# Dynamic Data Filtering of Long-Range Doppler LiDAR Wind Speed Measurements
## 4 Results
### Evaluation of Filtering Based on Staring Measurements
#### 4.1.1 Data Availability  
We define the here titled data availability as the ratio of the amount of data for one point in space of the filtered to the unfiltered LiDAR data within a time interval:  
\[\lambda=\frac{n_{u_{rfiltered}}}{n_{u_{rawfiltered}}} \tag{15}\]  
Only 10 min time intervals were considered that amounts to the theoretically number of measurement points. A data availability of 100% within a time interval implies that all measurement points are marked as valid. To calculate the data availability, a spatial based comparison (Figure 10) for all ranges and the corresponding closest volume to the ultrasonic anemometer has been made and was summarised in Table 1. For the data availability calculation we considered only in non-overlapping time intervals of 10 min. While all filters show a consistent mean result above 75% data availability, the behaviour with respect to the range is dependent on the type of filter. All filters using the CNR-threshold approach show the same decay in availability related to the distance dependency of \(\alpha\). With the decrease of the CNR over the distance, temporal fluctuations of \(\alpha\) are partially filtered out if they exceed the CNR-threshold. By this, the data availability decreases continuously. We assume that the here shown behaviour of all CNR-threshold containing filters is similar to the theoretical and empirically stated data availability decay with increasing distance described by [PERSON] (1997). Figure 10: Data availability of staring mode measurements for different filter methods. (**a**) time dependent behaviour for range at 2864 m and (**b**) averaged data availability over all ranges. The dashed line marks the distance of the anemometer at FINO1. It appears that the combined filter by [PERSON] et al. (1998) does not produce any visible deviation from the CNR-threshold filter even when they applied an addition iterative standard deviation filter that, when applied alone, provides an availability of 98.5%. It seems that as well the filter approach by [PERSON] et al. (2017) leads to a higher data availability compared to a sequential calculation from the individual availabilities. The output of the two-sigma standard deviation filter exhibits an overall availability of over 95% for the entire distance and increases slightly with more distant range gates. Because it is based on the deviation around the average of wind speed, this behaviour can be explained with the geometric correlation of the measurement setup. From a distance of approximately 2100 m, the laser beam measured outside the wind farm where the flow was not affected by wind turbine wakes. In contrast, the data availability of the iterative standard deviation filter decreases by 1% over distance. It is shown that the interquartile-range filter produces a smaller availability of 94% compared to 99.3% in theory for normal distributions. This may be an indication that the data distribution within the 10 min intervals does not exactly follow a normal distribution. If we neglect all filters that do not take into account the distance dependency of \(\alpha\), we can compare all CNR-based filter with the dynamic data filters. It can be seen that the histogram-based filter results in a nearly constant data availability of 90%. The kernel-based dynamic data filter shows a drop of data availability in closer distances followed by a constant slight decrease over the distance. From this behaviour it cannot be confirmed that the data availability of the dynamic data filters follow the decay stated by [PERSON] (2014). We assume that the main reason for this is based on the temporal and spatial normalisation of the LiDAR data. By normalising \(\alpha\) with the most probable value \(\overline{\alpha\;_{d}^{\;t}}\) within the normalisation interval, measurement points close to \(\overline{\alpha\;_{d}^{\;t}}\), which would exceed the CNR-threshold, are marked as valid and contribute to high data availability.