# Uncertainties of the 50-year wave height estimation using generalized extreme value and generalized Pareto distributions in the Indian Shelf seas

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## Abstract

Information about waves with specific return period in a region is essential for the safe design of marine facilities. In this study, significant wave height for 50-year return period is estimated using generalized extreme value (GEV) distribution and generalized Pareto distribution (GPD) based on the 15-year wave hindcast data. In order to realize the dependency of nature of the time series data on return value estimation, three types of data series: daily maxima (DM), monthly maxima (MM) and annual maxima (AM) are considered for GEV, whereas for GPD, threshold values are estimated from the parent data set at 6 h and the DM series. The GEV distribution shows that AM predicts higher significant wave height followed by MM and then DM. The large number (~ 50%) of smaller wave height value (< 1 m) in the DM leads to smaller estimate in wave height for 50-year return period for DM series compared to other data series. Among the locations studied, the maximum value of the significant wave height with 50-year return period by GEV with AM data series is 7.15 m in the western shelf seas and is 7.36 m for the eastern shelf seas, whereas the values based on GPD with peak over threshold are 6.94 and 7.42 m, respectively. Case studies are also done to know the influence of tropical cyclone on the estimated 50-year return value.

## Keywords

Extreme value distribution Surface waves Design wave height Return period Indian Ocean## Notes

### Acknowledgements

Wave model data was generated under the research project ‘Technical Criteria Atlas (TCA)’ sponsored by the Ministry of Earth Sciences (MoES), Govt. of India. We thank the two reviewers and the Editor for the suggestions which improved the scientific content of this paper. This manuscript is a part of the Doctoral thesis of the first author registered with Bharathidasan University, Tiruchirappalli and is NIO contribution 6433.

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