Surface Wind-Speed Statistics Modelling: Alternatives to the Weibull Distribution and Performance Evaluation

Abstract

Wind-speed statistics are generally modelled using the Weibull distribution. However, the Weibull distribution is based on empirical rather than physical justification and might display strong limitations for its applications. Here, we derive wind-speed distributions analytically with different assumptions on the wind components to model wind anisotropy, wind extremes and multiple wind regimes. We quantitatively confront these distributions with an extensive set of meteorological data (89 stations covering various sub-climatic regions in France) to identify distributions that perform best and the reasons for this, and we analyze the sensitivity of the proposed distributions to the diurnal to seasonal variability. We find that local topography, unsteady wind fluctuations as well as persistent wind regimes are determinants for the performances of these distributions, as they induce anisotropy or non-Gaussian fluctuations of the wind components. A Rayleigh–Rice distribution is proposed to model the combination of weak isotropic wind and persistent wind regimes. It outperforms all other tested distributions (Weibull, elliptical and non-Gaussian) and is the only proposed distribution able to catch accurately the diurnal and seasonal variability.