The link between European warm-temperature extremes and atmospheric persistence

Holmberg, Emma; Messori, Gabriele; Caballero, Rodrigo; Faranda, Davide

doi:https://doi.org/10.5194/esd-14-737-2023

Articles | Volume 14, issue 4

https://doi.org/10.5194/esd-14-737-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/esd-14-737-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 14, issue 4

Research article

|

04 Aug 2023

Research article |

| 04 Aug 2023

The link between European warm-temperature extremes and atmospheric persistence

Emma Holmberg, Gabriele Messori, Rodrigo Caballero, and Davide Faranda

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Final revised paper (published on 04 Aug 2023)
Preprint (discussion started on 16 Nov 2022)

Interactive discussion

Status: closed

CC1:
'Comment on esd-2022-50', Alexandre Tuel, 28 Nov 2022

This manuscript investigates the link between summer and winter warm spells in Europe and the persistence of the associated atmospheric circulation. The authors rely on metrics inspired by dynamical systems theory to show that while in winter, warm spells do tend to be generally related to persistent large-scale circulation favouring warm advection, in summer, they are not necessarily associated with persistent flow configurations.

This manuscript is overall well-written, and the methods and results are clear to follow. However, I have some strong reservations regarding the results and their physical interpretation, which I detail below.

Main comments

My main issue with this manuscript is that you start from an incorrect assumption, which is that “European” summer heatwaves are related to persistent blocking. The use of the word “Europe” here is misleading – it is by now well-known that summer heatwaves across Europe are driven by different processes, and are not systematically associated with blocking. Specifically, one must distinguish between Northwestern Europe/Scandinavia/Western Russia on the one hand and Southwestern/Southern Europe on the other hand. In the first group of regions, summertime heatwaves are known to be strongly related to blocking, with adiabatic warming and clear-sky radiative warming playing an important role. In the second group, blocking is not particularly relevant; instead, summer heatwaves are linked to persistent subtropical ridges (e.g., Carril et al. 2008 https://doi.org/10.1007/s00382-007-0274-5, Stefanon et al. 2012 https://doi.org/10.1088/1748-9326/7/1/014023, Sousa et al. 2018 https://doi.org/10.1007/s00382-017-3620-2). Blocking, for instance, was not relevant for the 2003 European heatwave (e.g., García-Herrera et al. https://doi.org/10.1080/10643380802238137). Admittedly, there is still some debate as to where the boundary between a block and a persistent ridge is, but “blocking” is generally not deemed to be an appropriate term for most persistent ridges below 45°N in summer. I am therefore quite uncomfortable with you writing at various points that your results go against the “conventional” view on European heatwaves.

Second, it seems that, when calculating analogues and persistence indices, you use the whole record (i.e., including both winter and summer days). Is that so? This might be a problem, because there is no a priori reason why the same flow pattern should have the same persistence in winter than it does in summer (you discuss for instance the role of land-atmosphere feedbacks and how they can affect the persistence of the circulation). One might argue that circulation analogues for a summer day would be more likely to be found in summer itself than in winter, but there is no guarantee that this is the case. Based on the results alone, it is also impossible to judge the quality of the selected analogues.

One thing that bothers me in your results and that may be related to this winter/summer issue is the lack of a strong persistence signal for so much of the area during summer heatwaves. Summer heatwaves are almost mechanically associated with strong anomalous ridges above the warm region (since the warm air column expands). There is a strong one-to-one relationship between the circulation and surface conditions. Even when the heatwave is influenced by surface conditions (dry soils, for instance), one would nevertheless expect a strong and persistent anomalous ridge to develop. So I wonder if the lack of persistence that you find is related to the fact that you include winter data to calculate persistence indices. Your summer results are for instance quite different from those of Hoffmann et al. (2021) https://doi.org/10.1038/s41598-021-01808-z who actually find that hot summer spells in the Mediterranean and Southern Europe are linked to very persistent atmospheric flow, while over Scandinavia, it is the opposite. Can this be reconciled with your approach?

One other possible reason for the discrepancy with Hoffmann et al. might also be that your method characterises the “average” persistence of a given flow pattern, which might occur sometimes in conjunction with warm spells (in which cases it could be very persistent) and sometimes not. So while atmospheric circulation would still be very persistent (in the traditionally accepted sense of the term) during warm spells, with your index you might not find a very strong persistence anomaly.

Third, following on this last comment, I wonder to what extent your persistence metric is able to systematically capture atmospheric circulation persistence. The metric is based on a fixed domain, which means that:

(a) It characterises persistence for this whole domain, which is not necessarily relevant for all grid point within this domain (at the edges, for instance)

(b) It only focuses on large-scale circulation, not small-scale.

(c) The analogue selection may be biased by the fact that SLP variance is quite uneven across the domain.

In particular, to illustrate why points (a) and (b) may be problematic, we can look at the case of the British Isles in winter. You find that warm spells there are associated with weaker-than-average persistence. But the warm advection from which these warm spells result is still persistent. It may not be related to a persistent large-scale circulation pattern over the European continent, but still related to locally very persistent conditions, or to persistent large-scale conditions over the North Atlantic ocean to the west.

Your figure 6 is also a good illustration of the problem raised in (b). Even though theta is large for the June 2016 heatwave, the ridge over Germany seems very persistent. This suggests that your results may be sensitive to the choice of region (and potentially distance metric). For instance, what happens if you let the region on which you calculate theta vary to be always centred on the grid point or region under analysis?

Minor comments

ll. 43-44 You may also cite Röthlisberger and Martius (2019) https://doi.org/10.1029/2019GL083745

ll. 75-77 I don’t know if this is such a “discrepancy”. As you mention later in the paper, a blocking system can be very persistent from a Lagrangian perspective, without being necessarily persistent from a Eulerian perspective. For continental blocking there is also a strong difference between winter and summer. In summer, positive feedbacks act to make blocking more persistent than in winter. Hochman et al. (2021) for instance analyse summer and winter together, but for Scandinavian/Northern European blocking, I am not sure this is relevant.

ll. 130-131 Which package exactly?

l. 163 It is difficult to conclude without looking at the other terms of the temperature budget. Meridional temperature gradients are much weaker in summer than in winter, as are the rescaled temperature anomalies (smaller daily variance in summer than in winter).

l. 165 Over topography, the adiabatic term would likely be as much if not more important. For an air parcel traveling downwards by 1000 meters, the advection component would be of the order of 5-7°C, and the diabatic component around 8°C (assuming an initial pressure of 900 hPa and temperature of 0°C). At such small scales and over complex orography, SLP is also not ideal to estimate surface temperature advection.

ll. 171-172 “The one exception is Russia, although we observe warm air in the Black Sea and Baltic Sea regions during warm spells in the Russian region. Anomalies over land are comparatively weak” Unclear what this means and refers to.

ll. 202-203 But your analysis should exclude blocking onset and decay days (when surface temperature are not maximized)

ll. 225-226 “We suggest that, for heatwaves predominantly driven by radiative or local effects, it is not a necessary requirement to have highly persistent large-scale atmospheric configurations” I am not sure I follow you here. Over Scandinavia, for instance, summer heatwaves are linked to very persistent conditions (your Figure 2b) but also strong radiative warming (clear-sky forcing below the block; Figure 5e).

+ the DOI is missing from a handful of references.

Citation: https://doi.org/10.5194/esd-2022-50-CC1
- AC1:
  'Reply on CC1', Emma Allwright, 14 Dec 2022
  Dear Alex, thank you for your feedback. If we are invited to provide a revised version of our manuscript we will certainly consider and incorporate your comments. We provide a more detailed answer to each of your points below:
  We agree that European heatwaves are driven by different processes, hence why we consider multiple separate regions in this analysis. The key point we wanted to make is that, in a large part of the literature, the atmospheric features driving the heatwaves – whether they are blocking or ridges – are highlighted as persistent. The exact nature of these features does not affect the conclusions we draw in the paper. We nonetheless agree that it is important to use a precise nomenclature of large-scale circulation structures associated with heatwaves, and will revise the manuscript to highlight the different atmospheric features conducive to European heatwaves, encompassing both blocking-like structures and persistent ridges.
  
  When calculating analogues and persistence indices we are indeed using the full time series of SLP maps. We agree that there is no a priori reason that all analogues must fall in the same season. However, we would like to draw your attention to the fact that these calculations are performed on absolute values of SLP rather than anomalies. Consequently, one would expect that the flow patterns should be distinguishable between winter and summer, and that the algorithm should typically select analogues with both a similar structure and amplitude. In reply to your comment we have repeated the calculation of the mean theta for heatwaves using summer analogues only. We find that the theta values for heatwaves calculated only on summer month analogues are on average slightly larger (i.e. lower persistence) than those calculated using the full data set, please see the attached figure showing a scatter plot of the theta values using the two methods of calculation, with the diagonal marked in red and the means shown in black. This only goes to strengthen our key conclusion. We therefore do not think that our results depend on mixing analogues between different seasons. On a more theoretical level, we are assuming that the atmospheric circulation corresponds to one continuous dynamical system for all time values, as opposed to two systems with discontinuous switches between seasons (or a system with clearly separated basins of attraction). Seeing as our key result is not qualitatively affected by this choice, we therefore prefer to avoid artificially stipulating that all recurrences must fall within a given season. The method of Hoffman et. Al. (2021) presents an intriguing way of considering persistence, however there are methodological differences with our manuscript. In particular, the persistence we calculate is estimated using the time between recurrences or similar maps, in other words, how often does the atmospheric system return to a given state. It is, in other words, based on an unbiased estimator of the extremal index. This is contrasted with the method of Hoffman et. al. (2021) who instead look at similarity between 10 consecutive maps, which is effectively a nuanced autocorrelation metric. We thank you for having brought our attention to this manuscript, which we will make sure to include in the discussion section of the revised manuscript. However, we would argue that the method we adopt here, which allows probing local properties of the attractor of chaotic dynamical systems (see e.g. Moloney et al. (2019) for a detailed discussion of this) provides a more theoretically-grounded insight as to the expected persistence behavior of any given circulation pattern.
  
  We believe that the last part of your comment stems from a misunderstanding of our methodology. The extremal index characterizes local properties of the attractor. If we took each analogue of a given heatwave and calculated its persistence, it would have a persistence different from that of the heatwave itself. In other words, we are not taking an average of the persistence of configurations similar to those of the heatwave and assigning that average persistence to the heatwave itself. This is a very important point that we will make sure to clarify in the revised methods section of our manuscript.
  The quality of the selected analogues is a point we would like to address separately. The algorithm is based on the l2 distance, and in computing such distance it provides a quantitative, precise definition of “similarity” of maps, for all that it may differ from a Lagrangian style tracking of a specific structure. Since our whole approach is based on a limit theorem (the Freitas-Freitas-Todd theorem) for how the analogue distances should be distributed in phase space, we take “good” analogues to be analogues that follow the theoretical limit distribution – which we have verified and indeed is the case for the analogues found in this study. If the analogues were poor, e.g. because we were using too short a dataset, then they would presumably not follow the limit distribution
  Our methodology is designed to investigate the link between the persistence of large-scale atmospheric configurations and heatwaves. Capturing small scale persistence is beyond the scope of this methodology, and indeed the view we challenge is that of large-scale blocking (or ridges) leading to the heatwaves needing to be highly persistent. We are not addressing any local or small-scale drivers of heatwaves. It is true that the approach computes persistence for a fixed domain, and we agree that the domain we present in the main paper may miss some persistent features to the west – as in the example of the British Isles you bring in your comment. To this end, we have conducted a sensitivity analysis to the choice of a westward-shifted domain in the Appendix. We would like to add that the choice of domain is arguably as arbitrary a choice as any of the parameters one needs to fix in algorithms that detect single atmospheric features – for example having to define how far a block can move in space to still be the same block, which is a parameter included in many blocking algorithms. As such, different domains need to be tested to ensure the results are robust, but we do not see this as a flaw in the methodology more than any other algorithm requiring the choice of a parameter. Choosing a smaller domain centred on the region being analysed would presumably aggravate the issue with missing persistent features outside of the domain. Moreover, if the persistent feature leading to the heatwaves is so local that it does not show up as persistent on a relatively narrow continental domain such as the one we are using in our analysis, it probably does not qualify as a large-scale persistent feature. Indeed, we are not arguing against the possibility that local atmospheric features may be persistent. We thank you for having raised this point, which is central to our argument and not stated clearly enough in the current manuscript. We will make sure to clarify this in the updated introduction and discussion sections of the manuscript. Concerning the variance of SLP, the unequal variance across the domain is a property of the dynamical system we are analysing, and trying to normalise the variance in some way would distort the phase space we are conducting our analysis in. Selecting analogues in a normalized variance space would thus result in a considerable difficulty in interpreting the results.
  
  The sensitivity to various distance metrics is an interesting exercise, and a brief discussion of the properties the chosen distance metric should have is provided in the Appendix of Faranda et al. (2019). Ultimately, we would argue that if the selected analogues distance follows the theoretical limit distribution, this shows that the choice of distance metric is appropriate. However, we wish for this paper to help bridge the gap between mathematics and meteorology. Thus, we would rather avoid a detailed discussion on the choice of distance metrics here.
  
  Minor comments:
  Thank you for your comments, we will endeavor to clarify the manuscript during the process of revision. The specific package you enquire about on lines 130-131 is called CDSK and is available on github.
  
  Faranda, D., Messori, G., & Vannitsem, S. (2019). Attractor dimension of time-averaged climate observables: insights from a low-order ocean-atmosphere model. Tellus A: Dynamic Meteorology and Oceanography, 71(1), 1554413.
  
  Freitas, A.C.M., Freitas, J.M. & Todd, M. Hitting time statistics and extreme value theory. Probab. Theory Relat. Fields 147, 675–710 (2010)
  
  Moloney, N. R., Faranda, D., & Sato, Y. (2019). An overview of the extremal index. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(2), 022101.
  
  Citation: https://doi.org/10.5194/esd-2022-50-AC1
  - CC2: 'Reply on AC1', Alexandre Tuel, 19 Dec 2022
    
    Thank you Emma for these detailed comments which helped me better understand your work. It is nice to see that the results remain the same when based on summer data only. Out of curiosity, did you use the raw SLP data or did you remove an annual cycle?
    You wrote "In other words, we are not taking an average of the persistence of configurations similar to those of the heatwave and assigning that average persistence to the heatwave itself. This is a very important point that we will make sure to clarify in the revised methods section of our manuscript." I agree that this is important and might cause a lot of confusion, because clearly what "persistence" means for the average atmospheric scientist is very different from your definition. In particular, persistent patterns in the "traditional sense" may not be classified as very persistent with your dynamical systems approach. This also relates to my earlier comment about heatwaves and persistence, and this is why you should be careful when writing that heatwaves in Western Europe are not associated with much atmospheric persistence (e.g., "We thus argue that atmospheric persistence is not a necessary requirement for summertime heatwaves") What you argue, if I understood well, is that the states of the circulation that tend to occur during heatwaves are not persistent from the attractor perspective. However, this does not imply that during a heatwave, the circulation does not tend to remain stuck in a small part of the attractor (and Hoffmann et al's metric would capture this case). Is that correct? If yes, the point needs to be made clearly in the manuscript.
    For future research, it would be nice to use Z500 (with the seasonality taken out) instead of SLP. For summer heat extremes, SLP is not quite as relevant , especially in the lower half of your domain. Z500 would be a better proxy for atmospheric circulation. Heatwaves may indeed be associated with heat lows while Z500 exhibits a pronounced ridge. The SLP analogues might thus not be very physically meaningful since low SLP at other times could be associated with cyclonic activity.
    One last point (motivated by personal curiosity, no need to change the manuscript): analogues are selected based on some low percentile of L2-distance across the whole trajectory. So, the number of analogues is the same for all time steps, but the average distance between the analogues and the target value is not fixed. In particular for some rare states, it could end up being high. Or is the threshold reasonably constant with time?
    
    Citation: https://doi.org/10.5194/esd-2022-50-CC2
    
    AC5: 'Reply on CC2', Emma Allwright, 23 Feb 2023
    
    Dear Alex,
    Thank you for your valuable time and follow up comment. Please find our reply in the attached pdf.
    Best regards,
    Emma Holmberg and all co-authors
    
    Citation: https://doi.org/10.5194/esd-2022-50-AC5
RC1:
'Comment on esd-2022-50', Anonymous Referee #1, 20 Dec 2022

The authors present an analysis of atmospheric circulation persistence with a focus on summer heat waves and winter warm spells in Europe. Their method is based on atmospheric circulation analogues that are used to estimate the persistence of a atmospheric circulation configuration. The study is overall very interesting and the approach appears to be promising. In the current version there is a lack of clarity in the interpretation of results and the conclusions drawn from the analysis.

Major comments:

In the current state, the manuscript lacks some clarity on the interpretation of the main findings. Some passages indicate, that the presented analysis that is based on a dynamical systems viewpoint contradicts main findings coming from the atmospheric blocking community (line 158-160, line 180-183, line 196-197). In the discussion the authors explain the methodological differences between their approach and the blocking approach (line 197-...). I would say that the main difference is the definition of "persistence". The authors use a definition of persistence that analyses the atmospheric circulation over a larger region. They can therefore quantify persistence for any day in the observations and compare the persistence of heat-wave days to other days. When analyzing the persistence of blocking there is a focus on a specific atmospheric circulation pattern and the persistence of blocking is not analyzed relative to the persistence of other flow patterns. It seems as if two approaches that are useful for different research questions are compared to each other which makes some of the interpretations of the paper misleading.

I would suggest to describe the research question more precisely and frame the interpretation of the results and the discussion along this research question. Is the research question "Is the atmospheric circulation observed during heat waves more persistent than the average persistence?" or is it "Does longer persistence of a atmospheric circulation pattern that favors heat waves lead to more intense heat waves?" or is the research question "would it be more appropriate to describe the persistence of heat waves with a dynamical systems approach".

If the main focus of the paper is a comparison with statements from the blocking literature I would also recommend to explain these statements in a bit more detail in the introduction to allow for more clarity in the discussion.

One example of an interpretation that I would question:

As the authors explain, the most persistent atmospheric flow is zonal flow (see line 71-72). If summertime heat waves occur when the zonal flow is blocked, one would expect, that the atmospheric circulation during heat waves is not anomalously persistent. To me everything seems to be as expected so far. Therefore, I would write the sentence in line 157-158 differently. To me this seems to be a misunderstanding: It might be true, that more persistent blocking leads to more severe heat waves. And this can be true irrespective of whether zonal flow is generally more persistent than blocking. I therefore also disagree with line 180-182.

Advection analysis and figure 4:

Looking at figure 4 it seems as if the advection that is analyzed here shows rather small scale features. Do these small scale features really represent the large scale flow that is shown in figure 1? Due to this (potential?) inconsistency I do not find the lines 160-166 convincing. In my view, more analysis would be needed to really interpret the role of warm air advection.

I would assume that the analysis is sensitive to the domain over which the atmospheric circulation is analyzed. A justification or an explanation of the choice of the Europe wide domain is lacking in section 2.1. There is one sensitivity test with a shifted domain which is great, but the interpretation of this sensitivity analysis is lacking in the main part of the manuscript. Furthermore, I think it would be more interesting to test the sensitivity to the size of the domain.

Minor comments:

L11: exact?

L129: Is it relevant that the reader understands the method of Süveges? If yes, please explain it in more detail. If no, I'm not sure if you need to compare it to another method (Ferro and Segers) which is not expleained either?

L130: Please write the package name here (I assume it is not "Robin")

L184-185: This formulation could lead to a misinterpretation of the results (see my major comments above). The presented analysis does not study the link between more persistent anti-cyclonic configurations and the intensity and persistence of heat-waves.

Figure A1: This sensitivity test is helpful and important. Would it also be possible to do a sensitivity test where the domain over which atmospheric circulation is analyzed is smaller, for example only the Mediterranean?

Citation: https://doi.org/10.5194/esd-2022-50-RC1
- AC2: 'Reply on RC1', Emma Allwright, 23 Feb 2023
  
  Dear Reviewer 1,
  Thank you for your valuable time and helpful comments. Please find our reply in the attached pdf.
  Best regards,
  Emma Holmberg and co-authors
  
  Citation: https://doi.org/10.5194/esd-2022-50-AC2
RC2:
'Comment on esd-2022-50', Anonymous Referee #2, 23 Dec 2022

Please see the attached pdf.

Citation: https://doi.org/10.5194/esd-2022-50-RC2
- AC3: 'Reply on RC2', Emma Allwright, 23 Feb 2023
  
  Dear Reviewer 2,
  Thank you for your valuable time and feedback. Please find our reply in the attached pdf.
  Best regards,
  Emma Holmberg and all co-authors
  
  Citation: https://doi.org/10.5194/esd-2022-50-AC3
RC3:
'Comment on esd-2022-50', Anonymous Referee #3, 26 Dec 2022

This paper examines the links between heat extremes and a metric of atmospheric persistence from dynamical systems theory. Using this metric, it is argued that there is no evidence of a link between heat extremes and anomalously persistent circulation patterns. Some assessment of the role of different terms in driving temperature anomalies is also provided and it is argued that there is an important role for zonal temperature advection in driving wintertime heat extremes, while in the summertime temperature advection does not play an important role. I can see that it's useful to quantify atmospheric persistence by this dynamical systems measure, although I have some questions about the methodology. My primary concern is about the interpretation and the conclusions when using this measure. I think there are two potential intepretations. One is that persistent circulation patterns are not closely linked to heat extremes, which is the interpretation the authors have provided. The other is that this dynamical systems metric is actually not a very good measure of persistent circulation patterns. I'm not totally convinced by the authors argument that this second interpretation can be ruled out, so my more major suggestion is that either a clearer demonstration of this being a preferred metric for atmospheric circulation persistence should be provided, or the discussion should be changed to be a bit more balanced on whether this metric is accurately measuring persistence of atmospheric circulation anomalies.

General comments:

(1) As mentioned above, my primary concern is whether the interpretation that "atmospheric persistence is not a necessary requirement for summertime heatwaves" (l9) is actually correct, or whether an alternative interpretation is that this dynamical systems theory metric of atmospheric persistence does not adequately capture persistent atmospheric circulation anomalies. I feel like the demonstration in Figure 6 supports that this metric might not be very good at capturing persistent atmospheric circulation anomalies. It is clear that Figure 6b and d demonstrate a persistent block, as indeed the authors state. But it seems like it could be argued that this dynamical systems metric is, therefore, just not a very good metric for persistent atmospheric flow anomalies. I'd question whether it can really be used to argue that "highly persistent configurations are not a necessary criterion for European summertime heatwaves to occur" (l242) when clearly there is a case in Figure 6 that does have a persistant atmospheric flow configuration but is considered not persistent by this metric. I'm left a bit confused about what argument is exactly being made. If I read the paper in a cursory manner, I might think that the conclusion is that you don't need persistent atmospheric circulation patterns to produce heatwaves, but if readers think more about it and pay attention to Figure 6, it seems the conclusion should actually be that this particular dynamical systems metric of persistence doesn't really capture persistence in atmospheric flow patterns of relevance to heatwaves. I suggest the authors either need to make a clearer case for why this metric is preferable to those based on persistent flow regimes or alter the wording in places to make clear that actually this dynamical systems metric of persistence doesn't do that good a job of picking out persistant blocking highs or other flow regimes that are relevant for heatwaves. I think either conclusions is worthy of publication, but I'm confused about which one is being drawn. Another example of a confusing conclusion is lines 247-249 where it's stated that "our results appear to contrast the conventional view of heatwaves being associated with very persistent blocked configurations" when above, in reference to Fig 6, it's stated that a blocking algorithm would detect a block in the low persistence case for several days (l238). It seems, then, that this metric is not a very good metric of blocking, so how can it be used to contrast the conventional view of very persistent blocked configurations being connected to heatwaves?

(2) One aspect of the methodology that I wondered about was is it easier to have higher persistence when there are less anomalies overall in the spatial field. I'm imagining that if you have a really large amplitude anomaly but that moves slightly, the spatial Euclidian distance between days that have a relatively small movement may end up being a lot larger than the Euclidian distance between days where there's much less going on in the spatial field. If so, then maybe this isn't a particularly good measure of the persistence of relevance to heat extremes. Persistence of nothing much going on over the region wouldn't be very meaningful, whereas having a persistant blocking high that stays around for a long time in the region, even if it moves slightly, would likely be more impactful for heat extremes. Or perhaps there's something in the methodology that prevents this from happening. I recommendt this be discussed or assessed.

Minor comments by line number:

l94: I don't think "345-45W" is correct. Maybe 15W-45E?

Figure 1 caption: I think this could be a bit clearer if it stated "warm spells during winter (top) and heatwaves during summer (bottom)". (It took me a while to notice the winter and summer in the titles).

l160: In the discussion of the role of advection starting here and referring to Figure 4, "the role of warm air advection toward the region of interest during warm spells" is not entirely obvious to me in a causal sense. Couldn't there also potentially be a role for the temperature anomaly itself being produced by some other cause actually leading to temperature advection anomalies. I feel like the reds next to blues in this figure may be indicative of that i.e., you get some warm anomaly set up and if the zonal flow is westerly then you end up with cold advection to the west of the warm anomaly and warm advection to the east. Even if that's not the case, the dominant role of warm advection isn't totally clear to me from the figure since it's very noisy. Is the intention that readers should be paying attention to the larger spatial scales, as oposed to the small scale noise? If so, maybe some filtering to retain only larger spatial scales could be performed?

l165-166: You mention the potential role of advection over topography for engendering large temperature anomalies here. But couldn't this also potentially be an artefact of using SLP? SLP will involve some extrapolation below the surface making an assumption about the lapse rate, I think. So SLP will be an approximation over topography and will be affected by the temperature at the surface, so is it possible that this could be playing a role here?

Citation: https://doi.org/10.5194/esd-2022-50-RC3
- AC4: 'Reply on RC3', Emma Allwright, 23 Feb 2023
  
  Dear Reviewer 3,
  Thank you for your valuable time and helpful suggestions. Please find our reply in the attached pdf.
  Best regards,
  Emma Holmberg and all co-authors
  
  Citation: https://doi.org/10.5194/esd-2022-50-AC4

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reconsider after major revisions (24 Feb 2023) by Christian Franzke

AR by Emma Holmberg on behalf of the Authors (29 Apr 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (03 May 2023) by Christian Franzke

RR by Anonymous Referee #2 (08 May 2023)

RR by Anonymous Referee #3 (14 May 2023)

ED: Publish subject to minor revisions (review by editor) (22 May 2023) by Christian Franzke

AR by Emma Holmberg on behalf of the Authors (01 Jun 2023) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (06 Jun 2023) by Christian Franzke

AR by Emma Holmberg on behalf of the Authors (13 Jun 2023) Author's response Manuscript

Short summary

We analyse the duration of large-scale patterns of air movement in the atmosphere, referred to as persistence, and whether unusually persistent patterns favour warm-temperature extremes in Europe. We see no clear relationship between summertime heatwaves and unusually persistent patterns. This suggests that heatwaves do not necessarily require the continued flow of warm air over a region and that local effects could be important for their occurrence.

The link between European warm-temperature extremes and atmospheric persistence

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