# 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
This could be indicating that the filters sort out physical reasonable values. While all filters have increased errors in determining the correct velocity standard deviation, the two-sigma standard deviation filter produced noticeably low values in this region. The increase of the errors for this inflow range may be explained due to different measuring volumes. While the anemometer is exposed to increased fluctuation directly in the mast wake, the LiDAR measures a mixed  
Figure 12: Behaviour of the 10 min averaged filtered staring mode measurements of (**a**) the projected wind speed over time; (**b**) the standard deviation over time; (**c**) average wind speed error over wind direction; (**d**) average standard deviation error over wind direction. Vertical dashed lines indicate the wind direction of possible wake shading of the anemometer on FINO1 based on geometrical correlations. velocity of free and affected flow within the elongated volume. It can further be seen from Figure 12c,d that the LiDAR is not capable of capturing perpendicular wind speed components (216\({}^{\circ}\) inflow direction) in a good manner. According to the errors shown in Figure 12c,d an undisturbed inflow occurred from 180\({}^{\circ}\) to 210\({}^{\circ}\) and from 220\({}^{\circ}\) to 265\({}^{\circ}\). In Figure 13a,b linear correlation of the ultrasonic anemometer data and the LiDAR data has been done for the velocity and the standard deviation. Here, all data are presented without a containment of wind direction. Therefore, these results include situations where the ultrasonic anemometer, as well the LiDAR measurement is in free flow, in wake flow of the mast and in the wake of the wind farm. We observe regression slopes in the range from 0.866 to 0.974 and regression coefficients from 0.78 to 0.9. These relatively low coefficients are driven by outliers, which are not very frequent, but have a large deviation. These wrong data points evidence in our opinion the discrepancy between point and volumetric flow interrogation in complex flows. In effect, these large deviations occur for data in the mast wake predominantly. In the study of [PERSON] et al. (2016) a subset of these data, specifically restricted to free flow, showed a very high correlation. These results are confirmed here as shown in Table 12. Since this is mainly a physical effect, it is impossible for any of the filters to reduce the error. It is to be noted that the large deviations concentrate in a certain wind speed range. This is due to the wind conditions during the measurement period, where wind speeds above 6 m/s were found very often for wind directions where the ultrasonic anemometer was shaded by the mast, whereas lower velocities occurred in free flow conditions. Figure 13: Behaviour of the 10 min averaged filtered staring mode measurements of (**a**) the projected wind speed over time, (**b**) the standard deviation over time, (**c**) average wind speed error over time, (**d**) standard deviation error over time. While the velocities correlate quite well, the regression of the standard deviation is widely spread for the different filters. All linear regression parameters are reported in Table 2. In combination with Figure 13a,b, Figure 13c,d extend the linear regressions with an uncertainty interval equal to the RMSE. For better visibility, we omit these ranges in Figure 13a,b, and plotted them separately in Figure 13c,d. It can be recognized that ultrasonic anemometer data in a wide range around 10 m/s is associated with high deviations of LiDAR velocities (Figure 13a). A corresponding behaviour is also present in Figure 13c. Even Figure 13c,d give the RMSE for specific velocities respectively velocity standard deviations a conclusion about the overall performance needs to consider the error frequencies in Figure 14.  
In general, it can be said that the application of the combined and dynamic filter approaches leads to smaller errors of the velocity and velocity standard deviation compared to other filters.