Multifractalidade dos rios brasileiros

Abstract

Many time series exihibit multifractal scale properties with important physical implications. We use the method for the multifractal characterization the MF-DFA (Mutifractal- Detrended Fluctuation Analysis) to calculate the generalized Hurst exponent [11] of water levels series of sixteen hydrological stations of the main Brazilian rivers, located in the cities of Manaus, Obidos, Lad ario, Porto Velho, Fonte Boa, Tucuru , Marab a, Santar em, Cruzeiro do Sul, Xambio a, Concei c~ao do Araguaia, Gua ra, Altamira, C aceres, Barra e Piranhas. These stations are placed in cities with di erent climate zones in Brazil. From this analysis, we concluded that all series exhibit multifractality and non-stationary behavior. We also show that the type of multifractality involved in this process is mainly due to the presence of di erent types of correlations in hydrological time series. We derive an analytic equation that generates the multifractal spectra for all the stations studied, with maximum errors of 1%, from the generalization of the d-Process Multiplied Multinomial. It suggests the existence of a universal multifractality in the hydrologic cycle of the Brazilian rivers and why not of the planet? This work shows that it is possible to treat the time series of water levels of the Brazilian rivers from a multifractal perspective, and therewith to have a better understanding of the complex aspects of the scale properties that these series exhibit.