## 3 Results
### Downscaled Model Validation  
The metrics, which are shown in Table 1, were the BIAS, RMSE, and correlation coefficient, and concluded with a definitive improvement on average of all the stations. The validation ran operationally for the first 6 months of the year 2023, considering daily forecast runs with a 1 day ramping-up period and 3-day forecasting horizon, and we averaged the results in hindcast mode by collecting observations from the nine METAR stations that fell within the bounding box area of the finer and smaller domain of 3 km (D02), as seen in Figure 1, but eventually removing three stations that did not offer a continuous data stream in the same 3 h resolution that the other six had. Although anomalies, such as those observed at the SAMOS station, may arise, they did not negate the overall enhancement that the dynamically downscaled 3 km model shows, as evidenced by metric averaging across all stations. Thus, in the last line, we averaged the error metrics of all available stations, finding all three of the considered metrics to favor the downscaled model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**BIAS**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**Correlation Coefficient**} \\ \hline
**Station Name** & GFS (27 km) & WRF (3 km) & GFS (27 km) & WRF (3 km) & GFS (27 km) & WRF (3 km) \\ \hline SAMOS & \(\mathbf{-1.276}\) & \(-1.751\) & 4.415 & **3.451** & **0.242** & 0.008 \\ \hline SYROS & \(-1.060\) & \(\mathbf{-0.299}\) & 4.804 & **3.844** & 0.048 & **0.332** \\ \hline
**EL VENIZELOS** & \(-2.578\) & \(\mathbf{-1.515}\) & 5.250 & **3.915** & 0.029 & **0.400** \\ \hline
**NIKOS KAZANTZAKIS** & \(-2.922\) & \(\mathbf{-0.490}\) & 5.676 & **4.063** & 0.127 & **0.210** \\ \hline
**KARPATHOS (AIRPORT)** & \(-0.368\) & \(\mathbf{0.202}\) & 4.132 & **4.000** & **0.271** & 0.259 \\ \hline
**PAROS** & \(-3.258\) & \(\mathbf{-0.968}\) & 5.706 & **3.510** & 0.268 & **0.371** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of error values for the GFS model, which was run with a 27 km spatial resolution and WRF 3 km downscaled model on wind speed data utilizing the BIAS, RMSE, and correlation coefficient metrics for the first six months of 2023 (the better result is denoted with a bold font).  
More specifically, the validation of the downscaled atmospheric model, as shown in Table 1, demonstrated a notable improvement of approximately 24% in RMSE, averaged across all stations. The bias improvement cannot be expressed as a percentage, given that bias encompasses both positive and negative values, indicating when the model overpredicts (positive bias) or underpredicts (negative bias). Correlation coefficients were computed at each individual validation station, showing larger values indicating better performance in all but two stations.  
This underscores the significance of higher-resolution models in enhancing atmospheric forecasting accuracy in practical applications. However, it is important to note that the efficacy of such models is contingent upon various factors, including downscaling ratio [13], terrain, and orographic resolution [36], which may vary across different test cases.  
Following the successful validation of the 3 km WRF hereby mentioned as the Control case study, we proceeded by introducing the operational parametrizations for the 3D-Var case, subsequently comparing the extent of improvement observed, using the Control case as a reference. To be able to express the improvement of the models percentagewise, the remaining comparative results between the control and 3D-Var cases are presented in terms of absolute bias.