# Can LiDARs Replace Meteorological Masts in Wind Energy?
## 3 Comparison of LiDAR Measurement with Sonic and Cup Anemometer
### Mean Wind Speed and Turbulence Intensity
Figure 5: Comparison of 10-min average horizontal wind speeds at 40 m height. **(a)** Sonic anemometer and cup anemometer; **(b)** Sonic anemometer and V2 profiling LiDAR. Figure 6 presents a comparison of the standard deviation of the horizontal velocities measured by the cup anemometer and the V2 LiDAR against the measurements collected by the sonic anemometer at 40 m height. The variation in the comparison of the standard deviation is higher than that for the mean wind speed. This larger difference comes from the definition of the standard deviation (\(\sigma\)), which is the square root of the second central moment of velocity, i.e.,  
\[\sigma=\sqrt{\frac{1}{N_{\mathrm{T}}}\sum_{i=N_{\mathrm{t}}}^{N_{\mathrm{t},T} }(V_{i}-\overline{V})^{2}}=\sqrt{\frac{1}{N_{\mathrm{T}}}\sum_{i=N_{\mathrm{t} }}^{N_{\mathrm{t}+T}}V_{i}^{2}-\overline{V}^{2}}. \tag{4}\]  
The square of the velocity fluctuation in \(\sigma\) means the differences between the \(\sigma\) measured by the two devices will also be larger compared to the mean wind speed. The slope and offset of the regression line from the cup and sonic anemometers comparison are 0.91 and 0.001 respectively, while \(R^{2}\) is 0.99. As it is clear from Figure 6b, the standard deviation from the LiDAR has a larger variation compared to the sonic anemometer; the slope, offset and \(R^{2}\) are 0.91, 0.107 and 0.952 respectively. The variation in the LiDAR and the sonic anemometer comparison increases with increasing \(\sigma\). Earlier studies also showed the same degree of difference or larger difference between LiDAR and conventional wind speed sensors like cup or sonic anemometers (see e.g., [PERSON] [14; 15]). However, the measurement periods in earlier studies were very short-from a few days to one or two months. It should be noted that statistics related to uncertainty obtained from Linear regression are not very meaningful for a long term comparison. For example, the relation for the regression line indicates that the LiDAR should under-estimate the \(\sigma\) values when compared against sonic anemometer measurements larger than 1.19 m/s. However, the distribution is spread over a large band. This may be because of the variety of atmospheric conditions--including the stability--that the site experiences during a long-term comparison as performed in the current study. Thus, the least square fitting or the coefficient of determination are not sufficient to quantify the performance of LiDAR for their long term deployment. Figure 7 presents the distribution of turbulence intensity as a function of mean wind speed. Turbulence intensity (\(I\)) is defined by  
\[I=\frac{\sigma}{\overline{V}}. \tag{5}\]  
Measurements from all three instruments show a similar trend; the higher turbulence intensities occur during lower wind speeds and they gradually decrease with increasing mean wind speed. Furthermore,  
Figure 6: Comparison of standard deviation at 40 m height. (**a**) Sonic anemometer and cup anemometer; (**b**) Sonic anemometer and V2 profiling LiDAR. variation of the turbulence intensity is larger when the wind speed is low. Variation is particularly large for the cup anemometer measurements with too many points close to or even larger than \(I=1.0\), but it should be noted that the measurements from cup anemometer as well as from LiDAR are not very reliable when the wind speed is low. Regarding the LiDAR, the turbulence intensities are mainly concentrated below \(I=0.8\) even at the lowest mean wind speed. Although not presented explicitly in the paper, the 90 th percentile line of the LiDAR data shows better agreement than that of the cup anemometer data when compared against the sonic anemometer measurement. Figure 7d shows the bin-averaged turbulence intensities for mean wind speed bins of size 1 m/s, and Figure 7e shows the number of turbulence intensity data per bin. Among the three instruments, the cup anemometer has the lowest turbulence intensity for almost all wind speed bins.