Wind Energy

Log10 E(k)*k**(5/3)
6
4
2
0
5/3 corrected spectra
for Hayange data
Log10 E(k)*k**(5/3)
17 Wind Extremes and Scales 101
5
4
3
2
1
5/3 corrected spectra
for St. Médard d’Aunis data
−2
−3 −2 −1 0
0
−3 −2 −1 0
Log10 k Log10 k
(a) (b)
Fig. 17.2. Compensated spectra of the two horizontal components of the data of
Fig. 17.1a and of Fig. 17.1b, respectively. The horizontal plateau correspond to the
Kolmogorov scaling
Log10 Pr (⏐dV⏐>A)
0
−1
−2
−3
−1
Probability distributions for modulus
of horizontal components of the wind
Straight lines have slope of −7
0
Log10 A
1
2
Log10 Pr (⏐dV⏐>A)
0
−1
−2
−3
0
Probability distributions for modulus
of horizontal components of the wind
Straight line have slopes of −7
1
Log10 A
Fig. 17.3. Probability tails of the wind increments of the two horizontal components
of the data of Fig. 17.1a and of Fig. 17.1b, respectively
that the wind maxima distribution is a Frechet law [21], often called Generalized
Extreme Value distribution of type 2 (GEV2), instead of the more
classical Gumbel law (GEV1). GEV1 and GEV2 are quite distinct, since
GEV1 has the same power law exponent qD as the original series, whereas
GEV2 has a very thin tail corresponding to a double (negative) exponential.
This sharp contrast results from the fact that a Frechet variable corresponds
to the exponential of a Gumbel variable, therefore its distribution is often
called “Log-Gumbel.” We will illustrate this with the help of Météo-France
wind data, in particular those collected during the two “inland hurricanes”
2
3