## 2 Data and Methods
### Estimation of Extreme Value  
In order to understand the spatial distribution of the extreme wave height using the EVA in the Northwest Pacific, SWH data measured along satellite altimeter tracks were sub-sampled within a bin of \(2^{\circ}\times 2^{\circ}\)[24; 28; 50]. In this study, the PoT method was utilized to estimate extreme SWHs using buoy measurements and satellite altimeter data (Figure 4). The PoT method, which uses data exceeding a defined threshold, alleviates the limitations of the AM method while maintaining data as being independent and identically distributed.  
Figure 3: Time series of the significant wave height (SWH) measurements from (**a**) the IORS and (**b**) the Donghae buoy, year–month plots of SWH (m) from (**c**) the IORS and (**d**) the Donghae buoy, and monthly average of SWHs from (**e**) the IORS and (**f**) the Donghae buoy.  
The data greater than the threshold follow a generalized Pareto distribution (GPD) in the EVA [17]:  
\[G(z)\ =\ 1-\left[1+\xi\left(\frac{z-\mu}{\sigma}\right)\right]^{-1/\xi}, \tag{1}\]  
where \(\mu\) is the location parameter, \(\sigma\) is the scale parameter, and \(\xi\) is the shape parameter. As the threshold \(\mu\) is a factor that affects the result of EVA, it is of considerable importance to select an appropriate threshold value. Too low a threshold causes the estimated extreme value to have a low bias, while too high a threshold does not maintain stability because of excessive suppression of the amount of data [17; 21]. Therefore, the stability of parameters should be tested. The parameters were estimated for every value of the threshold [17]. For the selection of the threshold, the shape parameter (\(\xi\)) and modified scale parameter (\(\sigma^{*}\ =\ \sigma-\ \xi\mu\)) were presented in Figure 5. Based on the results of the stability test, the 99.5 th percentile SWH suggested by [PERSON] et al. [21] was selected among the various threshold values proposed in previous studies [21; 24; 25; 28].  
To perform the PoT analysis, it was hypothesized that the data should satisfy the precondition of independence between the data. However, a satellite altimeter along the track would be likely to observe similar SWH values within a bin, which may violate the precondition. Taking this into account, we selected one maximum value for each track of the satellite within a given bin. Nevertheless, other satellites were likely to undermine this independence by observing similar SWHs within a given spatial range.  
Figure 4: Flowchart of estimation of extreme SWH using Peak over Threshold analysis with a generalized Pareto distribution, where n and N represent the 2 degree and 3 days, respectively.  
Figure 5: (a) Shape parameter (\(\xi\)) and (b) modified scale parameters (\(\sigma^{*}\ =\ \sigma-\ \xi\mu\)) with 95% confidence intervals for every value of threshold. The red dot indicates the 99.5 th percentile SWH.  
As such, an additional constraint was given to use a temporal range for the selection of only one maximum value among the previously selected maximums. Previous studies have mentioned that the independence of data could be ensured by separating these data into specific time intervals such as two days [35; 51] or three days [21]. In this study, data separated at three-day time intervals were used for the EVA.  
In the PoT method, the probability level for the 100-year return period SWH is determined as follows:  
\[P\Big{(}H_{s}<H_{s}^{100}\Big{)}\ =\ 1-\frac{N_{Y}}{100N_{\text{PoT}}}, \tag{2}\]  
where \(N_{\text{PoT}}\) is the number of exceedances used in the PoT analysis, and \(N_{Y}\) is the number of years covered by the analysis. As mentioned above, the PoT method complements the defects of the annual maximum method, but also has a limitation in that this method shows an extreme dependency on the threshold, and variations of the estimated extreme value were amplified if insufficient data were available for this approach.