## 3 Results
### Ocean and Wave Model Validation  
We performed a validation of the ocean circulation (NEMO) and wave model (WWIII) in Figure 6 for two model set-ups: one that uses WRF atmospheric forcing (Control run) and one that used WRFDA (DA run), for the same time period that the DA validation was performed. A comparison is shown for the values of sea surface temperature (SST) and  
Figure 4: Absolute bias error metric compared to observations per validation meteorological station in D02 averaged for all forecast hours for wind speed magnitude. Blue and orange indicate control and 3D-Var case, respectively. Figure 5: Absolute bias error metric compared to observations per validation meteorological station in D02 averaged for all forecast hours for temperature. Blue and orange indicate control and 3D-Var case, respectively. significant wave height (SWH) against in situ, satellite, and model reanalysis products. For the in situ dataset, buoy measurements from Data Source III (Section 2.1) falling within the set-up's domain were used. For the satellite comparison, values of the CMEMS SST satellite Level 4 data product ([[https://doi.org/10.48670/moi-00172](https://doi.org/10.48670/moi-00172)]([https://doi.org/10.48670/moi-00172](https://doi.org/10.48670/moi-00172)), last accessed online 28 October 2024), closest to the buoys' coordinates, were used. In the SWH case (Figure 6b), satellite values were not available. For the reanalysis dataset, the coarser resolution (approximately 4 km) CMEMS analysis-forecast products were used ([[https://data.marine.copernicus.eu/product/MEDSEA_ANALYSISFORECAST_PHY_006_013/description](https://data.marine.copernicus.eu/product/MEDSEA_ANALYSISFORECAST_PHY_006_013/description)]([https://data.marine.copernicus.eu/product/MEDSEA_ANALYSISFORECAST_PHY_006_013/description](https://data.marine.copernicus.eu/product/MEDSEA_ANALYSISFORECAST_PHY_006_013/description)), [[https://doi.org/10.25423/cmcc/medsea_analysisforecast_wav_006_017_medwam4](https://doi.org/10.25423/cmcc/medsea_analysisforecast_wav_006_017_medwam4)]([https://doi.org/10.25423/cmcc/medsea_analysisforecast_wav_006_017_medwam4](https://doi.org/10.25423/cmcc/medsea_analysisforecast_wav_006_017_medwam4)), last accessed online 28 October 2024) as a validated model closer to the ground truth. The first day of each daily forecast, for the grid point closest to the buoy coordinates, was considered to reconstruct the time-series shown in Figure 6a of SST (NEMO results) and Figure 6b of SWH (WWIII results) for both model runs that used the WRF and the WRF-DA atmospheric forcing. Figure 6: Validation of the (**a**) sea surfac e temperature (SST) variable computed with Nemo 3.6 (first day of each forecast) forced by WRF Control and Nemo forced by WRF-DA and compared to CMEMS SST (analysis), satellite values, and buoy observations with 3-hourly frequency at the location of the Buoy ID 61277 near Santorini (25.1307\({}^{\circ}\) E, 35.7263\({}^{\circ}\) N) and (**b**) sea surface significant wave height of WWIII forced by WRF Control WWIII forced by WRF-DA (first day of each forecast) compared to CMEMS SWH (analysis) and the same buoy measurements. The SST results (Figure 5(a); Table 2) exhibit strong agreement between NEMO outputs (both configurations) and the observational datasets, with the greater discrepancies observed during the summer periods. The addition of WRF-DA as the model's forcing slightly improved the agreement of NEMO with the observational and reanalysis datasets, as reflected by reduced deviations in temporal patterns. Specifically comparing the model results to the BUOY data, the RMSE dropped from 0.52 \({}^{\circ}\)C (number of samples, N = 703) to 0.49 \({}^{\circ}\)C when WRF-DA was included (Table 2). Similarly, for the comparison to the SATELLITE observations, the RMSE decreased from 0.62 \({}^{\circ}\)C (N = 92) to 0.57 \({}^{\circ}\)C when WRF-DA were used (Table 2). Lastly, for the comparison to the CMEMS analysis, the RMSE dropped from 0.62 \({}^{\circ}\)C (N = 2208) to 0.59 \({}^{\circ}\)C with WRF-DA (Table 2).