## 3 Results
### Estimation of Extreme SWH Using PoT Method  
Figure 7 shows the results of extreme SWH estimates by applying the PoT method using the GPD to the satellite observed SWH data from the sea surrounding in situ measurement stations of the IORS and the Donghae buoy. The small plot on the upper right side of each figure presents a comparison between the quantile of the observed data and the quantile of the PoT estimated value of altimeter-observed SWH data from the seas surrounding the IORS and Donghae buoy. Since relatively high SWH data were selected by excluding the SWHs smaller than the threshold value, as shown in red curves of Figure 7, the fitting of GPD was expected to represent the characteristics of the distribution of extreme wave heights. The quantiles estimated using the determined probability density function (PDF) were in good agreement with the observed quantiles from altimeter data near the IORS and the Donghae buoy. The estimated 25-year and 50-year return period SWHs were 11.83 m and 13.95 m for the satellite SWH data near the IORS, respectively (Table 2). The 100-year return period SWHs were estimated to be 16.49 m for the altimeter data near the IORS. The estimated extreme SWHs were higher than the maximum SWHs with difference values of 3.66 m and 0.20 m around the IORS and the Donghae buoy, respectively. Considering that the estimated 100-year return period SWHs were higher than the maximum values, it may be reasonable to estimate extreme SWH by applying the PoT method for the study area.  
Figure 6: Comparison between altimeter-observed SWH and in situ measurements from (**a**) the IORS and (**b**) the Donghae buoy; time series of (**c**) monthly mean SWH, (**d**) monthly maximum SWH at the IORS, (**e**) monthly mean SWH, and (**f**) monthly maximum SWH at the Donghae buoy, within a bin of 2\({}^{\circ}\times\) 2\({}^{\circ}\) including the in situ measurement stations.  
Figure 8 shows the estimated SWHs, marked red lines, as a function of the return periods from 1 year to 100 years using satellite data near the IORS and the Donghae buoy. The dash lines represent the upper and lower limits of the estimated SWHs within 95% confidence interval. The confidence interval was calculated by using variance-covariance matrix and the delta method as described in [17]. In the sea near the IORS, the satellite-based extreme SWH at 100-year return period was relatively large of 16.49 m with a confidence interval of approximately 5.04 m. In the region near the Donghae buoy in the eastern coastal region of the Korean Peninsula with deep water depth, however, the 100-year return period of SWH was 7.43 m with the upper and lower limits of the estimated return level amounted to 7.94 m and 6.93 m.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Station** & \(\mathbf{H_{s}^{Max}}\) & \(\mathbf{H_{s}^{25}}\) & \(\mathbf{H_{s}^{50}}\) & \(\mathbf{H_{s}^{100}}\) & \(\mathbf{H_{s}^{100}}\)\(-\mathbf{H_{s}^{Max}}\) \\ \hline IORS & 12.83 & 11.83 & 13.95 & 16.49 & 3.66 \\ \hline Donghae Buoy & 7.23 & 7.03 & 7.25 & 7.43 & 0.20 \\ \hline \end{tabular}
\end{table}
Table 2: SWH maximum (\(H_{s}^{Max}\)) and \(H_{s}^{25}\), \(H_{s}^{50}\), and \(H_{s}^{100}\) (m) estimated by Peak over Threshold analyses using satellite altimeter data in the seas around the IORS and Donghae buoy, where \(H_{s}^{Max}\) represents the maximum value of measurements, and \(H_{s}^{25}\), \(H_{s}^{50}\), and \(H_{s}^{100}\) are 25-year, 50-year, and 100-year return period wave heights, respectively.  
Figure 7: Distribution of probability density of significant wave height values from satellite altimeter data in the sea around (**a**) the IORS and (**b**) the Donghae buoy, where the red line represents the generalized Pareto distribution fitted to the data. The inner plots are the comparisons between observed quantiles and retrieved quantiles from Peak over Threshold analysis.