the same event may overcome the centroid 

latitude threshold on days -1:2. I would say that the latter is the better 

classification (i.e., wave-1) as it occurs continuously around the actual FSW date.

Further, what if the number of days are equal for the aspect ratio and centroid

latitude fulfilment?  

Lines 145-151; Just to clarify, when you say 50-hPa classification here, you only

mean for determining wave-1 and wave-2, right? (This is valid for the whole manuscript as

it can sometimes be a bit confusing). If not, then my point just above

will be redundant! 

Figure 1; I won't go into details here as I realise that both Darryn and Nick have

mentioned this substantially in their reviews/comments, but I was aware that there is

a well-known trend in the SH final warming dates, linked to ozone depletion. This trend

is lacking in fig. 1c and I am wondering why. As Nick states, it may be related to

the FSW definition, so discussing the sensitivity of your dates to the level of FSW definition,

as aforementioned in a previous comment of mine, would be useful.

Figure 2; What do the composites look like? Do they show typical wave-1 and wave-2

patterns, or does the longitudinal location of the vortices vary too much between

each FSW so that there is cancellation? During SSWs, the vortex locations are pretty

constant between events, so I wonder here if it is similar during FSWs. I also think it 

would be good to show this to see if there are indeed statistically-significant differences

between the wave-1 and wave-2 FSWs.

Line 170; 'positive' -> do you mean ratios greater than one?

Line 181; Not strictly a deceleration as has units of m/s. It is just the difference between

the two time periods right?

Lines 183-190; Are the differences between the wave-1 and wave-2 events statistically significant?

Lines 193-194; I cannot see this from the plot. It appears that the mean lines (thick) cross

zero at 50hPa after ~20days or so (panel c). Is this what you are referring to? 

Figure 5; Can you perhaps include a PV contour marking the 'edge' of the polar vortex to see

how it compares with the ozone anomalies?

Lines 231-232; Can this be shown explicitly? Figure 5 does suggest it, but I would rather it be 

shown. For instance, you could calculate the years that have stronger ozone depletion compared

to some mean and compare and perhaps calculate a correlation with the years that have a late FSW.

Just a suggestion for a figure, but I think this point could be better shown in the manuscript. 

Lines 260-264; It appears to me that the wave-1 and wave-2 events lead to nearly identically 

opposite 500-hPa GPH anomalies in the SH. Any idea why this is? Is this also the case at levels

above, perhaps in the stratosphere? Figure 5g,h did not show such an opposite-signed pattern in 

the TCO. Further, are there significant differences lower down, perhaps in the MSLP?