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arxiv: 2505.00835 · v2 · submitted 2025-05-01 · 📊 stat.AP · cs.LG· stat.ML

Multi-site modelling and reconstruction of past extreme skew surges along the French Atlantic coast

Nathan Huet , Philippe Naveau , Anne Sabourin This is my paper

Pith reviewed 2026-05-22 16:44 UTC · model grok-4.3

classification 📊 stat.AP cs.LGstat.ML
keywords extreme value theoryskew surgesmultivariate GPDthreshold selectioncoastal extremeshistorical reconstructionextremal dependenceFrench Atlantic coast
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The pith

A novel threshold selection method together with multivariate generalized Pareto modeling and angle-based regression reconstructs historical extreme skew surges at limited-data stations from long-record neighbors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a peak-over-threshold approach for multivariate extremes along the French Atlantic coast, where an event counts as extreme if at least one station records a large value. A new procedure is introduced to choose the threshold above which observations are treated as extremes. The multivariate generalized Pareto distribution then supplies a generative model that produces predicted extremes at one station from observed extremes at others, while a separate regression framework makes point predictions using only the direction, or angle, of the input variables. These tools are combined to fill in missing historical extreme skew surge values at stations that have short records by borrowing strength from stations such as Brest and Saint-Nazaire that hold more than 150 years of data.

Core claim

The central claim is that a new threshold choice for multivariate extremes, the generative properties of the multivariate generalized Pareto distribution, and an angle-only extreme regression together permit accurate reconstruction of past extreme skew surge time series at data-sparse coastal stations by transferring information from nearby long-record stations.

What carries the argument

The multivariate generalized Pareto distribution for joint extremes, paired with an angle-based extreme regression that uses only the normalized direction of the inputs for point predictions.

If this is right

  • Historical extreme skew surge series become available at stations that previously had too few observations for reliable analysis.
  • Coastal risk assessments gain from longer and more complete records of joint extremes across the station network.
  • Information from over 150 years of data at Brest and Saint-Nazaire can be propagated to other sites along the French Atlantic coast.
  • Extremal dependence between stations is explicitly modeled rather than treated as independent.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reconstruction pipeline could be tested on other coastal networks where some gauges have short histories but neighbors have long ones.
  • Adding covariates such as sea-level rise or storm-track changes might extend the method to future-projection settings.
  • Validation against any newly recovered archival surge records at the target stations would provide an external check on the reconstructions.

Load-bearing premise

The dependence pattern among extreme skew surges at different stations stays stable enough over time to be captured by the multivariate generalized Pareto distribution and the angle representation.

What would settle it

Direct comparison of the reconstructed extreme values at a short-record station against any independent historical observations or against the physical patterns expected from the nearest long-record stations would show large systematic mismatches.

Figures

Figures reproduced from arXiv: 2505.00835 by Anne Sabourin, Nathan Huet, Philippe Naveau.

Figure 1
Figure 1. Figure 1: Five French tide gauge locations along the French Atlantic coast. Brest and Saint-Nazaire (red dots) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pairwise skew surge exceedances for all pairs of stations from 01/12/2000 to 31/12/2023. Dark orange [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Histograms of skew surge exceedances at the three stations Brest (left), Saint-Nazaire (middle) and [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: After thresholding, the final training sets consist of 3,310 skew surge exceedances, while final test sets [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: QQ-plots comparing observed skew surge exceedances of the Port Tudy test set (x-axis), ranging from [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Predicted skew surge exceedances at Port Tudy station for the years 1989 (left), 1978 (middle), 1977 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Histograms of skew surge exceedances above the threshold specified in Table 1 at the three stations Brest [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: QQ-plots comparing predicted skew surge exceedances of the Port Tudy test set, ranging from 10/08/1966 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Extreme skew surge time series at Brest (left) and Saint-Nazaire (right). The dotted vertical black line [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Extreme skew surge time series at Port Tudy. The dotted vertical black line represents the deployment [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Predicted skew surges (y-axis), by the ROXANE procedure with OLS algorithm (top row) and the MGP [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Scatter plots showing sea levels (left) and skew surges (right) at each station plotted against one another [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Rolling means (brown) and rolling standard deviations (light orange) of the detrended skew surge time [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Goodness-of-fit diagnostics for the prediction of extreme skew surges using ROX OLS: PIT plot (left), [PITH_FULL_IMAGE:figures/full_fig_p029_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Goodness-of-fit diagnostics for the prediction of very extreme skew surges using ROX OLS: PIT plot [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Goodness-of-fit diagnostics for the prediction of extreme skew surges using the MGPRED procedure: [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Goodness-of-fit diagnostics for the prediction of very extreme skew surges using the MGPRED procedure: [PITH_FULL_IMAGE:figures/full_fig_p030_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Histograms of the EGP parameter estimators computed from [PITH_FULL_IMAGE:figures/full_fig_p031_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Histograms of the 100-year return level (left and middle), computed using the EGP parameter estimates [PITH_FULL_IMAGE:figures/full_fig_p031_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Rolling means (dark blue) and rolling standard deviations (light blue) of the detrended skew surge time [PITH_FULL_IMAGE:figures/full_fig_p032_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Histograms of sea level exceedances at the three stations Brest (left), Saint-Nazaire (middle) and Port [PITH_FULL_IMAGE:figures/full_fig_p033_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Histograms of sea level exceedances above the threshold specified in Table 7 at the three stations Brest [PITH_FULL_IMAGE:figures/full_fig_p033_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: QQ-plots comparing observed sea level exceedances of the Port Tudy test set (x-axis), ranging from [PITH_FULL_IMAGE:figures/full_fig_p034_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: QQ-plots comparing predicted sea level exceedances of the Port Tudy test set, ranging from 10/08/1966 [PITH_FULL_IMAGE:figures/full_fig_p034_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Predicted sea levels at Port Tudy station for the years 1996 (left), 1987 (middle), 1985 (right). These [PITH_FULL_IMAGE:figures/full_fig_p035_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Goodness-of-fit diagnostics for the prediction of extreme sea levels using the ROXANE routine with [PITH_FULL_IMAGE:figures/full_fig_p035_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Goodness-of-fit diagnostics for the prediction of very extreme sea levels using the ROXANE routine with [PITH_FULL_IMAGE:figures/full_fig_p035_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Goodness-of-fit diagnostics for the prediction of extreme sea levels using the MGPRED procedure: PIT [PITH_FULL_IMAGE:figures/full_fig_p036_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Goodness-of-fit diagnostics for the prediction of very extreme sea levels using the MGPRED procedure: [PITH_FULL_IMAGE:figures/full_fig_p036_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Histograms of the EGP parameter estimators computed from [PITH_FULL_IMAGE:figures/full_fig_p037_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Histograms of the 100-year return level (left and middle), computed using the EGP parameter estimates [PITH_FULL_IMAGE:figures/full_fig_p037_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Histograms of sea level (right) and skew surge (right) exceedances at the three stations Brest (top row), [PITH_FULL_IMAGE:figures/full_fig_p039_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: QQ-plots comparing observed sea level (left) and skew surge (right) exceedances of the Concarneau [PITH_FULL_IMAGE:figures/full_fig_p040_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Histograms of sea level (right) and skew surge (right) exceedances at the three stations Brest (top row), [PITH_FULL_IMAGE:figures/full_fig_p042_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: QQ-plots comparing observed sea level (left) and skew surge (right) exceedances of the Le Crouesty [PITH_FULL_IMAGE:figures/full_fig_p043_34.png] view at source ↗
read the original abstract

Appropriate modelling of extreme skew surges is crucial, particularly for coastal risk management. Our study focuses on modelling extreme skew surges along the French Atlantic coast, with a particular emphasis on investigating the extremal dependence structure between stations. We employ the peak-over-threshold framework, where a multivariate extreme event is defined whenever at least one location records a large value, though not necessarily all stations simultaneously. A novel method for determining an appropriate level (threshold) above which observations can be classified as extreme is proposed. Two complementary approaches are explored. First, the multivariate generalized Pareto distribution is employed to model extremes, leveraging its properties to derive a generative model that predicts extreme skew surges at one station based on observed extremes at nearby stations. Second, a novel extreme regression framework is assessed for point predictions. This specific regression framework enables accurate point predictions using only the 'angle' of input variables, i.e., input variables divided by their norms. The ultimate objective is to reconstruct historical skew surge time series at stations with limited data. This is achieved by integrating extreme skew surge data from stations with longer records, such as Brest and Saint-Nazaire, which provide over 150 years of observations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a multi-site framework for extreme skew surges on the French Atlantic coast. It introduces a novel threshold selection method in the peak-over-threshold approach, models joint extremes via the multivariate generalized Pareto distribution (GPD) to enable generative predictions at one station from observed extremes at others, and develops an angle-based extreme regression that performs point predictions using only normalized input directions. The central objective is to reconstruct historical extreme skew surge series at short-record stations by borrowing strength from long-record stations such as Brest and Saint-Nazaire (>150 years).

Significance. If the dependence structure proves stable and the models are properly validated, the generative multivariate GPD and angle-based regression could provide a practical way to extend extreme-event records for coastal risk assessment, leveraging the network of stations with heterogeneous record lengths.

major comments (3)
  1. [Results / validation sections] No quantitative validation (error metrics, cross-validation scores, or out-of-sample reconstruction accuracy) is reported for either the generative predictions from the multivariate GPD or the angle-based point reconstructions, so the claim of 'accurate reconstruction' remains unverified.
  2. [Dependence modeling and results] No formal test of temporal stability of the extremal dependence structure is presented (e.g., split-sample fits before/after 1950, trend tests on dependence parameters, or stationarity checks over the 150-year window), which is load-bearing for the historical reconstruction claim.
  3. [Extreme regression framework] The angle-based regression framework asserts that normalized directions alone suffice for accurate tail predictions, yet no direct comparison is given showing that this representation retains predictive power relative to the full vector input for extreme events.
minor comments (2)
  1. [Abstract] The abstract describes objectives and methods but supplies no empirical results or performance metrics; adding a brief statement of key findings would improve clarity.
  2. [Threshold selection method] Clarify the precise algorithmic steps and any tuning parameters of the proposed novel threshold method, and contrast it explicitly with standard diagnostics such as mean residual life plots.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We address each of the major concerns point by point below, proposing specific revisions to enhance the validation and robustness of our multi-site extreme modeling framework.

read point-by-point responses

  1. Referee: [Results / validation sections] No quantitative validation (error metrics, cross-validation scores, or out-of-sample reconstruction accuracy) is reported for either the generative predictions from the multivariate GPD or the angle-based point reconstructions, so the claim of 'accurate reconstruction' remains unverified.

    Authors: We agree that quantitative validation is essential to substantiate the reconstruction claims. In the revised manuscript, we will add a dedicated validation subsection including error metrics such as root mean squared error and continuous ranked probability scores for the generative multivariate GPD predictions. Additionally, we will report cross-validation results and out-of-sample accuracy for the angle-based reconstructions at stations with shorter records, using data from long-record stations like Brest. revision: yes

  2. Referee: [Dependence modeling and results] No formal test of temporal stability of the extremal dependence structure is presented (e.g., split-sample fits before/after 1950, trend tests on dependence parameters, or stationarity checks over the 150-year window), which is load-bearing for the historical reconstruction claim.

    Authors: The referee correctly identifies a key assumption in our historical reconstruction approach. Although the physical drivers of skew surges along the Atlantic coast suggest relative stability, we will incorporate formal tests of temporal stability. This will include split-sample fits comparing dependence parameters before and after 1950, as well as trend analyses on the extremal dependence measures to confirm the validity of extending records over the 150-year period. revision: yes

  3. Referee: [Extreme regression framework] The angle-based regression framework asserts that normalized directions alone suffice for accurate tail predictions, yet no direct comparison is given showing that this representation retains predictive power relative to the full vector input for extreme events.

    Authors: To strengthen the justification for the angle-based approach, we will include a comparative analysis in the revised paper. Specifically, we will contrast the predictive performance of the normalized direction inputs against the full vector inputs for extreme events, using metrics focused on tail behavior such as the accuracy of predicted exceedance probabilities and conditional expectations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines a novel threshold selection procedure and then applies standard multivariate GPD properties to construct a generative model that predicts values at one station conditional on extremes observed at others. The angle-based regression is separately defined as a model that takes only normalized direction vectors as input and is fitted to produce point predictions. Neither step reduces by construction to a quantity that was already defined in terms of the target output; the generative predictions and reconstructions are obtained from fitted parameters whose estimation is independent of the final reconstructed series. No load-bearing uniqueness theorem or ansatz is imported solely via self-citation, and the central reconstruction claim rests on the empirical stability of the fitted dependence structure rather than on a definitional identity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Only abstract available so details are limited; relies on standard extreme value theory assumptions plus new methodological choices for threshold and regression.

free parameters (1)
  • threshold level
    A novel method is proposed for determining the appropriate level above which observations are classified as extreme.
axioms (2)
  • domain assumption The multivariate generalized Pareto distribution adequately captures the joint tail behavior of skew surges across stations.
    Employed within the peak-over-threshold framework to model extremes and derive the generative model.
  • ad hoc to paper The angle (direction) of input variables contains sufficient information for accurate extreme point predictions.
    Central to the novel extreme regression framework described.

pith-pipeline@v0.9.0 · 5743 in / 1404 out tokens · 54754 ms · 2026-05-22T16:44:34.815457+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · 1 internal anchor

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    For conciseness, we assumeI“ t1,...,nuin the main text. Finally, the origin is shifted: we subtract, from each component of the observations, the minimum value recorded overI, i.e., the observations considered in the main paper are pXB,i,XN,i,Yiq:“ pX ori B,i ´mB,Xori N,i ´mN,Y ori i ´mY q, foriPIand wherem B “min iPIXori B,i,m N “min iPIXori N,i andm Y “...

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    Table 3: p-values of the ADF test (alternative hypothesis: stationarity) and the KPSS test (alternative hypothesis: non-stationarity) for the time series at the three stations

    shows the rolling means and standard deviations at each station for the detrended data, visually confirming that the stationarity assumption is reasonable. Table 3: p-values of the ADF test (alternative hypothesis: stationarity) and the KPSS test (alternative hypothesis: non-stationarity) for the time series at the three stations. Bold values indicate str...

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    For the diagnostics on the full test set, the overestimation of small values is clearly visible, although the boxplot means remain close to zero

    These diagnostics are shown for the MGPRED procedure and the ROXANE routine with the OLS algorithm; results for the RF algorithm are omitted, as they are very similar to OLS. For the diagnostics on the full test set, the overestimation of small values is clearly visible, although the boxplot means remain close to zero. For the subset of the most extreme o...

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    Refer to Sections 5, B and E.1 for details about the figures

    After thresholding, the final training set consists of 2,465 sea level exceedances, while final test set consists of 2,315 sea level exceedances. Refer to Sections 5, B and E.1 for details about the figures. E.2.1 Stationarity tests Table 5: p-values of the ADF test (alternative hypothesis: stationarity) and the KPSS test (alternative hypothesis: non-stat...

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    The darkblue curves represent the fitted EGP densities above the thresholds, with parameters specified in Table

    Figure 21: Histograms of sea level exceedances above the threshold specified in Table 7 at the three stations Brest (left), Saint-Nazaire (middle) and Port Tudy (right), from 01/12/2000 to 31/12/2023. The darkblue curves represent the fitted EGP densities above the thresholds, with parameters specified in Table

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    Table 7: Point estimates of the parameters of the fitted EGP distribution for sea level exceedances at the three stations

    The green curves represent the fitted GP densities. Table 7: Point estimates of the parameters of the fitted EGP distribution for sea level exceedances at the three stations. The chosen thresholds, determined using via Algorithm 1, are shown in thetrows. The data used for inference are from the training set ranging from 01/12/2000 to 31/12/2023. Parameter...

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    39 Figure 32: QQ-plots comparing observed sea level (left) and skew surge (right) exceedances of the Concarneau test set (x-axis), ranging from 28/06/1999 to 31/12/2010, to predicted data (y-axis) from the algorithms of Sections 4.2 and 4.3. The plots show results from the ROXANE procedure with RF regression (top row), ROXANE procedure with OLS regression...

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    42 Figure 34: QQ-plots comparing observed sea level (left) and skew surge (right) exceedances of the Le Crouesty test set (x-axis), ranging from 14/03/1996 to 31/12/2014, to predicted data (y-axis) from the algorithms of Sections 4.2 and 4.3. The plots show results from the ROXANE procedure with RF regression (top row), ROXANE procedure with OLS regressio...

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