## 4 Remote Sensing Techniques
### Doppler Lidar
For turbulence measurements, Doppler lidar scanning frequency and scanning strategies pose limitations, and methods to estimate turbulence parameters have been  
Figure 4: WindCube V2 Doppler lidar by Leosphere measures along five lines of sight, one vertical and four inclined with a fixed zenith angle \(\varphi\) = 28\({}^{\circ}\) (elevation angle \(\alpha\) = 62\({}^{\circ}\)) and with an azimuth angle of \(\theta\) = 90\({}^{\circ}\) between the inclined beams. Using radial velocities \(v_{\pi}\) along at least three different beams, it is possible to derive the three-dimensional wind vector \((u_{1},u_{2},u_{3})\)[79; 84]. developed [77]. The same limitations apply also for wind gust measurements. [PERSON] et al. (2017) [39] used a short-range (measurements up to 300 m height) pulsed Doppler lidar to obtain wind gust profiles. The DBS scanning technique consisted of five beams, one vertical and four inclined with \(\theta=90^{\circ}\) azimuth angles and an elevation angle of \(\alpha=62^{\circ}\). The resolution of wind speed observations was 3.8 s, which is the time it takes to measure all five beams. The observed wind speed maxima from the Doppler lidar were clearly higher than those from sonic anemometers at a nearby meteorological mast (the difference between the blue and black curves in Figure 5). [PERSON] et al. (2017) [39] developed a scaling method to correct for this positive bias, which is shown as a red curve in Figure 5. This novel method not only scales the lidar gusts, but also provides estimates for wind gusts with variable gust durations including the shorter durations (of the order of a second), which are beyond the limits of the lidar measurement frequency. The input parameters for the scaling method include the wind gust speed, mean wind speed and the standard deviation of the horizontal wind speed from the lidar. The wind gust speed is calculated as the maximum of the moving-averaged horizontal wind speed. For the WindCube V2 Doppler lidar used by [39], an average over five samples (corresponding to gust duration \(t_{g}=19\) s) was found to be adequate, but this depends on the lidar type and the scanning technique and must be tuned separately for each lidar setup. Using Doppler lidar data only for the scaling method will provide reasonable gust factor estimates, with a small positive bias (about 0.03) and RMSE of about 0.06, but it is possible to further reduce this bias by better estimates of the velocity variance. The improved performance of the scaling method was most noticeable in turbulent daytime conditions, but it also improved the estimation of gustiness in precipitating conditions, which are a challenge for Doppler lidars. In the case of Doppler lidars, data quality is traditionally assessed based on the Carrier-to-Noise-Ratio (CNR). However, [PERSON] et al. [39] found that better results were obtained with a spike detection algorithm typically used for sonic anemometer data. The algorithm effectively removes outliers (including unrealistically high values) that may arise for example from incorrect instrument's  
Figure 5: Median peak factor as a function of gust duration as observed by sonic anemometers (black), lidar (blue) and the theoretical peak factor (red) derived from the parallel measurements from lidar and sonic anemometers. All peak factors are normalized by the standard deviation of the wind speed from the sonic anemometers. The standard error of the mean is given by the shadowed region underlying the points in each median curve. Redrawn with permission from [39]. internal calculation of CNR [87]. The outliers (the spikes) were replaced by linear interpolation using neighboring non-spike values. An example of the wind gust speed and the gust factor measured by a Doppler lidar during a two-day period is shown in Figure 6. During the first day, good data were obtained through the entire measurement range, but on the second day, when there were rainy conditions, the data availability was limited.