## 3 Results
### Wind Speed Calibration Results  
This section shows the results of the different types of calibration for only the closest grid point and using only the testing data set.  
Figure 14 is the Taylor diagram that shows the correspondence of the uncalibrated wind speed time series and its various calibrated versions with the measurements.  
Figure 14: Taylor diagram of the various calibrations and the uncalibrated wind speed time series from the closest grid point against the measurements.  
Figure 13: Wind rose that combines the measured wind speed with the predicted wind direction from the testing data set.  
Table 5 shows the error metrics of the uncalibrated data and the calibrations against the wind measurements.  
The calibrations can also be evaluated through their probability distributions. This is specially suitable for our purposes, since it is more important to get a realistic overall probability distribution from which to calculate the wind resource rather than to accurately predict wind at any given moment. In this case, the Weibull distribution was used, which is one of the types of distributions usually used in wind data analysis [30]. It was fitted for each of these wind speed times series: the measurements, the reanalysis data, and all 4 calibrations. That gave the coefficients showed in Table 6, and with those the probability density functions were plotted, as shown in Figure 15.  
As the error metrics already showed, the directional calibration stands out by underestimating the wind speed. The rest of the calibrations have almost identical PDFs to that of the measured wind speed.  
These distributions were fitted using the whole testing data set, without taking into account the measured nor the reanalysis' wind direction. This is helpful for evaluating the calibrations themselves, but, if we want to better understand how the calibration helps estimating the production of any wind direction dependent wind turbine, we have to separately analyze the performance of the calibration using only the data points in which wind direction falls within the absorption range explained in Section 2.2.2. For that purpose, another series of Weibull distributions were fitted. In the case of the  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **ERA5-GD1-1 yr** & **Anem** & **QM** & **QM Dir** & **QM Season** & **QM Comb** \\ \hline \(k\) & 1.808 & 1.301 & 1.277 & 1.253 & 1.281 & 1.315 \\ \(c\) & 3.291 & 1.472 & 1.466 & 1.236 & 1.448 & 1.488 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Coefficients of the Weibull distributions of various wind speed time series covering a 1-year period.  
Figure 15: Probability density functions of the Weibull distributions of various wind speed series covering a 1-year period.  
measured wind speed series, the measured wind direction was used for selecting the data points. For the calibrated series, the predicted direction was used. Table 7 shows the coefficients of these distributions, while Figure 16 shows the probability density functions.  
In both Figures 15 and 16, we clearly see that the measured wind speed is significantly lower than that of the reanalysis. This can be due to the different locations: the closest ERA5 grid point is located outside of the town, while the anemometer is inside the town and located at the roof of a building away from the edge, a place where CFD simulations, like that of [PERSON] et al. (2014), indicate a low wind speed.