Multifractalidade e criticalidade auto-organizada da precipitação pluvial em Piracicaba-SP, Brasil

Abstract

Rainfall can be understood as an end product of a number of complex atmospheric processes, which vary in space and time, and it may be considered one of most important dominant factor of the meteorological-climatic features of an specified investigated area. In this study, we observed if the dynamics of rain in Piracicaba, São Paulo - Brazil is generated by a multifractal process and / or belongs to classes of Self-Organized Criticality systems. To detect long-term correlations and multifractal behavior, we apply MF-DFA method that systematically detect nonstationarities and overcome trends in the data at all timescales. We calculated the generalized Hurst exponent, h(q), and Renyi exponent, (q). The results showed the existence of power-law long-term correlations which are described by a hierarchy of scaling exponents, that is the consequence of an underlying multifractal stochastic process. For smaller scales of about 8 months, the dynamics of rain is generated by a multifractal process (the generalized Hurst exponent, h(q), decreases with the increase in order (q) meaning it can be modeled using the cascade models. For larger scales, the value of h(q) is between 0:35 �� 0:55 indicating a weaker multifractality. The hypothesis that rainfall may be a case of Self-Organized Criticality is assessed. We analyze two events: the daily amount of rain and drought events (days without rain), both are weather phenomena that are strongly linked to rainfall. It appears that the distribution of the daily amount of rain displays two different scaling regimes for small and large intensities. The value of the ratio of these exponents confirms the results that were obtained in regions with tropical and subtropical climates. However, for the distribution of drought events we find two distinct scaling exponents with values that are closer than those observed in the daily amount of rain. The multifractal properties and self-organized criticality should be incorporated into theoretical models and computer simulations of the dynamics of rainfall and related phenomena.Rainfall can be understood as an end product of a number of complex atmospheric processes, which vary in space and time, and it may be considered one of most important dominant factor of the meteorological-climatic features of an specified investigated area. In this study, we observed if the dynamics of rain in Piracicaba, São Paulo - Brazil is generated by a multifractal process and / or belongs to classes of Self-Organized Criticality systems. To detect long-term correlations and multifractal behavior, we apply MF-DFA method that systematically detect nonstationarities and overcome trends in the data at all timescales. We calculated the generalized Hurst exponent, h(q), and Renyi exponent, (q). The results showed the existence of power-law long-term correlations which are described by a hierarchy of scaling exponents, that is the consequence of an underlying multifractal stochastic process. For smaller scales of about 8 months, the dynamics of rain is generated by a multifractal process (the generalized Hurst exponent, h(q), decreases with the increase in order (q) meaning it can be modeled using the cascade models. For larger scales, the value of h(q) is between 0:35 �� 0:55 indicating a weaker multifractality. The hypothesis that rainfall may be a case of Self-Organized Criticality is assessed. We analyze two events: the daily amount of rain and drought events (days without rain), both are weather phenomena that are strongly linked to rainfall. It appears that the distribution of the daily amount of rain displays two different scaling regimes for small and large intensities. The value of the ratio of these exponents confirms the results that were obtained in regions with tropical and subtropical climates. However, for the distribution of drought events we find two distinct scaling exponents with values that are closer than those observed in the daily amount of rain. The multifractal properties and self-organized criticality should be incorporated into theoretical models and computer simulations of the dynamics of rainfall and related phenomena.