Nonlinear and multifractal behaviour of atmospheric parameters and particulate matter in South Africa

Abstract

This study investigates the nonlinear and multifractal behavior of atmospheric parameters and particulate matter (PM10) in South Africa. We employed nonlinear techniques such as Sample Entropy, Lyapunov Exponent, and Correlation Dimension, alongside Multifractal Detrended Fluctuation Analysis (MFDFA) on hourly data of atmospheric parameters and PM10. Our results indicate that the air pollution time series exhibits significant disorder and chaos across all sites. Nonlinear analysis revealed chaos in all the parameters considered with Sample entropy ranging between 0.31 and 1.94, the largest Lyapunov exponent in the range 0.03–0.18 and the correlation dimension ranges from 0.03 to 1.88 showing the complex nature of the system. The Hurst exponent (H > 0.5) demonstrated persistence in the time series, suggesting long-range correlations. The multifractal analysis confirmed strong correlations and a fine multifractal structure in all variables, with multifractal strength ranging from 0.36 to 0.86 with Holder exponent (α0) values exceeding 0.5, demonstrating high regularity and complexity in the atmospheric data. These findings highlight the effectiveness of nonlinear and multifractal analyses in uncovering the complexity of atmospheric conditions, particularly in South Africa.