## 2 Materials and Methods
### Model Validation  
Field observations of tidal level and current were used to verify the hydrodynamic model. The water levels were collected from the Shanhaiguan station during the spring tide (11-12 May 2013) and neap tide (16-17 May 2013). The current data were collected at five field stations, SDL01 to SDL05, during the neap tide, 16-17 May 2013. These observation stations are shown in Figure 1. Figure 3 shows the comparison of simulated results and measured data including tidal level and current speed and direction. The hydrodynamic model results were quantitatively assessed against observed values using the _skill_ model [44].  
\[skill=1-\frac{\sum\lvert X_{m}-X_{o}\rvert^{2}}{\sum\left(\lvert X_{m}-\overline {X_{o}}\rvert+\lvert X_{o}-\overline{X_{o}}\rvert\right)^{2}} \tag{5}\]where \(\overline{D}\) is the mean value, in situ, of the observed data; \(M\) and \(D\) are the computed result and in situ observed data, respectively; and \(N\) is the number of data entries. A _skill_ value of 1.0 indicates a perfect performance of the model: _skill_ between 0.65 and 1 is considered excellent, _skill_ in the range of 0.5-0.65 is considered very good, _skill_ in the range of 0.2-0.5 is considered good, and _skill_ of less than 0.2 is considered poor.  
The model results generally matched the measured values very well with the excellent performance of _skill_ evaluation summarized in Table 1. The _skill_ of tidal level at Shanhaiguan during the spring and neap tides were all 0.99, and those of current speed at SDL01, SDL02, SDL03, SDL04, and SDL05 were 0.90, 0.87, 0.85, 0.94, and 0.86, respectively. The _skill_ values of current direction at the same stations were 0.97, 0.98, 0.95, 0.97, and 0.95, respectively. All _skill_ values (over 0.90) were much larger than 0.65, implying the excellent predictive efficiency of the model.  
Figure 3: _Cont._  
In order to evaluate the transport model, which shares the same computational mesh as the hydrodynamic model of Qinhuangdao, the validated TN concentration data were collected from Qinhuangdao during the period 16-23 July 2013. The simulated result of TN concentration is shown in Figure 4. Given that the measured data at 20 stations were from different dates, the time series was discontinuous, we calculated the average error, and all of the numbers were below 11% (shown in Table 2), which means the present model can accurately predict the TN distribution.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Time** & **Station** & **Period** & **Skill** & **Performance** \\ \hline tidal level & May, 2013 & Shanhaiguan & Neap tide & 0.99 & excellent \\  & & Station & Spring tide & 0.99 & excellent \\  & & SDL01 & & 0.90 & excellent \\  & & SDL02 & & 0.87 & excellent \\ speed & May, 2013 & SDL03 & Neap tide & 0.85 & excellent \\  & & SDL04 & & 0.94 & excellent \\  & & SDL05 & & 0.86 & excellent \\  & & SDL01 & & 0.97 & excellent \\  & & SDL02 & & 0.98 & excellent \\ direction & May,2013 & SDL03 & Neap tide & 0.95 & excellent \\  & & SDL04 & & 0.97 & excellent \\  & & SDL05 & & 0.95 & excellent \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hydrodynamic model evaluation.  
Figure 3: Model validation of tidal level and current velocity.