# Carrier-to-Noise-Threshold Filtering on Off-Shore Wind Lidar Measurements
## 3 Data Analysis
### Wind Speed Dependence on Carrier-to-Noise-Ratio  
Contrary to measurements by a cup-anemometer, wind speed measurements performed by a wind lidar are assigned a quality indicator expressed as the Carrier-to-Noise-Ratio. Reference [31] pointed out a consequence of the choice of a CNR threshold value on the wind observations; increasing the threshold value increases the estimated mean wind speed. The effect was found over land, in coastal areas, and off-shore. The findings of Reference [31] will be extended to consider the effect that filtering of the data with a CNR threshold value has on the distribution of the wind speed and direction as well as the wind power density; the latter indicates how much power is available for conversion to energy by a wind turbine. To investigate how the filtering effect of the CNR threshold value acts on the wind speed data-series, Figure 3a shows the cumulative probability distribution of the wind speed observations at 126 and 626 m height. It can be observed that the wind-speed for the factory setting threshold value of \(-35\) dB is always smaller as compared to \(-22\) dB over the whole cumulative distribution at both heights. The effect is also illustrated for low, medium, and high wind speeds exemplified by the percentiles. This is illustrated in Figure 3b, showing the 25%, 50%, and 75% percentiles of the wind speed profiles for CNR threshold values of \(-22\) dB and \(-35\) dB, respectively. It can be observed that the profile of the wind speed is persistently larger for a CNR threshold value of \(-22\) dB when compared to \(-35\) dB. Figure 3: Panel (**a**) shows the cumulative distributions of wind speed observations. The full lines represent observations for a CNR threshold value of \(-35\) dB, and dashed lines for \(-22\) dB. Black lines represent measurements from 126 m height, and red lines from a height of 626 m. Panel (**b**) illustrates profiles of wind-speed percentiles for CNR \(>\)\(-35\) dB (diamonds) and CNR \(>\)\(-22\) dB (squares). The lines and symbols represent: blue 25%, black 50%, and red 75% percentiles. Solid symbols represent wind lidar measurements and open symbols mast observations. To further illustrate the effect on the choice of CNR threshold value, Figure 4 shows the wind speed distribution at 126 and 626 m height. It can be observed that the wind speed distribution is shifted towards higher values when applying the \(-\)22 dB threshold value as compared to a \(-\)35 dB threshold, thus, the filtering does not just remove low wind speed values but operates on all wind speeds in such a way that the wind speed distribution is shifted towards higher values. The effect can be observed at all heights covered by the campaign (50 to 626 m) and is here illustrated for heights of 126 and 626 m.  
Figure 5 further illustrates the sensitivity of the mean wind speed and power density to the CNR threshold value. The effect is illustrated in Figure 5 a showing the mean wind speed (full lines) and the corresponding uncertainty (dashed lines) as a function of the CNR threshold value. The brown lines are when the CNR threshold is imposed on the full profile of lidar measurements up to 626 m, the other lines illustrate the relationship when the CNR threshold is not imposed on the full profile but only at the wind lidar measurements at 126 m (black), 626 m (blue), and the concurrent wind speed measurements from the cup anemometer at 90 m (red). The uncertainty is here taken as the standard error of the mean wind speed and is illustrated by the dashed lines above and below the mean wind speed. As pointed out by [31] for, e.g., lidar measurements at 126 m, being a typical height of a wind turbine, the use of a CNR threshold value of \(-\)22 dB in this off-shore case resulted in an overestimate of the mean wind speed of 12% for the full profile and 9% as compared to a CNR threshold value of -35 dB.