Publishers version - DTU Orbit

4.5 Ground based, vertical scan configuration wind field
parameter determination
4.5.1 Least-squares fitting routine
The data that are fed to the fitting routine consist of up to 150 pairs of values of 〈VLOS〉 and
azimuth angle φ. In conditions of uniform wind flow, this gives rise to a rectified cosine wave
of the form:
〈VLOS〉 = |acos(φ−b)+c|. (100)
Thederivationofthisfunctionisstraightforwardandcanbefoundinanumberofpublications,
e.g. Banakh et al. (1993). The peaks of the function correspond to the azimuth angle aligned
parallel or anti-parallel to the wind direction. The function passes through zero when the
azimuth angle is perpendicular to wind bearing since there is no component of velocity along
the line of sight. The data are also conveniently displayed on a polar plot (Figure 46), which
provides information at a glance on the speed, direction and vertical wind component. A
standard least-squares fitting routine provides the best estimates of the values of the three
floating parameters (a, b and c).
Figure 46: Wind lidar output for a ground-based, vertical scan ZephIR, illustrating many of
the features of a wind profile measurement. This example has been obtained at a height
150 m above ground level, one of several heights being probed in sequence. The lower trace
shows 147 individual line-of-sightwind speed values, obtained over a total period of 3 seconds
(plotted as white squares against azimuth scan angle). The same data, along with the leastsquares
fit in red, are displayed above in polar coordinates on the figure-of-eight plot showing
the wind bearing to lie slightly to the East of North. The wind parameters, derived from the
fit, appear in the table on the right; the horizontal wind speed at this height is determined
to be 9.1 m s −1 . The plot on the upper left shows one of the spectra from which each point
on the other graphs is derived.
The high level of redundancy in the fitting process is advantageous and can be used to
identify non-uniform flow. The root mean square deviation of the points from the optimum
solution gives an indication of the quality of fit, and this can be related to the value of
turbulent kinetic energy (TKE; see Wagner et al. (2009)). More work is needed to establish
a full understanding of the turbulence information available from lidar signals (Banakh et al.,
1999). Note that information on turbulence is also available from the spectral widths of the
84 DTU Wind Energy-E-Report-0029(EN)