the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Aug 2025
Cold spells induced by slow and amplified atmospheric waves
Abstract. Cold spells in the Northern Hemisphere mid-latitudes have been linked to planetary waves. Yet the mechanisms by which these waves impact cold-spell formation remain unclear. Here we develop novel metrics to separately measure the amplitude and speed of ridges and troughs, examining the behavior of planetary waves during winter cold spells. Our findings indicate that while the planetary waves across the entire mid-latitudes experience significant changes during cold spells, local wave dynamics play a major role in developing these events. The nearest upstream ridge and downstream trough of the cold-spell region are located in a way that facilitates development of the extreme cold anomaly. This ridge and trough amplify and slow, enhancing and prolonging southward advection of cold air from the Arctic into the cold-spell region. The slow and amplified upstream ridge and downstream trough occur several days before the region’s minimum temperature, suggesting these local wave anomalies induce cold-spell formation.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-3867', Anonymous Referee #1, 18 Sep 2025
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RC2: 'Comment on egusphere-2025-3867', Anonymous Referee #2, 26 Sep 2025
Review of "Cold spells induced by slow and amplified atmospheric waves" by Babaei et al.
General assessment
This concise manuscript focuses on the connection between Rossby waves and surface cold extremes, with the aim of systematically connecting such extremes with specific wave properties (i.e., amplitude, speed). To achieve this objective, a geometric method to track individual ridges and troughs is proposed and employed. The main outcome of the study emphasizes the equatorward advection of cold air by slow-moving, amplified ridges as crucial for cold spell occurrence.
First of all, I believe that the manuscript needs to be substantially revised, so that the novelty of the approach and of the results can be made more visible and assessed more properly. This can be done by:
1) extending the description of the ridge/trough tracking method, including a specific case study where, at different time steps, the wave properties and their connection with the occurrence of a cold spell are explicitly shown;
2) reworking the motivation of the study and the exposition of the results to highlight novel aspects, as the role of advection by slow-moving, amplified waves is a rather known mechanism for the occurrence of cold spells (e.g., Bieli et al. 2015; Fragkoulidis and Wirth, 2020; Roethlisberger and Papritz, 2023; Tuel and Martius, 2024, just to cite a few recent ones). In this sense, the performed analysis does not add (at least from reading the current version of the manuscript) much novel understanding.
In addition to the novelty aspect, there is some ambiguity concerning the type of Rossby waves that are analyzed in this study, as the reader is often left wondering whether stationary or transient (e.g., Rossby wave packets, RWPs) waves are being considered.
Given the conceptual and methodological unclarities, I conclude that publication in Weather and Climate Dynamics can only be granted after the resubmission of a substantially reworked manuscript: this would point to a recommendation between "Rejection" or, if the handling editor sees it fit, of "Reconsideration after major revision". More specific suggestions and requests for clarification are listed below.
Major points
- Need for a clearer explanation of the methodology, involving a real case study: If one of the aim of this paper is to introduce the novel methodology to track Rossby waves, the space dedicated to it is too short to actually appreciate its improvement with respect to other metrics. It would really help if the general explanation were to be complemented by a "real" case study, so that the approach can be actuallly understood. I would also suggest to incorporate some parts from the Supplementary Text in the main to improve the explanation. The explanation of the methodology is complicated to follow and the Fig. 1 does not help much to understand it, in particular for the part about the amplitude of the waves. A possibility would be to include a modified version of Fig. S3 as part of the panel in Fig. 1, removing the Fig. 1b. Furthermore, to better support the statement that the developed metric provides a "unique methodology compared to other metrics" (line 236), a comparison -even qualitative, but specific- with other metrics would be needed.
- Novelty aspect: the results section is quite short and does not focus too much on the novel aspects: it needs to be reworked to include more specific analysis, ideally by contrasting two/three different regions or groups of regions with analogous characteristics, rather than only showing the average. Topics that might be deepened include, for instance, the potential importance of retrograding patterns (whose presence is hinted in Fig. 3), the specificity of Northern Siberia (l. 132) or the Rossby wave dynamics during low- vs high-latitude cold spells. Some paragraphs in the Results section, furthermore, belong more to the Introduction than to the Results part (e.g., l. 141-147,l. 156-167), making it unnecessary lengthy and further blurring the explanation. In addition to the Results part, the conclusions do not stand out as novel enough: maybe, for a start, the authors can elaborate on the aspects in which this study provides a different perspective than, e.g., Fragkoulidis and Wirth (2020) who also concluded that "persistent [...] cold extremes are associated with an above-normal RWP amplitude and a below-normal RWP phase speed."
- Theoretical issue about the nature of the waves involved in cold spells: as far as I understand, the authors identify three main ridges and troughs over the Northern Hemisphere, corresponding to the stationary waves resulting from orography, land-sea contrast and eddy/mean flow forcing, and interpret the occurrence of cold spells as a shift in their position (as discussed in detail, e.g., in Supplementary Text "Wave location", at lines 96-115, a paragraph that helps the interpretation and that would fit more appropriately in the Results part). However, when performing the analysis, what is being tracked are transient ridges and troughs (more or less slow-moving) of fundamentally different origin that the ones by stationary wave theory: instead, they would be physically closer to RWPs. Although the authors might object that filtering on low wavenumbers (Z1-5) allows to consider longer waves than RWPs, most of the considered regions are located at high latitudes and, thus, baroclinic RWPs would project on similarly low wavenumbers due to the meridians getting closer and closer together towards the North Pole. Consequently, the interpretation of dynamics in terms of amplification/deepening of the six stationary wave features (ENA, EAsia, EMed, WNA, TP, NAO) is not well posed. On the other hand, what is being tracked are the transient features evolving on top of the stationary waves, whose presence should be considered more explicitly to explain the dynamics and remove ambiguities in interpretation.
- Excessive reminders to the Supplementary Information: the readers are often sent to look at the Supplementary information, often without additional explanation of how the linked content is relevant for the logical flow of the manuscript (l. 101-102, 132, 149, 167). Given that the manuscript now is quite short, I would suggest the reader to enrich the description of the method and the analysis of the results with material from the Supplement, properly introduced and discussed. Some detailed suggestions are scattered across the review.
Specific comments
l. 4-5 and following: what is the difference between "planetary wave" and "local wave dynamics" (line 4-5)? Are the ridges and the waves being tracked and analyzed part of the local or of the planetary?
l. 15: "influenced by pressure differences": this sound imprecise, in which sense "influenced"? Would "local and planetary vorticity gradients" be more adequate? Also, the Holton and Hakim (2013) textbook is cited three times in the manuscript, would it be possible to add more specific literature?
l. 25: in which sense negatively tilted troughs are "generated through strengthening of the wind shear"? Do the authors refer to meridional wind shear in a context of LC1/LC2 life cycles and/or of Rossby wave breaking?
l. 33-38: "Cold spells and heavy snowfalls across the Northern Hemisphere have increased" is a misleading statement, and the presence of few regional trends cannot mask the overall decrease in their intensity and frequency (e.g., Easterling et al. 2016, van Oldenborgh et al., 2019), and their occurrence is predicted to globally decrease according to climate projections (e.g., IPCC 2021, Fig. SPM.9). The purported examples in the following lines are anecdotal and not necessarily representative of a broader trend. The answer might be more nuanced for heavy snowfall (e.g., O'Gorman, 2014; Quante et al., 2021), but snowfall is a more complex phenomenon than cold spell as it involves moisture changes, and is anyway not the main focus of this article.
l. 46: the citation of van Mourik et al. (2025) needs to be contextualized a bit more: first of all, because the authors of that study question in their limitation whether rapidly moving "blocks" (as diagnosed by their methodology) actually represent cases of atmospheric blocking, and secondly because in the conclusions of that paper is written that "In winter, the coldest temperatures are associated with quasi-stationary blocks", so there is no particularly visible "inconsistency" (l.48).
l. 66: a more detailed explanation of the logic behind the choice of the regions would be helpful here, ideally moving some parts of the Supplementary Information here and by adding a figure showing the "cold anomaly contribution to the historical extreme cold days".
l. 83: in which sense "bottom-trough" and "top-ridge"?
l. 85-87: difficult to follow, would it be possible to mark the +/- 8% lines in Fig. 1a to visualize how it is computed?
l. 92: would it be possible to see the lat/lon tracks of the ridges/troughs tracked using this method?
l. 101: what is the nature of these interpretation errors?
Fig. 2: It is not clear whether the contours are representative of the winter climatology or of vertical extremes, as from the caption one would expect a double set of contours. Also, what are "vertical extremes"?
l. 169-173: if the trough speed is computed only over trough regions, what is the value attributed to "trough speed" in Fig. S8 (and consequently in Fig. 4) for cold spells occurring over the UK (R04) or the NW US (R01) that are located almost completely under a ridge? It would be great if these longitude bands were to be shown explicitly in a Figure.
Fig. 4: I find interesting that at low latitudes troughs decelerate during cold spells (as discussed at line 191), but at the same time the ridge move significantly faster. I am wondering whether this puzzling aspect is due to the averaging across different regions: looking at Fig. S8 it seems that this behavior is related particularly to N Siberia and US cold spells, but could not figure out the logic of it. Could the authors explain more in detail what is happening? Would it make sense to have separate discussion for some peculiar regions?
l. 224-231: the ambiguity between stationary and transient waves is also well visible in this concluding paragraph, where the word "wave" is used sometimes to mean Rossby wave packets (e.g., citing Fragkoulidis 2018) and sometimes in terms of climatological stationary waves (l. 228). This leaves quite some confusion in the reader about what has been the object of this study, whether stationary or transient waves: the use of tracking approaches would indicates focus on the latter type, but the emphasis on the climatological wave-3 pattern points towards the former.
Grammar/Technical/Typos
L. 39: increase. Also, increase in what? Frequency, intensity, etc...
l. 60-69: consider starting the paragraph with the full sentences starting between lines 65-69 and then explain why IPCC regions were not chosen.
Bibliography:
Bieli, M., Pfahl, S. and Wernli, H. (2015), A Lagrangian investigation of hot and cold temperature extremes in Europe. Q.J.R. Meteorol. Soc., 141: 98-108. https://doi.org/10.1002/qj.2339
Easterling, D.R., K.E. Kunkel, M.F. Wehner, and L. Sun, 2016: Detection and attribution of climate extremes in the observed record. Weather and Climate Extremes, 11, 17–27, doi:10.1016/j.wace.2016.01.001
Fragkoulidis, G., and V. Wirth, 2020: Local Rossby Wave Packet Amplitude, Phase Speed, and Group Velocity: Seasonal Variability and Their Role in Temperature Extremes. J. Climate, 33, 8767–8787, https://doi.org/10.1175/JCLI-D-19-0377.1.
IPCC, 2021: Summary for Policymakers. In: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 3−32, doi:10.1017/9781009157896.001
O’Gorman, P. Contrasting responses of mean and extreme snowfall to climate change. Nature 512, 416–418 (2014). https://doi.org/10.1038/nature13625
Quante, L., Willner, S.N., Middelanis, R. et al. Regions of intensification of extreme snowfall under future warming. Sci Rep 11, 16621 (2021). https://doi.org/10.1038/s41598-021-95979-4
Röthlisberger,M. and Papritz,L. (2023). A global quantification of the physical processes leading to near-surface cold extremes. Geophysical Research Letters, 50, e2022GL101670. https://doi.org/10.1029/2022GL101670
Tuel, A. and Martius, O. (2024). Persistent warm and cold spells in the Northern Hemisphere extratropics: regionalisation, synoptic-scale dynamics and temperature budget, Weather Clim. Dynam., 5, 263–292, https://doi.org/10.5194/wcd-5-263-2024
van Oldenborgh, G.J. et al., 2019: Cold waves are getting milder in the northern midlatitudes. Environmental Research Letters, 14(11), 114004, doi:10.1088/1748-9326/ab4867.
Citation: https://doi.org/10.5194/egusphere-2025-3867-RC2
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Thank you for preparing this manuscript. Please find the comments attached.