Chaos and Predictability in Ionospheric Time Series

Modelling the Earth's ionosphere is a big challenge, due to the complexity of the system. Different first principle models have been developed over the last 50 years, based on ionospheric physics and chemistry, mostly controlled by Space Weather conditions. However, it is not understood in depth if the residual or mismodelled component of the ionosphere's behaviour is predictable in principle as a simple dynamical system, or is conversely so chaotic to be practically stochastic. Working on an ionospheric quantity very popular in aeronomy, we here suggest data analysis techniques to deal with the question of how chaotic and how predictable the local ionosphere's behaviour is. In particular, we calculate the correlation dimension (Formula presented.) and the Kolmogorov entropy rate (Formula presented.) for two one-year long time series of data of vertical total electron content (vTEC), collected on the top of the mid-latitude GNSS station of Matera (Italy), one for the year of Solar Maximum 2001 and one for the year of Solar Minimum 2008. The quantity (Formula presented.) is a proxy of the degree of chaos and dynamical complexity. (Formula presented.) measures the speed of destruction of the time-shifted self-mutual information of the signal, so that (Formula presented.) is a sort of maximum time horizon for predictability. The analysis of the (Formula presented.) and (Formula presented.) for the vTEC time series allows to give a measure of chaos and predictability of the Earth's ionosphere, expected to limit any claim of prediction capacity of any model. The results reported here are preliminary, and must be intended only to demonstrate how the application of the analysis of these quantities to the ionospheric variability is feasible, and with a reasonable output.