Analysis of the stochastic model of the Markov chain on daily rainfall occurrence in the state of Santa Catarina, Brazil

Abstract

Purpose The purpose of this paper is to evaluate the seasonal and spatial variations in the statistical descriptors of the Markov chain model as well as the expected values of the length of dry and wet days and to estimate the probability of dry and rainy sequences in the state of Santa Catarina. Design/methodology/approach Daily rainfall data from 1970 to 2013 of five rainfall stations in the state of Santa Catarina were used. To model the sequence of dry and wet days, the first order of the Markov chain was used. The statistical descriptors of the Markov model were evaluated, as well as the expected values of the length of dry and wet days and the number of dry and rainy days for each month. Along with geometric distribution, the probability of occurrence of sequences of dry and rainy days was determined. The adherence of the data to geometric distribution was evaluated using the Kolmogorov-Smirnov test. Findings The results showed that there is a seasonal and spatial variation in Markov model descriptors and also in the duration of the dry and rainy periods. These variations may be related to the mechanisms responsible for the formation and distribution of rainfall in the state, such as the air masses and relief. The Lages station, located in the Plateau of Santa Catarina, had the highest P00 values, reflecting more stable conditions of the atmosphere. In autumn and winter, no marked differences were found between the coastal stations and west of the state. The geometric distribution was adequate for estimating the probability of dry and rainy days. Originality/value Although some work has already been carried out on the modeling of the Markov chain in the state of Santa Catarina, this study was found to be more complete with the use of various statistical descriptors of the model and its application in estimating the duration of the cycles of dry and wet periods and the number of rainy days in the period.