Joint Probability Distribution Model of Wind Velocity and Rainfall with Mixed Copula Function

The aerodynamic characteristics of high-speed railway bridges and vehicles vary under wind and rain in special areas, then affecting the operation safety and comfort of trains. To comprehensively describe the joint distribution law and spatiotemporal correlation features of wind velocity and rainfall, this paper presents a joint probability distribution model of wind velocity and rainfall with mixed Copula function based on monitoring data from the natural disaster monitoring system of the Lanzhou-Xinjiang high-speed railway. The mixed Copula function was constructed using the Gumbel, Clayton, and Frank Copula functions. The marginal distribution functions of extreme wind velocity and rainfall were then estimated using the nonparametric kernel density estimation method. The weight and dependence parameters of mixed Copula function were estimated according to the Bayesian weighted average method and minimum of sum square variation. The goodness of fit of mixed Copula function was tested using the K-S and minimum distance methods. Finally, taking the monitoring data of the extreme wind velocity and rainfall along the Lanzhou-Xinjiang high-speed railway as an example, the joint probability distribution models of wind velocity and rainfall with different copula functions were established and compared. The results show that the joint probability distribution models of wind velocity and rainfall with mixed Copula function can more accurately describe the various correlations between the extreme wind velocity and rainfall. The joint probability distribution model of wind velocity and rainfall with three mixed Copula functions is the best model to describe the joint distribution law of the extreme wind velocity and rainfall. The correlations between the extreme wind velocity and rainfall monitored by the base station along the Lanzhou-Xinjiang high-speed railway are main left tail, secondary right tail, and secondary symmetry. © 2021, Editorial Department of China Journal of Highway and Transport. All right reserved.