Jensen‐Shannon Complexity and Permutation Entropy Analysis of Geomagnetic Auroral Currents

Abstract

In this study we determine whether auroral westward currents can be characterized by low-dimensional chaotic attractors through the use of the complexity-entropy methodology developed by Rosso et al. (2007, https://doi.org/10.1103/PhysRevLett.99.154102) and based on the permutation entropy developed by Bandt and Pompe (2002, https://doi.org/10.1103/PhysRevLett.88.174102). Our results indicate that geomagnetic auroral indices are indistinguishable from stochastic processes from time scales ranging from a few minutes to 10 hr and for embedded dimensions d < 8. Our results are inconsistent with earlier studies of Baker et al. (1990, https://doi.org/10.

Dynamical Properties of Peak and Time‐Integrated Geomagnetic Events Inferred From Sample Entropy

“…These results suggest the persistence of an important stochastic component in the hourly index during both moderately and strongly disturbed periods, whereas and become much more regular/organized during stronger disturbances. This corresponds to the higher variability of substorm field‐aligned currents (responsible for magnetic field perturbations in the auroral region) than the ring current, but it likely corresponds also to a higher stochasticity of than or during higher geomagnetic activity—in agreement with recent results from Osmane et al (). But in this case, how to explain the good correlation between and or entropies, if the intermediary auroral indices and are themselves significantly stochastic?…”

“…It is also consistent with the somewhat lower SampEn(AE) during smaller Int(ap) and Int(AE) intervals in Figure 1 (bottom row): relatively quiet 10-day periods are simply less stochastic than a random succession of substorms and injections. A recent study has also shown that AE and AL are practically indistinguishable from stochastic processes in terms of hourly dynamical complexity 10.1029/2019JA027599 (Osmane et al, 2019). Apparently, AE mainly describes the directly driven, partly stochastic response of the magnetosphere to solar wind forcing, whereas higher organization arises in the delayed and entangled consequences occurring well within the inner magnetosphere-ionosphere system itself.…”

“…In some aspects, as in the time series of the 1‐min auroral electrojet index, the Earth's magnetosphere resembles a low‐dimensional chaotic system (Vassiliadis et al, ). However, considering permutation entropy and assuming an embedding dimension of the reconstructed phase space, Osmane et al () found that auroral geomagnetic indices and reach a much weaker degree of organization/complexity and become essentially indistinguishable from stochastic fractional Brownian processes over time scales longer than 1 hr.…”

Radial Evolution of Magnetic Field Fluctuations in an Interplanetary Coronal Mass Ejection Sheath

“…To further verify the statistical robustness of the analysis, we confirmed that the studied data intervals satisfied the criteria N/d! > 10 and d!/(N − (d − 1)τ ) < 0.2 (Osmane et al 2019) for every value of τ . Figure 4 shows the values of H and C versus τ for the 1 s fluctuation amplitudes of the magnetic field magnitude and RTN components.…”

Compacting the description of a time-dependent multivariable system and its multivariable driver by reducing the state vectors to aggregate scalars: the Earth's solar-wind-driven magnetosphere

“…In other words, one can seek timescales upon which coherent structures/fluctuations/modes arise. In some instances, coherent modes are signatures of deterministic chaos (Maggs and Morales, 2013) or a reduction to the number of degrees of freedom (Osmane et al, 2019). Readers with little familiarity with these two information theoretic measures can consult the reviews of Riedl et al (2013) and Zanin et al (2012) or the pedestrian methodology section found in Osmane et al (2019).…”