Copula-Based Joint Distribution Analysis of Wind Speed and Direction

This paper presents a novel copula-based approach to model the joint cumulative distribution function (JCDF) of wind speed and direction for wind-resistant design of engineering structures. Copula functions enable the JCDF to be obtained with the corresponding marginal distributions of wind speed and wind direction. The daily maximum wind speed recorded during 1971-2017 in Dali, China, was collected and used as the data source. The Weibull distribution was applied to represent the marginal distribution of wind speed; meanwhile, the marginal distribution of wind direction was modeled by the von Mises distribution. The Farlie-Gumbel-Morgenstern (FGM) and four commonly used Archimedean copulas were employed to construct the continuous bivariate JCDF of wind speed and direction. The simulation results were compared with those obtained using the traditional methods, i.e., the approaches based on multiplication rules and angular-linear (AL) model. The statistics of the coefficient of determination R2 and root-mean-squared error (RMSE) obtained in the regression analysis were used to judge the goodness of fit of each approach. The analytical results show that the approach based on copulas can not only yield good JCDF estimations of wind speed and direction, but also provide an effective and practical way to predict the extreme wind speed at a certain return period. Moreover, the estimated extreme wind speed varies significantly in the 16 directions and the predicted extreme wind speed in the studied region will be unreliable when neglecting the joint effect of wind speed and direction.