# Fast Numerical Wind Turbine Candidate Site Evaluation
## 3 Results
### Results Related to Wind Speed Distribution  
The role of the MSE(\(\bar{v}\)) value is comparing the average wind speed during the 11 month test period as predicted by the models with the actual average wind speed. Each modelling method results in 12 average wind speeds, and Table 4 provides the MSE of these results. The third power of the wind speed is likewise averaged and its MSE is presented in the column MSE(\(\bar{v}^{3}\)). The models that better predict the wind speed time series (see Table 3) tend to also predict average values that are closer to the true average.  
Predictions of one of the LS lin models from each site are statistically compared to the measured wind speeds and NWP predictions in Figures 8-10. Scatter plots, Q-Q plots, and sunflower diagrams showing the daily wind patterns are presented. The shown LS lin model is the one with the choice of the training month that resulted in the best MSE at each site.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Name** & **MSE(\(\bar{v}\)) [m\({}^{2}\)/s\({}^{2}\)]** & **MSE(\(\bar{v}^{3}\)) [m\({}^{6}\)/s\({}^{6}\)]** \\ \hline LS lin & **0.003** & **1.177** \\ GP lin & 0.011 & 1.399 \\ GP SE+lin & 0.005 & 1.210 \\ GP SE & 0.004 & 1.421 \\ NWP & 1.004 & 645.327 \\ \hline LS lin Stolp & 0.003 & 14.179 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Wind speed distribution-related figures of merit for various models of wind speed at Brezice meteorological station and for LS lin model at Stolp meteorological station. The wind speed and the cube of the wind speed are averaged over the 11-month test period for each model to obtain \(\bar{v}\) and \(\bar{v}^{3}\). The difference between \(\bar{v}\) or \(\bar{v}^{3}\) obtained with model prediction and \(\bar{v}\) or \(\bar{v}^{3}\) obtained from the measurement is computed, squared, and the 12 squares that correspond to the 12 train/test data set selections are averaged.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model Name** & **R** & **R\({}^{2}\)** & **MSE [m\({}^{2}\)/s\({}^{2}\)]** & **MSLL** \\ \hline LS lin & **0.685** & **0.454** & **0.243** & **\(-\)0.285** \\ GP lin & **0.685** & 0.435 & 0.251 & \(-\)0.266 \\ GP SE+lin & 0.636 & 0.378 & 0.276 & \(-\)0.198 \\ GP SE & 0.601 & 0.341 & 0.293 & \(-\)0.190 \\ NWP & 0.418 & 0.000 & 2.842 & - \\ \hline LS lin Stolp & 0.811 & 0.652 & 0.442 & \(-\)0.514 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Figures of merit for various models of wind speed at Brezice meteorological station and for LS lin model at Stolp meteorological station. The values given are the values obtained on the test data averaged over the 12 models with different train/test data set selections and the Brezice models are ordered in ascending MSE.  
Figure 8: Scatter plots and Q–Q plots of wind speeds for the Brežic meteorological station. The measurements are compared to the numerical weather prediction (NWP) model (**left**) and to the linear regression with least squares model trained on November 2017 data (**right**). The experimental model used is the same one as in Figure 6. The shown LS lin model predictions are for the test data. The black line is the line of equality, and the red line is the least-squares linear fit of all the data points.  
Figure 9: Scatter plots and Q–Q plots of wind speeds for Stolp meteorological station. The measurements are compared to the NWP model (**left**) and the linear regression with least squares model trained on May 2017 data (**right**). The shown LS lin model predictions are for the test data. The black line is the line of equality, and the red line is the least-squares linear fit of all the data points.