# Measurement and Prediction of Wind Fields at an Offshore Site by Scanning Doppler LiDAR and WRF
## 3 Results and Discussion
### Measurement and Prediction of Wind Turbine Wake
The distribution of the yaw misalignment during the evaluation period was roughly symmetrical on the two sides of 0\({}^{\circ}\) and the maximum yaw error was \(\pm\)10\({}^{\circ}\). The wake model proposed by [PERSON] and [PERSON] [34] is able to account for the yaw misalignments. Therefore, for an accurate comparison, the yaw error distribution is used to construct weighted average velocity profiles from this wake model. Note that [PERSON]'s model, which assumes top-hat distribution of velocity deficit, is simply a function of \(C_{T}\) and downstream distance from the turbine. The model proposed by [PERSON] et al. [32] is based on the conservation of mass and momentum but is also a function of \(C_{T}\) and assumes top-hat velocity deficit distribution. In the model by [PERSON] and [PERSON] [33], they employed Gaussian distribution to represent velocity deficit profiles. Although the model of [PERSON] and [PERSON] also employed Gaussian distribution for velocity deficit, the model and the wake growth rates are the function of both \(C_{T}\) and inflow turbulence intensity. Figure 21 shows the horizontal profiles of normalized velocity deficit at the hub height in the wake of the wind turbine. Here, the normalized velocity deficit is defined as:  
\[\frac{\Delta\mathrm{U}}{U_{0,h}}=\frac{U_{0,h}-U}{U_{0,h}}, \tag{7}\]  
Figure 20: **(a,b)**: Time series of 10-min-averaged wind speed and turbulence intensity at the height of 90 m measured by the met mast. The dark lines are mean wind speed and turbulence intensity over the time range. **(c)** Time series of one-minute-averaged wind and yaw directions at the wind turbine nacelle. **(d)** Time series of yaw misalignment. where \(U_{0,h}\) is the average inflow velocity which is equal to 8.2 m/s during the current comparison period, \(U\) is the streamwise velocity, and \(\Delta\)U is the velocity deficit. Profiles obtained from scanning LiDAR are compared with those predicted by the wake models. The models of [PERSON] and [PERSON] et al. underestimate the velocity deficit--compared to the measurement--around the wake center. Similar tendency has been observed in other studies on comparison of these two wake models with the large-eddy simulations (LES) (see, e.g., Ref. [33]). The performance of these models can be further improved by tuning the wake growth rate parameter, as done in some other studies (see Ref. [36] for the review), but the top-hat assumption of velocity deficit will never allow them to reproduce the Gaussian nature of the measured profiles. It can be appreciated that the velocity-deficit profiles predicted by the models of [PERSON] and [PERSON] and [PERSON] and [PERSON] show similar trend as the measured profiles. The model of [PERSON] and [PERSON], however, overestimates the velocity deficit at x/D =1 and significantly underestimates the profiles further downstream. The discrepancy can be attributed to the fact that, in this study, the wake growth rate parameters were not obtained from fitting them to the current measurements, instead the parameters from the closest LES case in Ref. [33] were used. The model of [PERSON] and [PERSON] shows the most favorable agreement with the measured profiles, though even this model visibly overestimate or underestimate the velocity deficit compared to the measured profiles. The velocity deficit is maximum at \(x/D=3\), though a deficit can be observed even at \(x/D=6\). At \(x/D=1.0\), close to the rotor, a horizontal profile with a dual peak can be observed in the measurement. This dual peak is the result of an uneven distribution of force on the rotor in the radial direction. The near-wake flow is significantly affected by the specific blade aerodynamics, especially when the ambient turbulence is low. This has also been observed in experimental studies as shown by [PERSON] and [PERSON] [37]. However, these differences between the wake model and measurements in the near wake region are not very relevant when considering engineering applications of the model.