## 2 Materials and Methods
### Model Validation  
The hydrodynamic performance of the large, medium, and small models (i.e., Bohai, Qinhuangdao, and Jinmeng Bay models, respectively) was validated against the observeddata, including the tidal amplitude and phase, and the time series of the water level, and current speed and direction. For the Bohai model, the tidal amplitude and phase of four major tidal constituents, M2, S2, K1, and O1, at 10 tidal stations around the Bohai Sea land boundary (Figure 2a) were evaluated by the method proposed by [PERSON] et al. (1993), which is shown as follows:  
\[Diff=\sqrt{\left(a_{o}\cos g_{o}-a_{m}\cos g_{m}\right)^{2}+\left(a_{o}\sin g_{o }-a_{m}\sin g_{m}\right)^{2}} \tag{11}\]  
where \(a\) is the tidal amplitude and \(g\) is the tidal phase. Subscripts \(o\) and \(m\) represent the observed and modeled values, respectively. The calculated values of \(Diff\) are listed in Table 1, in which the average values of \(Diff\) for M2, S2, K1, and O1 are 8.03 cm, 1.75 cm, 2.60 cm, and 1.91 cm, respectively, and were reasonable compared with previous studies [46; 52; 53]. For the evaluation of the Qinhuangdao model, the time series of the observed current speed and direction from 9:00 15 December 2020, to 9:00 16 December 2020, at two measuring points, i.e., QVMP1 and QVMP2, were compared with the simulated values extracted from the model. The _skill_ model was employed for quantifying the model's performance [54]; the equation of _skill_ is shown as follows:  
\[skill=1-\frac{\sum\lvert X_{m}-X_{o}\rvert^{2}}{\sum\left(\lvert X_{m}-\overline {X_{o}}\rvert+\lvert X_{o}-\overline{X_{o}}\rvert\right)^{2}} \tag{12}\]  
where \(X\) is the given variable to be validated and the overbar denotes the average operator. The subscripts \(m\) and \(o\) denote the modeled and observed values. A _skill_ value of 1, 0.65-1, 0.5-0.65, 0.2-0.5, and 0-0.2 indicates that the model performance is perfect, excellent, very good, good, and poor, respectively. As shown in Figure 3, the simulated current speed and direction at QVMP1 and QVMP2 fit well with the observed values. The _skill_ values of the current speed and direction at QVMP1 are 0.88 and 0.90, respectively, and those at QVMP2 are 0.98 and 0.97, respectively, which indicate the excellent performance of the Qinhuangdao model. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Tidal Station**} & \multicolumn{4}{c}{_Diff of Tidal Constituents (cm)_} \\ \cline{2-5}  & **M2** & **S2** & **K1** & **O1** \\ \hline Dongying & 0.84 & 0.25 & 2.17 & 0.73 \\ Huanghua & 10.38 & 2.72 & 2.43 & 2.10 \\ Tanggu & 9.10 & 3.28 & 3.51 & 2.13 \\ Jingtang & 10.02 & 2.19 & 3.47 & 1.27 \\ Shanhaiguan & 2.90 & 0.35 & 1.98 & 0.95 \\ Jinzhou & 9.37 & 0.72 & 2.22 & 3.46 \\ Bayuquan & 17.16 & 2.49 & 3.88 & 4.49 \\ Changxingdao & 13.80 & 2.09 & 3.07 & 1.02 \\ Laizhou & 2.44 & 1.08 & 2.23 & 2.05 \\ Penglai & 4.28 & 2.35 & 1.03 & 0.93 \\ \hline Average & 8.03 & 1.75 & 2.60 & 1.91 \\ \hline \end{tabular}
\end{table} 
Table 1: Evaluation of the Bohai model based on the _Diff_ values of four major tidal constituents, M2, S2, K1, and O1, at 10 tidal stations around the Bohai Sea land boundary. As for the Jinmeng Bay model, the observed and simulated values for the current speed and direction from 12:00 5 September 2017, to 12:00 7 September 2017, at the measuring point JVMP, and the water level during August 2021, at the tidal station QTS were compared, as shown in Figure 4. The _skill_ values of the current speed and direction at JVMP and the water level at QTS are 0.88, 0.90, and 0.94, respectively, which indicate the excellent hydrodynamic performance of the Jinmeng Bay model.