## 4 Discussion
### Wave Setup in the Taiwan Strait during Soudelor and Dujuan  
Wave setup is the change in mean water level due to the presence of breaking waves. In this study, wave setup was taken as the water level rise driven by the spatial variation of wave radiation stress, which is also called the wave radiation stress gradient. The wave radiation stress is the depth-integrated and phase-averaged excess momentum flux caused by waves, which is exerted on the mean flow. The variation of the radiation stress also induces change in the mean flow [32].  
According to [PERSON] et al. [16], the wave setup on the northeast coast of Taiwan could reach 1.0 m because of offshore giant (>20 m) waves. [PERSON] et al. [9] studied wave-induced surge in Tampa Bay (Florida), while [PERSON] et al. [10] studied the wave setup in the Bay of Biscay; their results showed that the regional maximum wave setup could be >0.3 m. These studies found that wave setup is considerable in storm surge modeling when large wave heights occur in a region with a steep sea bottom slope. The Taiwan Strait lies on the continental shelf of the East China Sea with average depth of 60 m; therefore, there has been little study of wave-induced surge in this area.  
Figures 14 and 15 shows the wave setup simulation for the western bank of the Taiwan Strait during the passage of both Soudelor and Dujuan. The wave setup was enhanced as the typhoons approached and reached its highest value when the typhoons made landfall. Although the spatial distribution of the wave setup was similar in each case, wave action was stronger and the wave setup was greater during the passage of Typhoon Soudelor.  
In the deep ocean, the radiation stress gradient can be neglected because of the depth integration. However, in nearshore areas, waves break with the rapidly changing bathymetry and the radiation stress varies considerably, which means the wave setup generated by the radiation stress gradient is obvious in such areas. Wave radiation stress reaches its maximum value before the waves break and it then decreases afterward. The radiation stress gradient is directed onshore in the zone of breaking waves and directed offshore in the area of wave growth. Figure 16 shows maximum wave setup of all simulation area during the Typhon Soudelor and Dujuan. The maximum of wave set-up is about 15 cm and the minimum of wave set-up is about \(-8\) cm during the typhon process. Consequently, wave setup, which was found positive (negative) in the nearshore (offshore) area, was over 15 (\(-8\)) cm in this study.  
Figure 14: Wave setup in the Taiwan Strait during the passage of Soudelor.  
Figure 16: Maximum (red dot) and minimum (blue dot) wave setup during the Typhon Soudelor (**a**) and Dujuan (**b**).  
Figure 15: Wave setup in the Taiwan Strait during the passage of Dujuan.  
It is notable that the wave setup in Sanduao Bay (26.3-26.9\({}^{\circ}\) N, 119.5-120\({}^{\circ}\) E), which was very low in comparison with the adjacent area, could also be explained by the local topography (Figure 17). The effect of shoaling is diminished at the mouth of Sanduao Bay because of a trend of deepening. Therefore, wave breaking in this zone was weakened and the wave radiation stress gradient was low, which resulted in a small wave setup. The principal finding of this study was that the distribution of wave setup was determined primarily by local topography. The wave setup also oscillated within tidal period because the waves were affected by the tide. In this study, the oscillation of the wave setup reached 3 cm at most. In the nearshore area, wave breaking was weakened at high tide, which reduced the radiation stress gradient and decreased the wave setup. Conversely, the wave setup was increased during low tide.