Bayesian updating for Copula-based joint probability modeling of wind speed, wind direction, and air temperature under parameter uncertainty

Accurate estimation of environmental extremes is challenged by limited data availability and complex dependence among environmental variables. To address this issue, a Bayesian updating framework integrating optimal parametric marginal distributions with nonparametric Bernstein Copula-based joint modeling is proposed and validated through a case study. First, the marginal distributions of wind speed, wind direction, and air temperature are identified using a tail-feature-based selection method, and three Bernstein Copula-based joint modeling strategies are developed to characterize nonlinear dependence structures. The model parameters are then dynamically updated through Bayesian inference, and directional environmental contours are constructed using the IFORM approach. The results show that the strategy directly constructing the trivariate joint distribution achieves the best performance. The posterior distributions progressively converge toward the full-data results, accompanied by a reduction in parameter uncertainty. Comparisons with MCMC-based posterior inference further confirm the accuracy of the proposed MAP–Laplace approach. In addition, environmental contours obtained at successive updating stages gradually approached the complete-data results, demonstrating the capability of the proposed framework to provide reliable environmental contour estimates throughout the updating process. Although the maximum wind speeds obtained from different methods are similar, the corresponding temperatures differ by more than 10°C when dependence is ignored. These findings highlight the importance of accounting for both dependence structures and parameter uncertainty in environmental probabilistic modeling and environmental load assessment.