Joint distribution of wind speed and direction over complex terrains based on nonparametric copula models

Understanding the distribution of wind field parameters over various terrains is important for kinds of applications including condition monitoring of high-speed railways and pollutant dispersion modeling. Based on Empirical Bernstein Copula (EBC), a nonparametric joint distribution model of wind speed and direction adaptable for complex wind field is proposed. Four commonly used parametric models are introduced for comparison, including the angular-linear model, Frank Copula, Gaussian Copula, and the model without considering interdependence. Yearly data measured from wind monitoring stations at 19 sites with various wind fields alongside the Lanzhou-Xinjiang high-speed railway in China is adopted for studying. The EBC model shows an overall best goodness-of-fit with the comprehensive metric value reaching 4.9586 (full score 5). Particularly, the superior performance of the EBC model is retained while the parametric models fail to predict the joint distribution in regions where wind speed and direction are highly dependent. In addition, when dealing with cases that the fitting goodness of marginal distribution is relatively poor (i.e. R2 = 0.488), a desired accuracy of joint distribution can be obtained with EBC. Further discussion about the optimal parameters and Copula structure of EBC is conducted to reveal reasons for the model showing adaptability to highly variable wind environments.