# High Spatial and Temporal Resolution Bistatic Wind Lidar
## 3 Validation and Characterisation
### PTB Bistatic Lidar/Sonic Anemometer (CSAT3B) in Turbulent Flow  
In 2019, a comparative measurement between the PTB bistatic lidar and a CSAT3B ultrasonic anemometer mounted on top of a 30 m mast was conducted over flat terrain at the site of the Johann Heinrich von Thunen Institut (the German Federal Research Institute for Rural Areas, Forestry and Fisheries) in Braunschweig, Germany [3]. At this height, the PTB bistatic lidar's measurement volume (diameter \(d=2\) mm and length \(l=50\) mm) is comparable to that of the used sonic anemometer. The PTB bistatic lidar was positioned 9 m away from the mast, and both devices sampled wind velocity data at a rate of 10 Hz over a period of about two weeks. Figure 11 shows the orthogonal linear regressions of the average horizontal wind velocity component \(\overline{u}\), of the fluctuation of the vertical wind velocity component \(\overline{w^{\prime}w^{\prime}}^{1/2}\), and of the shear stress velocity \(u_{*}\). Table 1 shows the corresponding statistical parameters. Figure 10: Results of the 2018 comparative measurement between the PTB bistatic lidar and an LDA in the wind tunnel at PTB’s Competence Center for Wind Energy, showing an average deviation of 0.37% between both devices. In order to verify that the PTB bistatic lidar is free of any angular dependence, an additional sample was recorded at 10 m \(\cdot\) s\({}^{-1}\) (shown in pink) after the PTB bistatic lidar trailer was rotated 90\({}^{\circ}\). Figure 9: Results of the 2016 comparative measurement between the PTB bistatic lidar and the top anemometer and between the monostatic lidar (WindCube) and the top anemometer in _undisturbed flow_ at a measurement height of 135 m, evaluated according to IEC 61400-12-1 using 1 s intervals. The monostatic lidar shows large deviations, while the PTB bistatic lidar’s deviation only increases significantly beyond 1% at very low or very high wind speeds. Both devices showed very good agreement, especially for the fluctuation of the vertical wind velocity component, with a mean deviation of only \(0.017\) m \(\cdot\) s\({}^{-1}\) at an intercept of \(-0.009\) m \(\cdot\) s\({}^{-1}\) and a slope of \(0.989\). There was also good agreement for the average horizontal wind velocity component \(\overline{u}\) with an intercept of \(0.044\) m \(\cdot\) s\({}^{-1}\) and a slope of also \(0.989\). However, at a slope of \(0.973\), the shear stress velocity \(u_{*}\) exhibited a slightly larger deviation from unity. This is demonstrably due to the angular dependence inherent to ultrasonic anemometers. The dynamics of fully developed turbulence in the inertial subrange (an intermediate range of scales within the underlying energy cascade) can be described by certain similarity laws [26]. Specifically, the ensemble cospectrum (spectrum of the cross-correlation of two orthogonal velocity components) follows a \(-7/3\) power law [27]. Figure 12 shows the ensemble cospectra \(Co_{uw}\) between the wind velocity components \(u\) and \(w\) of the PTB bistatic lidar and the CSAT3B sonic anemometer. The PTB high-resolution bistatic lidar is in excellent agreement with the theoretical distribution, showing a drop-off in cospectral power density consistent with the theoretical \(-7/3\) law. However, due to its angular dependence, at higher frequencies, the CSAT3B sonic anemometer deviates significantly from the theoretical distribution. Overall, although both the PTB bistatic lidar and the employed ultrasonic anemometer have proven to be well suited for measurements in turbulent flow, the PTB bistatic lidar is the more favourable option if high precision is desired. This is due to its distortion-free measurement capability, which is free of any angular dependence.