The Long-Range Memory and the Fractal Dimension: a Case Study for Alc\^antara

TL;DR

This study analyzes the long-range memory and fractal properties of the Southern Oscillation Index, revealing persistent climate behavior and potential links to wind variability at the Alcântara Launch Center using advanced time series techniques.

Contribution

It introduces a comprehensive analysis of the Southern Oscillation Index's long-memory and chaotic behavior, applying novel techniques to understand climate dynamics and their regional impacts.

Findings

Southern Oscillation Index exhibits long-range persistence.

Wind speed at São Luís correlates with Southern Oscillation Index variability.

Chaotic behavior detected in the time series through Lyapunov exponent analysis.

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, such 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 complex dynamic behavior in climate effects at global-scale level and specifically its influence in northeastern Brazil, in the region of the Alc\^antara Launch Center. The R package \texttt{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 S\~ao Lu\'is airport, Maranh\~ao State, and the Southern Oscillation Index. The permutation test results showed that the time series of monthly average wind speed in the S\~ao Lu\'is airport is correlated with the variability of Southern Oscillation Index, statistically significant at the 5\% confidence level. The results also indicate the possibility of using autoregressive models to represent average meteorological variables in behavioral analysis, as well as trends in the climate, more specifically a possible climatic influence of El Ni\~no--Southern Oscillation on wind strength in the Alc\^antara Launch Center.