Quantifying error of lidar and sodar Doppler beam swinging measurements of wind turbine wakes using computational fluid dynamics

Wind-profiling lidars are now regularly used in boundary-layer meteorology and in applications such as wind energy and air quality. Lidar wind profilers exploit the Doppler shift of laser light backscattered from particulates carried by the wind to measure a line-of-sight (LOS) velocity. The Doppler beam swinging (DBS) technique, used by many commercial systems, considers measurements of this LOS velocity in multiple radial directions in order to estimate horizontal and vertical winds. The method relies on the assumption of homogeneous flow across the region sampled by the beams. Using such a system in inhomogeneous flow, such as wind turbine wakes or complex terrain, will result in errors. To quantify the errors expected from such violation of the assumption of horizontal homogeneity, we simulate inhomogeneous flow in the atmospheric boundary layer, notably stably stratified flow past a wind turbine, with a mean wind speed of 6.5 m s at the turbine hub-height of 80 m. This slightly stable case results in 15 of wind direction change across the turbine rotor disk. The resulting flow field is sampled in the same fashion that a lidar samples the atmosphere with the DBS approach, including the lidar range weighting function, enabling quantification of the error in the DBS observations. The observations from the instruments located upwind have small errors, which are ameliorated with time averaging. However, the downwind observations, particularly within the first two rotor diameters downwind from the wind turbine, suffer from errors due to the heterogeneity of the wind turbine wake. Errors in the stream-wise component of the flow approach 30 % of the hub-height inflow wind speed close to the rotor disk. Errors in the cross-stream and vertical velocity components are also significant: crossstream component errors are on the order of 15 % of the hubheight inflow wind speed (1.0 m s) and errors in the vertical velocity measurement exceed the actual vertical velocity. By three rotor diameters downwind, DBS-based assessments of wake wind speed deficits based on the stream-wise velocity can be relied on even within the near wake within 1.0 m s (or 15 % of the hub-height inflow wind speed), and the cross-stream velocity error is reduced to 8 % while vertical velocity estimates are compromised. Measurements of inhomogeneous flow such as wind turbine wakes are susceptible to these errors, and interpretations of field observations should account for this uncertainty.