# Coastal Wind Measurements Using a Single Scanning LiDAR
## 3 Results
### Validation of 10-Minute Mean Wind Speeds and Wind Directions
#### 3.2.2 Sensitivity to Elevation Angle Setting  
Figures 8 and 9 show the scatter plots of the V1 and 100s wind speeds and directions for Case 6 (\(\theta\) = 14.11\({}^{\circ}\)) and Case 7 (\(\theta\) = 26.05\({}^{\circ}\)). The evaluation heights for Case 6 and Case 7 are 107 and 207 m ASL, respectively. The azimuth angle settings in these cases were identical to Case 2, i.e., \(\varphi_{\text{range}}\) = 45\({}^{\circ}\). The two-parameter fitting VVP, which ignores the vertical wind speed component (_cf._ Equation (6)) included in the original equation, was used for the analysis. Thus, if the vertical component of wind speeds was not negligibly small compared to the horizontal components, the accuracy of the wind speeds and directions should decrease as the elevation angle increases. However, these figures show that the accuracy of the 100s wind speeds and directions aloft did not deteriorate as the elevation angle increased. In fact, the accuracies for Case 6 and Case 7 increased in comparison to Case 2. This may be associated with the tendency of the wind to become more homogeneous at higher altitudes.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Case** & \(\mathbf{U_{\text{ref}}}\) & \begin{tabular}{c} \(\mathbf{N}\) \\ **(-)** \\ \end{tabular} & \begin{tabular}{c} \(\overline{\mathbf{D}}_{\text{V1}}\) \\ **(\({}^{\circ}\))** \\ \end{tabular} & \begin{tabular}{c} \(\overline{\mathbf{D}}_{\text{100s}}\) \\ **(\({}^{\circ}\))** \\ \end{tabular} & \begin{tabular}{c} \(\overline{\mathbf{\epsilon}}_{D}\) \\ **(\({}^{\circ}\))** \\ \end{tabular} & \begin{tabular}{c} \(\sigma(\epsilon_{D})\) \\ **(\({}^{\circ}\))** \\ \end{tabular} & \
\begin{tabular}{c} \(\mathbf{y}\) = \(\mathbf{mx}\) + \(\mathbf{b}\) \\ **(-)** \\ \end{tabular} &
\begin{tabular}{c} \(\mathbf{R^{2}}\) \\ **(-)** \\ \end{tabular} \\ \hline
1 & V1 & 644 & 128.8 & 130.0 & \(-\)0.5 & 2.5 & 0.998 & \(-\)0.263 & 1.000 \\
2 & V1 & 436 & 266.0 & 268.1 & \(-\)0.4 & 2.8 & 1.006 & \(-\)1.900 & 0.999 \\
3 & V1 & 424 & 271.2 & 270.2 & \(-\)0.2 & 5.4 & 1.004 & \(-\)1.372 & 0.995 \\
4 & V1 & 411 & 250.0 & 245.6 & \(-\)0.9 & 8.3 & 0.994 & 0.676 & 0.988 \\
5 & V1 & 754 & 207.4 & 205.0 & \(-\)2.0 & 7.8 & 0.998 & \(-\)1.495 & 0.996 \\
6 & V1 & 540 & 84.6 & 83.4 & \(-\)0.5 & 2.0 & 0.999 & \(-\)0.354 & 0.999 \\
7 & V1 & 505 & 185.7 & 186.8 & \(-\)0.3 & 2.5 & 1.000 & \(-\)0.178 & 1.000 \\
8 & V1 & 8039 & 114.9 & 114.0 & \(-\)0.7 & 3.7 & 0.997 & \(-\)0.329 & 0.998 \\
9 & SA & 3557 & 158.7 & 157.8 & 1.4 & 12.1 & 0.995 & 2.254 & 0.984 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistics of the 10-minute wind direction from 100s for Cases 1–9.  
Figure 8: Scatter plots between the V1 and the 100s wind speeds for **(a)** Case 6 and **(b)** Case 7.  
Figure 10 shows the time series of the horizontal and vertical wind speed components observed by V1 at a height of 107 m ASL for the period from 5 to 8 February 2019. The \(w\) component of velocity was not directly observed by V1, as it is calculated from a transformation conversion of the line-of-sight wind speed using the DBS method. From Figure 10, it appears that the magnitude of \(w\) is mostly less than 10% of the horizontal wind speed. Thus, these results indicate that neglecting the vertical wind speed component in the two-parameter fitting VVP is quite acceptable for measuring offshore winds, which have a small vertical wind speed component. Therefore, we concluded that the elevation angle setting between 5\({}^{\circ}\) and 26\({}^{\circ}\) did not produce any significant difference in the measurement accuracy for the same distance from the position of the scanning LiDAR.