Jones et al. (2026) Collective risk modelling of multi-peril events: correlation of European windstorm gust and precipitation annual severity

Identification

• Journal: Natural hazards and earth system sciences
• Year: 2026
• Date: 2026-02-13
• Authors: Toby Jones, David B. Stephenson, Matthew D. K. Priestley
• DOI: 10.5194/nhess-26-775-2026

Research Groups

• Department of Mathematics & Statistics, University of Exeter, Exeter, United Kingdom

Short Summary

This study develops and tests three collective risk frameworks to model the correlation between annual aggregated wind gust and precipitation severities from European windstorms. It finds that interannual modulation of hazard variables is crucial to accurately capture the observed negative correlations at high severity thresholds.

Objective

• What assumptions are required for a collective risk model to be able to capture the correlation between aggregate losses at all spatial locations?
• Can such a collective risk model quantitatively account for how the correlation changes for more extreme events?
• What are the key drivers of the changes in correlation with threshold?

Study Configuration

• Spatial Scale: Europe and the North Atlantic, analyzed at a 0.25° spatial resolution grid point level. A specific region covering France (4.75° W–8.5° E, 42.25–51.75° N) was used for detailed analysis.
• Temporal Scale: 40 years (1980–2020) of 1-hourly reanalysis data, with annual aggregation over calendar years (1 January–31 December). Extended winter seasons (1 October–31 March) were also considered in supplementary analysis.

Methodology and Data

• Models used:
  • Three collective risk frameworks of increasing complexity:
    • Framework A: Assumes uncorrelated hazard variables (Frequency-Severity Independence, Hazard Independence, Serial Independence).
    • Framework B: Allows for correlated hazard variables within an event (Frequency-Severity Independence, Serial Independence).
    • Framework C: Allows for correlated hazard variables within an event and between-year correlation caused by interannual modulation of hazard variables (Frequency-Severity Independence).
  • Severity Indices (SI) defined as g(X) = X - uX for Xi > uX, and 0 otherwise, where uX is a threshold.
  • Aggregated Severity Indices (ASI) calculated as the sum of SIs over all events in a given period.
  • Cyclone identification and tracking using the TRACK algorithm at 850 hPa.
• Data sources:
  • ERA5 reanalysis data (Hersbach et al., 2020) at 0.25° spatial resolution and 1-hourly temporal resolution.
  • Hazard variables: Maximum 3-second wind gust speeds and total accumulated precipitation for each cyclone within a 5° radius of a grid point.

Main Results

• The correlation between annual wind and precipitation severity indices decreases with increasing thresholds, becoming negative over land regions at high thresholds (e.g., 20 m/s wind gust, 20 mm precipitation).
• Framework A (uncorrelated hazards) consistently produced non-negative correlations and failed to capture the observed negative correlations.
• Framework B (correlated hazards) showed some negative correlations but underestimated their magnitude compared to observations.
• Framework C (correlated hazards with interannual modulation) was the only framework capable of quantitatively reproducing the observed correlations across all thresholds and spatial patterns, including the extensive negative correlations over land.
• The correlation in Framework C is driven by three components: within-year dependency (positive at low thresholds, negative at high), event dispersion (positive, decreases with threshold), and interannual dependency (strongest decrease to negative values at high thresholds).
• At low thresholds, event dispersion is the main contributor to positive correlation. At high thresholds, interannual dependency becomes the dominant factor, driving the negative correlations.
• Storm transit duration is proposed as a plausible driver for the interannual modulation. Extreme precipitation events (>100 mm) are associated with longer storm durations (>40 hours) and more meridional tracks, while extreme wind events (>37 m/s) are linked to shorter durations (<20 hours) and more zonal tracks.
• Annual mean storm duration shows a negative correlation with annual mean wind intensity and a positive correlation with annual mean precipitation intensity, especially over European land, intensifying with increasing thresholds and explaining the negative correlation between wind and precipitation.

Contributions

• Introduced and rigorously tested three collective risk frameworks for modeling the correlation of aggregated severities from multi-peril events, providing a diagnostic tool for understanding underlying drivers.
• Demonstrated that incorporating interannual modulation of hazard variables (Framework C) is critical for accurately capturing the complex, threshold-dependent correlations, including negative correlations, between annual wind and precipitation severities.
• Identified storm transit duration as a key physical mechanism driving the interannual modulation and the observed differential impacts on wind and precipitation extremes.
• Provided insights relevant for improving risk management in the insurance industry by challenging the common assumption of independent annual losses from different perils.

Funding

• Engineering and Physical Sciences Research Council (grant no. EP/R513210/1)
• WTW Research Network

Citation

@article{Jones2026Collective,
  author = {Jones, Toby and Stephenson, David B. and Priestley, Matthew D. K.},
  title = {Collective risk modelling of multi-peril events: correlation of European windstorm gust and precipitation annual severity},
  journal = {Natural hazards and earth system sciences},
  year = {2026},
  doi = {10.5194/nhess-26-775-2026},
  url = {https://doi.org/10.5194/nhess-26-775-2026}
}