Return period of bivariate distributed extreme hydrological events

Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either separate single random variables or two joint random variables. In the latter case, the return periods can be defined using one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical models and observed flood data.