Bayesian rainfall frequency analysis with extreme value using the informative prior distribution

Determination of the frequency and the magnitude of the extreme rainfall events are very important for water resources management and the designs of the hydraulic structures because the extreme rainfall events and the resulting floods usually cause a lot of damage to life and properties of human society. Recently an increase in the occurrence of extreme events due to global warming has been observed all over the world. Therefore, it is required that the conventional rainfall frequency analysis methods may be reconsidered in two ways. Firstly, the conventional probability distributions used in the frequency analysis should be evaluated again whether the probability distribution can represent the effect of the extreme value or not. Also, the uncertainty in the rainfall frequency analysis should be quantified for the flexible water resources management. Therefore, the comparative study with the Gumbel distribution and the GEV(Generalized Extreme Value) distribution are performed to evaluate the efficiency of the GEV distribution in this article. Also, the Bayesian MCMC(Markov Chain Monte Carlo) scheme and the MLE with a quadratic approximation for parameter estimation are compared to show the advantage of the Bayesian MCMC in the aspect of uncertainty analysis. Especially, the informative prior distributions using the additional information are elicited in the process of the Bayesian MCMC.