A combined storyline-statistical approach for conditional extreme event attribution

León-FonFay, Dalena; Lemburg, Alexander; Fink, Andreas H.; Pinto, Joaquim G.; Feser, Frauke

doi:10.5194/egusphere-2025-4976

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https://doi.org/10.5194/egusphere-2025-4976

Preprints

27 Oct 2025

| 27 Oct 2025

A combined storyline-statistical approach for conditional extreme event attribution

Dalena León-FonFay, Alexander Lemburg, Andreas H. Fink, Joaquim G. Pinto, and Frauke Feser

Abstract. Quantifying the influence of anthropogenic global warming on extreme events requires both physical and statistical understanding. We present a framework combining two complementary conditional attribution methods: spectrally nudged storylines and flow-analogues. Applied to the 2018 Central European heatwave, storylines project an area-mean intensification of 1.7 °C per degree of global warming. Despite no detected changes in atmospheric blocking, the flow-analogue approach further indicates that heatwaves exceeding the storyline-projected intensities become far less rare at their corresponding warming levels than the factual 2018 event was under present conditions. Specifically, the 2018 heatwave, with an intensity of 2.2 °C and a return period of 1-in-277-years today, becomes a 6.6 °C event with a 1-in-26-year probability in a +4 K world. We conclude that this combined framework is promising for climate change attribution of individual extreme events, offering both a physical assessment of anthropogenic warming and its associated likelihood while accounting for potential shifts in atmospheric dynamics.

Received: 08 Oct 2025 – Discussion started: 27 Oct 2025

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

Journal article(s) based on this preprint

16 Apr 2026

A combined storyline-statistical approach for conditional extreme event attribution

Dalena León-FonFay, Alexander Lemburg, Andreas H. Fink, Joaquim G. Pinto, and Frauke Feser

Weather Clim. Dynam., 7, 597–613, https://doi.org/10.5194/wcd-7-597-2026,https://doi.org/10.5194/wcd-7-597-2026, 2026

Short summary

Dalena León-FonFay, Alexander Lemburg, Andreas H. Fink, Joaquim G. Pinto, and Frauke Feser

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4976', Anonymous Referee #1, 30 Oct 2025

Please find my comments attached.

Citation: https://doi.org/10.5194/egusphere-2025-4976-RC1
- AC1: 'Reply on RC1', Dalena Leon, 08 Dec 2025
  
  Dear Referee,
  We appreciate the recognition of the contribution of combining storylines and flow-analogues for conditional attribution. Your comments have been valuable for strengthening the manuscript.
  Kind regards,
  Dalena, on behalf of all Co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-4976-AC1
RC2:
'Comment on egusphere-2025-4976', István Dunkl, 21 Nov 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4976/egusphere-2025-4976-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-4976-RC2
- AC2: 'Reply on RC2', Dalena Leon, 08 Dec 2025
  
  Dear Istvan,
  Thanks for your positive feedback on our combined attribution methodology. Your comments have been constructive and helped with the improvement of the manuscript. We have addressed your points in the following document.
  Kind regards,
  Dalena, on behalf of all Co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-4976-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4976', Anonymous Referee #1, 30 Oct 2025

Please find my comments attached.

Citation: https://doi.org/10.5194/egusphere-2025-4976-RC1
- AC1: 'Reply on RC1', Dalena Leon, 08 Dec 2025
  
  Dear Referee,
  We appreciate the recognition of the contribution of combining storylines and flow-analogues for conditional attribution. Your comments have been valuable for strengthening the manuscript.
  Kind regards,
  Dalena, on behalf of all Co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-4976-AC1
RC2:
'Comment on egusphere-2025-4976', István Dunkl, 21 Nov 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4976/egusphere-2025-4976-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-4976-RC2
- AC2: 'Reply on RC2', Dalena Leon, 08 Dec 2025
  
  Dear Istvan,
  Thanks for your positive feedback on our combined attribution methodology. Your comments have been constructive and helped with the improvement of the manuscript. We have addressed your points in the following document.
  Kind regards,
  Dalena, on behalf of all Co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-4976-AC2

Peer review completion

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

AR by Dalena León-FonFay on behalf of the Authors (12 Dec 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (22 Jan 2026) by Camille Li

RR by Anonymous Referee #1 (26 Jan 2026)

RR by István Dunkl (03 Feb 2026)

ED: Publish subject to revisions (further review by editor and referees) (17 Feb 2026) by Camille Li

I have read the revised manuscript and the authors' responses to the reviewers. The authors have made substantial revisions and the reviewers
are for the most part satisfied. There remain two main issues (reviewer 1) which are closely related, and have to do with the interpretation of
the results.

There is no doubt that reviewer 1 sees the nudged storyline approach as a valuable one for studying extreme event attribution. The reviewer is, however, highlighting that different approaches giving slightly different messages could be meaningful, and that this is in fact a strength of combining approaches. The definition of a "class" of event could thus be seen to depend on how strongly an approach conditions on dynamics (Thompson et al. doi: 10.1002/wea.7779). In addition, for the nudged storyline approach, uncaptured dynamics may still be important (e.g., van Garderen et al., 2020).

A suggestion is that the authors keep the framing of their study as is (e.g., the question posed in L159), as it aligns with published studies such as Feser & Shepherd, but that they remain open to the points raised by reviewer 1 in their presentation of the results. The Thompson et al. report, which is very new, could be a useful additional reference. I don't feel that this will require lengthy text additions, but rather just adjustments to the current text, particularly in the introduction and conclusions/discussion sections, as well in certain statements in the results sections.

Finally, given that the study should appeal to a broad audience, the manuscript could benefit from a round of copyediting and proofreading to make it as clear and readable as possible. English language editing is no longer provided by EGU journals. Some examples for illustration:
- L28: "In contrast, non-heatwave events shaped by complex dynamical processes - in particular when associated with modification of the large-scale atmospheric circulation like windstorms..." - “like windstorms” relates to "non-heatwave events"? sentence needs to be restructured if so.
- L32-33: extra article "either a counterfactual or future warmer worlds"
- L33-35: "counterfactual" should be explained the first time the term is introduced (L33), not the second time (L35)
- Could section 4.3.1 be its own subsection (4.4)? I realize it pertains directly to 4.3, but it is also a wrap-up and contains its own figure, so I think it would be appropriate.

I would like to emphasize that all of us (both reviewers and myself) are very positive about this study, and feel it represents a valuable contribution to the literature. What I believe reviewer 1 is asking for is a more open and considered interpretation of the results that balances various viewpoints. I'd be happy to help - perhaps in consultation with reviewer 1 - if the authors would like clarifications on any of the points. I would offer reviewer 1 the chance to see the revised manuscript if they are able to provide feedback in a timely manner.

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AR by Dalena León-FonFay on behalf of the Authors (06 Mar 2026) Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (13 Mar 2026) by Camille Li

RR by Anonymous Referee #1 (19 Mar 2026)

For final publication, the manuscript should be

accepted as is

accepted subject to technical corrections

accepted subject to minor revisions

reconsidered after major revisions

rejected

Were a revised manuscript to be sent for another round of reviews:

I would be willing to review the revised manuscript.

I would not be willing to review the revised manuscript.

Suggestions for revision or reasons for rejection

The authors have partially addressed my previous comments. They have partially recognized that the storyline approach may not project the correct intensity change (in their words: "they are hypothetical and should not be regarded as future projections"), but not all framing of the results are adapted to this new way of considering their results so that the paper reads sometimes strangely from one paragraph to another (see below for some examples). I still disagree quite strongly with the framing of their storyline simulations as representing "a physically consistent plausible scenario in which our climate could have developed under an alternative thermodynamic background" (L139). As I argued in my previous review, this is not physically possible under our current understanding of the physics of the atmosphere because it basically ignores any dynamical trend in the climate system and reduces any trend to a thermodynamic change. This is the reason why the storyline approach does not give the correct intensity change. At this stage I have expressed my reservations regarding the method and even though I encouraged the authors to take seriously my arguments and reconsider some of their assertions with regards to them, I recommend accepting the paper after some minor revisions. Please find them below:
- L9 in the abstract: this framing of the probabilities assumes that the storyline approach gives the correct intensity change
- L139: "Each storyline represents a physically consistent, plausible scenario in which our observed climate could have developed under an alternative thermodynamic background" -> I still think this sentence is incorrect
- L231: the use of a GEV is still not justified, neither statistically (no test is employed to estimate the quality of the fit), nor mathematically (why should a GEV fit your data and not a simpler Gaussian, or any other 3 parameters distribution ?). I insist that I previously explained that you do not really need to fit any distribution here to give probabilities given how many analogues you have.
- L279: "Here, we state that the 2018 heatwave with a mean intensity of 2.2 °C would have been 6 days shorter and with a 0.5 °C mean intensity in the absence of human-induced global warming" -> this statement still assumes that the projection with the storyline approach gives the correct intensity change with climate change
- paragraph L355: the way the paragraph is framed, as explained in my previous reviews, assumes that the storyline approach gives the correct intensity change
- L402: the authors say that the two methods do not disagree, which, as explains above and in my previous reviews, is pretty strange given that the two methods address a similar question for a similar event and give different answers
- L507: "Because storylines are hypothetical experiments, they cannot be regarded as projections or claimed to happen exactly as projected in the future" -> I have to say I pretty much agree with this statement, but it seems contradictory to a lot of the other statements provided above in the paper (including, most importantly, in the abstract). In particular, it implies that the storylines do not give the correct intensity change and thus that they cannot be used to assess the change in probability of this event, including when conditioning on the analogues. I think the authors should clarify their position on how to interpret the storylines intensity change.

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RR by István Dunkl (23 Mar 2026)

EF by Anna Mirena Feist-Polner (18 Mar 2026) Author's response

ED: Publish subject to technical corrections (01 Apr 2026) by Camille Li

Thanks to the authors for submitting a revised manuscript. I appreciate the thorough consideration of the remaining comments in the response document. At this point, I believe there remain 2 open issues: a technical point on whether fitting the data to a GEV is necessary, and a conceptual point on how exactly to interpret results from the combined attribution method bringing together the nudged storyline and flow analogue approaches. There are nuanced arguments on both sides of the discussion. I don’t believe that either issue undermines the fundamental results presented in the manuscript. I would thus suggest publication subject to the following minor revisions/corrections, which pertain to 1) a request for clarification on some of the statistics performed, and 2) some small wording changes to make certain statements in the body of the manuscript consistent with revised text in the conclusions. I will classify this as technical corrections; if the authors have any objections to these corrections, they may contact me to discuss.

Interested readers may refer to the three rounds of public review for more a more in-depth discussion of these issues.

Line numbers refer to version 3 of the manuscript.
- L8-9 in the abstract: Replace “According to our study, …” with “Our results show that the 2018 heatwave, with an intensity of 2.2 °C and a return period of 1-in-277-years today, becomes a 6.6 °C event with a 1-in-26-year probability in a +4K world in the absence of other dynamical trends.”
- L122: “Each storyline represents a physically consistent, plausible scenario in which the event could have developed under an alternative thermodynamic background while holding the circulation fixed.”
- L210-212: Could the authors please add a sentence or two to comment on the quality of the GEV fit?
- L261-263: “Here, it indicates that the dynamical pathway leading to the 2018 heatwave with a mean intensity of 2.2 °C would have produced an event that was 6 days shorter and with a 0.5 °C mean intensity in the absence of human-induced global warming.”
- L378-379: I don’t think you need the sentence “The fact that the upper tail…” to make your point, and removing it would also eliminate what I believe is a point of contention with the reviewer. The information given in the following two sentences lays out very nicely what’s different about the approaches, and why this could lead to different answers, while still demonstrating the utility of combining the approaches.

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AR by Dalena León-FonFay on behalf of the Authors (07 Apr 2026) Author's response Manuscript

Journal article(s) based on this preprint

16 Apr 2026

A combined storyline-statistical approach for conditional extreme event attribution

Dalena León-FonFay, Alexander Lemburg, Andreas H. Fink, Joaquim G. Pinto, and Frauke Feser

Weather Clim. Dynam., 7, 597–613, https://doi.org/10.5194/wcd-7-597-2026,https://doi.org/10.5194/wcd-7-597-2026, 2026

Short summary

Dalena León-FonFay, Alexander Lemburg, Andreas H. Fink, Joaquim G. Pinto, and Frauke Feser

Supplement

https://doi.org/10.5194/egusphere-2025-4976-supplement

Dalena León-FonFay, Alexander Lemburg, Andreas H. Fink, Joaquim G. Pinto, and Frauke Feser

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Short summary

We combine physical (spectrally nudged storylines) and statistical (flow-analogue) methods to show how global warming affects the intensity and likelihood of historical extreme events. By conditioning on the circulation pattern, we minimize uncertainties linked to atmospheric dynamics. Using the 2018 Central European heatwave, we find that while the weather pattern remains equally likely, its intensity and frequency rise sharply with warming, making such events far more common in the future.


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