Comparison of bivariate distribution construction approaches for analysing wind speed and direction data

Statistical distribution models for estimating wind energy potential spurred a great interest among researchers and practitioners recently. Bivariate statistical models for representing both wind direction and speed are helpful for the design and implementation of more efficient systems for harnessing wind energy. In this study, we construct seven different bivariate joint distributions based on three construction approaches, namely, angular‐linear (AL), Farlie‐Gumbel‐Morgenstern (FGM) and anisotropic lognormal approaches, and then compare them using the adjusted R 2 and root mean square error (RMSE) as measures of goodness of fit. For both AL and FGM approaches, the distributions of wind speed and direction need to be obtained separately before the construction of joint distribution. While using the mixture of von Mises distribution for representing the wind direction, we utilize two different mixtures of distributions for representing the wind speed, with one being the mixture of singly truncated below Normal and Weibull distribution, and the other being the mixture of three‐parameter inverse Gaussian and lognormal distributions. A case study is conducted for this purpose on multiple sites in North Dakota, USA. It indicates that the two mixtures of distributions for wind speed have comparable performances. Meanwhile, there is little difference in terms of adjusted R 2 and RMSE values in modelling wind direction with AL and FGM approaches. Although the anisotropic approach significantly lags behind AL and FGM approaches, the adjusted R 2 and RMSE values provided by the latter two approaches are comparable.