Modelagem estocástica da distribuição de probabilidade da precipitação pluvial via métodos computacionalmente intensivos

Abstract

In this work, it was made a statistical modeling of precipitation. This is a methodological work that uses stochastic simulations to estimate the probability distributions related to this atmospheric variable. In order to estimate the parameters of these distributions, Markov chain Monte Carlo methods were used to generate large size synthetic samples from observed data. The used methods were the Metropolis-Hastings algorithm and the Gibbs sampler. The simulations were performed under the hypothesis that the days of of the same period of the year (month or rainy season) can be considered to be identically distributed concernig the probability of precipitation. This research allowed the production of four papers. The first paper used the Metropolis-Hastings algorithm to model the probability of occurrence of precipitation on any day of the month. The simulations of this paper were perfomed with observed data of some Brazilian cities. The other papers used the Gibbs sampler and the proposed methods were applied to data from cities in the Northeast Brazil. In the second paper, Beta and Binomial distributions were used to model the number of days of the month with occurrence of precipitation. In the third paper, the Poisson distribution was used to model the number of days with precipitation extreme values in the rainy season. An alternative method for estimating these extreme values and their distribution is presented in the fourth paper, using the Gamma distribution. According to the results obtained by these researches, the Gibbs sampler was considered to be adequate to estimate distributions in the modeling of precipitation on cities for which there are few historical data.