{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T00:56:15Z","timestamp":1776992175814,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Modelling the Earth\u2019s 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\u2019s 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\u2019s behaviour is. In particular, we calculate the correlation dimension D2 and the Kolmogorov entropy rate K2 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 D2 is a proxy of the degree of chaos and dynamical complexity. K2 measures the speed of destruction of the time-shifted self-mutual information of the signal, so that K2\u22121 is a sort of maximum time horizon for predictability. The analysis of the D2 and K2 for the vTEC time series allows to give a measure of chaos and predictability of the Earth\u2019s 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.<\/jats:p>","DOI":"10.3390\/e25020368","type":"journal-article","created":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T02:27:24Z","timestamp":1676600844000},"page":"368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Chaos and Predictability in Ionospheric Time Series"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7070-333X","authenticated-orcid":false,"given":"Massimo","family":"Materassi","sequence":"first","affiliation":[{"name":"Consiglio Nazionale delle Ricerche-Istituto dei Sistemi Complessi (CNR-ISC), Via Madonna del Piano 10, Sesto Fiorentino, 50019 Firenze, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6096-0220","authenticated-orcid":false,"given":"Tommaso","family":"Alberti","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Rome, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5290-7235","authenticated-orcid":false,"given":"Yenca","family":"Migoya-Oru\u00e9","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1907-3715","authenticated-orcid":false,"given":"Sandro Maria","family":"Radicella","sequence":"additional","affiliation":[{"name":"Boston College, USA (BC), Institute of Scientific Research, Chesnut Hill, MA 02467, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3403-647X","authenticated-orcid":false,"given":"Giuseppe","family":"Consolini","sequence":"additional","affiliation":[{"name":"National Institute of Astrophysics (INAF), Institute for Space Astrophysics and Planetology (IAPS), Tor Vergata, Via del Fosso del Cavaliere 100, 00133 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,17]]},"reference":[{"key":"ref_1","unstructured":"Kelley, M.C. 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