Bayesian modeling of the maximum rainfall of Petrópolis (RJ) and Poços de Caldas (MG)

ABSTRACT

The cities of Petrópolis (RJ) and Poços de Caldas (MG) are located in the mountain range regions of their respective states in Brazil. They frequently suffer from damage caused by heavy rains. Therefore, analyzing and predicting the occurrence of maximum rainfall for these locations is fundamental for planning activities that are vulnerable to its occurrence. The modeling of this variable is done, generally, through the generalized distribution of extreme values (GEV), which the Bayesian methodology has shown good results in estimating its parameters. Therefore, the present study aimed to fit the GEV distribution to the historical series of maximum rainfall in Petrópolis and Poços de Caldas, and to evaluate different structures of prior distributions, informative and non-informative, in predicting the maximum rainfall expected for different return times. The number of successes and precision were analyzed in order to evaluate the predictions obtained with the information from the maximum rainfall of different locations to elicit the prior distribution. To obtain the posterior marginal distributions, the Monte Carlo method via Markov Chains was used. The use of informative prior distribution based on data from Poços de Caldas was more precise and accurate to predict the maximum rainfall for Petrópolis, while for Poços de Caldas, the informative prior based on information from São João da Boa Vista (SP) provided the best results. For both locations, it is expected that, in an average time of 5 years, there will be at least one day with maximum rainfall equal to or greater than 100 mm.

Keywords:
extreme rainfall; generalized distribution of extreme values; informative prior; return time