# Measurement and Prediction of Wind Fields at an Offshore Site by Scanning Doppler LiDAR and WRF
## 3 Results and Discussion
### Measurement and Prediction of Vertical Wind Profiles  
Before presenting the comparison and analysis of vertical wind profiles, the quality of LiDAR measurements is assessed. To that end, the effect of carrier-to-noise-ratio (CNR) on the quality of measurement, particularly for different availability limits (\(\eta_{\rm lim}\)), is discussed. Here, \(\eta_{\rm lim}\) is the lower limit of the availability (\(\eta\)) set for the scanning LiDAR data (cf. Equation (3)). Figure 5 shows the distribution of CNR for the measurements at the height of 140 m. As is clear from the figure, the minimum threshold value of CNR is \(-\)25 dB. However, in order to investigate the effect of CNR, the minimum threshold values are increased to \(-\)23 dB and \(-\)20 dB. Figure 6 presents comparisons of 10-min-averaged horizontal velocities measured by scanning LiDAR and V1 LiDAR, for these three CNR limits and for \(\eta_{\rm lim}=80\%\). A comparison of statistical parameters for an \(\eta_{\rm lim}=20\%\) and \(80\%\) and for all three CNR limits is summarized in Table 1. It can be appreciated from the comparison that the quality of measurements degrades when the minimum threshold value of the CNR is increased. Figure 4: \(u_{r}\) as a function of azimuth angle (\(\theta\)) for elevation angle (\(\phi\)) = 50\({}^{\circ}\)and range of 100 m. Red circles indicate peak \(u_{r}\). In particular, the RMSE increases significantly when the minimum threshold of the CNR is increased for the same \(\eta_{\text{lim}}\). This is due to the distribution of CNR, as shown in Figure 4. Setting a higher value for the minimum threshold of the CNR means discarding data below that CNR. Figure 5: Distribution of Carrier-to-Noise-Ratio (CNR) for the measurements at the height of 140 m. Period: 1 April 2016 to 15 April 2016. Figure 6: Comparison of 10-min-average wind speeds of scanning Doppler LiDAR and V1 LiDAR at 140 m height for different CNR thresholds (**a–c**). Next, Table 2 summarizes a comparison of 10-min-averaged horizontal velocities measured by scanning LiDAR and V1 LiDAR for four different availability limits (\(\eta_{\text{lim}}\)) for the minimum threshold value of CNR of \(-25\) dB. Note that, for \(\eta_{\text{lim}}=0\%\), even if one data is measured in a 10-min time slot, then that time slot is considered valid. It can be appreciated from the table that, for lower \(\eta_{\text{lim}}\), the variation is larger and the coefficient of determination (\(R^{2}\)), as a result, is also smaller. However, the difference between \(R^{2}\) for \(\eta_{\text{lim}}=20\%\) and that for \(\eta_{\text{lim}}=80\%\) does not change too much. A further comparison between the 100S and V1 LiDARs is presented quantitatively using root mean square error (RMSE) in Figure 7. The RMSE increases with decreasing \(\eta_{\text{lim}}\). The availability of scanning Doppler LiDAR data is further analyzed as a function of height. Figure 8a shows data availability in the form of number of data measured every 10 min, i.e., \(N_{\text{mes}}\) as the function of height. It is obvious from the figure that the \(N_{\text{mes}}\) is higher at the lower height and reduces with height. Figure 8b shows the vertical profiles of the availability (\(\eta_{10}\)) of 10-min-averaged wind speeds. \(\eta_{10}\) is given by:  
\[\eta_{10}=\frac{N_{10,\eta_{\text{lim}}}}{N_{10,\,\text{max}}}. \tag{6}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **\(\eta_{\text{lim}}\) (\%)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Minimum** \\ **Number of Data** \\ \end{tabular} } & \multirow{2}{*}{**Offset**} & \multirow{2}{*}{**Slope**} & \multicolumn{2}{c}{**Coefficient of**} & \multirow{2}{*}{**RMSE** **(m/s)**} \\  & & & & & **Determination (\(R^{2}\))** & **(m/s)** \\ \hline
0 & 1 & 0.14 & 0.996 & 0.9549 & 0.924 \\
20 & 28 & 0.13 & 0.996 & 0.9607 & 0.868 \\
40 & 56 & 0.126 & 0.99 & 0.9612 & 0.844 \\
60 & 82 & 0.124 & 0.996 & 0.9672 & 0.806 \\
80 & 112 & 0.122 & 0.996 & 0.9694 & 0.784 \\ \hline \hline \end{tabular}
\end{table}