# Dynamic Data Filtering of Long-Range Doppler LiDAR Wind Speed Measurements
## 4 Results
### Evaluation of Filtering Based on Staring Measurements
#### 4.1.2 Comparison of LiDAR and Anemometer Velocity Measurements  
In the following section, we quantify the accuracy of all filtering methods. For this we assess the discrepancy of estimated velocities taking into account filtered, unfiltered data and the reference data of the ultrasonic anemometers. We distinguish between the average error, which is defined as the arithmetic mean, and the RMSE. As we mentioned previously the assumption of LiDAR data behaviour is included in every filter. The resulting errors of the following comparison can be seen as a measure of correctness of this filter included LiDAR data behaviour. Because the fixed LiDAR measurements can strictly measure the in-beam directed wind vector, the ultrasonic anemometer data has been projected to the LiDAR measurement geometry. The original anemometer velocity information has been adjusted on the basis on the study of [PERSON] (1966) to compensate the mast wake. Due to the marginal changes of the wind speed magnitude of the low elevation measurement of the LiDAR of \(\theta=0.2^{\circ}\)  
\[1-\cos(0.2^{\circ})=5.48\cdot 10^{-5} \tag{16}\]  
we used the filtered radial line-of-sight velocities of the LiDAR without additional projection to the horizontal plane. By this assumption, the projection of the ultrasonic anemometer is reduced to a single rotation around the z-axis. The index \(lrf\) refers to the LiDAR reference frame, whereas index \(mrf\) stands for the meteorological reference frame. \[\left( \begin{array}{c}u\\ v\end{array} \right)_{lrf}=\left[ \begin{array}{cc}\cos(\gamma)&-\sin(\gamma )\\ \sin(\gamma)&\cos(\gamma)\end{array} \right]\left( \begin{array}{c}u\\ v\end{array} \right)_{mrf} \tag{17}\]  
where \(\gamma=-53.53^{\circ}\) is the directional offset of the LiDAR reference frame and the meteorological reference frame. In advance, we carried out correlations of wind speed time series of each range gate with the ultrasonic anemometer time series to find the closest measurement range gate. The direct comparison of wind speed and the calculation of deviations of the filter associated time series show that all filters behave in a similar manner for the greater part (Figure 12a,b). The CNR threshold and both standard deviation filter did not select all outliers as accurate as the dynamic data and combined filter approaches. High average velocity errors seem to correlate with recognisable peaks in the velocity standard deviation curve (Figure 12a,b), which is an indicator of high scattering in the filtered data. This may occur when the invalid data from the \"comb\"-shaped data distribution (Figure 1) is classified as valid. Figure 11: Absolute error of staring mode measurements in dependency of data availability. Markers represent 10 min values of (**a**) the velocity error and (**b**) the velocity standard deviation. The velocity error and the velocity standard deviation error over the wind direction show high values for several inflow directions (Figure 12c,d). Based on the turbulence intensity distribution from Figure 9 and the standard deviation error from Figure 12d, it cannot be differentiated whether the visible increase between 110-145\({}^{\circ}\) is due to the mast shadow or by the wake of the turbines AV09, AV08, AV12 and AV11. Indicated by peaks of the average velocity error (Figure 12c) close to the theoretical turbine directions we could conclude that these arise by wake shading. Meandering effects, wake-induction-zone interaction, turbine and wind farm circulation could not be taken into account; thus, differences in the turbine positions and the corresponding peaks may occur. The smallest increases can be determined for AV09 in a distance of 2230 m and AV11 (2069 m), whereas significant peaks may be caused by AV10 (1669 m), AV08 (1512 m) and AV07 (916 m). Because AV08 and AV12 are close to each other, we cannot differentiate individual proportion of the wakes to the error. It is surprising that the average error in the mast wake (<145\({}^{\circ}\)) is less for unfiltered LiDAR data than for processed ones.