{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T10:05:13Z","timestamp":1781690713385,"version":"3.54.5"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T00:00:00Z","timestamp":1582848000000},"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>The interaction between the solar wind and the Earth\u2019s magnetosphere\u2013ionosphere system is very complex, being essentially the result of the interplay between an external driver, the solar wind, and internal processes to the magnetosphere\u2013ionosphere system. In this framework, modelling the Earth\u2019s magnetosphere\u2013ionosphere response to the changes of the solar wind conditions requires a correct identification of the causality relations between the different parameters\/quantities used to monitor this coupling. Nowadays, in the framework of complex dynamical systems, both linear statistical tools and Granger causality models drastically fail to detect causal relationships between time series. Conversely, information theory-based concepts can provide powerful model-free statistical quantities capable of disentangling the complex nature of the causal relationships. In this work, we discuss how to deal with the problem of measuring causal information in the solar wind\u2013magnetosphere\u2013ionosphere system. We show that a time delay of about 30\u201360 min is found between solar wind and magnetospheric and ionospheric overall dynamics as monitored by geomagnetic indices, with a great information transfer observed between the z component of the interplanetary magnetic field and geomagnetic indices, while a lower transfer is found when other solar wind parameters are considered. This suggests that the best candidate for modelling the geomagnetic response to solar wind changes is the interplanetary magnetic field component B z . A discussion of the relevance of our results in the framework of Space Weather is also provided.<\/jats:p>","DOI":"10.3390\/e22030276","type":"journal-article","created":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T04:16:16Z","timestamp":1583122576000},"page":"276","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Measuring Information Coupling between the Solar Wind and the Magnetosphere\u2013Ionosphere System"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6303-5329","authenticated-orcid":false,"given":"Mirko","family":"Stumpo","sequence":"first","affiliation":[{"name":"Department of Physics, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy"},{"name":"INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00133 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3403-647X","authenticated-orcid":false,"given":"Giuseppe","family":"Consolini","sequence":"additional","affiliation":[{"name":"INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00133 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6096-0220","authenticated-orcid":false,"given":"Tommaso","family":"Alberti","sequence":"additional","affiliation":[{"name":"INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00133 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7288-1087","authenticated-orcid":false,"given":"Virgilio","family":"Quattrociocchi","sequence":"additional","affiliation":[{"name":"INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00133 Roma, Italy"},{"name":"Dipartimento Scienze Fisiche e Chimiche, Universit\u00e0 degli Studi dell\u2019Aquila, 67100 L\u2019Aquila, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2","DOI":"10.12942\/lrsp-2006-2","article-title":"Space Weather: The Solar Perspective","volume":"3","author":"Schwenn","year":"2006","journal-title":"Living Rev. Sol. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0273-1177(97)01096-X","article-title":"The effects of geomagnetic disturbances on electrical systems at the Earth\u2019s surface","volume":"22","author":"Boteler","year":"1998","journal-title":"Adv. Space. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1029\/2018SW002065","article-title":"A preliminary risk assessment of geomagnetically induced currents over the Italian territory","volume":"17","author":"Tozzi","year":"2019","journal-title":"Space Weather"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1023\/A:1005160129098","article-title":"Interplanetary origin of geomagnetic storms","volume":"88","author":"Gonzalez","year":"1999","journal-title":"Space Sci. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1023\/A:1005105831781","article-title":"Particle acceleration at the Sun and in the heliosphere","volume":"90","author":"Reames","year":"1999","journal-title":"Space Sci. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"25261","DOI":"10.1029\/2000JA004025","article-title":"Near-Sun and near-Earth manifestations of solar eruptions","volume":"106","author":"Gopalswamy","year":"2001","journal-title":"J. Geophys. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s11207-005-4980-z","article-title":"The 1859 Solar Terrestrial Disturbance And the Current Limits of Extreme Space Weather Activity","volume":"224","author":"Cliver","year":"2004","journal-title":"Solar Phys."},{"key":"ref_8","first-page":"S02004","article-title":"Effects of space weather on technology infrastructure","volume":"2","author":"Daglis","year":"2004","journal-title":"Space Weather"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1029\/GL017i003p00279","article-title":"The nonlinear response of AE to the IMF Bs driver: A spectral break at 5 hours","volume":"17","author":"Tsurutani","year":"1990","journal-title":"Geophys. Res. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13089","DOI":"10.1029\/96JA00563","article-title":"The organized nonlinear dynamics of the magnetosphere","volume":"101","author":"Klimas","year":"1996","journal-title":"J. Geophys. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4266","DOI":"10.1002\/2016JA023175","article-title":"Timescale separation in the solar wind-magnetosphere coupling during St. Patrick\u2019s Day storms in 2013 and 2015","volume":"122","author":"Alberti","year":"2017","journal-title":"J. Geophys. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"A56","DOI":"10.1051\/swsc\/2018039","article-title":"On fast and slow Earth\u2019s magnetospheric dynamics during geomagnetic storms: a stochastic Langevin approach","volume":"8","author":"Alberti","year":"2018","journal-title":"J. Space Weather Space Clim."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1142\/S0218348X02001397","article-title":"Self-organized criticality: A new paradigm for the magnetotail dynamics","volume":"10","author":"Consolini","year":"2002","journal-title":"Fractals"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1029\/2001JA000281","article-title":"Scale- free statistics of spatiotemporal auroral emissions as depicted by POLAR UVI images: The dynamic magnetosphere is an avalanching system","volume":"107","author":"Uritsky","year":"2002","journal-title":"J. Geophys. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"9065","DOI":"10.1029\/2018JA025952","article-title":"On the Forecast Horizon of Magnetospheric Dynamics: A Scale-to-Scale Approach","volume":"123","author":"Consolini","year":"2018","journal-title":"J. Geophys. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"033025","DOI":"10.1088\/1367-2630\/12\/3\/033025","article-title":"Recurrence networks\u2013a novel paradigm for nonlinear time series analysis","volume":"12","author":"Donner","year":"2010","journal-title":"New J. Phys."},{"key":"ref_17","first-page":"A08225","article-title":"An information theory approach to the storm-substorm relationship","volume":"116","author":"Consolini","year":"2011","journal-title":"J. Geophys. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1002\/2015GL067325","article-title":"Time scales of the European surface air temperature variability: The role of the 7-8 year cycle","volume":"43","author":"Jajcay","year":"2016","journal-title":"Geophys. Res. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"075307","DOI":"10.1063\/1.5019944","article-title":"Causality, dynamical systems and the arrow of time","volume":"28","author":"Palus","year":"2018","journal-title":"Chaos"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"424","DOI":"10.2307\/1912791","article-title":"Investigating Causal Relations by Econometric Models and Cross-Spectral Methods","volume":"37","author":"Granger","year":"1969","journal-title":"Econometrica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"056211","DOI":"10.1103\/PhysRevE.75.056211","article-title":"Directionality of coupling from bivariate time series: How to avoid false causalities and missed connections","volume":"75","author":"Palus","year":"2007","journal-title":"Phys. Rev. E"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1016\/j.asr.2010.10.026","article-title":"Predictive Space Weather: An information theory approach","volume":"47","author":"Materassi","year":"2011","journal-title":"Adv. Space. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5748","DOI":"10.1002\/2014GL060928","article-title":"External versus internal triggering of substorms: An information-theoretical approach","volume":"41","author":"Johnson","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"9378","DOI":"10.1002\/2016JA022711","article-title":"Information theoretical approach to discovering solar wind drivers of the outer radiation belt","volume":"121","author":"Wing","year":"2016","journal-title":"J. Geophys. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"16987","DOI":"10.1038\/s41598-018-35250-5","article-title":"Common solar wind drivers behind magnetic storms-magnetospheric substorm dependency","volume":"8","author":"Runge","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1111\/j.1365-246X.1978.tb05494.x","article-title":"A study of geomagnetic storms","volume":"54","author":"Perreault","year":"1978","journal-title":"Geophys. J. Roy. Astron. Soc."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.5636\/jgg.42.1249","article-title":"Storm-time magnetospheric currents inferred from midlatitude geomagnetic field variations","volume":"42","author":"Iyemori","year":"1990","journal-title":"J. Geomagn. Geoelectr."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1029\/JZ071i003p00785","article-title":"Auroral electroject activity index AE and its universal time variations","volume":"71","author":"Davies","year":"1966","journal-title":"J. Geophys. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"107","DOI":"10.3847\/1538-4357\/aab712","article-title":"A Short-term ESPERTA-based Forecast Tool for Moderate-to-extreme Solar Proton Events","volume":"857","author":"Laurenza","year":"2018","journal-title":"Astrophys. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_31","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience. [2nd ed.]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","article-title":"Measuring Information Transfer","volume":"85","author":"Schreiber","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wibral, M., Pampu, N., Priesemann, V., Siebenh\u00fchner, F., Seiwert, H., Lindner, M., Lizier, J.T., and Vicente, R. (2013). Measuring Information-Transfer Delays. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0055809"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"066138","DOI":"10.1103\/PhysRevE.69.066138","article-title":"Estimating mutual information","volume":"69","author":"Kraskov","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1209\/epl\/i2004-10483-y","article-title":"Hierarchical clustering using mutual information","volume":"70","author":"Kraskov","year":"2005","journal-title":"Europhys. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/S0167-2789(00)00043-9","article-title":"Surrogate time series","volume":"142","author":"Schreiber","year":"2000","journal-title":"Phys. D"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"27039","DOI":"10.1029\/97JA02639","article-title":"Coordinated observations demonstrating external substorm triggering","volume":"102","author":"Lyons","year":"1997","journal-title":"J. Geophys. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"729","DOI":"10.5636\/jgg.48.729","article-title":"Auroral ionospheric ion feeding of the inner plasma sheet during substorms","volume":"48","author":"Daglis","year":"1994","journal-title":"J. Geophys. Geoelectr."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1029\/1999RG900009","article-title":"The terrestrial ring current: Origin, formation, and decay","volume":"37","author":"Daglis","year":"1999","journal-title":"Rev. Geophys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/B:SPAC.0000042938.57710.fb","article-title":"Several controversial issues on substorms","volume":"113","author":"Akasofu","year":"2004","journal-title":"Space Sci. Rev."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1029\/97EO00162","article-title":"Terrestrial agents in the realm of space storms: Missions study oxygen ions","volume":"24","author":"Daglis","year":"1997","journal-title":"Eos Trans. AGU"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"989","DOI":"10.5194\/angeo-24-989-2006","article-title":"Geomagnetic Dst index forecast based on IMF data only","volume":"24","author":"Pallocchia","year":"2006","journal-title":"Annales Geophys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2244","DOI":"10.1016\/j.pss.2007.05.017","article-title":"Thermodynamics of rare events and impulsive relaxation events in the magnetospheric substorm dynamics","volume":"55","author":"Consolini","year":"2007","journal-title":"Planetary Space Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/276\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:02:36Z","timestamp":1760173356000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,28]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["e22030276"],"URL":"https:\/\/doi.org\/10.3390\/e22030276","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,28]]}}}