## 2 Materials and Methods
### SWAN Model Validations and Implementation of Data Assimilation Techniques
The parameters presented in Table 4 are: mean measured and simulated values of the significant wave height, bias, mean absolute error, RMS (root mean square) error, scatter index (_SI_), correlation coefficient (_R_), and the regression slope (_S_), all of them being computed according to their standard definitions. In Table 4, \(N\) represents the number of data points considered in the statistical analysis. As it is known the bias, mean absolute error, RMS error and scatter index are better when the values are smaller, while the correlation coefficient and the regression slope are better when they are closer to the unity. From this perspective, it can be seen from Table 4 that the results with data assimilation appeared improved for all parameters. Figure 3 illustrates the corresponding scatter diagrams (the 15-year time interval 1999-2013) for the significant wave height. On the left side of this figure, the results of the SWAN model without data assimilation are presented while on the right side the results after performing the assimilation of the satellite data are given. The results presented in Figure 3 also indicate a clear improvement in the case when the data assimilation technique is used. Detailed information concerning the techniques considered for assimilating satellite data in the Black Sea wave modeling is given in [17; 42; 43; 44]. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{\begin{tabular}{c} **MeanObs** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **MeanSim** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Bias** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **MAE** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **RMSE** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **_SI_ \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **_R_ \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} \(S\) \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} \(N\) \\ \end{tabular} } \\ \hline SWAN _H_s (m) & \multirow{2}{*}{\(1.04\)} & \(0.97\) & \(-0.07\) & \(0.27\) & \(0.35\) & \(0.35\) & \(0.88\) & \(0.98\) & \multirow{2}{*}{\(316\),\(920\)} \\ SWAN\({}_{\rm DA}\)_H_s (m) & \multirow{2}{*}{\(1.00\)} & \(-0.04\) & \(0.21\) & \(0.29\) & \(0.28\) & \(0.91\) & \(0.99\) & \\ \hline \end{tabular}
\end{table} 
Table 4: Statistical results obtained for the _H_s values simulated with SWAN and the _H_s values obtained after the application of the DA (data assimilation) method, against altimeter measurements used for validation across the Black Sea, results corresponding to the 15-year time interval (1999–2013). Finally, as previously mentioned, an alternative multi parameter assimilation scheme was also designed, especially for the computational domain Sph4, considering in the assimilation process the in situ measurements carried out at the Gloria drilling unit [40,41]. In this case three different wave parameters have been assimilated. These are significant wave height, mean period and mean wave direction. This approach is based on the successive correction method (SCM) and its main advantage consists in the fact that the corrections are not limited to the significant wave height but operate on other two important wave parameters, which are wave direction and period. As shown in [40,41] this assimilation method improves the reliability of the wave predictions. On the other hand, the main inconvenience in relationship with the assimilation of the satellite data consists in the fact that it is directly related to a permanent source for in situ measurements. That is why from the computational domains considered in the present work, the above assimilation approach is effective only for Sph4 and the subsequent domains Sph5 and Cart3.