## 2 Materials and Methods
### SWAN Model Validations and Implementation of Data Assimilation Techniques  
Extensive calibrations and validations have been carried out for the wave modeling system against both 'in situ' and remotely sensed measurements [16; 33; 34; 35; 36]. While the validations against the satellite data considered only the significant wave height, those carried out against in situ measurements, besides this wave parameter, considered also the mean wave period and the wave direction [15; 16; 32; 33; 34; 35]. As it is known, an increased wave period leads to higher celerity, enhancing as a consequence the wave power. From this perspective a brief discussion will be focused next on the model capability in predicting with an acceptable accuracy this important wave parameter. Since the Black Sea is an enclosed basin, the fetch is significantly smaller than in the ocean environment. This means that the value of the mean period is not so large, an average value for the western coast of the Black Sea being about 4 s. This is almost half the average value of the mean period close to the European oceanic coasts [18]. The results presented in [15; 16; 32; 33; 34; 35], considering validations and  
Figure 2: The computational domains defined in Cartesian: (**a**) Cart1—the nearshore in front of Sulina arm of the Danube River; (**b**) Cart2—Sacalin Peninsula and the Saint George arm of the Danube River; (**c**) coastal environment close to Mangalia city, the south of the Romanian nearshore. calibration studies against data provided by two directional buoys: Gelendzhik (37.98\({}^{\circ}\) E, 44.51\({}^{\circ}\) N) and Hopa (41.38\({}^{\circ}\) E, 41.42\({}^{\circ}\) N), show that the wave modeling system implemented predict the mean wave period with a reasonable accuracy, in some statistical parameters, as for example the scatter index the results being systematically better than for the significant wave height. Furthermore, also on the west coast of the Black Sea, a comparison of the SWAN results with the data measured at the Gloria drilling platform, which operates in the western sector (44.31\({}^{\circ}\) N, 29.34\({}^{\circ}\) E) at a location where the water depth is about 50 m shows also a relatively good accuracy of the model predictions in terms of mean wave periods. Furthermore, for increasing the accuracy and reliability of the wave predictions, techniques for assimilating the satellite data have been designed and implemented for the first two computational levels corresponding to the SWAN domains Sph1 and Sph2 [42; 43; 44]. These assimilation techniques are based on the optimal interpolation method [45]. The main idea behind these assimilation techniques is to combine the information coming from measurements with the results of the numerical models into an optimal estimation of the field of interest. For these two computational domains, the assimilation of the wave data has been performed in terms of the significant wave height (_H_s). It has to be highlighted that the satellite observations provided by the multimission system were considered for data assimilation. These comprise measurements from seven satellites. Thus, the data coming from the satellites: ERS-2 (European Remote Sensing), Poseidon, JASON-1, JASON-2 and GEOSAT (GEOdetic SATellite) Follow-On (GFO) were considered in the assimilation process, while the data from ENVISAT (Environmental Satellite) and TOPEX (TOPography Experiment) were used for validations. From this perspective, Table 4 presents the statistical results obtained for the _H_s values simulated with SWAN and the _H_s values obtained after the application of the data assimilation method, against the altimeter measurements used for validation across the Black Sea. The results correspond to the 15-year time interval 1999-2013.