the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 Jul 2025
Dynamical System Metrics and Weather Regimes explain the seasonally-varying link between European Heatwaves and the large-scale atmospheric circulation
Abstract. Global warming is projected to increase the frequency and intensity of heatwaves in the extended summer period. To better predict heat extremes, it is important to explore the seasonal variations in their drivers. Therefore, we analyze heatwaves in Central Europe using ERA5 reanalysis data over the historical period (1950–2023) for the extended summer months (May–September). We quantify atmospheric persistence, and the link between near-surface temperatures and large-scale atmospheric circulation patterns using dynamical system metrics. This approach is further contextualized by the consideration of weather regimes, which represent the low-frequency variability of the atmosphere over the North Atlantic and Europe.
Our results show a maximum in atmospheric persistence in July and August, associated with higher occurrence of Scandinavian Blocking, and relative minima in spring and autumn. The relationship between the large-scale atmospheric circulation and near-surface temperatures exhibits similar seasonal characteristics. For heatwave days, we find a statistically significant anomalous strong link between large-scale atmospheric circulation and surface temperatures from June to September. This relationship is generally not attributable to the occurrence of specific weather regimes. However, heatwaves in July and August are associated with higher atmospheric persistence due to an enhanced frequency of the persistent Scandinavian and European blocking weather regimes. Beyond atmospheric circulation, additional physical drivers of daily maximum temperature during heatwaves are analyzed: While surface net solar radiation shows a particularly strong link in June and July, soil moisture exhibits an anomalously high link in July and August. These findings highlight the critical role of intra-seasonal variations in shaping heatwave dynamics.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-3379', Anonymous Referee #1, 09 Sep 2025
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RC2: 'Comment on egusphere-2025-3379', Anonymous Referee #2, 13 Oct 2025
Review of manuscript: “Dynamical System Metrics and Weather Regimes explain the seasonally-varying link between European Heatwaves and the large-scale atmospheric circulation” by Ines Dillerup et al.
Recommendation: Accept after minor revision.
This paper investigates the links between the atmospheric circulation and near-surface air temperature during the extended summer season. The authors use the ERA5 reanalyses and a methodology based on dynamical system metrics and the weather regime approach to study the seasonality of the association between large-scale atmospheric circulation and summer European heatwaves.
The main results of the paper are interesting and deserve to be published. The methods used in the paper are not new but their combination makes the originality of the study. However, I do think that the paper would benefit from a small amount of additional work regarding sensitivity tests and the discussion.
Main comments:
Sensitivity to the choice of the regime approach: the authors have chosen to use the fixed (static) 7-regime approach of Grams et al. 2017. It would be interesting to test a different approach based on a larger number of regimes, for instance with an approach similar as the one (based on sea level pressure) used in Neal et al. (2016) with 30 weather regimes (or weather types). That would allow the presence of more intra-seasonal summer-like regimes (like the Atlantic-low or southerly flow anomaly regime, that is known to be strongly associated with heatwaves over Western Europe, see Vautard et al. 2023 for a recent study) and perhaps of a more refined description of the association between circulation and heatwaves.
If a given regime (its centroid pattern) is strongly connected to heatwaves, I would expect that some of the heatwave properties should depend in some ways of a distance (to be defined, for instance using a simple pattern correlation) between the stream function pattern of the heatwave day and the regime centroid pattern. It would be interesting to see such a diagnostic for the two regime approaches.
My second comment is about the dynamical system metrics. I know that these metrics have been proposed and used in many recent papers but I have to say that I am still a bit unclear/skeptical on their exact meaning and relevance. With the threshold (2%) you have chosen, you are using 541 analogues per day (this means that you are searching analogues throughout the whole year). It is also well known that given the size of ERA5, even the “best” analogues (based on Euclidean distance or other metrics) are not really good analogues, raising questions about the derived state persistence. I’d be curious to see the mean fraction (relative to the whole set of 541 analogues) of days with the same regime as the reference day. Can you also run the Süveges algorithm on the days of the same regime (as the day of consideration) instead of the analogues obtained with the Euclidean distances? Do you get similar results ?
My third comment is about the last part of the study and the discussion regarding the soil moisture, surface solar radiation and minimum temperature. I would suggest to reframe a bit this section while trying to provide more explanation behind some of your results. While the soil moisture and surface solar radiation can be considered as additional factors influencing the severity and/or persistence of heat waves, the minimum temperature is part of the heatwave characteristics. I would first describe the results about tasmin, then the ones about the additional factors.
Can you explain why there is such large intra-monthly variability during July and August in the co-occurrence of soil moisture with tasmax? Is it just due to the fact that you are only considering the upper soil layer? If you include also the second layer, do you get the same result?
When you explain the seasonality and high values of co-occurrence between tasmax and tasmin (line 411), you could also mention the release of the heat trapped during daytime to explain the high values during July and August. Finally, I am not sure than the co-occurrence metric has a direct and simple link with the quantification of the respective contribution of solar radiation and soil moisture to heatwaves (lines 421–422). As the authors mention earlier in the text, no causality and quantification of the effect magnitude can be deduced from the co-occurrence metrics.
Minor comments:
A general comment: in several instances, a “from” is missing before specific months, see for example line 337: “…but varies only slightly June to August.”
(1) Abstract: page 1, line 9: why spring and autumn here? May and September instead?
(2) page 3, lines 59: why coupling here? I do not see in the paper any analysis related to the influence of heatwaves or surface temperature patterns on the atmospheric flow. The same comment also applies to other uses of the word coupling throughout the manuscript (e.g page 9, line 246).
(3) page 4, line 109: why “throughout the year”. throughout the extended summer instead ? Most of the paper concerns the extended summer, and there is very little discussion of the other seasons.
(4) page 5, line 127: please specify how exactly you have detrended the different variables (period, method of detrending etc…)
(5) page 5, line 132: “for better comparability” – with what?
(6) page 5, lines 131–136: I do not see the point of having two different domains for calculating heatwaves and dynamical metrics. It seems to me that using the same domain would be much better. Finally, you have chosen to extend much more the latitudinal than the longitudinal span of the red box to get the dashed box. Can you justify this choice ?
(7) page 6, line 154: 5% is a rather small area (only a few grid points since you are using 0.5° data) given that your geographical domain is also small.
(8) Section 2.4, lines 176–178: you haven’t clearly mentioned if you classify all days or if you are using a metric with a threshold to identify regime and transition days. Can you detail exactly what you have done? Based on Figure 2e, it seems that you are using the index IWR to define regime and transition days?
(9) Section 2.5: are you using the full fields or the anomalies for the analogue computation? Have you tested the sensitivity of your approach to other distances (than the Euclidean)?
Co-occurrence ratio, lines 209–210: again, coupling implies a two-way interaction and here there is no evidence of such a thing. Furthermore, I do not clearly see why alpha “provides valuable insights into the physical system under investigation”.
(10) page 9, lines 228–229: either “over a 5–day period” or “over 5-day periods”
(11) page 9, lines 242–247: how do you interpret the strong decline of the co-occurrence starting on the 24, while the heatwave is not yet fully developed?
(12) page 9, lines 248–250: this statement may be true, but at this point in the paper, one case study is not enough to make it true.
(13) page 9, lines 257–258: “stream” should be “stream function”. Note that this need to be corrected in many instances throughout the paper.
(14) page 12, lines 301–303: it seems to me that the second sentence and the bootstrap test shown in figure 4b contradicts the first sentence.
(15) page 17, line 386: change the word “probable” as the role of land-atmosphere interactions and their influence on heatwaves has been shown by multiple studies.
(16) page 18, line 398–399: I would suggest to use a different predictor for the soil moisture availability in order to see whether it can explain the high co-occurrence ratio. What matters is not just the soil moisture anomaly but also how far you are from a shift between soil moisture regimes (dry, transitional, and wet regimes).
(17) page 18, line 409: “governed”. The beginning of the sentence is not really bringing anything new, please rephrase.
(18) page 18, line 429: I’d rather use “association” instead of “coupling”
(19) page 20, lines 490-494: it would be very nice to use sea level pressure instead of the stream function to replicate Figure 4.
(20) page 21, line 517: not always as indicated below and by many previous works looking at the dynamical role of transition days between regimes.
Figures:
Figure 5: middle column: it is very difficult to clearly identify the different colors (specifically the different pink and orange colors). Can you explain why the frequency of GL for all days in August is less than that of EuBL while the climatology of IWR is greater for GL than EuBL?
References:
Neal, R., Fereday, D., Crocker, R. and Comer, R.E. (2016), A flexible approach to defining weather patterns and their application in weather forecasting over Europe. Met. Apps, 23: 389-400. https://doi.org/10.1002/met.1563
Vautard, R., Cattiaux, J., Happé, T. et al. Heat extremes in Western Europe increasing faster than simulated due to atmospheric circulation trends. Nat Commun 14, 6803 (2023). https://doi.org/10.1038/s41467-023-42143-3
Citation: https://doi.org/10.5194/egusphere-2025-3379-RC2
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- 1
In this study, the authors investigate the link between European heatwaves and the large-scale atmospheric circulation through a combination of diagnostics grounded in dynamical systems theory with weather regime analyses. The approach builds on previous work (such as Holmberg et al., 2023) using similar dynamical systems metrics for the investigation of extreme events and extends those by studying seasonal variations and combining the metrics with empirically defined weather regimes that allow for a more accessible interpretation of the large-scale circulation. By doing so, it makes a somewhat incremental, but, in my view, useful contribution to the literature. The results are not clear-cut (e.g., different weather regimes become important during the seasonal cycle), providing evidence of the complexity of the circulation leading to heat waves. The paper is well-written and -structured, and I particularly appreciate the detailed and instructive explanation of the methodology (e.g., the concept behind the dynamical system metrics). Nevertheless, I have a few, mostly minor comments for the authors to consider before I'd recommend the manuscript for publication, as detailed below.
Major comment:
In a recent study, Brunner and Voigt (https://doi.org/10.1038/s41467-024-46349-x) identified pitfalls when studying extreme events through percentiles defined over rolling time windows. If I'm not mistaken, the authors' heatwave definition is based on the approach criticized in this paper. Moreover, Brunner and Voigt emphasize that analyses of seasonal variability, as done here, can be particularly problematic in this context. I thus think that the authors should include a sensitivity analysis showing that the pitfalls identified by Brunner and Voigt do not substantially affect their findings.
Minor comments:
- Line 45: Daily mean temperature is more important for the impacts than for understanding the development of heatwaves, right? Maybe mention this here.
- L 57: Consider noting already here that the transition between these patterns (advection vs. local processes) in the transition seasons are less-well studied.
- L 71-74: This is very technical for an introduction section and could be omitted here (it is explained in the methods).
- L 248: I think this summary goes too far. It is not evident form a single example that the metrics and regimes are "clearly connected", as this is only one data point and could likely be a coincidence. I'd suggest using more cautious language here.
- L 257 and elsewhere: I find it confusing to use "stream" as a short form of "stream function".
- Fig. 2: The caption should indicate the fields that are displayed. Furthermore, is there a reason why you always show inverse persistence, although the actual persistence is discussed? This requires the reader to flip everything in their head.
- L 310: "partly explained" indicates a connection between re-occurrence and persistence, which is not easy to understand without further explanation
- L 323: "low persistent": I cannot see this in the figure. There is no cluster of points on the right-hand side of the plot.
- L 324: I'd suggest to not mention the weather regimes here, as they are only discussed in more detail later.
- Section 4: I would appreciate a brief discussion about potential linkages of these findings to the mechanisms discussed in the introduction, such as the role of advection throughout the seasonal cycle. This could be added at the end of this section or in section 6.
- Section 5: The least conclusive part, in my view, is the linkage between maximum and minimum temperature, which is described, but not really interpreted. It would be helpful to add some discussion on potential mechanisms here.
- L 517: "might usually represent an atmospheric state close to climatology": I have some doubts about this statement. The fact that the mean over the "no regime" category is similar to climatology does not tell that this is also true for individual cases. In fact, such cases can be quite different from the climatological mean; the reason that they are in this category is that they do not project on any of the patterns of the selected regimes.