# Carrier-to-Noise-Threshold Filtering on Off-Shore Wind Lidar Measurements
## 3 Data Analysis
### Wind Speed Dependence on Carrier-to-Noise-Ratio
For the wind power density (Figure 5b) the effect is even more pronounced than for the wind speed, being 32% larger for a CNR threshold value of -22 dB compared to -35 dB when the threshold is imposed on the entire wind profile between 126 m and 626 m and 18% larger when the CNR threshold is applied to the observations at 126 m only. The wind power density was calculated by use of the Wind Atlas Analysis and Application Program (WAsP) [3] using an air density of 1.225 kg m\({}^{-3}\). For wind energy assessment applications the Weibull distribution is commonly used to describe the variability of the wind speed. It is reported in [31] that filtering the wind speed observations with a CNR threshold also affects the shape parameter in the Weibull distribution. To investigate if any wind direction dependency exists in the general relationship between the mean wind speed and the CNR threshold value, the mean wind speed was plotted for Northerly (325\({}^{\circ}\)-45\({}^{\circ}\)), Easterly (45\({}^{\circ}\)-135\({}^{\circ}\)), Southerly (135\({}^{\circ}\)-225\({}^{\circ}\)), and Westerly (225\({}^{\circ}\)-345\({}^{\circ}\)) wind directions (Figure 6). The relationship is illustrated for wind lidar measurements at 126 m (full lines) and the concurrent cup- anemometer observations at 90 m (dashed lines). A general tendency for the mean  
Figure 4: Wind speed distributions for (**a**) 126 m and (**b**) 626 m height. Red line represents the distribution for CNR \(>\)\(-\)22 dB and black for CNR \(>\)\(-\)35 dB, respectively. Note that the curves that are filtered with CNR \(>\)\(-\)22 dB (red) contain less data than the curves for CNR \(>\)\(-\)35 dB (black). wind speed to decrease for decreasing CNR values can be observed in all the wind direction sectors, but for the eastern sector, the effect is not as pronounced as in the other sectors. High wind speeds in the western sectors and low wind speed in the eastern sector are typical for the meteorological conditions over the North Sea. It can be observed from Figures 5 and 6 that the mean wind speed decreases as the CNR threshold decreases from -17 dB to about -29 dB and then remains near constant as the CNR threshold is further decreased. This general behavior is observed in the wind lidar measurements at both 126 m, 626 m and for the concurrent cup anemometer observations at 90 m (Figure 5) as well as for all the wind direction sectors (Figure 6). Figure 5: Panel (**a**) shows the mean wind speed plotted as a function of the CNR threshold. Full lines illustrate the relationship when filtering the measurements at 126 m (black), the concurrent cup anemometer measurements at 90 m (red), the measurements at 626 m (blue) with the CNR threshold value, and the full brown line when the CNR threshold is imposed at all levels between 126 m and 626 m. The uncertainty corresponding to the standard error of the mean wind speed is shown by dashed lines. The panel (**b**) illustrates the wind power density at 126 m height as a function of the CNR threshold value. The meaning of the line colors is similar in both panels. There are no measurements smaller than -35 dB which corresponds to the factory setting threshold value. Figure 6: Mean wind speed as a function of the CNR threshold value for separate wind sectors as measured with the wind lidar at 126 m height (full lines) and the cup anemometer at 90 m height (dashed). Northern sector (325\({}^{\circ}\)–45\({}^{\circ}\), blue lines), Easterly sector (45\({}^{\circ}\)–135\({}^{\circ}\), red lines), Southerly sector (135\({}^{\circ}\)–225\({}^{\circ}\), green lines) and Westerly sector (225\({}^{\circ}\)–345\({}^{\circ}\), black lines). Further investigation of the effect of the CNR threshold is performed by comparing the wind speed measured by the cup anemometer at 90 m with the wind lidar measurements at 126 m. Figure 7 shows the standard deviation of the difference between cup-anemometer (90 m) and the wind lidar (126 m) measurements of the wind speed.