The Long-Range Memory and the Fractal Dimension: a Case Study for Alcântara

Cleber Souza Corrêa,Mariane Mendes Coutinho,Gilberto Fernando Fisch,Daniel Andrade Schuch,Felipe Do Nascimento Corrêa,Antonio Paulo De Queiroz

doi:10.5028/jatm.v9i4.683

Abstract

This study aimed to analyze the time series behavior of the Southern Oscillation Index through techniques using Fast Fourier Transform, computing the autocorrelation function, and the calculation of the Hurst coefficient. The methodology of Hurst Exponent calculation uses different lags, which are computed in the time series of Southern Oscillation Index. The persistent behavior in the time series can be characterized by calculating the Hurst Exponent, seeking for more behavioral information, as the existence of persistence and/or terms of long-range memory in the series. The results show a persistence of the climate in terms of long-memory Southern Oscillation Index time series, which can help to understand a complex dynamic behavior in climate effects at global-scale level and specifically its influence in northeastern Brazil, in the region of the Alcântara Launch Center. The R package tseriesChaos was used in the analysis of the Southern Oscillation Index time series, estimating the largest Lyapunov exponent, which indicates the existence of chaotic behavior in time series. The resampling technique was used in a permutation test between the surface wind data in the Sao Luis airport, Maranhao State, and the Southern Oscillation Index. The permutation test results showed that the time series of monthly average wind speed in the Sao Luis airport is correlated with the variability of Southern Oscillation Index, statistically correlated to the confidence interval at the 5% level. The results showed the possibility of using autoregressive models to represent average variable meteorology in the behavior analysis as well as trends in the climate, more specifically a possible climatic influence of El Nino-Southern Oscillation in wind strength in the Alcântara Launch Center.

Highlights

Sea surface temperature conditions in the tropical Pacific are important drivers of the atmospheric circulation and can have a major influence on the global climate
The function lyap estimated with Lyapunov regression coefficient for Southern Oscillation Index (SOI) time series is ʎ1 = 0.40. These results show that SOI time series presents a chaotic behavior, which is consistent with Chang et al
The application of the H methodology can capture the trends of SOI time series with significant results

Summary

Introduction

Sea surface temperature conditions in the tropical Pacific are important drivers of the atmospheric circulation and can have a major influence on the global climate. The dynamic behavior of ENSO is very complex, and it is difficult to predict its time series variations. The Southern Oscillation Index (SOI) time series signal is composed of a set of geophysical forcing with different temporal scales, some of long time as the cycles of solar activity and/or the interaction atmosphere-ocean, involving a planetary scale. The Southern Oscillation is a seesaw in surface air pressure between the tropical eastern and the western waters of the Pacific Ocean. SOI is calculated as the standardized anomaly of the surface air pressure difference between Tahiti, in the Pacific Ocean, and Darwin, Australia, in the Indian Ocean

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