Weibull wind speed distribution: Numerical considerations and use with sodar data

Two analyses have been performed of the use of the Weibull distribution to describe wind speed statistics. The first is a combination of theoretical considerations in a common domain of c and k parameters concerning some robust indicators of position, spread, skewness, and kurtosis. The second is a calculation of the Weibull parameters using three differing methods based on a 3‐a sodar database. The modified maximum‐likelihood method is direct, the method of weighted probability moments considers order statistics, and the method based on the minimum RMSE is iterative. As a result of the theoretical analyses, we propose some simple relationships involving Weibull parameters and the range of a fraction of central data, the variation coefficient, and the Yule‐Kendall index, which may be applied practically. The calculation of Weibull parameters has revealed the sharp contrast between day, where the fit was highly satisfactory, and night, mainly below 300 m. Moreover, a seasonal pattern was also observed. The comparison between the methods used also proved satisfactory, particularly during day, whereas a slight disagreement was observed during the night for the method based on the minimum RMSE. Finally, randomly generated samples were used to check the accuracy of the Weibull parameters in the domain analyzed, resulting in small residuals and standard deviations of the values calculated.