Analysis of hydrological time series using the horizontal visibility graph method
Precipitation, Horizontal Visibility Graph, Standardized Precipitation Index.
Precipitation is one of the most important climatic variables to characterize the climate of a region, its abundance or scarcity has serious consequences on activities and human life. Recently, because of global warming, precipitation patterns have changed in several regions. Droughts and floods have occurred more frequently, especially in tropical countries such as Brazil. Therefore, this work seeks to evaluate the dynamics of precipitation and the standardized precipitation index (SPI) in the state of Pernambuco, located in the Brazilian Northeast. To understand the dynamic behavior of the precipitation and SPI time series, the Horizontal Visibility Graph method was used, which transforms the time series into a network, allowing the application of graph theory techniques to analyze the phenomenon. In particular, the Clustering Coefficient, Average Shortest Path Length and the slope of the semi-logarithmic line of the node's degree distribution (Lambda) were used. The HVG was applied to the time series of precipitation (original and anomalies) and the standardized precipitation index in the periods of 1,3,6 and 12 months recorded in 5 representative stations of the Metropolitan Region, Zona da Mata, Agreste, Sertão Pernambucano and Sertão São Francisco, which characterize each mesoregion of the state of Pernambuco in the period between 1962 and 2012. For precipitation series, was observed that the capacity to form groups in the network, given by the clustering coefficient decreased in coast-sertao direction. The rainfall in the Metropolitan and Sertão São Francisco region presented characteristics of chaotic process. With regard to anomaly series, little variability was observed between the mesoregions for clustering coefficient and average shortest path. Furthemore, Metropolitan and Sertão Pernambucano regions were governed by stochastic processes. Evaluating the measures for SPI, the result of the clustering coefficient was similar to observed for the anomalies. Also, by increasing the SPI period, the networks became less connected. The 1-month period of the standardized precipitation index generated networks belonging to chaotic regimes, which changed in SPI-3, in which all regions presented stochastic characteristics. However, Sertão São Francisco was chaotic when considering SPI in the 6-month period, while Sertão Pernambucano and Sertão de São Francisco demonstrated similar behavior in SPI-12. Therefore, network theory is an efficient method to analyze hydrological phenomena. Thus, based on analysis of topological indices of the networks obtained, it is possible to identify important characteristics of the processes that govern precipitation and the standardized precipitation index.