# Measurement and Prediction of Wind Fields at an Offshore Site by Scanning Doppler LiDAR and WRF
## 2 Measurement and Prediction Methods
### Wind Field Measurement by Scanning Doppler LiDAR  
In order to retrieve vertical profiles of wind speeds and directions, line-of-site (LOS) wind speeds (\(u_{r}\)) were measured in the Doppler Beam Swinging (DBS) scanning configuration, shown schematically in Figure 2. In this configuration, the LiDAR beam is swung from north to east to south to west and to vertical directions. The wind speed can then be calculated at each measurement height using:  
\[u=\frac{u_{rE}-u_{rW}}{2\cos\phi},\quad v=\frac{u_{rN}-u_{rS}}{2\cos\phi},\quad w =u_{rV}, \tag{1}\]  
where \(u,\ v,\ w\) are wind speed components in west to east, north to south, and vertical directions, respectively. \(u_{rE},\ u_{rW},\ u_{nN},\ u_{rS},\ u_{rV}\) are radial wind speeds along the LOS measured in east, west, north, south, and vertical directions, respectively. Finally, \(\phi\) is the elevation angle and, except for the  
Figure 1: Choshi offshore wind energy test facility. (a) Google map, (b) picture of wind turbine and the met mast tower. vertical scan, it is set to 62\({}^{\circ}\). Note that some LiDARs in DBS mode do not perform vertical scans and instead compute the vertical velocity from the following relation:  
\[w=\frac{u_{rE}+u_{rN}+u_{rW}+u_{rS}}{4\sin\phi}. \tag{2}\]  
Using the DBS mode, the vertical velocity profiles were collected for a period of four months between March and July of 2016. It should be noted that the scanning speed of the scanning LiDAR is 20 s per cycle, whereas the V1 LiDAR completes one scan cycle every five seconds. Consequently, the number of data collected by the scanning LiDAR is 1/4 th of the data collected by the V1 LiDAR. This is because the range of the scanning LiDAR is 3000 m, while the maximum range of the V1 LiDAR is 186 m, thus requiring a longer processing time for the former. Furthermore, atmospheric conditions (aerosol concentration, presence of cloud, or mist layers) strongly influence the availability of the LiDAR data. Therefore, it is necessary to evaluate how availability influences the quality of measured wind speed. To this end, a 10-min availability of wind speed data is defined as [19]:  
\[\eta=\frac{N_{\text{mes}}}{N_{\text{max}}}\times 100\%, \tag{3}\]  
where \(\eta\) is availability, \(N_{\text{max}}\) is the maximum number of data that the LiDAR can measure in 10 min, and \(N_{\text{mes}}\) is the actual number of data measured by the LiDAR in a 10-min time period. For the scanning LiDAR, \(N_{\text{max}}\) is 140. When \(\eta\) is small, the number of samples for computing the 10-min-averaged wind speed is also small, and this may result in a higher error in the mean wind speed. In addition to its application as a profiling LiDAR with a very high measurement range, scanning LiDAR can also perform conical and vertical slice scans [17]. Figure 3 shows two commonly employed scan modes, i.e., range height indicator (RHI) and plan-position indicator (PPI), of scanning Doppler LiDAR. In the range height indicator (RHI) scan, the azimuth angle is fixed, and the elevation angle is varied to sweep the beam through the vertical slice. In the plan-position indicator (PPI) scan, the LiDAR beam sweeps over a range of azimuth angles, while maintaining the elevation angle at a constant value. Usually, in an RHI scan, high resolution samples are acquired in the direction of the elevation angle, whereas, in a PPI scan, high resolution samples are acquired in the azimuthal direction [20]. Multiples  
Figure 2: Schematic representation of the Doppler beam swinging (DBS) configuration. of such scans by varying azimuth angle for RHI mode (or elevation angle for PPI mode) are necessary to construct a three-dimensional flow field. However, care should be taken in that multiple RHI or PPI scans can result in a significantly low time resolution, thus making it difficult to construct reliable turbulence fields from scanning LiDAR measurements.