# Dynamic Data Filtering of Long-Range Doppler LiDAR Wind Speed Measurements
## 4 Results
### Evaluation of Filtering Based on Staring Measurements  
For the error calculation of ultrasonic anemometer data and the LiDAR data, the initial question arises how different measurement concepts can be mutually compared. The metric used to validate the new and other filters is based on average velocities. We present also results for the velocity standard deviation for sake of completeness. However, we consider that the data available is not adequate for drawing conclusions in our ability to derive turbulence properties. Although both devices measure within a certain volume--in an idealised case, the same volume--this differ in spatial dimensions. While we estimate the ultrasonic measurement volume from technical drawings as a cylinder with \(V_{USA}\approx\pi\cdot\left(0.24\text{ m}\right)^{2}\cdot 0.48\text{ m}\), the corresponding equivalent volume for the LiDAR laser beam of the Leosphere device in the here used configuration is approximately \(V_{L}\approx\pi\cdot\left(0.1\text{ m}\right)^{2}\cdot 60\text{ m}\). By this, the LiDAR measurements use around 22 times the ultrasonic anemometer volume. If we consider that the individual ultrasonic transmitter and receiver heads measures on the surface shell of this cylinder, the ratio \(\frac{V_{L}}{V_{USA}}\) is in the magnitude from 10 to 100. The effect of spatial averaging of LiDAR measurements on the variance of the line-of-sight measurements and the associated challenge of deriving turbulent properties, in a substantial scientific manner, from LiDAR measurements is discussed in a plurality of publications. First, LiDARs filter out high frequencies depending on the effective sampled volume. This distorts the velocity variance. Moreover, [PERSON] and [PERSON] [28] show that atmospheric conditions play an important role affecting the ability to measure turbulence. [PERSON] and [PERSON] [28] published an extensive review of turbulence measurements since the beginning of LiDAR based remote sensing in which they highlight that the variance is very dependent on atmospheric conditions. We conclude from the work of [PERSON] [9] and [PERSON] and [PERSON] [28] that an adequately determination of the wind speed variance is possible, with a comprehensive approach including raw LiDAR data. Such treatment was out of the scope of this work, wherefore we focused in the following inter-comparison of the LiDAR filter on the average wind speed. To minimise the different volume averaging effects and to comply with other comparisons of LiDAR measurements and met mast anemometers [29; 30; 31; 32; 33], we applied filtering in clustered temporal segments of \(\Delta T\ =10\) min. We have deliberately refrained a data availability pre-filtering for the calculation of the 10 min average velocity and velocity standard deviation. This is intended to create a greater transparency to the overall filter behaviour. We evaluated the effect of variable averaging times for all filters with a smaller data set from the already presented campaign. The impact on the total error in combination with the normalisation time \(\Delta t\) for the dynamic data filters can be seen in the Appendix B. We conclude from Figures 13-13 that the results of the dynamic data filters vary depending on the used parametrisation. The parameters should be adjusted with respect to the purpose of data analysis and the desired error calculation, as can be seen in the Appendix C.  
be seen in Figure A3. For a better readability, we opted for one parameterisation each. The selection of the validity value \(\
u\) regarding the error behaviour in Appendix A was chosen as a compromise between the average error and the root-mean-square error (RMSE) of each, velocity and velocity standard deviation. The histogram-based dynamic filter has been used with a lower filter threshold of 0.02% and an upper filter threshold of 0.29%, through the Gaussian kernel based implementation was set to a validity level of 16.94%. In total 4325 10 min time intervals have been processed for the following results.