Causal drivers of alpine flood variability from 1300 to 2020 revealed by climate time series analysis

Peña-Rabadán, Juan Carlos; Schulte, Lothar; Miró-Cubells, Josep Ramon; Casellas-Masana, Enric; Carvalho, Filipe

doi:10.5194/egusphere-2026-303

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https://doi.org/10.5194/egusphere-2026-303

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02 Feb 2026

| 02 Feb 2026

Causal drivers of alpine flood variability from 1300 to 2020 revealed by climate time series analysis

Juan Carlos Peña-Rabadán, Lothar Schulte, Josep Ramon Miró-Cubells, Enric Casellas-Masana, and Filipe Carvalho

Abstract. Understanding flood variability in the European Alps is critical for risk management, yet causal mechanisms linking climate drivers to floods remain unclear. Previous studies have largely relied on correlations, limiting causal attribution. Here we apply a constraint-based causal inference framework using the PC-stable algorithm, combined with bootstrap stability analysis and Granger causality validation, to multi-centennial climate and flood proxy records from the Hasli-Aare catchment (1300–2020 CE). Our results reveal that total solar irradiance modulates summer atmospheric circulation, notably the summer North Atlantic Oscillation, which causally influences alpine flood frequency. These relationships are strongest during the preindustrial period and weaken under modern anthropogenic forcing, indicating a shift in dominant flood drivers. Our study demonstrates the utility of causal inference methods in paleoclimate research and offers a framework for investigating changes in the drivers of hydrological extremes, important for climate attribution and risk assessment in mountain environments.

Received: 19 Jan 2026 – Discussion started: 02 Feb 2026

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Juan Carlos Peña-Rabadán, Lothar Schulte, Josep Ramon Miró-Cubells, Enric Casellas-Masana, and Filipe Carvalho

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-303', Anonymous Referee #1, 02 Mar 2026

The authors investigate the potential causal linkage between climate drivers and flood frequency in the Hasli-Aare catchment from 1300 to 2020 CE. Based on different sources of climate and flood proxy records, the PC-stable algorithm combined with bootstrap stability analysis and Granger causality validation is used to detect the climate-flood relationships. The results show that total solar irradiance modulates the summer atmospheric circulation, which may causally influence the flood frequency. Under modern anthropogenic forcing, these relationships are weaker than those during the preindustrial period.
In general, the structure of the manuscript is clear and the proposed causal inference framework sounds technically promising. However, there are some concerns, as well as some more specific comments that should be addressed by the authors (please see the relevant section below), before it can be considered for publication.
Major concerns:
For the Introduction section, it clearly outlines the analytical framework adopted in the manuscript and provides sufficient background to understand the methodological steps that follow. However, in its current form, it reads more as a retrospective summary of the authors’ previous work than as a critical positioning of the present study within the broader literature. A substantial proportion of the cited references derive from earlier publications by the same research group in the same catchment, which limits the integration of this study into the wider scientific context. Regarding the stated research gap of moving beyond correlations to identify causal mechanisms linking climate drivers and floods, this objective is relevant but not sufficiently substantiated. The Introduction does not clearly explain why correlation-based approaches are inadequate in this specific context, nor does it discuss how other studies have addressed similar questions and where key challenges persist. I encourage the authors to incorporate a broader range of external literature to demonstrate what has been achieved in this field, where traditional correlative methods face limitations, and why formal causal identification provides added value in disentangling the complexities of Alpine flood attribution.
All datasets used in this study are currently described in the Supplementary Material, presumably to maintain a streamlined structure in the Methods section. While this intention is understandable, given that the analysis relies on multiple paleo-reconstructed datasets and model simulations for several key variables, I suggest moving Sections S1.1 and S1.2 into Section 2 of the main text. This would improve transparency and allow readers to more easily connect the variables introduced in the Methods with the results presented later, particularly in Section 4. As it stands, it is difficult to directly link specific outcomes to the corresponding time series without repeatedly consulting the supplementary material.
In addition, Flood_F1, which represents flood frequency and could be one of the core variables in the analysis, is only briefly described with reference to previous publications. Given its central role, more detailed information should be provided in the main text, including its temporal resolution, exact coverage period, construction method, and associated uncertainties. Similar issues apply to several other time series used in the study. This is particularly important because the title specifies 1300–2020 as the study period, whereas the end years listed in Table S2 for several series appear to fall between 1800 and 2005 and the others remain unclear. The manuscript does not clearly explain how these discrepancies in temporal coverage are handled, nor how differences in time span and resolution across datasets are reconciled within the causal analysis.
Finally, the inferred causal relationships are derived from multiple reconstructed time series based on different paleoclimate proxies and model simulations, each of which carries its own methodological and reconstruction uncertainties. These uncertainties arise from proxy calibration, dating errors, spatial representativeness, and model assumptions, and they may propagate into the causal discovery framework. At present, these datasets appear to be treated implicitly as ground truth, with limited discussion of how their uncertainties might influence the robustness of the inferred causal links. At least, the manuscript should discuss this issue more explicitly. I am also curious whether the identified causal linkages persist when referring to the recent observational period, where instrumental data are available. Testing the proposed relationships using modern observations could provide an important consistency check and help evaluate whether the inferred mechanisms are robust.
Specific comments:
Line 65, Fig. 1: It is a bit hard to find the relevant information in this figure and I suggest separating the two panels into two figures.
Line 77, Fig. 2: It is also hard to see the context in this figure and I suggest restructuring the layout to place the input data in the left panel and the part of the causal framework in the right panel. Furthermore, there is a lack of consistency between the figure and the Supplementary Material, as several variables in TIER 3 and TIER 5 are missing corresponding descriptions in Tables S1 and S2. Lastly, it should be “Spring Precipitation” in TIER4.
Line 90 and the other lines: The references to tables and figures in the main text should be checked because their numbering does not match that in the supplementary materials.
Line 168: The results provided in Table 1 are the same as in Supplementary Material 2.
Lines 171 and 186: The choice of 0.58 as highly stable edges for the unconstrained DAG and 0.41 for the constrained DAG requires clearer statistical justification. With 100 bootstrap replicates, an edge strength of 0.58 implies absence in 42% of resamples, which may not constitute strong stability given the inherent dating uncertainties of ±20 years. The relaxation to 0.41 further raises concerns regarding the empirical support for the constrained model.
Fig. 3, Fig. S6 and Fig. S9: I would appreciate clarification regarding the apparent inconsistency between the causal network results and the Granger causality analysis. Specifically, the DAGs show either no link or an inconsistent link between the flood proxy (Flood_F1) and Alpine precipitation (Pamj_Alps), whereas the Granger causality test indicates a statistically significant relationship (p < 0.001).
Line 205: For section 4.5, what is the bootstrap stability threshold for the DAG? While differences in DAG topology between pre-industrial and industrial periods demonstrate structural evolution in the inferred network, further caution is needed before interpreting these changes to anthropogenic forcing since no explicit anthropogenic variables were included in the network.
Lines 277-282 and Lines 290-294: These parts appear to contain repetitive content.
Lines 359 and 427: There are some symbol errors.

Citation: https://doi.org/10.5194/egusphere-2026-303-RC1
- AC1:
  'Reply on RC1', Juan Carlos Peña, 12 Jun 2026
  Manuscript: EGUSPHERE-2026-303
  
  Title: Causal drivers of alpine flood variability from 1300 to 2005 revealed by climate time series analysis
  
  Response to: Referee #1 (RC1)
  General thanks:
  
  We thank the reviewer for the thorough and constructive review. We have addressed all comments and provide a detailed point‑by‑point response in the attached PDF. Below is a summary of the main changes.
  Main revisions in response to RC1:
  
  Introduction rewritten – Reduced self‑citations, added external literature on causal inference (Hannart et al., Runge et al., Kretschmer et al., Su et al.) and Alpine flood studies (Blöschl et al., Wilhelm et al., Merz et al.). Explicitly justified limitations of correlation (confounding, non‑stationarity, directionality).
  
  Flood_F1 description expanded – Added detailed description of core AA‑05 (Table 1) including temporal resolution, construction method, uncertainties, and handling of 1300‑2020 vs 1300‑2005 period (Section 2.2 and Section 3.1).
  
  Bootstrap threshold justification – Clarified that thresholds 0.58 and 0.41 derive from elbow analysis; revised terminology (“moderately stable”, “weakly stable but retained”). Added sensitivity analysis with stricter thresholds (0.7, 0.8) in Supplementary Material S2.3 (Table S4).
  
  Proxy uncertainties and instrumental validation – Added Section 4.2 on handling of uncertainties (calibration, dating, spatial representativeness, model assumptions). New instrumental consistency check (Section 6.1) using 1900‑2020 data confirms core causal pathway. Partial correlations (Supplementary S2.4, Table S5) support TSI→Flood_F1 link.
  
  Figure separation and numbering – Separated original Fig. 1 into Fig. 1 (location and core) and Fig. 2 (multi‑proxy reconstruction). All references checked.
  
  Figure 2 (now Fig. 5) layout – Redesigned into two‑panel layout (input data left, causal framework right). All acronyms defined in caption and Table 2.
  
  Repetitive content removed – Merged two overlapping paragraphs in Discussion into a single concise statement (lines 697‑703 in revised manuscript).
  
  Conclusion:
  
  We believe the manuscript has been substantially improved.
  
  Citation: https://doi.org/10.5194/egusphere-2026-303-AC1
RC2:
'Comment on egusphere-2026-303', Anonymous Referee #2, 21 May 2026

The manuscript addresses a highly relevant topic and contains potentially significant and interesting findings, particularly regarding the possible role of total solar irradiance in shaping flood variability. The combination of paleoflood reconstructions with causal inference methods is potentially promising and could provide useful insights into long-term climate–flood interactions. However, in its current form, the manuscript is difficult to follow methodologically and conceptually, and several aspects of the causal interpretation require more careful justification before the work can be considered robust.
The presentation and organization of the manuscript would benefit from substantial revision. The Introduction relies heavily on cross-referencing to previous publications by the same research group and to supplementary figures and tables very early in the text, which hinders readability and makes the rationale of the study difficult to follow. The motivation for specifically examining these drivers, and particularly for moving from correlation-based analyses toward causal inference, is not sufficiently explained. Several figures are overloaded with information and contain extensive embedded text (e.g., the inclusion of research-group information in Figure 2). Also, the manuscript relies excessively on supplementary material for understanding the main analysis, while the extensive use of acronyms further reduces accessibility (e.g., AL and AH in Figure 3 are not explained in the main manuscript but only in the supplement). I encourage the authors to substantially revise the structure and presentation of the paper to improve transparency and readability.
The methodological assumptions underlying the causal framework also require further scrutiny and discussion. In particular, the imposed hierarchy and expert-defined blacklist constraints used to guide the causal graph construction raise concerns regarding circularity. While some excluded causal directions may indeed be physically implausible (e.g., floods affecting solar forcing), the extent to which the inferred structure depends on these imposed assumptions remains unclear. Given the complexity and multiscale coupling of the climate system, the assumptions embedded in the blacklist design require more explicit justification. The imposed blacklist constraints and their influence on the resulting network topology and causal interpretation should be reported and discussed more explicitly.
Related to this point, the manuscript does not sufficiently discuss how autocorrelation, long-term persistence, and shared low-frequency variability among climate series may affect conditional independence testing and inflate apparent causal structure. This is particularly important in paleoclimate applications where proxy smoothing and persistence may induce shared covariance patterns even in the absence of direct mechanistic causality.
The interpretation of structural differences between the pre-industrial and industrial periods also appears somewhat overstated. The manuscript repeatedly interprets changes in DAG topology as evidence of anthropogenic restructuring of the climate system. However, no explicit anthropogenic variables are included in the network, and the term “anthropogenic effects” remains rather vague throughout the text. It is unclear whether the authors refer to recent warming, land-use changes, river engineering, or broader climatic shifts. Alternative explanations such as differences in data quality, proxy uncertainty, sample size, or methodological instability are not sufficiently examined. Therefore, more caution is required when interpreting edge appearance/disappearance as evidence of anthropogenic reorganization of climate–flood relationships.
Finally, while the Discussion section is generally informative and demonstrates appropriate hydrological and climatological background, the Conclusions section appears repetitive and occasionally somewhat stronger in tone than warranted by the methodological limitations discussed earlier in the manuscript. I believe the Conclusions could be made more precise and better aligned in tone with the more balanced Discussion section.

Citation: https://doi.org/10.5194/egusphere-2026-303-RC2
- AC2:
  'Reply on RC2', Juan Carlos Peña, 12 Jun 2026
  Manuscript: EGUSPHERE-2026-303
  
  Title: Causal drivers of alpine flood variability from 1300 to 2005 revealed by climate time series analysis
  
  Response to: Referee #2 (RC2)
  General thanks:
  
  We thank the reviewer for the detailed and constructive critique. We have substantially revised the manuscript to improve transparency, readability, and methodological rigor. A point‑by‑point response is attached as a PDF. Below is a summary of the main changes.
  Main revisions in response to RC2:
  
  Presentation and readability
  
  Rewrote Introduction, reduced self‑citations, added extensive external literature (Runge et al., Kretschmer et al., Su et al., Silini et al.).
  
  Removed early references to supplementary material; moved core descriptive content (AA‑05 record, glossary, SLP grids) into main text (Sections 2.2, 3; Tables 1‑3).
  
  Defined all acronyms (AL, AH, OM, etc.) in Table 2 and figure captions.
  
  Blacklist constraints and circularity
  
  Explicitly justified each blacklist category (Section 4.5) based on physical principles.
  
  Quantified impact: blacklist removed 23 % of spurious edges without affecting core pathway (Section 5.4).
  
  Added sensitivity test with reduced blacklist (Supplementary S2.6); core pathway unchanged.
  
  Autocorrelation, persistence, and low‑frequency variability
  
  Added methodological discussion (Section 4.7) and partial correlation analysis (Section 5.5, Supplementary S2.4, Table S5).
  
  Core pathway remains robust; weak edges disappear as expected.
  
  Pre‑whitening tests (AR(1)) showed insufficient removal of autocorrelation; results not reported but robustness confirmed via alternative tests.
  
  Cautious interpretation of structural shifts (anthropogenic forcing)
  
  Replaced deterministic language (“anthropogenic forcing disrupted…”) with cautious phrasing (“coincident with industrial era”, “consistent with emerging anthropogenic influence”, “cannot be uniquely attributed”).
  
  Added explicit caveat that network lacks explicit anthropogenic variables (CO₂, land‑use).
  
  New paragraph in Discussion (Section 6.5) lists alternative explanations (volcanic forcing, solar activity, proxy non‑stationarity).
  
  Conclusions
  
  Completely rewritten (Section 7): shorter, non‑repetitive, balanced tone.
  
  Explicitly acknowledges limitations (21‑year resolution, dating uncertainties, absence of anthropogenic predictors).
  
  Conclusion:
  
  We believe the manuscript has been significantly improved
  
  Citation: https://doi.org/10.5194/egusphere-2026-303-AC2
AC3: 'Comment on egusphere-2026-303', Juan Carlos Peña, 12 Jun 2026

To the Editor

Hydrology and Earth System Sciences (HESS)

European Geosciences Union (EGU)
Dear Editor,
Revised manuscript EGUSPHERE-2026-303

"Causal drivers of alpine flood variability from 1300 to 2005

revealed by climate time series analysis"
Thank you very much for the positive evaluation of our manuscript. We are very

grateful to the two anonymous referees for their extensive, thorough and

constructive reviews. Their comments and suggestions have been invaluable in

improving the clarity, methodological transparency, and interpretational

caution of our study.
In addition, we have taken the opportunity to add a new co-author, Laura

Barbería Oivanen, who has participated very actively in the revision process,

contributing significantly to the re-analysis of data, the improvement of

figures, and the refinement of the causal interpretation. All authors have

approved this addition and the current version of the manuscript.
We have carefully addressed all the points raised by both reviewers. The main

changes made in response to their comments include:
- Comprehensive revision of the Introduction – reduced self-citations, added

extensive external literature on causal inference and Alpine flood

attribution, and explicitly justified the limitations of correlation-based

approaches.
- Improved transparency of data handling – moved key descriptive content

(AA-05 sedimentary record, glossary of variables, SLP grids) from the

Supplementary Material into the main text, and clarified the temporal

harmonisation of datasets (1300-2005 common period).
- Enhanced methodological justification – provided explicit justification for

the bootstrap stability thresholds (0.58 and 0.41) using elbow analysis,

added sensitivity tests with stricter thresholds (0.7, 0.8), and included a

partial correlation analysis to address autocorrelation concerns.
- Quantified the influence of domain constraints (blacklist) – reported that

the blacklist removed 23% of spurious edges without affecting the core

causal pathway, and added a sensitivity test using a reduced blacklist

(Supplementary Material S2.6).
- Added an instrumental consistency check – using purely observational data

(1900-2020) to confirm that the core causal pathway

(TSI -> EOF1 -> Pamj_Alps -> Flood_F1) is robust and not an artefact of

proxy uncertainties (Section 6.1).
- Revised the language on anthropogenic attribution – replaced deterministic

statements with cautious phrasing (e.g., "consistent with an emerging

anthropogenic influence", "cannot be uniquely attributed"), and explicitly

noted that our network does not include explicit anthropogenic variables.
- Shortened and re-balanced the Conclusions – removed repetitions, moderated

the tone, and added a clear statement of limitations.
In addition, we have restructured several sections (Introduction, Study area,

Climate Variables, Methods, Results, Discussion) and redesigned figures

to improve readability and accessibility. All changes

are highlighted in the revised manuscript.
A point-by-point response to the reviewers' comments is attached as a separate

PDF.
Thank you very much for your continued handling of our manuscript. We look

forward to hearing from you soon.
Yours sincerely,
Juan Carlos Peña-Rabadán

Corresponding author

Meteorological Service of Catalonia / University of Barcelona

juancarlos.pena@gencat.cat

Citation: https://doi.org/10.5194/egusphere-2026-303-AC3

Juan Carlos Peña-Rabadán, Lothar Schulte, Josep Ramon Miró-Cubells, Enric Casellas-Masana, and Filipe Carvalho

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https://doi.org/10.5194/egusphere-2026-303-supplement

Juan Carlos Peña-Rabadán, Lothar Schulte, Josep Ramon Miró-Cubells, Enric Casellas-Masana, and Filipe Carvalho

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Short summary

1. Total Solar Irradiance is a key external driver modulating summer atmospheric modes, which in turn influence alpine flood frequency. 2. These causal pathways are strongest in preindustrial era, suggesting enhanced solar-atmospheric coupling in the absence of strong anthropogenic forcing. 3. The causal structure is statistically stable and physically consistent, validated across methods and time periods.


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