## 3 Results
### Validation: Tides  
The tidal constants (amplitude and phase) were validated with hourly observations collected at 42 tidal stations in the SIS using the R\({}^{2}\) and NRMSE (normalized root-mean square error) values. We restricted our analysis to observational data collected during the same period as the numerical model run, thereby allowing us to compare the model outputs to the observed data while considering seasonal effects on tides. The model results were also extracted every 12 min at the locations of the tidal stations.  
The major harmonic tidal constituents (M\({}_{2}\), S\({}_{2}\), K\({}_{1}\), and O\({}_{1}\)) in the SIS [30], including N\({}_{2}\), are compared in Figure 3. The semidiurnal constituents, M\({}_{2}\) and S\({}_{2}\), were found to be major components in the SIS with maximum magnitudes of approximately 1.08 m and 0.58 m, respectively. Then, K\({}_{1}\), O\({}_{1}\), and N\({}_{2}\) followed with relatively small values less than 0.5 m. The tidal phases of the major constituents are distributed between 120\({}^{\circ}\) and 360\({}^{\circ}\).  
Table 15 presents the locations of the tidal stations and the R\({}^{2}\) and NRMSE results obtained from the observed and calculated surface elevations. The NRMSE values ranged from 0.07 to 0.15 (the RMSE values ranged from 0.07 to 0.19 m, not shown here), a greater improvement than that obtained in the previous study with an RMSE value of 40 cm inside the SIS [21]. The R\({}^{2}\) values were higher than 0.9 at almost all tidal stations except for Kobe,  
Figure 3: Comparison of tidal constants ((a) amplitude and (b) phase) between the major tidal components observed at 42 tidal stations and those modeled.  
Murotomisaki, Osaka, Sumoto, and Tannowa, all of which are, interestingly, located in the eastern part of the SIS.  
Figure 4a,b shows comparisons of the time series between the observations and model results at the Hiroshima and Osaka tidal stations. The Hiroshima tidal station is located in the western part of the SIS, while the Osaka tidal station is located in the eastern part, as indicated in Figure 1a.  
These two locations have different tidal characteristics. Basically, the amplitude of the tides is higher in the western part of the SIS, with a maximum value of approximately 4 m in the modeled period, and the semidiurnal tide was dominant in this area. The eastern part of the SIS showed a maximum amplitude of less than 2 m during the spring tides, only half the amplitude obtained at Hiroshima. The reason for the relatively low R\({}^{2}\) values derived from the eastern tidal stations can be attributed to this result. The model still might not describe very detailed fluctuations superposed onto tidal signals. However, the tides near Osaka showed mixed, mainly semidiurnal patterns that matched the observations well. Semidiurnal tides dominated during the spring tides, while diurnal tides dominated around near tide periods (5 and 22 September in Figure 4b).  
The surface elevations were also affected by atmospheric forces, such as winds and air pressure. The blue line and vectors in Figure 4 show the air pressure and wind velocity, respectively, recorded at the Osaka tidal station and derived from the MSM dataset of the JMA for utilization in the simulation. On the 3 rd of September, a typhoon event accompanying northerly winds induced a rise in sea level. Additionally, other atmospheric events occurred on the 22 nd and 30 th of September.