the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Apr 2026
Improved Estimation of Extreme Sea Levels via Non-asymptotic Statistical Methods for Coastal Hazard Assessment
Abstract. Understanding the likelihood of extreme sea level events intensified by climate change is vital for effective coastal management. This study focuses on the Mediterranean and part of the European Atlantic coastline. Because sea level records are often short, non-asymptotic extreme value modeling is more accurate, as it does not depend on large-sample limiting assumptions. However, selecting independent events (IEs) is critical and depends on the chosen threshold sea level (TSL) and time window width (TWW) used. Existing literature often lacks a definitive methodology for IE selection. This study aimed to fill this gap by proposing two methodologies for selecting IEs (overlapping and sorting approaches) and a methodology to find the optimal combination of TWW and TSL. The identified IEs were employed to model extreme sea level events utilizing the Peak Over Threshold-Generalized Pareto Distribution (POT-GPD) and the metastatistical extreme value distribution (MEVD) approaches. A cross-validation approach, along with statistical metrics, was used to rigorously assess performance. Findings indicate that MEVD outperforms POT-GPD and is effective in estimating extreme events with longer return periods (RPs). Overall, MEVD with the overlapping method proved more effective at predicting long RP events, although MEVD with the sorting approach had comparatively lower uncertainty.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1243', Anonymous Referee #1, 04 Jun 2026
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RC2: 'Comment on egusphere-2026-1243', Anonymous Referee #2, 22 Jun 2026
The paper “Improved Estimation of Extreme Sea Levels via Non-asymptotic Statistical Methods for Coastal Hazard Assessment” by Sithara et al. presents a comparative analysis of four different approaches aimed at extrapolating extreme sea levels from gauges located in the Mediterranean Sea and the Atlantic Ocean. The paper is clear and well written, and the figures support the narrative effectively. The topic is well suited to NHESS; therefore, I am positive about its publication. There are, however, some aspects that I recommend addressing before the paper is published.
First, and most importantly, the authors refer to “new” declustering approaches (line 248) and “novel independent event selection methodologies” (line 434). However, the use of windows centred on the peak of an event has been adopted in a number of previous publications. Regarding the sorting method, I recall, for example, https://doi.org/10.1016/j.wace.2024.100701 and https://doi.org/10.1002/2016WR019426, among many others. It would perhaps be more accurate to state that such a selection procedure is applied for the first time in conjunction with the MEVD (if this is indeed the case), since the data extraction method is not new per se.
Second, a linear trend is used to detrend the time series (line 140). Is this assumption reliable? At some locations, acceleration effects may lead to exponential growth. Please comment on this aspect.
Finally, the core of the research is the identification of the best TSL–TWW combination based on the alignment between observed and predicted quantiles. However, Figure 3 suggests that different combinations yield very similar errors. Since the subsequent comparisons focus on the best-performing setting, this raises the question of whether a meaningful improvement is actually achieved. Perhaps colour bars with fewer classes would improve clarity, and this aspect should be discussed in greater detail. In addition, Figure 4 appears to show that the data are characterised by multiple ties. Does this introduce any bias in parameter estimation?
See below a list of minor comments:
- In the abstract, line 8 (“This study” to “coastline”) would be better placed later in the text. In the second line, it appears somewhat abruptly.
- I am not a native speaker, but I believe that “Threshold Sea Level” should be changed to “Sea Level Threshold”. Consider making this change throughout the manuscript.
- Line 53. Up to this point, the manuscript has referred to POT-GEV (see line 41); therefore, the GPD should be introduced and contextualised more clearly.
- More context about the present study should be provided in the Introduction, particularly from line 72 (“Here we study”). At a minimum, please introduce the dataset, even if it is described in detail in Section 2.
- Line 81. Add a reference to Figure 1 alongside Table 1.
- In Section 2, thirteen lines are devoted to introducing the Mediterranean basin, whereas only two lines describe the Atlantic coast. The discussion of the two study areas should be more balanced.
- Line 250. Complete the sentence (the verb is missing).
- Line 324. Please explain the NSE index.
Citation: https://doi.org/10.5194/egusphere-2026-1243-RC2
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- 1
In this paper, titled “Improved Estimation of Extreme Sea Levels via Non-asymptotic Statistical Methods for Coastal Hazard Assessment”, the authors performed a comparative assessment of extreme value analysis approaches to evaluate the likelihood of coastal extreme sea levels. The paper is well written and well structured, and the results are clearly presented, with figures and tables being all relevant. Despite this, the manuscript presents some points that need to be clarified before being considered for publication. In what follows, some comments and suggestions are given.
My first concern relates to the lack of a clear description of the cross-validation procedure used to select the optimal TSL and TWW, as well as to evaluate the performance of the MEVD and POT-GPD approaches. I strongly recommend clarifying which variables are used to compute the performance indicators (e.g., those presented in Figures 3 and 4).
Secondly, the authors should discuss in greater detail the variability and uncertainty associated with the selection of the optimal TSL-TWW combination. According to the results presented in Figure 3, several TSL-TWW combinations - even those with substantially different values - yield very similar RMSE*. This raises the question of how sensitive the return period estimation is to the choice of TSL-TWW combination.
Thirdly, the authors should more clearly link the results regarding the selection of independent events to the underlying physical processes governing extreme sea levels at the coast, namely tides and storm surges. In particular, the choice of an appropriate TWW should be discussed in relation to the dynamics of the meteorological drivers (primarily extratropical cyclones) that control extreme sea levels in the Atlantic and the Mediterranean Sea. In this context, I suggest that the authors assess whether the use of relatively large TWW values (8-10 days) may inadvertently mask independent events.
Minor comments:
References
Arns, A. et al. Non-linear interaction modulates global extreme sea levels, coastal flood exposure, and impacts. Nat. Commun. 11,1918. https://doi.org/10.1038/s41467-020-15752-5 (2020).
Ferrarin, C., D. Bellafiore, G. Sannino, M. Bajo, and G. Umgiesser (2018), Tidal dynamics in the inter-connected Mediterranean, Marmara, Black and Azov seas, Prog. Oceanogr., 161, 102–115, doi: 10.1016/j.pocean.2018.02.006
Ferrarin, C., P. Lionello, M. Orlić, F. Raicich, and G. Salvadori (2022), Venice as a paradigm of coastal flooding under multiple compound drivers, Sci. Rep., 12, 5754, doi: 10.1038/s41598-022-09652-5