Stochastic simulation for the precipitation frequency over some Brazilian cities through the Metropolis–Hastings algorithm

Abstract

This work analyses precipitation patterns in Brazilian cities with different climatic classifications, according to Köppen–Geiger, in order to estimate the probability of precipitation on any day of a particular month. It is focused on the frequency of precipitation and its probability. For this aim, the R software was used to perform stochastic simulations by the Metropolis–Hastings algorithm, assuming that the days of a particular month are distributed identically regarding the frequency of rainfall. It is also assumed that this frequency can be modelled by the Beta distribution, with adjusted parameters. The distribution proposed in this work is suitable for adequately estimating the frequency of precipitation when the average chosen rates are higher than 50%. However, this frequency could not be approximated by the proposed method, because the average chosen rates were <50%. The results can contribute to numerical prediction models for cities with a shortage of or missing rainfall data, providing information that contributes to urban planning in these cities.