Multi-Time-Scale Analysis of Chaos and Predictability in vTEC

Theoretical modelling of the local ionospheric medium (LIM) is made difficult by the occurrence of irregular ionospheric behaviours at many space and time scales, making prior hypotheses uncertain. Investigating the LIM from scratch with the tools of dynamical system theory may be an option, using the vertical total electron content (vTEC) as an appropriate tracer of the system variability. An embedding procedure is applied to vTEC time series to obtain the finite dimension (m is an element of N) of the phase space of an LIM-equivalent dynamical system, as well as its correlation dimension (D2) and Kolmogorov entropy rate (K2). In this paper, the dynamical features (m,D2,K2) are studied for the vTEC on the top of three GNSS stations depending on the time scale (tau) at which the vTEC is observed. First, the vTEC undergoes empirical mode decomposition; then (m,D2,K2) are calculated as functions of tau. This captures the multi-scale structure of the Earth's ionospheric dynamics, demonstrating a net distinction between the behaviour at tau <= 24h and tau >= 24h. In particular, sub-diurnal-scale modes are assimilated to much more chaotic systems than over-diurnal-scale modes.