Wind Energy

96 H. Kantz et al.
# of occurences per day
100000
10000
1000
100
10
day 191
1
0 1 2 3 4 5 6 7
increase of wind speed during 2 s [m/s]
Fig. 16.3. The distribution of wind gusts for different days. Results shown below
are obtained for the gusty day 191
against changes of this interval. The histograms of these gust strengthes
show approximately an exponential distribution (Fig. 16.3). The previously
discussed prediction schemes are not suitable to predict strong gusts, i.e. a
coming gust does typically not cause a large positive difference between predicted
and actual value, ˆvt+k − vt (the persistence predictor trivially predicts
this difference to be 0). However, the Markov chain approach offers a probabilistic
way of forecasting: One can extract, for every time instance, a probability
of a gust to come. This is done by straightforwardly interpreting the
conditional probability densities of the Markov chain or evident variants of
these. In order to estimate the probability of a gust to happen during the
following 2 s, one selects all data segments at past times lvt + g, i.e. which fulfil our gust criterion,
gives the actual probability of a gust of strength g to come.
This is a probabilistic prediction scheme, and despite a large predicted
probability no gust might follow. This illustrates the difficulty of verification:
The prediction scheme yields a probability, the actual observation will yield
a yes/no result. In order to check the predicted probabilities, we apply the
technique of the reliability plot: We create sub-samples of data for which the
predicted gust probabilities are in some small interval pgust(t) ∈ [r − ∆r, r +
∆r]. If the predicted probabilities are without any bias, then the relative
number of gust events inside such a sample should be in good agreement with
r (for sufficiently small ∆r). Indeed for r smaller than 1/2 this property is