# Coastal Wind Measurements Using a Single Scanning LiDAR
## 2 Materials and Methods
### Leveling Calibration of the Scannig LiDAR  
It is best to have the scanning LiDAR installed in a perfectly level position, as a tilted device results in differences between the target and the actual measurement points. In particular, a tilt angle in the vertical direction can significantly affect the accuracy of wind speed measurements taken with a scanning LiDAR due to the strong vertical wind shear that exists within the surface layer. The impact of a tilt angle increases linearly with the distance from the device. For instance, a device deployed with a tilt angle of 1\({}^{\circ}\) leads to vertical height errors of 17.5 and 35 m, respectively, at the ranges of 1000 and 2000 m. This will consequently introduce extra uncertainty into the wind speed measurements. Field measurement environments differ from laboratory environments, and it appears difficult to deploy a scanning LiDAR with a tilt angle error of less than 0.1\({}^{\circ}\) (the impact of which can be assumed to be negligibly small), even using extremely precise digital levels. Therefore, a calibration method referred to as hard target calibration (HTC) [19] was used for the leveling calibration. In HTC, the tilt angle is generally estimated by analyzing the carrier-to-noise ratio (CNR) values, which are used for checking the quality of measurements. Generally, the CNR values peak near the device, then decrease as the distance increases. Moreover, it is also known that scanning LiDARs record dramatically higher CNR values when the laser is reflected by obstacles such as a meteorological tower or light house. By using characteristics of the CNR recorded by scanning LiDARs when striking an obstacle, the pitch and roll angles of the device, which are the tilt angles in the x and y directions, respectively, can be estimated from the difference between the actual location of the obstacle and the position detected by the CNR distribution of the scanning LiDAR. After calculating the pitch and roll angles, they are added to the original LiDAR-registered azimuth and elevation angles as an offset. This approach, using the reflection from obstacles, is applicable with fewer constraints over land, but is difficult to apply to offshore wind measurements due to the difficulty of finding suitable targets offshore. Therefore, in the current study, another characteristic of the CNR distribution of the LiDAR was used to estimate the pitch and roll angles misalignment. At the time of installation, we noticed that the CNR appeared to rapidly decline when the laser beam hit the sea surface. Figure 2 shows a snapshot of the CNR distribution obtained from the 100s with an azimuth width of 45\({}^{\circ}\) and for an elevation angle of 0\({}^{\circ}\). The Japanese Local Standard Time (LST), which is +9 hours from UTC, is used in this study. The high CNR values at the x and y positions of 0 and 400 m were due to the reflection from the observational hut on the pier. Much lower CNR values are observed in the upper right region of the figure. As an elevation angle of 0\({}^{\circ}\) was set in this case and no obstacle was present, this must be the result of the laser beam hitting the water surface in this region. From this CNR distribution, we were able to estimate the pitch and roll error using planar fitting, as the horizontal and vertical positions of the LiDAR device are the given information. The equation of the planar fitting is given by  
\[z=x\tan\theta_{x}+y\tan\theta_{y}+z_{0} \tag{1}\]  
where \(z_{0}\) is the deployment height of the 100s (= 11.5 m ASL), and \(\theta_{x}\) and \(\theta_{y}\) are the pitch and roll angles. For the LiDAR installation in the current study, a pitch angle of \(-0.092^{\circ}\) and a roll angle of