Wind Energy

21 Extreme Events Under Low-Frequency Wind Speed Variability 121
only on the scale ratio λ and not on the absolute scale ∆t. Although breakdown
coefficients do not assume any particular model for the analyzed field,
their results may be used to characterize and evaluate parameters of scaling
models, such as multiplicative cascades. It should be noted that breakdown
coefficients represent the measurable values of the weights in a multiplicative
cascade model, which are not identical to the generating cascade weights, except
in the restrictive case of a microcanonical cascading process. The fact
that breakdown coefficients only depend on the weights’ generator in the case
of a multiplicative cascade [3], allows for their use not only for scale-invariance
testing, but also for generator stationarity probing. This is to say that, while
multifractal fields are, as such, typically nonstationary, we can nevertheless
unveil the possible stationarity of the field generator, and make use of it for
prediction purposes.
21.3 Results and Conclusions
The data used for this study comprise wind velocities measured at a deforested
site in the state of Rondônia, Brazil (10 o 45 ′ S, 62 o 22 ′ W) during January
and February 1999. The land is dominated by short grasses, about 25 cm
tall; isolated indigenous trees are scattered throughout the landscape. The
measurements were obtained as part of the NASA TRMM-LBA (Tropical
Rainfall Measuring Mission – Large scale Biosphere-Atmosphere) project in
the Amazonia. To measure the three components of the wind speed, a sonic
anemometer (Solent A1002R, Gill Instruments, Lymington, UK) was deployed
on a tower at 6 m above the surface. The sonic anemometer recorded wind
speed at a frequency of 10 Hz. These fast-response data were obtained via
data acquisition and electronic signal condition systems (model SCXI 2400,
National Instruments, Austin, TX) which were interfaced with a computer.
The breakdown coefficient analysis has been performed on daily data, in
order to distinguish whether the energy cascading process can be regarded as
similar between day and night. While the absolute values of velocities certainly
look very different, the breakdown coefficient distributions of energy dissipation
(Fig. 21.1) are very similar, and a Kolmogorov-Smirnov test indicates that
the hypothesis of the two empirical distributions having the same underlying
probability distribution function can be accepted at high significance levels
(e.g. 20%).
We conclude therefore that the multifractal cascade generator of energy
dissipation in the atmosphere can be regarded as stationary (which implies
stationarity of the fluctuations field up to a multiplicative intensity modulation),
in this case between day and night, with implications on the mechanism
underlying Taylor’s hypothesis that are being discussed elsewhere [3]. The
same method of breakdown coefficient analysis can be used to determine the
stationarity of atmospheric turbulent energy cascade generators at larger temporal
scales, thereby drawing conclusions on the interplay of climatic indexes,
possible climate change, and others.