Statistical models for extreme waves: Comparison of distributions and Monte Carlo simulation of uncertainty

Abstract

This study evaluates the extreme waves in the Mediterranean and the Black Sea. Annual Maximum Series (AMS), and Partial Duration Series (PDS) of the significant wave heights (Hm0) are used from the ERA5 dataset. Generalized Extreme Value (GEV), Gumbel, Weibull, Lognormal, and Generalized Pareto Distribution (GPD) models are used to predict Hm0 for 50, 100, and 500-years of return periods. The statistical models are compared by using Anderson-Darling test statistics and the best-fitting AMS and PDS models at each grid cell is mapped to depict spatial variability within the study area. The uncertainty of the return levels is estimated by using the Monte Carlo simulation technique. The effect of varying width and temporal location of data window on the results is studied. The highest return levels of Hm0 are found in the Algerian basin, offshore Libya, the Tyrrhenian Sea, and offshore Crimea. The relative performance of statistical models showed that GEV outperformed other AMS models in the 43% of the study area, followed by Gumbel (29%), Lognormal (24%), Weibull (4%). In case of PDS models, Weibull dominates the region by covering 93% of the study area, with the remaining regions being characterized as GPD.