# Generic Methodology for Field Calibration of Nacelle-Based Wind Lidars
## 5 LOS Velocity Calibration and Uncertainties
### Measurement Uncertainties Assessment Procedure
#### 5.6.4 Uncertainty Sources and Budget  
The uncertainty evaluation of the cup-measured reference speed \(V_{hor}\) follows the IEC-61400-12-1 standard (Annex E in [14]). It should be mentioned that most of the numeric values used in this standard are empirical and somewhat arbitrary. For the LOS velocity calibration procedure, the HWS uncertainty sources are:  
1. **Wind tunnel calibration uncertainty**: \[u_{cal}=\sqrt{u_{cal,1}^{2}+\left(\frac{0.01}{\sqrt{3}}V_{hor}\right)^{2}}\] (12) where \(u_{cal,1}\) is the uncertainty specified by the calibration certificate for a coverage factor \(k=1\). We used \(u_{cal,1}\approx 0.025\) m\(\cdot\)s\({}^{-1}\). The 2 nd term is due to the variability of cup anemometers calibration results for _Measnet_ accredited wind tunnels. _Measnet_ requires the tunnels to be within \(\pm 1\%\) of each other. Hence a 1% uncertainty is added with an assumed rectangular--or uniform--distribution of uncertainty yielding the \(1/\sqrt{3}\) factor. 2. **Operational--also called classification--uncertainty**: \[u_{ope}=\frac{k_{class}}{\sqrt{3}}\cdot(0.05+0.005V_{hor})\] (13) where \(k_{class}\) is the anemometer's classification number characterising the systematic deviations due to environmental conditions, e.g., angular response, turbulence, temperature (influence on bearing friction), etc. The cup anemometer used in this study is of type _'Thies First Class Advanced'_ which has a class of 0.9A (\(k_{class}=0.9\)). 3. **Mounting uncertainty**: \[u_{mast}=0.5\,\%\cdot V_{hor}\] (14) related to the mounting of the sensor on the mast. The 0.5 % uncertainty is the default value for top-mounted instruments suggested in the revision of the IEC 61400-12-1. The only source of **wind direction uncertainty** from the sonic anemometer is the calibration. Indeed, the LOS direction is evaluated in the frame of reference of the wind direction sensor (see Section 5.4). The North mark and boom orientation uncertainties are thus irrelevant. At \(k=1\), the calibration certificates specify a wind direction uncertainty of  
\[u_{\theta}=0.4^{\circ} \tag{15}\]  
Uncertainty sources in the calibration measurement process are:  
1. LOS direction uncertainty, related to the statistical evaluation of \(\theta_{los}\) (Section 5.4) and roughly estimated to: \[u_{\theta_{los}}=0.1^{\circ}\] (16)
2. Uncertainty of physical inclination angle characterising the uncertainty of the angle used in the vertical projection of the HWS in (Equation (2)) and estimated via the inclinometers' calibration (see [4; 5]) to: \[u_{\varphi}=0.05^{\circ}\] (17)
3. Vertical beam positioning uncertainty: characterises how close to the reference instruments height the beam is positioned. Here, modelling the vertical shear profile with the power law, using a shear exponent \(\alpha_{exp}=0.2\), a height uncertainty \(u_{H}=10\,\)cm at \(H_{ref}=8.9\,\)m, the wind speed uncertainty due to the height error is: \[u_{pos}=\alpha_{exp}\cdot\frac{u_{H}}{H_{ref}}\cdot V_{hor}\approx 0.23\%\cdot V _{hor}\] (18)
4. Inclined beam and range uncertainty: practically, the inclined beam implies that the laser light travels, within the probe volume, through a range of heights. The lidar thus senses different wind speeds if there is a wind shear. Additionally, the range uncertainty along the LOS moves the probe volume's center slightly away from the reference instruments' height. A model of this uncertainty can be found in Annex A of [18]. Configuring this model with the 5B and ZDM lidars setup in Hovsore and a conservative 5 m range uncertainty, we obtained respectively: \[\left\{ \begin{array}{l}u_{inc,5B}=0.052\%\cdot V_{hor}\\ u_{inc,ZDM}=0.104\%\cdot V_{hor}\end{array} \right.\] (19)
5. Spatial separation uncertainty: the spatial separation between the two reference sensors infers an uncertainty whose magnitude increases with the separation distance. In our case, the two masts are 5 m apart and the terrain is flat. The spatial separation effects can reasonably be neglected.