| 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.
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.