Extreme value analysis for waves in the Persian Gulf: Skill assessment of different methods for a fetch-limited basin

Estimating the design wave height with specific return period using extreme value analysis (EVA) is of significant importance in coastal and marine engineering. The purpose of this study is to compare different methods such as the Maximum Likelihood, the L-Moment and the least square methods to estimate the parameters of Generalized Pareto Distribution (GPD), Gumbel, and Weibull distributions in order to determine 100 years return period wave height at 16 selected points within the Persian Gulf. The Peaks Over Threshold (POT) method was employed for all tests. The hourly wave data were available for the total period of 30 years from 01/01/1990 to 31/12/2019 using reanalyzed ECMWF-ERA5 dataset as well as hindcast results from a calibrated local WAVEWATCH-III model. In order to find the threshold cutoff value, one of the pivotal parameters in EVA, adaptive approaches were employed which determined the threshold value based on the distribution function and the goodness of fit for extreme data at specific site. It was shown that subjective constant values used in most of previous studies in this water body were much less than what should be used to have the best fit. Moreover, the determined threshold value was not constant at different points and varied depending on the type of distribution employed. The results showed superiority of the Gumbel distribution in most of the points in the Persian Gulf. Sensitivity Analysis to the threshold values showed that using a low threshold value would lead to increasing the return wave height, which was significant in the case of Pareto and Gumbel distributions. Sensitivity analysis to input data confirmed that ECMWF-ERA5 underestimated the wave height and consequently, the underestimation of designed wave height at some locations by more than 40%. Also, the results from Annual Maxima Method (AMM) was similar to POT method but with ±20% differences in values.