## 6 Flow Distortion due to Offshore Platform and Terrain
As shown in Table 6 the height to which the platforms caused distortion was not the same. Horns Rev 2, a transformer platform, caused distortion in the magnitude of the velocity vector in the horizontal plane, \(U_{mag}\), up to a height equivalent to that of the rig whereas Schooner created distortion \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & & \multicolumn{6}{c}{**Height above Lidar in m**} & \multicolumn{2}{c}{**Height AMSL for**} \\  & & \multicolumn{6}{c}{**(Height Normalized by Rig Height)**} & \multicolumn{2}{c}{**2.5\% Free-Stream**} \\ \hline \multirow{3}{*}{**Platform**} & **Rign** & **Lidarm** & **Wind Tunnel** & \multicolumn{2}{c}{**CFD Results**} & \multicolumn{2}{c}{**CFD Results**} \\ \cline{3-10}  & **Height** & **Height** & **Point** & \multicolumn{2}{c}{**Point**} & \multicolumn{2}{c}{**Lidar**} & \multicolumn{2}{c}{**Lidar**} \\ \cline{3-10}  & **(m)** & **(m)** & \(u\) & \(u\) & \(\theta\) & \(u\) & \(\theta\) & \(u\) & \(\theta\) \\ \hline
**Babbage** & 42 & 42 & 33 (0.8) & & & & & 75 & \\
**Beatrice** & 62 & 42.5 & 64 (1.0) & 30 (0.5) & \(>\)64 (1.0) & 34 (0.5) & 59.5(1.0) & 76.5 & 102 \\
**HornRev 2** & 26 & 26 & 30 (1.2) & 44 (1.7) & 57 (2.2) & 25 (1.0) & 55 (2.1) & 50 & 80 \\
**Jacky** & 28 & 28 & & 20 (0.7) & 19 (0.7) & 10 (0.4) & 18 (0.6) & 38 & 46 \\
**Schooner** & 38 & 36.25 & 24 (0.6) & 24 (0.6) & 35 (0.9) & 9 (0.2) & 24 (0.6) & 39 & 54 \\
**Taqa** & 31.4 & 30 & 37 (1.2) & 30 (1.0) & 36 (1.1) & 33 (1.1) & 27 (0.9) & 63 & 57 \\
**Utsira** & 26 & 26 & & 108 (4.2) & 192 (7.4) & 150 (5.8) & 300 (11.5) & 176 & 326 \\ \hline \end{tabular}
\end{table} 
Table 6: Height above lidar installation level and AMSL for undisturbed flow measurement from wind tunnel and CFD point measurement and by lidar based simulation from CFD where u is the magnitude of the wind velocity and \(\theta\) is flow angle in the horizontal plane. The values in the columns are height in meters AMSL at which this measurement is unaffected (\(\pm\)2.5% free-stream) by distortion. Numbers in brackets are the height at which distortion is negligible non-dimensionalised by the platform height. up to 0.2 times the rig height only. The extent to which distortion was created appeared to be a function of the solidity of the rig. The open lattice type structures created significantly less distortion than the more solid structures such as Horns Rev 2. It should be noted that the CFD simulations indicated that the lidar measurements were less susceptible to flow distortion than a point measurement at the same height. Also of note was the height to which the island of Utsira created distortion. From the simulation of the lidar measurements in the distorted flow field it was possible to calculate correction factors and addends that could be applied to the data measured by the lidars situated on the offshore platforms. To correct the magnitude and direction of the free stream velocity vector in the horizontal plane, \(u\) and \(\theta\) respectively, to the undisturbed free stream values Equations (1) and (2) were derived. In the simulation the values of \(u\)-free stream and \(\theta\)-free stream in the undisturbed flow were known and the measurements made by a lidar, \(u\)-lidar and \(\theta\)-lidar in the distorted flow field could be determined from the lidar simulation. Substituting these values into Equations (1) and (2) allowed the corrections, _cff\({}_{u}\)_ and _cff\({}_{\theta}\)_ to be determined. \[\mathrm{u_{free\ stream}} = \mathrm{cff_{u}}\times\mathrm{u_{lidar}} \tag{1}\] \[\theta_{\mathrm{free\ stream}} = \theta_{\mathrm{lidar}}+\mathrm{cff_{\theta}} \tag{2}\]  
Correction factors were a function of height and free stream flow angle as shown in Figure 10. Flow corrections were only applied to data where the correction required was greater than 2.5%, for the flow magnitude and 0.5\({}^{\circ}\) for the flow direction as this was considered to be the limits of the accuracy of the CFD simulation data.