## 4 Discussion  
### Tide and Storm Surge Interaction  
Two sets of numerical experiments were conducted to assess the model performance and to analyze the mechanism of tide storm surge interaction: (a) Full run: The model was driven by both the tidal forcing at the ocean boundary and the atmospheric forcing. The resultant water level from this model run is the storm tide. (b) Storm-only run: Only the blended atmospheric forcing was used to drive the model, while the tidal forcing was turned off. The resultant water level from this model run is called pure storm surge. (c) Tide-only run: Only the tidal forcing was included. The resultant water level is the pure astronomical tide level.  
In the Taiwan Strait, large tidal range and severe storm surge are observed and tide-surge interaction is remarkable, especially near the western bank. The storm surge observations always show tidal oscillation because of the tide-surge interaction [6; 29]. According to experiments conducted by [PERSON] et al. [6], nonlinear bottom friction is a major factor that should be considered when predicting these oscillations. In addition, the presence of the island of Taiwan enhances tide-surge interactions.  
During the passage of both Soudelor and Dujuan, the storm surge showed oscillation within the tidal period that was inversely proportional to the tide elevation, i.e., low at high tide and high at low tide. It confirms that tide-surge interaction is inevitable in coastal areas with shallow water depth and large tides. The predicted water level matched the observations well, especially the predictions that considered tide-surge interaction. Without consideration of tide-surge interaction, the predictions were higher at high tide and lower at low tide, which resulted in overprediction of the tidal range.  
The peak water levels at Xiamen and Dongshan occurred earlier than the astronomical high tide owing to tide-surge interaction. The tides from the northern and southern entrances of the Taiwan Strait mix in the district between Dongshan and the Penghu shallows [1; 11]. In the northern part of the Taiwan Strait, tidal wave propagation was accelerated because the water depth was increased by the storm surge, which caused the peak to arrive earlier. This type of pre-arrival was also evident at Xiamen and Dongshan.  
Discrete Fourier transform (DFT) analysis, applied to both the astronomical tide and the interaction residual (difference between the predicted water level simulated with and without consideration of tide-surge interaction), showed that tide-surge interaction led to oscillation within the tidal period. Oscillation around the period of the M2 tidal constituent was most remarkable (Figures 8 and 9). Table 3 shows the DFT results for typhoons Soudelor and Dujuan. In comparison with Typhoon Dujuan, tide-surge interaction was stronger during the passage of Typhoon Soudelor because of typhoon intensity.  
Figure 8: Time series of astronomical tide water level (solid lines), predicted water level without consideration of tide-surge interaction (dotted lines), predicted water level simulated with consideration of tide-surge interaction (green solid dots), and interaction residual (red dashed lines) during the passage of Soudelor (**a**–**e**), together with discrete Fourier transform of astronomical tide (black solid lines) and interaction residual (red solid lines) of each station (**f**–**j**).  
Figure 9: Time series of astronomical tide water level (solid lines), predicted water level without consideration of tide-surge interaction (dotted lines), predicted water level simulated with consideration of tide-surge interaction (green solid dots), and interaction residual (red dashed lines) during the passage of Dujuan (**a**–**e**), together with discrete Fourier transform of astronomical tide (black solid lines) and interaction residual (red solid lines) of each station (**f**–**j**).