A comparative study to determine the optimal copula model for the wind speed and precipitation of typhoons

Typhoon is usually one of main reasons to damage the buildings, infrastructures, water operations, and human life in summer in East Asia, which includes China, Japan, and Korea. Typhoons can be considered multivariate extremes that consists of climate variables that affect wind and precipitation. Copula models can be used to investigate the dependence between random variables. In this study, we used copula models to investigate the optimal marginal distribution for the relations between the wind speed and the precipitation of typhoons at the Jeju weather station in South Korea. We used the 10-min average wind speed (W10) and the total precipitation (PT) from 65 typhoon events that had affected the Jeju station. Two case studies were considered using the typhoon data. Case one included all typhoon events, and case two included 39 typhoon events with the following thresholds: W10 ≥ 10 m s⁻¹ and PT ≥ 50 mm. The marginal distributions for the copula models included the generalized extreme value (GEV), generalized logistic (GLO), generalized Pareto (GPA), and Weibull (WBU) distributions as well as three copula models: Clayton, Frank, and Gumbel copulas. Each step was checked by the robust diagnostic, the probability plot correlation coefficient (PPCC) test, and the goodness-of-fit test (S_n statistic). The Frank copula model with GLO (W10) – GPA (PT) had the best performance in both cases. The results of this study present the key steps needed to identify an optimum copula for a bivariate distribution in applications related to atmospheric sciences and provides an example of how this applies to wind velocity and precipitation from typhoons.