On the selection of bivariate parametric models for wind data

The joint modelling of wind speed and direction in an area is important for wind energy projects and a variety of ocean engineering applications. In the context of wind resource assessment, the analytical description of wind climate is usually confined to the description of wind speed; however, the accurate joint description of the directional and linear wind characteristics is also essential at the candidate sites for wind farm development. In this work, three families of models for the joint probabilistic description of wind speed and wind direction are examined and thoroughly evaluated, namely Johnson-Wehrly and two families of copulas, Farlie-Gumbel-Morgenstern and Plackett families. These models are applied on long-term wind data obtained by different measuring devices (five oceanographic buoys and one meteorological mast) for six different locations of the Greek and Spanish waters in the Mediterranean Sea. The proposed bivariate models are theoretically sound and tractable, since they are defined by closed relations and are constructed by considering the marginal (univariate) distributions of wind speed and wind direction along with an appropriate dependence structure of the involved variables. In the univariate case, wind speed modelling is based on a wide range of conventional and mixture distributions, while wind direction is modelled through finite mixtures of von Mises distributions. The evaluation of the bivariate models is based on seven bin-specific goodness-of-fit criteria, namely root mean square error, relative root mean square error, mean absolute error, index of agreement, chi-square statistic, adjusted coefficient of determination and normalized deviation. The obtained results suggest that the performance of the Johnson-Wehrly model is rather superior, since it provides better fits compared to the other two families of bivariate distributions for the overwhelming majority of the examined cases and criteria. The most efficient bivariate models are then implemented to estimate the detailed structure of wind power density at three selected locations.