Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall

摘要

The use of copulas as flexible tools for constructing marginal-free distribution functions for multivariate phenomena, such as rainfall, recently enjoys substantial attention by researchers in hydrology. In this study, commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall, observed at Uccle, Belgium. In the analysis, various problems that can occur are highlighted, and opportunities for further research are outlined. After selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data, a detailed seasonal dependence analysis is provided, together with a study on tail dependence. Further, different existing parameter estimation techniques and goodness-of-fit methods for selecting the most appropriate bivariate copulas are applied and compared. Finally, attention is given to the presence of asymmetric dependence and nonexchangeability.