## 3 Results
### Validation: Currents  
Flow velocity modeling results were obtained at each layer (5, 10, 20, and 30 m below the surface) for comparison with the observations, as shown in Figure 14. The locations of the observations are indicated in Figure 14. The results of diverse statistical analyses, such as the R\({}^{2}\), current NRMSE, linear regression, and beta distribution analyses, are shown in Figure 6. In terms of the beta distribution, even if the same data were analyzed, the distribution can be manipulated if different bin widths are applied. Therefore, in this study, the bin widths for all data were fixed at approximately 0.05 m/s despite the varying ranges of each dataset. The number of bins for each dataset was determined based on the range of the data to maintain a bin width of 0.05 m/s. For instance, the observed velocity at a depth of 5 m had a minimum (maximum) value of approximately 0.008 (0.957) m/s, resulting in a range of approximately 0.949 m/s. In this case, the optimal number of bins was determined  
Figure 5: Box plots of water temperatures at thirteen stations: the observed, sampled, and raw temperatures. The depth labels indicate the observation depth at each station.  
to be 19, allowing the data range to be divided into 0.05 m/s increments. In this way, bin numbers between 19 and 21 were selected depending on the data ranges.  
The model outputs showed R\({}^{2}\) values approximately equal to or larger than 0.8 at the three layers closest to the surface. Although the near-bottom velocities exhibit a minimum R\({}^{2}\) value of 0.74, the numerical model could explain the real velocity reasonably well. From the positive y-intercepts (b in the linear regression equation in Figure 6), we could know that the model overestimated the velocities overall by approximately 0.06 m/s. However, the slopes (a in the linear regression equation in Figure 6) were nearly 1 in all cases, indicating the high reproducibility of the model for velocity variations.  
The vertical distributions of flow velocities are also important information for understanding sea characteristics. From the beta distributions of the observed velocities, the velocity at a depth of 30 m showed a distinct distribution from those at other depths. The maximum velocity was approximately 0.96 m/s at this depth (while those at other depths exceeded 1 m/s). The probability density was strongly concentrated near 0.26 m/s and then showed a steep decrease at high velocities. Other distributions, except for 30 m, showed less steepness and then exceeded the distribution of the 30 m depth when the velocity exceeded 0.47 m/s. Moreover, when the velocity exceeded 0.6 m/s, similar distributions were calculated for the 5 and 10 m depths, indicating no relative velocity (no shear) during ebb and flood tides when tidal currents were strong.  
The vertical distributions derived from the model results also showed similar distributions as the observations. The model illustrated the highest probability density near 0.30 m/s and decreased steeply at a depth of 30 m, as observed. The modeled steepness was weaker than the observed steepness. Similar to the observations, when the velocity exceeded 0.48, the probability densities of the distributions other than that corresponding to the 30 m depth were relatively high. In terms of high velocities, the model presented  
Figure 6: Scatterplot (transparent points) and linear regression results of the velocity profile at the mooring station. The dotted lines indicate 95% confidence boundaries. The beta distributions indicate the probability density of velocity in each layer of the observations and modeling outputs.  
a relatively high distribution of high velocities from the surface to bottom. The same probability density between 5 m and 10 m was not reproduced in the model results.