Statistical Modelling of Extreme Rainfall Indices using Multivariate Extreme Value Distributions

Environmental Modeling & Assessment - Multivariate extreme value models are used to investigate the combined behaviour of several weather variables. To investigate joint dependence of extreme...     

Modelling dependence structures of extreme wind speed using bivariate distribution: a Bayesian approach

When investigating extremes of weather variables, it is seldom that a single weather station determines the damage, and extremes may be caused from the combined behaviour of several weather stations. To investigate joint dependence of extreme wind speed, a bivariate generalised extreme value distribution (BGEVD) was considered from frequentist and Bayesian approaches to analyse the extremes of component-wise monthly maximum wind speed at selected weather stations in South Africa. In the frequentist approach, the parameters of extreme value distributions (EVDs) were estimated with maximum likelihood, whereas in the Bayesian approach the Markov Chain Monte Carlo (MCMC) technique was used with the Metropolis–Hastings algorithm. The results showed that when fitted to component-wise maxima of extreme weather variables, the BGEVD provided apparent benefits over the univariate method, which allowed information to be pooled across stations and resulted in improved precision of the estimates for the parameters and return levels of the distributions. The paper also discusses a method to construct informative priors empirically using historical data of the underlying process from weather characteristics of four pairs of surrounding weather stations at various distances. The results from the Bayesian analysis showed that posterior inference might be affected by the choice of priors that were used to formulate the informative priors. From the results, it could be inferred that the Bayesian approach provides a satisfactory estimation strategy in terms of precision, compared with the frequentist approach, because it accounts for uncertainty in parameters and return level estimations.     

Bayesian modelling of extreme wind speed at Cape Town,South Africa

In the framework of generalized extreme value (GEV) distribution, the frequentist and Bayesian methods have been used to analyse the extremes of annual maxima wind speed recorded by automatic weather stations in Cape Town, Western Cape, South Africa. In the frequentist approach, the GEV distribution parameters were estimated using maximum likelihood, whereas in the Bayesian method the Markov Chain Monte Carlo technique with the Metropolis–Hastings algorithm was used. The results show that the GEV model with trend in the location parameter appears to be a better model for annual maxima data. The paper also discusses a method to construct informative priors empirically using historical data of the underlying process from other weather stations. The results from the Bayesian analysis show that posterior inference might be affected by the choice of priors and hence by the distance between a weather station used to formulate the priors and the point of interest.