Circular-linear-linear probabilistic model based on vine copulas: An application to the joint distribution of wind direction, wind speed, and air temperature

Coupling of multiple environmental factors in the engineering sector, in particular, joint distribution modeling based on a high-dimensional environmental dataset containing circular data is very topical. We propose a modeling framework applicable to the 3D joint distribution of circular-linear-linear (C-L-L) dataset consisting of a parametric model based on copulas and a nonparametric kernel density estimation model. In the parametric model, the pair-copula decomposition concept of vine copulas represents the C-L-L dependence structure as a combination of C-L and L-L ones modeled by C-L and L-L copulas, respectively. This allows one to solve the circular variable's cyclicity problem in the trivariate joint distribution and assess C-L and L-L dependencies between paired variables in the C-L-L dataset. A case study is used to establish the joint distribution model based on annual observations of wind direction, wind speed, and air temperature via the structural health monitoring system of the Jiangyin Bridge, China. The modeling framework validity is proved by the case study, which reveals significant differences in the conditional univariate distribution features of wind speed and air temperature, and conditional joint distribution features of two variables under different wind directions. Therefore, in engineering problems sensitive to the wind direction, the latter's effect cannot be neglected.