Drought Analysis in Northeast Brazil - Probability Distribution Models and Markov Chain Approach
Markov Chain, standardized precipitation index, drought, Brazil.
Brazil is one of the tropical countries most affected by drought. The Brazilian territory contains 18.26% of dry lands concentrated mainly in Northeast Brazil (NEB). Droughts have been reported in NEB since the XVI century, and several facts about their impacts were observed during this period. Some facts that could be highlighted are livestock loss, people dying of famine, and people migrating to other regions. In this scenario, this study aimed to identify drought characteristics in the NEB that could provide beneficial information for hydrology professionals to plan possible measures to minimize drought’s negative impacts. To do that, an initial study was developed to analyze the fit of 2-parameter distributions gamma (GAM), log-normal (LNORM), Weibull (WEI), generalized Pareto (GP), Gumbel (GUM) and normal (NORM) to precipitation data from 293 rainfall stations across NEB, in the period 1988 - 2017. The maximum likelihood (ML) method was used to estimate the parameters to fit the models and the choice of the model was based on a modification of the Shapiro-Wilk statistic. The results showed that the LNORM, GAM, GP and WEI models were better fitted to the data. After that, the Standardized Precipitation Index (SPI) related to the 30 years of information was used with a Markov Chain approach to characterize drought. The results showed that a station that experienced a moderate drought recovered to a non-drought condition in about 10 to 19 months. The values increase when the initial state is severe, taking a minimum of 16 to 19 months to recover. The states of Ceará, the west portion of Rio Grande do Norte, Paraíba and Pernambuco are highlighted, presenting some spots where recovery to a non-drought condition can take up to 46 months. The mean residence time commonly varies between 1.1 to 1.2 months when the region has experienced a moderate drought condition and 1.1 to 2.2 months to recover from a severe drought condition. The probability of transitions from any category to a moderate or severe drought class was smaller than a transition to a non-drought or near-normal class. When analyzing the changes to a severe condition, the probabilities increased as the drought's severity increased. The same behaviour was observed in the moderate condition, highlighting some points in the north of NEB that showed a higher probability of transition from a state of severe drought to a state of moderate drought.