Statistical Tools - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 158

Fig. A.2 Turbulence intensities measured at 80 m height at FINO1 on November 17, 2005 from
20 to 21 h local time (left) and at 3.5 m height at Graswang (Upper Bavaria, Germany) on June
25, 2010 from 12 to 13 h local time (right). Full line shows turbulence intensity depending on the
averaging period, dotted line shows the standard deviation of the mean values normalized with
mean wind speed and the dashed line gives the total turbulence intensity (computed from the total
variance in Fig. A.1 )

left-hand figure in Fig. A.1 the mean wind speed was 5.2 m/s (mean wind speeds
decrease from about 11-4 m/s in the first 15 min of the evaluated time interval and
then oscillated around 5.5 m/s for the rest of the period), for the right-hand figure it
was 2.5 m/s.
The amplitude of wind fluctuations is usually proportional to the mean wind
speed. Therefore, the wind speed variance depends on the mean wind speed in this
period. In order to get rid of this dominating wind speed influence, the variance
can be normalized with the square of the mean wind speed. Normalization of the
standard deviation with the mean wind speed leads to the formation of a frequently
used variable: the turbulence intensity. The turbulence intensity is given by:

q

u 0 2 ð t ; T Þ

I u ð t ; T Þ¼ ð A : 6 Þ

u ð t ; T Þ

Figure A.2 shows the turbulence intensity for the two cases presented in Fig. A.1 .
Both situations were recorded during unstable thermal stratification. On November
17, 2005, cold air from the North was advected over the still rather warm waters in
the German Bight and on June 25, 2010 cool air was present in Upper Bavaria with
the sun in a cloudless sky heating the surface considerably. Therefore, turbulence
intensities are above average for both marine and land surfaces.
If the wind speed is measured by sonic anemometers rather than by cup
anemometers, all three fluctuating components of the wind speed are available for
data analysis. Usually, then u 0 denotes the longitudinal horizontal wind component
parallel to the mean wind direction, v 0 denotes the transverse horizontal wind
component perpendicular to the mean wind direction, and w 0 the vertical wind
component. In this case the variances, standard deviations and turbulence
intensities can be computed separately for all of these three components. The
normalisation of all three components leading to turbulence intensities is done
with the mean horizontal wind speed. The variable