Análise multifractal das correlações cruzadas entre séries temporais de precipitação e vazão

Abstract

Hydrological systems are composed of many components (precipitation, runoff, evaporation, transpiration, infiltration, etc.) and exhibit nonlinear behavior, with all individual components exhibiting non linear behavior as well. Although nonlinearity of hydrological processes has been recognized for many years, recent development of computational power and data acquisition technologies provide researches with powerful tools to evaluate existing methods and develop new more efficient techniques to study spatial and temporal variability and complexity of these phenomena. Considering that rainfall is the mayor natural factor that governs the stream flow regime, in this work we study non linear relationship between these components of the hydrological system, by examining multifractal correlations of individual rainfall and streamflow temporal series, as well as multifractal cross correlations between two processes. To this end we apply methods Multifractal Detrended Fluctuation Analysis (MF-DFA) and Multifractal Detrended Cross-Correlation Analysis (MF-DXA) on daily rainfall and streamflow temporal series registered in Piracicaba River Basin which is located in the state of São Paulo, Brazil. The results show that rainfall and streamflow temporal series exhibit multifractal correlations and cross correlations indicated by the generalized Hurst exponent, Renyi exponent and multifractal spectrum. The multifractal spectrum obtained by cross correlation analysis is similar to the multifractal spectrum of streamflow, for Corumbataí, Jaguari e Atibaia sub-basin, while for Camanducaia and Piracicaba sub-basin the cross correlation spectrum is more similar to the multifractal spectrum of precipitation. This difference could be related with land use and type of soil that affect the process of evapotranspiration and thus the whole hydrological cycle.