General Comments

Overall, I enjoyed reading this manuscript and the results were interesting and novel. I mostly have minor comments, with a few more broad suggestions for improvement.

First, while negative wave driving events (NWDs) are included in the study, they seem almost an after-thought. It would be nice to include something on NWDs in Figures 3 and 4 for example (or in a simple manner to Figures 3 and 4 but in an appendix). More discussion or even a separate section could be given to discussing these events. Or, another option would be to consider not including NWDs here but save these for another study (perhaps comparing to “vortex intensification” events instead of SSWs).

Second, I had quite a few comments on the Discussion/conclusions section below, that I hope the authors will consider also more broadly for the entire manuscript. While I find the results presented in the study very compelling, I also think that the primary goal of the study should not be to dismiss the major SSW definition. In particular, some of the text seems to imply that PWDs and SSWs are different phenomenon, while they really are just two different ways of measuring the same basic dynamical process. While I agree with the authors that the wave driving events do have advantages over SSWs particularly if the interest is in surface impacts, rather than trying to argue that SSWs are not important or the SSW definition not valid, I think the results of the study could be better used to argue for improved dynamical metrics output from forecasting/climate models in order to encourage use of this somewhat more complicated metric (and, I do think it worth acknowledging that while the wave activity metric is relatively straightforward to calculate, it does require much more data than u1060).

Specific Comments

Title: “sudden” appears twice. More generally, I suggest in the title and in the text (e.g., line 11, line 368) that the acronym for SSW is defined as “sudden stratospheric warming” rather than “stratospheric sudden warming”; reasons for which are described in Butler et al. 2015, footnote 1.

Line 12, line 35: “normal westerly”- to be clearer, specify “climatological wintertime westerly”

Line 13-14: Since the event date itself is presumably determined by the wave activity flux, remove “prior to the onset of the events”.

Line 15-18: phrasing is confusing, plus this point is repeated in the next line. Suggest instead just stating “About half of the wave events are identical to SSWs. However, there exist several advantages for defining stratospheric weak extremes based on wave events rather than using the common SSW definition:…”

Line 31: What is meant by “inner core”? In the NH the warming often seems to start in one particular extratropical sector and move inwards towards the polar cap.

Line 41: Could you be more specific in terms of latitude/level of the CP07 definition?

Line 48: Here, I think you mean “it is unclear how effective this definition of SSWs is in capturing events with downward influence…”

Line 51-52: If the zonal wind reverses, how can it be considered a relatively minor perturbation? According to your prior paragraphs, the reversal is why major SSWs are considered so intense. Since this sentence also repeats the sentiment of the prior one about downward impacts, I would just remove it. The point about it being a based on a fixed threshold is perhaps really only important in the context of climatological model biases; or regarding your next statement on lines 53-54, which is a valid one.

Line 55-57: Is this your wave driving definition applied here to the SH? If not, it seems somewhat out of place to bring this up here (I like the point about the SH in the conclusions, but I would remove it here and focus only on the NH).

Line 17, line 58, line 125, 405: Not sure about the word “traditional”. Technically the traditional WMO one is not exactly the same as the CP07 definition; see Butler et al. 2015, which describes the long history of SSW definitions. Perhaps you should instead use the word “common” to describe this definition and state somewhere that by “common SSW definition” you mean the Charlton and Polvani definition.

Line 60: This paper should be cited here or elsewhere in the manuscript; it is very relevant: https://journals.ametsoc.org/view/journals/clim/30/14/jcli-d-16-0465.1.xml

Line 60-62: I agree, the SSW definition is not based on what precedes the event, but on the other hand is also not based on “their effect”, at least at the surface, which is how this may be interpreted. Maybe “but instead on their stratospheric effect”. I would also argue that a wind reversal is very much a “dynamically-oriented” metric, so I would rephrase (see also, Butler and Gerber 2018, which showed that the particular latitude and height of the CP07 definition does maximize dynamic metrics, at least for definitions based on wind reversals).

Line 61: This is the first time the predictability of SSWs is brought up. Could you make a brief statement about what lead times are expected for SSW prediction? (e.g., Domeisen et al. 2020 part I).

Line 74-96: There are other studies that suggest caution about how to interpret the 100 hPa eddy heat flux, which should perhaps be mentioned in this section somewhere, see, e.g.:

https://journals.ametsoc.org/view/journals/atsc/74/9/jas-d-17-0136.1.xml

Line 86: Do you test different levels? What about the wave activity at 50 or 10 hPa, for example? 100 hPa could still be muddied by tropospheric variability potentially.

Line 121: what is the model lid height?

Line 125: The CP07 definition is not exactly the WMO-criterion. See Butler et al. 2015.

Line 129, line 151: this should read “separated by at least 20 consecutive days of westerlies”.  See CP07 corrigendum: https://journals.ametsoc.org/view/journals/clim/24/22/jcli-d-11-00348.1.xml. In your methodology described on line 151, are your events just separated by 20 days (regardless of wind or PWD sign?). Please clarify.

Line 134: This seems like a broad latitude range to calculate Fz. Did you also try 45-75N or 40-80N as many other studies use?

Lines 134-136: I don’t follow why multiplying by -1 ensures that a positive sign means upward propagation. Which term in Fp leads to upward propagation being negative?

Line 141: “of either sign”- this is confusing because the paragraph starts off describing “positive wave driving events” yet here you are looking for anomalies of Fz of either sign.

Line 150: What does it mean for this quantity to become negative? It’s not clear in a physical sense how that signals a positive  WD event. Perhaps an example would be useful? (it does become a bit more apparent in Figure 3).

Line 157: du_min is not mentioned on line 129-130 as being saved for SSWs; might do so for consistency. Also the statistics listed here don’t match what is listed in Table 1.

Line 199: This isn’t apparent from the figure (the EX-PWD line falls beneath the SSW value at the 12.9 threshold).

Figure 2: This is a really nice figure. What are the units of event frequency (is this number of events per year multiplied by 100?)

Line 202: It would be nice to at least briefly mention that especially the SLP response in ERA5 is much noisier due to the smaller sample size, which means that the SLP difference between PWD and SSWs and the selected threshold is not significant in ERA5. I think the overall good agreement with the model does support the idea that using ERA5 here alone would be difficult and provides support for needing many samples from model experiments.

Line 220: I don’t know if it will be clear to the general reader what is meant by the final warming here (I don’t think it’s been defined yet) and which zero-wind crossing you are referring to.

Line 229: I can see the “eastern” vs “western” dipole in the lag -15 panel but not so much in the lag -25 panel.

Line 248-253: Here, you have confused the sign of the NAM.  The positive values here represent negative values of the NAM (at least, I hope this is the case!). The text should be fixed here; and since the NAM here is approximated by the polar cap geopotential height anomalies, either these should be labeled as such on the figure (instead of as the NAM), or they should be multiplied by -1 to match NAM polarity conventions.

Figure 5: Instead of event day of year, which doesn’t seem that useful since it can be somewhat inferred from the location of the triangle, it would be more useful to put the accumulated wave driving value for each event as the small number.

Line 271: “when the polar vortex is weak” – would instead phrase as “when the polar vortex is climatologically weaker”

Line 283-286: I understand your point here, but on the other hand, each SSW also evolves differently, in terms of the morphology of the vortex, so in a similar fashion there is also much uncertainty about how that contributes to the surface response and timing of the response in terms of individual cold air outbreaks. This is of course underscored by your Figure 6 and the following discussion.

Figure 7: It’s hard to tell whether the SSW curve is flat at the top or extends above the y-axis. It may be preferable to extend the y-axis so the peak can be seen. Also for panel (d); it’s hard to see what is going on because the EX-SSW blocks the U+.

Line 311: Is the narrower seasonality of SSWs in part by construction? Since they cannot be defined past the end of March in the CP07 definition. For a better comparison, you could consider a similar definition that uses the full calendar year- see Butler and Gerber 2018 (this also has the advantage of removing weak March SSWs; which may influence your results on the surface responses to SSWs being slightly weaker).

Line 319: here, U- events are likely dynamic final warmings, correct? I would distinguish these events from radiative final warmings (this is done to later, on lines 361-365, but perhaps that discussion should be moved up to here).

Line 320-321: I think here you are referring to the fact that the CP07 definition doesn’t permit April SSWs, but perhaps that should be made clearer. I would find it hard to believe that the wind would reverse in April and still show a “complete vortex recovery”- since the climatological mean date for the final warming is ~April 12 and after that the winds are climatologically easterly, so what would a complete vortex recovery look like at that time of year? I would rephrase or remove this sentence.

Line 350: There appears to be no significant Pacific response to SSWs so I would remove that from the sentence. Could more be said about the NWD response? Intriguingly, the Pacific sector stands out much more strongly for NWDs (and for PWDs), compared to SSWs.

Line 350-354: Following the previous comment, could you show these patterns for ENSO-neutral years only as in Figure 4? It seems like for over >4000 samples as in most of the model composites, and *if* the model does not show a strong preference for SSWs/PWDs/NWDs in only one phase of ENSO, then ENSO should basically average out, meaning that Pacific signals shouldn’t really be associated with ENSO as suggested here. Is this the case? (i.e., what is the Nino 3.4 composite value for each of these maps?). Could the prominence of the Pacific signal instead be related to the wave driving itself in some way; a fingerprint of the wave driving response? I realize that the intention to investigate this further is mentioned for another paper, but given the strong differences in Pacific response here, I think it would be at least useful to mention the composite Nino 3.4 value in each case.

Lines 350-353: This statement is true but explains the ENSO related precursors to SSWs, not the response to SSWs, which is typically very North Atlantic-centric.  The SSW composite in ERA5 in fact shows the opposite anomaly over the N. Pacific (top left Fig 8); this is likely related to ENSO “noise” affecting the composite in the small reanalysis dataset.

Lines 368-69: This sentence overstates the conclusions/implications of this study. This sentence gives the impression that it’s the upward wave driving itself that is the most important source for stratospheric signals at the surface, but of course the wave driving has to first cause a change in the polar stratospheric circulation for it to have any influence. True, I think this study does show that that change does not have to be a full reversal of the winds as for the “major SSW” definition, but I think this sentence does a disservice to the role of SSWs in general, which has been well established in the literature. (The rest of the paragraph clarifies this point, but I would consider rewriting this sentence to better reflect the results of the study; lines 383-384 I think is a much better starting conclusion sentence for what the study shows).

Line 372: PWDs had the same frequency as SSWs but by construction of your chosen threshold, which should be clarified here.

Line 374-375: “just like SSWs, PWDs were preceded by increased amounts of wave activity flux” – this is also by definition

Line 377: Here it should perhaps be clarified “half of all PWDs did not concur with major SSWs”, since it’s very likely that the other half were minor SSWs or final warmings.

Line 378: the more even distribution at least partially comes from PWDs including final warmings, whereas the SSW definition does not include final warmings by construction. While I do think it’s an advantage that the PWD definition can detect dynamic final warmings that likely have similar impacts as SSWs, this distinction should be made clearer, as the SSW definition was purposefully designed to exclude final events, so it can’t really be considered as a fault of the definition.

Line 378-379: I don’t think this was shown anywhere. This assumes that the Pacific response in Figure 8 is from ENSO, but I think more will have to be provided (such as the composite value of Nino 3.4 for each plot in Fig 8) to make this statement.

Line 388: I disagree with this point. If there’s any reason to use the common SSW definition, it’s for its simplicity, particularly in model data because you just need daily u1060. It’s much more intensive to calculate Fz (for which you need gridded daily v and T). I think a stronger stance this study could take is that you’ve demonstrated that PWDs are valuable measures of stratosphere-troposphere coupling, so there should be more demand for models to output daily v’T’ (pre-calculated preferably on model time steps), and to participate in efforts to output these dynamical variables like DynVarMIP (few CMIP6 models did so).

            Additionally, while PWDs may include all these types of events, they don’t distinguish between them, which is not necessarily an advantage. Instead, perhaps this should be stated as, while other definitions focus on separately defining all these variations of polar vortex variability and looking at differences between them, this goal of this definition is to identify events with greater surface impact, no matter the particular timing or evolution of the polar stratospheric circulation.

Line 391: I don’t think this can be stated so strongly here unless you test this explicitly. I agree that Figure 3b hints some lengthening of wave activity flux prior to the event, but it’s not a guarantee that this will translate into better predictability of these events. I would soften this statement, e.g., “potentially lengthen the forecast horizon”…

Technical Corrections

Line 19, line 56, and throughout: capitalize Southern/Northern Hemisphere

Line 50: I don’t think NAM has yet been defined anywhere

Line 55-56: change to “stronger climatological polar vortex”

Line 97: change “date” to “dataset”

Line 106: change to “The results in Section 3…”

Line 145: “past the wave driving” – remove “the”

Line 157: “As for SSWs”- suggest instead “Similarly to SSWs”

Line 233, line 360: don’t need to capitalize “polar cap”

Review of ‘Stratospheric wave driving events as an alternative to sudden

stratospheric sudden warmings’ by Thomas Reichler and Martin Jucker

General Comments:

This is an interesting study that aims to introduce another definition of 

extreme polar vortex events, related to the magnitude of the lower-stratospheric 

wave flux. The authors compare the tropospheric response to the most-often used 

wind-reversal criterion, to their own wave driving definition and find that the

latter gives an overall stronger surface response. Although the suggested 

definition does have some advantages as the authors state, I do not think it is

as simple to calculate as the wind reversal criterion or indeed other definitions

that require a single zonal-mean field. In some places therefore, the language 

should be toned down so as to not over-sell this new definition. 

A bugging concern I have is that the presented diagnostic is not necessarily capturing a wave

driving event, rather an increased wave flux in the lower stratosphere. So the nomenclature 

should be changed from planetary wave driving (PWD) to planetary wave flux (PWF) events. Even 

though there is a strong EP flux in the lower stratosphere, it may not drive a weaker vortex

and the wave activity could just propagate and break farther equatorward. Indeed, it is the derivative 

of the wave flux that determines how much the mean flow is affected, and so this should be called

the wave driving, rather than your definition.

I would like to see how the presented definition compares to a more dynamical extreme vortex event

definition such as the wind tendency definition of Birner and Albers (2017; SOLAS). In my eyes,

that definition can more appropriately capture wave driving events, as the wind deceleration is

proportional to the wave flux convergence (in the transformed Eulerian mean sense). Nevertheless, 

the current study is already long enough and self-contained and so this is a suggestion for 

future work.

The paper is well-written and well thought out and so my comments are generally of a minor

nature. Hence, my overall recommendation is of publication subject to minor corrections 

which I list below. 

Comments: 

Lines 44-45; It is relatively well understood now that the wave-mean flow interactions associated 

with the critical layer mechanism for downward propagation (that originally propsed by Matsuno) 

only reaches the tropopause. See for instance, Hitchcock and Haynes (2016; GRL). So I would rephrase 

or remove this sentence. 

Lines 51-55: I think the following paper should be cited here:

"Defining Sudden Stratospheric Warming in Climate Models: Accounting for Biases in Model Climatologies"

by Kim et al. 2017, J. Clim. 

They make this point about the fixed threshold not being ideal for climate models as there are mean 

state biases present so that a model with a too strong vortex would likely simulate less SSWs. This is

a sort of similar point to that regarding NH vs SH differences. 

Lines 66-67; The heat flux itself is not referred to as the wave driving, as what happens if the wave 

activity simply propagates upward through a region? Rather, it is the derivative of the heat flux that 

weakens the polar vortex as this represents the convergence/divergence of said wave activity.

General comment on introduction: It is currently very long and I would shorten it to be more to the point.

Also, I think other definitions of extreme vortex events should be mentioned somewhere. There are many

but the current intro only focusses on the wind-reversal one. How does yours fit into the context of others?

I would add a paragraph to discuss previous definitions. Tendency based definitions such as that by 

Birner and Albers (2017; SOLAS) is one example that may be better suited to overcome the issue you mention

on defining SSWs in a warming world with underlying polar vortex changes (your lines 58-60). Sentences such 

as that on lines 62-64 make it seem that your definition is the only study that has attempted to use a more

dynamically-based definition. 

Lins 125-126: I think the WMO criterion also involves a reversal of the temperature gradient. The CP07 

definition is a simplification of that.

Lines 139-144: Is there a reason an e-folding timescale of 50 days is chosen? Is this something to do 

with radiative timescales in the lower stratosphere? Or perhaps related to the 40-day vertically 

integrated wave flux in Polvani and Waugh (2004)? It would be good to know if results are sensitive 

to varying this parameter to shorter timescales (which would be a more conservative criterion that 

reduces the accumulated wave flux). Intuitively 50 days sounds quite long, so would be good to have 

justification here.

Lines 148-150: 1) What does the timescale physically mean? The time taken for an average accumulated

wave packet to die out? 2) Why is a negative Fz set as the end of the wave driving event? I would think

that if the wave flux anomaly was close to zero but still positive then this is pretty much the end of

the event anyway. For instance, imagine a situation where the wave flux anomaly remained positive but

close to zero for an extended period; this would be erroneously counted as an extended event and contribute

to the summation. Would a more plausible end of event be related to a criterion on the standard deviations?

Lines 162-164: Physically a positive PWD in the 20 days after an SSW is surely not related to the driving 

of the SSW? Indeed, Fz remains positive for 2-3 days after an SSW event (as your figure 3 shows), but for 

1 week plus, I highly doubt it. How many of your common events fall into this category of large Fz in the 

20 days after an identified SSW? 

Line 189: What is this 58% and 62% SSW frequency? I presume you are referring to the number per decade 

which in ERA-5 would be 6.2 per decade and so translates to 62% of years having an SSW. Is that right?

I am not saying the statistics are wrong, rather the way they are presented is non-standard. 

Figure 2: I am not sure if it is to do with the way it is rendered on my screen, but the shading in this 

figure completely masks much of the figure. It not only masks the lines, but the writing next to the lines.

Please fix and make the confidence interval more transparent. Because of its current rendering, lines such

as 201-202 are impossible to make out.

Figure 3: I cannot distinguish the bold from the non-bold lines in panels a-f. You state that bolded lines

represent those differences that are statistically significant. Also, the panels b,e are cut off and do not 

show some of the lines around the onset date. Especially in panel e, the sharp increase in SLP just after 

day zero is interesting. Finally, what is NNR in the caption?

Lines 216-217: Are you reading off the anomalies in c-d by comparing the solid lines with the dashed lines

and seeing which lies lower? 

Lines 240-241: From the left column of figure 3, I would not expect to have such comparable SLP anomalies

to those in the model. In fact PWDs in ERA5 appear to have positive SLP anomalies, for up to 20-30 days 

before the onset date, presumably associated with a strong Siberian High.

Lines 267-270: 100hPa where you identify the PWDs is already well within the vortex. Hence, the PWDs events

you capture may also be due to 'stratospheric internal dynamics'. de la Camara et al. (2017) suggested that

300hPa was a better diagnostic level to say that there is cross-tropopause wave propagation. Nevertheless,

this brings up another point: how sensitive are your PWDs to choice of vertical level? It would be good to 

raise or lower the level and recalculate the numbers to check that 100hPa is representative of the lower

stratosphere.

Line 275: The word 'tend' here suggests that the majority of NWDs occur close to the onset date of the SSW 

(say within +-30 days). I do not see that in figure 5. Rather, there are around as many NWDs that are not 

close to an onset date as there are close to an onset date. Can you clarify what you mean here, perhaps 

quantitatively. Otherwise I would just consider removing the sentence. 

Lines 331-333: This is interesting but unsatisfyingly not further addressed! Do you have any idea as to 

why this is? By March-April the vortex is already starting to break down and wave activity to wane 

(figure 1a,b) and so is the weaker day 0-59 SLP response simply reflecting the seasonal cycle? The 

vortex recovery is too weak by this point as it is the transition time to easterlies and so the 

radiative recovery is cut off by the seasonal cycle. Many studies have shown that the persistent 

lower-stratospheric anomalies are important for a continued tropospheric response (Hitchcock and 

Simpson 2014, JAS; Maycock and Hitchcock 2015, GRL; White et al. 2020, JClim) with it being mechanistically 

attributed to the induced meridional circulation by the lower stratospheric radiative recovery (Thompson 

et al. 2006, JAS; White et al. 2022, JAS), and this may provide further evidence for that. A NAM index 

plot for SSWs occurring only in March-April would help to see if the extended recovery in the lower 

stratosphere is indeed cut off by the seasonal cycle with a shorter NAM timescale evidence for that.

Figure 7: Same problem as figure 2 with the shading. 

Lines 350-354: It does not look like the SSWs are associated with a SLP<0 response over the North Pacific 

compared to the PWDs (comparing panels in column 2) although you state this to be the case. Isn't the strong 

SLP<0 anomaly over the North Pacific in the PWDs compared to the SSWs just related to the fact that the PWDs 

are wave events themselves? As you say, it represents a deeper Aleutian Low but the difference between the 

PWDs and the SSWs is that the planetary wave driving is shut off in the SSWs whereas it continues in the 

PWDs until the Fz anomaly goes negative (which could take a while depending on your specified e-folding 

timescale). Hence, in the PWDs, I would likely expect a more negative Aleutian Low to persist well after the onset date. 

To clarify, my concern is that the presented SLP patterns for the PWDs are simply aliasing the planetary 

wave patterns that drove the weaker vortex in the first place and therefore not part of some downward response. 

Perhaps a simple way around this is not to use such a broad time-average window that goes all the way to the 

onset date (i.e., not use lags 0-59). Or, base the averaging window on the date the minimum stratospheric 

winds were found following the maximum Fz.  

Further, I thought you had removed the ENSO effects from the timeseries (lines 174-179). Please clarify as 

this affects the discussion here. It also affects for instance, line 359.

Line 388: I don't think this is such a simple metric to calculate, particularly compared to the wind reversal one.

The traditional definition can capture most of these events. I would not state that your definition trumps it 

so flippantly.

Line 391: Compared to the traditional measure, it appears that the PWD events hint at around an extra week of extreme

Fz (figure 3b) but I would hesitate to state that this so definitely. 

Technical Comments:

Title: You use 'sudden' twice!

Line 18: 'criterium' --> 'criterion'

Line 19: Duplicated 'that'

Line 97: 'data' --> 'data'

Line 106: Change the short sentence to 'The results in Section 3...'

Line 134: To clarify, did you use area weighting to average the EP flux?

Figure 1: I think I get it, but can you clarify what the lines mean? I presume thin lines represent

the +-SDs and the thick represents the full value, but it would be nice to not have to work it out...

Line 146: remove the first 'the' on this line.