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Keywords:

  • cascade models;
  • wind speed probability distribution;
  • Weibull statistics

ABSTRACT

Several known statistical distributions can describe wind speed data, the most commonly used being the Weibull family. In this paper, a new law, called ‘M-Rice’, is proposed for modeling wind speed frequency distributions. Inspired by recent empirical findings that suggest the existence of some cascading process in the mesoscale range, we consider that wind speed can be described by a seasonal AutoRegressive Moving Average (ARMA) model where the noise term is ‘multifractal’, i.e. associated with a random cascade. This leads to the distribution of wind speeds according to the M-Rice probability distribution function, i.e. a Rice distribution multiplicatively convolved with a normal law. A comparison based on the estimation of the mean wind speed and power density values as well as on the different goodness-of-fit tests (the Kolmogorov–Smirnov test, the Kuiper test and the quantile–quantile plot) was made between this new distribution and the Weibull distribution for 35 data sets of wind speed from the Netherlands and Corsica (France) sites. Accordingly, the M-Rice and Weibull distributions provided comparable performances; however, the quantile–quantile plots suggest that the M-Rice distribution provides a better fit of extreme wind speed data. Beyond these good results, our approach allows one to interpret the observed values of Weibull parameters. Copyright © 2011 John Wiley & Sons, Ltd.