# Dynamic Data Filtering of Long-Range Doppler LiDAR Wind Speed Measurements
## Appendix B Influence of the Averaging and Normalization Time on the Error  
For the investigation of the influence of the averaging interval \(\Delta T\) and the normalisation interval \(\Delta t\) on the error, corresponding combinations were calculated (Figures 18 and A1). We evaluated \(\Delta T\) for 15 s, 30 s, 60 s, 120 s, 300 s and 600 s and \(\Delta t\) for 0.5 s, 1 s, 5 s, 15 s, 30 s, 60 s, 120 s, 300 s and 600 s with a reduced data set. A time interval of 24 h was selected with the focus to represent a balanced ratio of wake and free flow situations. The data was captured from 04.01.2014 7:30 h (UTC) till 05.01.2014 7:30 h (UTC). Even if all other used filters are defined on prescribed time intervals, we have examined these for variable \(\Delta T\). A relation of the non-dynamic data filters to the normalisation time \(\Delta t\) was not given. While the average error and the RMSE behave contrary for the velocity error, there is no clear indication for the velocity standard deviation error. Regarding both implementations of the dynamic filter, it is only possible to derive a suggested parameter set directly from Figures A2a and A3a for the average error. The RMS velocity error reduces with increasing average time. To be able to choose a parameter set from Figures A1 and A2 that fulfil the  
Figure A2: Visualisation of the influence of the normalisation time \(\Delta t\) and the averaging time \(\Delta T\) on the resulting error of staring mode LiDAR data from 04.01.2014 7:30 h (UTC) till 05.01.2014 7:30 h (UTC) from the histogram-based dynamic data filter (**a**) Average velocity error; (**b**) average velocity standard deviation error; (**c**) RMS velocity error and (**d**) RMS velocity standard deviation error. Figure A4: Averaged and normalised error behaviour of the average velocity error, the RMS velocity error, the velocity standard deviation error of **(a)** the histogram-based dynamic data filter and **(b)** the Gaussian kernel based dynamic data filter. Staring mode LiDAR data from 04.01.2014 7:30 h (UTC) till 05.01.2014 7:30 h (UTC) form the basis for this calculation. * _[PERSON] et al. (1963)_ [PERSON]; [PERSON] The Laser and its Application to Meteorology. _Bull. Am. Meteorol. Soc._**1963**, _44_, 564-575. * [PERSON] (1997) [PERSON]; [PERSON] Quality control and flux sampling problems for tower and aircraft data. _J. Atmos. Ocean. Technol._**1997**, _14_, 512-526. [CrossRef]
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