Statistical modelling of directional wind speeds using mixtures of von Mises distributions: Case study

Abstract

A finite mixture model of continuous variable probability is used in this paper to represent the distribution of directional wind speed. The model is comprised of a finite mixture of von Mises (vM-pdf) distributions. The parameters of the model are estimated using the least squares method. The range of integration to compute the mean angle and the standard deviation of wind direction is adjusted to minimum variance requirements. The suitability of the distributions is judged from the coefficient of determination R 2. The model is applied in this paper to wind direction data recorded at several weather stations located in the Canary Islands (Spain). The conclusion reached is that the mixture distribution used in this paper provides a very flexible model for wind direction studies and can be applied in a widespread manner to represent the wind direction regimes in zones with several modes or prevailing wind directions. In the case of the Canary Islands, mixtures of two vM-pdfs provide better fits in all the cases analysed than those obtained with the models proposed in the specialised literature on wind energy. The conclusion is also drawn that when the number of components N of the mixture distribution increases, the value of R 2 increases. However, the variations in R 2 are not significant for values of N greater than six.