Modeling Bivariate Distribution of Wind Speed and Wind Shear for Height-Dependent Offshore Wind Energy Assessment

A joint statistical model of wind speed and wind shear is critical for height-dependent wind resource characteristic analysis. However, given the different atmospheric conditions that may be involved, the statistical distribution of the two variables may show multimodal characteristics. In this work, a finite mixture bivariate statistical model was designed to describe the statistical properties, which is composed of several components, each with a Weibull distribution and a normal distribution for wind speed and wind shear, respectively, with a Gaussian copula to describe the dependency structure between the two variables. To confirm the developed model, reanalysis data from six positions in the coastal sea areas of China were used. Our results disclosed that the developed joint statistical model can accurately capture the different multimodal structures presented in all the bivariate samples under mixed atmospheric conditions, giving acceptable predictions of the joint probability distributions. Proper consideration of wind shear coefficient variation is crucial in estimating height-dependent wind resource characteristics. Importantly, unlike traditional methods that are limited to specific hub heights, the model developed here can estimate wind energy potential across different hub heights, enhancing the economic viability assessment of wind power projects.