Complexity analyses of geomagnetic and solar activity indices time series

Abstract

The universal properties of the geomagnetic/solar indices critically describe their time series' dynamics. Here, we investigate the complexity behavior of the time series of the geomagnetic and solar activity indices Kp, DST, Ap, F10.7, [Formula: see text], AE, AL, AU, pc, and R. To do this, we apply multiscale entropy (MSE) analysis, detrended fluctuation analysis (DFA), rescaled range (R/S) test, and visibility graph (VG) to the time series of indices recorded daily from January 1st, 1996 to January 1st, 2020. MSE analysis reveals that AE exhibits the lowest entropy (minimal complexity), followed by F10.7, [Formula: see text], and R. Ap shows intermediate complexity, while AL, Dst, AU, and pc maintain higher entropy values. The range of Hurst exponents between 0.5 and 1 extracted from DFA and R/S analyses confirms the long-term memory of geomagnetic indices. In contrast, solar activity indices exhibit Hurst exponents consistent with pink noise or non-stationarity. VG analysis identifies AU, Dst, pc, and Kp as possessing "small-world" characteristics-corroborating strong long-range correlations. Synthesized results indicate that the indices Kp, Dst, AL, AU, and pc exhibit stronger evidence of long-term correlated memory, while the solar indices, along with the geomagnetic index AE, are comparatively suitable for studying transient phenomena.

Fig. 1

The daily average of OMNI2 data for Kp (1st row), Dst (2nd row), Ap (3rd row), F10.7 (4th row), and (last row) for the time period of 1 January 1996 to 1 January 2020.

Fig. 2

The daily average of OMNI2 data for AE (1st row), AL (2nd row), AU (3rd row), pc (4th row), and R (SSN) number (last row) for the time period of 1 January 1996 to 1 January 2020.

Fig. 3

The MSE analysis for the time series of geomagnetic and solar activity indices.

Fig. 4

Linear fitting are applied to the frequency distribution of links in a log-log scale resulting from visibility graph analysis of time series Kp (1th row), Dst (2nd row), Ap (3rd row), F10.7 (4th row), and Lyman (last row). The parameters of the model and the error ranges are listed in Table 3.

Fig. 5

Linear fitting are applied to the frequency distribution of links in a log-log scale resulting from visibility graph analysis of time series AE (1st row), AL (2nd row), AU (3rd row), pc (4th row), and R (last row). The parameters of the model and the error ranges are listed in Table 3.