Publishers version - DTU Orbit

Uconst wΑx
l h
Φ
h.tanΦ
Figure 161: Simplified lidar scanning geometry in a linearly changing mean flow. The lidar is
shooting upstream and downstream with a half opening angle φ.
has positive and the downstream has negative tilt relative to the top of the hill. The projected
wind speed on the upwind and downwind beams are
vup = −(U +hα)sinφ vdown = (U +hα)sinφ . (269)
Assuming horizontal inhomogeneity, the horizontal velocity can be calculated as
Ulidar = vdown −vup
2sinφ
= U +hα, (270)
which shows, in the case of a negative α that the horizontal wind is underestimated (Bingöl
et al., 2008a). A simplified three dimensional analysis of the error is derived by Bingöl et al.
(2008b), where the the mean wind field U = (u,v,w) is assumed to vary linearly. In such
case, the wind vector estimations become:
ulidar = u+h ∂w
∂x
vlidar = v +h ∂w
∂y
wlidar = w− l
2 tan2φ ∂w
∂z
(271)
(272)
(273)
where l is the focus distance h/cosφ. Eq. 273 shows that the error due to inhomogeneity of
the mean flow vanishes for the vertical component as the half opening angle φ goes to zero.
The errors on the horizontal components are independent of φ.
12.3.2 Predicting the error by means of a flow model
Conical scanning mode of the lidar can be simulated in flow models. An automated script
for commercial software WAsP Engineering has been written by the author for the ZephIR
and Windcube lidars and has been published (Bingöl and Mann, 2009). The method can be
simplified as below and can be adapted to different scanning regimes such as different φ.
A unit vector in the direction of the laser beam can be written as,
n = (cosθsinφ,sinθsinφ,cosφ) (274)
whereφishalfopeningangleandθ isthegeographicalangleinwhichthebeam ispointing.As
it is previously stated, assuming the flow field to be roughly homogeneous over the averaging
DTU Wind Energy-E-Report-0029(EN) 235