A non-asymptotic framework integrating novel independent event selection methodology for the prediction of extreme sea levels

The probability of extreme sea level events is critical for planning and devising suitable coastline protection strategies. The traditional asymptotic approaches require sufficiently long sea level records to yield accurate estimates of extreme water levels, particularly for the long return periods needed for risk mitigation interventions. However, sea level records are often short, leading to high uncertainty in estimating under asymptotic approaches based on the Generalized Extreme Value (GEV) distribution. These only utilize a small part of the data (e.g., yearly maxima or a few values exceeding a high threshold), thereby not making optimal use of scarce observations. Non-asymptotic methods, such as the Metastatistical Extreme Value Distribution (MEVD), are proposed, which use the scarce data efficiently. A critical part of such methods is selecting independent events (IEs). The existing literature lacks a definitive methodology for IE selection. This study proposes a new method that prioritizes the highest peaks and excludes nearby ones to ensure independence. With application to the Italian coastline, a stringent cross-validation approach is implemented to assess the predictive performance of the extreme value models. This study identifies an optimal time window and a threshold sea level for IE selection, and compares the performance of MEVD with that of the Peak Over Threshold (POT) approach. Results indicated that the proposed IE selection methodology is practical, showing that MEVD outperforms POT, particularly in high quantile estimation.