Global comparison of the goodness-of-fit of wind speed distributions

Abstract

The aim of this study was evaluating the goodness-of-fit of 24 one-component probability density functions and 21 mixture probability density functions to empirical wind speed probability density functions on a global scale. Era-Interim reanalysis wind speed data for the period 2011-01-01 to 2015-12-31 with a spatial resolution of 1°×1° were used to compare the goodness-of-fit of 69 combinations of probability density functions and mixture probability density functions fitted with four different parameter estimation methods. The distribution parameters were obtained by applying the moment method, the L-moment method, the maximum likelihood estimation method and the least-squares estimation method. Four goodness-of-fit metrics related to the probability-probability plot, three goodness-of-fit metrics related to the quantile-quantile plot and one goodness-of-fit metric related to the average wind power density were calculated to assess the suitability of distributions. One important result of this study is that mixture probability density functions like the seven-parameter Burr-Generalized Extreme Value, the seven-parameter Dagum-Generalized Extreme Value, the six-parameter Dagum-Weibull and the six-parameter Generalized Extreme Value-Weibull generally provide a superior fit to one-component probability density functions according to goodness-of-fit metrics related to the probability-probability plot. Another important result is that based on the evaluation of goodness-of-fit metrics related to the quantile-quantile plot, the five-parameter Wakeby probability density function is a suitable choice for onshore and the four-parameter Kappa probability density function for offshore wind speed regimes. The four-parameter Johnson system of distributions and Wakeby probability density functions provided the overall best fit for average wind power density. Only for few wind speed regimes, the often used two-parameter Weibull probability density function was identified as the most appropriate distribution. Maps were produced that country-by-country show the most appropriate on- and offshore distributions on a global scale.