## 4 Simulation and Experimental Results and Discussion
### WRF Simulation Analysis  
Our analysis of both the WRF atmospheric model predictions and wind observations indicates that wind speeds above 10 kts predominantly originate from the western sector, as illustrated in the wind rose in Figure 5. Additionally, it is worth noting that the WRF1 model predicts a direction approximately 60\({}^{\circ}\) more northerly and at higher velocities compared to the observed wind speeds and that WRF9 predicts winds that are lower than the observation and more varied in their direction. In the lower wind speed range, both WRF1 and WRF9 predict winds from the western sector, whereas a substantial portion of the wind measurements come from the eastern sector. Additionally, the WRF1 model forecasts a higher frequency (approximately 32%) of 10-15 kts winds compared to the 12% observed and roughly 5% more wind velocities in the range of 15-20 kts. For stronger winds, the WRF1 simulations generally indicate a W-NW direction, with a minor increase in the northern bias, as indicated by the higher frequency of the NW direction becoming dominant, whereas the observed data still indicate a SW-WSW direction. To conclude, the wind-rose investigation highlights the inaccuracies of the WRF simulation models. First and foremost, WRF1 presents a solid preference for the northern wind component throughout the day. This is important in two contexts:  
* Both resolutions of WRF fail to predict the morning to midday lake breezes, which are the ESE to SE winds that are visible at IMS wind roses, as illustrated in Figure 5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Learn rate & 0.0001, 0.0002, 0.0003, 0.0004 \\ Epochs & 100, 300, 500 \\ Activation function & Sigmoid, ReLU, Tanh \\ CNN number of filters in 1 st layer & 64, 128, 256 \\ CNN number of filters in 2 nd layer & 64, 128, 256 \\ MLP dense 2 nd layer size & 16, 32, 64 \\ MLP dense 3 rd layer size & 5, 10, 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Value ranges for model hyperparameters used through the grid search process. Due to the typical wind cycle [64], we expected both the WRF simulation and IMS observations for the noon winds to present stronger and more westerly. Although the velocity difference is less dramatic than the direction discussed earlier, it also plays a crucial role from a competitive sailing perspective. For clarity, even a relatively small velocity difference between two boats is crucial when it comes to boat speed and angle relative to the wind origin. The 60\({}^{\circ}\) direction difference between WRF1 and observations and the diversion of velocity and WRF1 velocity predictions are clearly significant and show that the basic WRF (WRF1) simulation can be greatly improved, especially for demanding applications such as sailing competitions where a relatively small wind velocity difference could result in victory [81]. The regression of direction between the simulation and observation, as depicted in Figure 6, shows that the WRF1 simulation was not able to identify any change in wind direction (\(r^{2}=0.01,p\leq 0.01\)) and that the WRF9 simulation was not able to predict wind direction in much the same way (\(r^{2}=0.00,p=0.99\)). As speculated previously, this inability to identify changes in wind direction is probably caused by the failure of the models to  
Figure 5: Wind roses of WRF1 (**a**, **left**) and the simultaneous observations (**a**, **right**) and WRF9 (**b**, **left**) and the simultaneous observations (**b**, **right**). The data are comprised of 3600 1 Km 1 h interval data points and 1340 9 Km 3 h interval data points. simulate the morning lake breeze [82]. The WRF1 simulation predicted changes in wind velocity better (\(r^{2}=0.47\), \(p<0.001\)), while the WRF9 simulation was not able to predict the velocity changes (\(r^{2}=0.01\), \(p<0.001\)). It is possible that WRF1 was able to resolve velocity changes because they are driven by larger scale phenomena such as intrusion of Mediterranean sea breeze.