This paper presents a systematic analysis of extremes in the zonally averaged meridional heat transport and how they are related to weather regimes and preferred zonal wavenumbers. The work is based on several decades of reanalysis data and draws on the results from earlier publications. Overall, the authors argue that their results are consistent with previous results regarding weather regimes, dominant wavenumbers, and how they are related to heat transport extremes. The current analysis makes explicit the role of planetary versus synoptic scales in this context. The question of extreme events is of primary importance in our science, and a detailed analysis such as the present one is welcome. I can see this as a publication in WCD.

Yet, I have a few issues. To be sure, I need to say that I am not an expert in the present topic, rather I consider myself as representative of a typical reader of WCD. As such, I had a hard time in several of the more technical sections to understand what the authors have really done. This is probably due to the fact that the text seems to be primarily directed at the expert, who is familiar with a string of earlier publications from the same group. I have no doubt that the analysis is performed in a proper way; however, I suspect that this is hard to appreciate by the average reader of WCD.

As a way out I suggest that the authors should make a serious attempt to more pedagogically introduce the concepts used in their analysis as well as in their results sections. Instead of just providing the references to multiple generations of previous publications, assuming that each reader is familiar with those papers, the authors should add some advice to the not-so-expert reader trying to introduce and/or summarize these earlier developments on a conceptual level. This would increase the readability of and add great value to the paper.

In addition, the paper would benefit if the authors could add some non-technical guidance to the reader as to what these results mean in more meteorological terms and what the implications are. To be sure, you draw a few interesting conclusions. However, you should make a more serious attempt to connect these conclusions to the more technical parts of the paper. Again, I do not doubt the validity of the results or the conclusions; I just feel that this paper would make a much stronger impact if such meteorological guidance were available and if the technical and the interpretatory parts of the paper are connected in a more seamless fashion. Also, you often point out the consistency with earlier results, and by doing so some readers may get lost and left unclear about what is really new about this paper; therefore, it would be good you could point our more explicitly what is new in the current paper.

Examples

Let me provide a few examples illustrating the major issue made above. As I said, some work for improvement would be appreciated in the interest of a broader readership.

For instance, equations (3) and (4) were unclear to me at my first reading. If you do a Fourier decomposition of a field and multiply two such fields (as you have to do to compute a heat flux), you obtain a double sum, one for each expansion. You can, then, sort this double sum according to the resulting zonal wavenumber, and this results in each Fourier coefficient of the heat flux being a sum of many terms from the individual terms (v and E) that just happen to add up to the zonal wavenumber in consideration. This is what I would have expected in equations (3) and (4), but your method is different.

To be sure, I could have read the quoted papers in order to educate myself (to be honest, a cursory look into Graversen and Burtu 2016 did not help me a lot), but I would not be too optimistic regarding the readiness of the average WCD reader to do so. Instead, I would have appreciated not just a short “summary” of those earlier methodological developments, but rather a conceptual introduction on a somewhat higher “meta-level”.

In the end, the point here is that you consider zonally integrated fluxes, and Parseval’s theorem allows one to express the zonal integral of a quadratic quantity as a single sum over all wavenumbers like in (4). The other important point here is that the sum of all individual components such as (3) and (4) is equal to the total, zonally integrated heat flux, which you refer to as “wavenumber decomposition” later in your text. Implicitly, you heavily draw on this property in the rest of the paper. A corresponding hint in the method’s section would have helped me a lot!

To provide a second example, in Fig. 4b it was not clear to me at first why the extremes do not just represent the tails of the distribution from the color fill (just like in a box-and-whisker plot). This is what I would have expected initially. The same problem arises in the text on line 232: how can possibly the “equatorward and poleward extremes largely overlap”? Shouldn’t the extremes represent opposing ends of a PDF? If so, it is hard to see how they can overlap. The solution to this problem probably depends on how you defined the extremes and their PDF: the extremes are defined without reference to a wavenumber, and this implies that the existence of an extreme does not have to be reflected in the PDF of each and every wavenumber. Is that right? Other readers may have a similar problem, and some explanation would be very helpful. In addition, reading this (and related) plots is made more difficult due to the fact that the caption does not give contour intervals for the dashed isolines.

In the last section, you draw some interesting conclusions, which I was not always able to relate to the core of your analysis. For instance, you say that “planetary scales determine the strength and meridional position of the synoptic-scale baroclinic activity with their phase and amplitude”: where exactly have you shown this? How can you make statements about the wave’s phase, which (as far as understand) is unavailable from just looking at the zonally integrated heat transport? Similar reservation I have with the conclusions on lines 371-373. I feel that you need to tell the reader somewhat more explicitly how you arrive at these conclusions and which part of the analysis your conclusion is based on. Take another example: you say on line 385 that “…our results emphasize that the modes related to energy transport extremes are hemispheric in scale”. What part of your analysis is this statement based on? My point here is that the chief instrument in your analysis is the investigation of the zonally integrated heat flux, and this leads (almost by design) to “modes” that can be expected to be hemispheric in scale rather than very local or small-scale. In summary, all of these conclusions may be well justified, it was just not easily visible for me. The authors should make an attempt for improvements in this direction.

Minor comments

Line 16: This is somewhat advanced material for the start of an introduction. Presumably you talk about vertically averaged moist static energy, right? In the tropics the vertical change of moist static energy is close to zero, because the increase of potential temperature with altitude is, to a large extent, compensated by a decrease of water vapor mixing ratio.

Line 125: you remove the linear trend only in certain latitude bands. Why does this not create awkward discontinuities at the boundaries of these ranges?

I suggest to increase the size of the panels in Fig. 1 and 2.

Panel 1c, y-axis-label: the threshold should have dimensions, right?! How about the physical dimensions of the scale and the shape parameter?

Fig 3 and 4: How did you normalize the PDFs? It seems to me that integrating by eye over the heat transport at a fixed latitude one may obtain values larger than 1. Or put the other way: what units does the plotted PDF have? Is it really (10^15 W)^(-1)? How should I read the red and blue dashed contours corresponding to the extreme situations (no contour interval given….).

Line 217: ”…. the PDF steeply decays towards the high latitudes….”, I understand what you want to say, yet, it is not really well expressed. You probably want to say that the mean or median of the PDF decreases as one goes to higher latitudes.

Line 232: (see my general marks earlier): Why can the positive and negative extremes overlap? In my simple-minded thinking, the extremes of a PDF represent the opposite tails of the PDF, so I do not understand why and how these can “overlap”. I probably did not understand your definition of “extreme”, but it may help other readers if you could say here why this is so.

Line 233: What do you mean here by “pattern”?

Line 268: shouldn’t it be “…. higher zonal variability in the former….”?!

Line 311 (and similar at some other line): you talk about a “midlatitude channel”, but this term is misleading as it should be reserved for a geometric setup with walls at the southern and northern boundary of the channel. As far as I can tell, you are dealing with spherical geometry, never with true “channel geometry”.

Line 318: a heatwave cannot possibly be a “case study”. You probably mean that this heat wave is a “case”.

Line 345: what are “higher-scale eddies”? I would prefer the term “smaller scales”.

Line 385 ff: (see my earlier remarks): Do your results really suggest that the modes associated with heat flux extremes are hemispheric in scale? It seems to me that this is a necessary consequence of your methodology that focuses on individual wavenumbers. If so, it cannot possibly be a result of your study.

Typos etc.

Line 34: must be “…. a poleward transport….”

Fig 9 and 10: letters a and b missing to denote the two different panels.

This study investigates the characteristics of the extreme meridional energy transport associated with various zonal scales, using the reanalysis data. Using Extreme Value Theory, extreme events of the meridional energy transports are identified, and their associated zonal wavenumbers and meteorological patterns are analyzed. They found that extreme energy transports are, in general, associated with planetary (synoptic) scale wave during boreal winter (summer). Further, they connect those extreme energy transport events with commonly known teleconnection patterns. The topic and the results of this paper generally fits the aim of the WCD and would improve the scientific community’s knowledge about the meridional energy transport.

However, I found that the manuscript's writing and the scientific results are vague. I think the Introduction needs more strong motivation and hypothesis, and the Methodology section should be written with more details as readers with meteorological background might not be familiar with advanced statistical method such as EVT. More importantly, I found it very difficult to digest the meteorological and dynamical interpretations of the extreme events presented in the Result and Discussion sections. My specific comments are presented below.

Introduction

First three paragraphs introduce general information of the meridional energy transport, and L48-51 only mentions the plan of this paper. Yet, I think the introduction can be improved by adding more motivations and hypothesis. Here are some suggestions.

• Why do we need to pay attention to the energy transport extremes at different length scales? I think L33-35 touches this issue, but it is not so clear to me how planetary waves can oppose the total transport. I think it just depends on the structure and the phase of the wave itself, and thus one cannot make a general statement about it. Can you provide some more references or more explanations?
• What is the main hypothesis? What do authors expect to find out by analyzing the different component of the meridional transport, for different seasons?

Method:

• L92: Authors have defined the planetary scale to be k=1 to 5, while some previous researches have defined waves with zonal wave number 1 to 3 as planetary scale waves and wavenumber 4 or higher as synoptic scale waves (cf. Baggett and Lee 2015; Shaw 2014 https://doi.org/10.1175/JAS-D-13-0137.1). Therefore, some discussion to justify the author’s choice of the threshold between planetary and synoptic scale wave number would be helpful. Also, in L276, authors refer k=5 as a synoptic scale wave which is not consistent with the definition of the synoptic scale used in this paper.
• L124-126: I think this is a serious issue. If authors decided to remove the trend, then they should remove it from the entire grid point. Removing trend only at certain latitudinal band may result a physical unrealistic field and further analysis based on these data would make the readers to suspect the results. So, I suggest either do not remove the trend or remove the trend from the entire grid point. Or at least, authors should provide some information (perhaps as a supplementary figures) that qualitative results don’t change regardless of the de-trending method (Even if the results may qualitatively remain same, authors would need to justify their choice anyway).
• L150-157: Authors argue that Figure 1 justifies the choice specific threshold values. However, even after looking at Figure 1, I cannot understand how authors have chose these specific threshold value (ex: 86% percentile for DJF poleward). So more detailed explain regarding this step would be helpful.
• L170: Can you explain why do you first apply EOF analysis before K-means clustering? Can’t you just apply K-means clustering to the raw data, or just use the PC timeseries of the first 4 EOFs?
• I question the purpose of finding the weather regimes using a clustering algorithm. It makes more sense to me to directly diagnose the dynamical characteristics of energy transport extremes using the composite map of z500 pattern. My interpretation is that authors are hypothesizing that energy transport extremes should be associated with the identified teleconnection patterns, but that is not 

  necessarily guaranteed. It is possible that each event may have their own circulation structure that may not resemble the known teleconnection patterns. Therefore, some discussion on why authors use clustering algorithm instead of directly diagnosing the circulation composite structures would be helpful.

Result

• L221: If the JJA PDF shows positive skewness, are you refereeing more colored contours toward left side of the yellow (mean) line? At least to me, the difference between high and low latitude are not so clear in Figure 4a.
• Can you add some scientific/meteorological interpretations of what it means to have positive skewness, and why positive skewness is an important finding?
• L251-253: Can you explain how PT regime (Fig. 2c) can be characterized as lower latitude negative anomalies and high latitude blocking? I think this pattern is rather zonally oriented without a prominent high latitude blocking-like structure or lower latitude signals.
• It is somewhat difficult to interpret the results presented in Figs 5 and 6, along with circulation structure presented in Fig. 2. For example, JJA NHC3 is similar to winter AO, and yet they show opposite results in Figs. 5e and 6e. Besides the seasonal difference, can you comment what makes such a difference in the poleward transport even when two circulation fields are dynamically similar? In addition, EATC3 shows increasing frequency in the 30-42°N degree band (Fig. 6b), while its strong circulation patterns are rather located at higher latitude near Greenland and Scandinavia (Fig. 2b). Can you explain how this circulation pattern can be related to the equatorward transport occurring near 30-40°N latitude?

• L286: Authors said ‘…JJA and DJF differ in the fact that the higher zonal variability in the latter…’. Shouldn’t this be opposite? Figs. 7 and 8 say that JJA is associated with higher zonal variability and higher zonal wavenumber, not DJF.
• L287-288: Authors claim that poleward extremes have more meridionally marked, or zonally uniform, structure compared to the structure of the equatorward extremes. I don’t see a clear difference between poleward and equatorward (there are no (a) and (b) in Figs. 9 and 10, so I assume the poleward is the left column and the equatorward is the right column). For example, in Fig.9, both panels of the 45°N-47°N band show zonal wave number 4~5 structure without prominent meridional structure. Also, it is little unclear to me how a relatively zonally uniform circulation structure would favor for a strong meridional energy transport. I would assume meridional wind in a zonally uniform circulation to be small. Providing more detailed reasoning for such an interpretation would be very helpful.
• Also, Figs. 9 and 10 shows the composite mean of z500 anomalies. Please indicate the sample size of the composite, and significance test of this composite sampled is also necessary.
• Regarding Figs. 9 and 10, the composite of z500 anomalies is helpful to diagnose the circulation structure, but it is yet difficult to tell where the energy transport is prominent. I think that plotting the composite of anomalous vE would help readers to diagnose the prime location(s) of the meridional energy transport.

Discussion

Comments on QRA and heatwaves: 

L302-328: Authors argue that the heat waves are related to the poleward energy transport and present the year 2010 as an example of the extreme poleward energy transport. I found this interpretation is somewhat subjective and lack of dynamical justifications.

My first concern is the choice of the sample. It looks like the energy transport in JJA, according to Fig. 8, is generally associated with the wavenumber 4 to 6. Accordingly, I would expect to find out energy transport to be associated with wavenumber of 4 to 6, regardless of the year. Therefore, the fact that dominant wavenumbers of the energy transport in 2010 is similar to the preferred zonal wavenumber of the quasi-resonant amplification (QRA) theory does not necessary mean that the energy transport and QRA theory are dynamically connected.

Also, according to the Figure 11, the extremes are computed with respect to 2010 mean, but shouldn’t they be computed with respect to the climatology?

The second question is the actual dynamical connection between energy transport, QRA mechanism, and heat waves. If I understand correctly, QRA mechanism requires a zonally oriented enhanced jet stream that can act as a strong waveguide. In line with the comments made earlier, with such a zonally oriented background flow, it is little unclear to me how meridional energy transport can be strong. In addition, heat waves are rather caused by processes such as temperature advection, enhanced solar radiation within an anticyclone, and etc. So, if you can discuss how meridional energy transport can dynamically cause (or be associated with) the heat waves, it will help readers to follow the manuscript.

Other Comments: 

• L329: It is confusing how composites based on the 30-33 band and 57-60 band can be characterized by negative NAO. The 30-33 band composite is more zonally oriented without a prominent anticyclonic feature over Greenland, and there are almost no signals in the composite by 57-60 band.
• Decomposing the zonal wavenumber of the energy transport into planetary and synoptic scale is an interesting, and perhaps, an important point, yet their dynamical origin is not discussed well. Therefore, I think the paper can have a broader impact by adding some more discussion on this topic. What are the causes of the planetary vs. synoptic scale meridional energy transports? Is it possible that planetary scale wave and energy transport can be excited by tropical forcing, whereas the synoptic scale waves can be associated with high-frequency transient eddy fluxes? If one can speculate the cause of those energy transport at different zonal scales, it might be beneficial to diagnose the variability and intraseasonal fluctuations of meridional energy transport and perhaps the long-term changes under anthropogenic warming. I will let the authors to decide whether to add a discussion on this topic.

Minor comment

• L179: Here, the patterns are based on the time period of 1979-2013, while L62 says that the analyzed time period is 1979-2012. If this is not a typo, then I think it is better to use the same time period for all analysis.
• L207, L337, and Figure 11 caption: It is better to spell out ‘with respect to’ instead of just writing wrt.
• L220 and L222: I think it is better to indicate specific latitudinal band instead of expressing as ‘edges of the mid-latitudinal channel’ or ‘high/low latitude’.
• For clarity, it would be good to clearly indicate which figures authors are referring to. For example, L252, “… frequency of NAO-(Fig5a), AO(Fig.5e), and PT (Fig. 5c)” and L253 “In JJA, NHC4(Fig. 6e)/EATC2(Fig.6a) …”. Same clarification in other lines will help readers to follow the manuscript better.
• It is somewhat difficult to remember the physical pattern of all the JJA pattern with the current names (for example, L276 and 278 EATC2 and NHC4 / EATC4, PACC4, NHC3). So, I suggest to re-name JJA patterns with more intuitive or commonly known names as in DJF, or explicitly explain in the text. For example, L276 can be re-written as ‘…EATC2 and NHC4(Scandinavia blocking-like pattern) …’.
• L381-398: In these paragraphs, references are written with out parenthesis. For example, L383 should be written as “… atmospheric features (Galfi et al. (2019); … et al. (2021))”.

Figures

• Figures 2 a-d / A1 / A2: I think it might be visually beneficial to use rectangular map instead of circular map if you wish to only plot certain designated domain. This is only a suggestion, so I will let the authors to decide.
• Figures 3b-e and 4b-c: having a same x-axis range for all four panels will make it easier to compare the relative magnitude of the transport for different wave number regimes. Also x-label should be ‘Meridional energy transport’, not heat transport.
• Figure 9 and 10: (a) and (b) are missing. Also, the unit of color bars in Fig. 9, 10, and 11a are [Pa], which is not [dam].