## 8 Selected Results of Hub Height Winds  
One of the objectives of the NORSEWInD array of wind lidars was to evaluate the ability of numerical models to predict winds at hub height (~100 m) and, in particular, the vertical wind speed profile, since the final wind atlas was merely produced from the model outputs. Therefore, there was a need to compare the model results with observations on places where the wind resource at such levels had never been measured. Although most wind resource assessment software, such as the Wind Atlas Analysis and Application Program (WAsP) [29], estimate the wind turbine/farm energy production based on wind speed distributions at hub height and with that respect the outputs of a mesoscale model are rather good [30], the mesoscale models have shown difficulties to reproduce the wind profiles and, therefore, the vertical wind shear [31]. The latter becomes more important for wind turbines with large rotor areas as the difference between the below and above hub height winds might have a great impact on the loads and energy yield. Thus, we decided to concentrate on the analysis of the vertical wind shear observed by the wind lidars. All NORSEWInD wind lidars were able to observe winds at 100 m and higher. Most of them were WindCube systems (Table 4), _i.e._, pulsed lidars; thus the availability of data decreases with height (Figure 5). In order to maximize the amount of data we decided to estimate the wind shear from the two closest wind speed observations to the 100 m height. The wind shear is estimated as the value of the shear exponent \(\alpha\) of the power law:  
\[\frac{u_{1}}{u_{2}}=\left(\frac{z_{1}}{z_{2}}\right)^{\alpha} \tag{3}\]  
where \(u\) is the magnitude of the wind speed, \(z\) the height, and 1 and 2 referred to two levels. \(\alpha\) can then be estimated as:  
\[\alpha=\frac{z}{u}\left(\frac{du}{dz}\right)\approx\frac{z}{u}\left(\frac{ \Delta u}{\Delta z}\right) \tag{4}\]  
Equation (4) is important because one can relate \(\alpha\) to Monin-Obukhov similarity theory and will find that (see [8,32]):  
\[\alpha=\frac{\Phi_{m}}{\ln\left(\frac{z}{z_{0}}\right)-\psi_{m}} \tag{5}\]  
where \(z_{0}\) is the surface roughness length and \(\Phi_{m}\) is the dimensionless wind shear, which is a function of the dimensionless stability parameter \(z\)/\(L\) and also some sort of the derivative with respect to height of \(\psi_{m}\) and \(L\) is the Monin-Obukov length. Based on Equation (5), we therefore expect that within the surface layer \(\alpha\) is a function of height and will vary as \(z_{o}\) increases with wind speed (among others) over the sea and \(\psi_{m}\) depends on the atmospheric condition. The relationship of \(\alpha\) and stability was investigated from offshore mast data Fino-1 at heights below 80 m and compared to Large Eddy Simulation results [33] and the dependence of the power-law exponent on surface roughness and stability in a neutrally and stably stratified surface boundary layer was described by [34]. Recently [35] compared one year of lidar data to Fino-1 meteorological data, and [36] studied wind shear from the wind lidar observations at Fino-1 as a function of stability, and [37] compared data to meteorological data in upland terrain. Figure 12 illustrates the distribution of \(\alpha\) at a height close to 100 m, estimated using Equation (4), for all the NORSEWInD nodes where data is available in the database. The graph is based on 10-min observations from [PERSON] (9034), [PERSON] (5347), [PERSON] (94,848), [PERSON] (28,572), [PERSON] (20,243), [PERSON] (47,317) and [PERSON] (59,908), the number of observations is given in brackets. There has not been any filtering related to the data in the sense that we have not used for example a minimum or maximum threshold of wind speed to be analyzed.