Statistical Modelling of Extreme Rainfall Indices using Multivariate Extreme Value Distributions

Multivariate extreme value models are used to investigate the combined behaviour of several weather variables. To investigate joint dependence of extreme rainfall events, a multivariate conditional modelling approach was considered to analyse the behaviour of joint extremes of rainfall events at selected weather stations in South Africa. Moreover, 1-day to 5-day indices of rainfall events were constructed to investigate the frequencies and intensities of rainfall events for selected weather stations. Then, the conditional multivariate modelling was fitted to investigate dependence between series of extreme rainfall events. The conditional multivariate modelling has provided all forms of dependence, using Laplace marginal transformations, for which all weather stations are not equally extreme. Bootstrap sampling was also employed to account for models uncertainty in computing the prediction standard errors and compared with the prediction obtained from the conditional modelling that was fitted to extreme data. The results obtained from predictions reflected both the marginal and the dependence features, as well as the extremal dependence structure described consistently for indices of rainfall events between weather stations. The modelling framework and results of this study contribute towards understanding the salient features on the extremal dependence of rainfall extremes which are associated with, e.g. flash floods and landslides. This knowledge has practical applications in disaster risk preparedness by communities.