Ionosphere fluctuations and global indices: A scale dependent wavelet-based cross-correlation analysis S.G. Roux a,n , P. Koucka´ Knı´zˇova´ b , Z. Moˇ sna b , P. Abry a a Laboratoire de Physique (UMR 5672), CNRS, Ecole Normale Supe´rieure, Lyon, France b Institute of Atmospheric Physics ASCR, Czech Republic article info Article history: Received 6 August 2011 Received in revised form 21 March 2012 Accepted 26 March 2012 Available online 5 April 2012 Keywords: Ionosphere F-layer foF2-measurements Global indices Solar activity Geomagnetic activity Cross-correlation Scale invariance Wavelet transform Wavelet coherence function abstract Ionosphere corresponds to the ionized upper part of atmosphere. Characterizing Ionosphere variations is of major importance to address both practical (radio-communications and navigation systems) and theoretical (Space–Earth coupling, climatological global change, and human activity impact) issues. Therefore, establishing a statistical description of Ionosphere variations and relating them to potential driving sources such as global solar and geomagnetic activities constitute important stakes. often, Ionosphere variations are described in terms of long-term trends versus short-term fluctuations. To better ground such a separation, instead of performing a classical and arbitrary low-pass versus high- pass filtering operation, it is here, instead, propose to recourse to a scale dependent analysis. It is based on a (continuous) wavelet transform and the wavelet coherence function. Applied to F2-region critical frequency data, locally measured at 11 mid-latitude European stations, as well as to five global solar and geomagnetic indices, these tools show that Ionospheric variations are well described by the superimposition of well-defined long-term cycles with highly correlated fractional Gaussian noise fluctuations. Also, they show that mid-latitude European stations display highly correlated variations even for short-term fluctuations and that, while solar activity mostly drives long-term cycles, short- term fluctuations and scaling properties are essentially controlled by geomagnetic activity. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Motivation Variability in (the F-region of) Ionosphere. Ionosphere consists of a plasma formed in the upper layers of the atmosphere, at heights corresponding to mesosphere and thermosphere, with high density of free electrons. Ionosphere therefore behaves as a large system showing a strong variability in its concentration fluctuations over a broad continuum of time-scales ranging from minutes (such as for e.g., Traveling Ionospheric Disturbances) to years (e.g., long-term variations such as those induced by the solar cycle). A comprehen- sive characterization of such fluctuations is of major importance notably for radio-communications and navigation systems. Indeed, with the increasing human activity in space, which degrades substantially the quality of satellite navigation systems (phase cycle slips, receiver loss of lock, etc., cf. e.g., Zolesi and Cander, 2004), Ionospheric variability appears of great importance because of its impact influence on communication with ground. Ionosphere variability analysis may also potentially bring new and significant knowledges related to Ionospheric climatology. The Ionospheric F-region variability notably has received increasing attention and efforts (cf. e.g., Forbes et al., 2000; Rishbeth and Mendillo, 2001; Mendillo et al., 2002), mostly due to the role Ionosphere plays into Earth environment mechanisms via coupling processes stemming from above and below. Solar and geomagnetic impact on Ionosphere. It is widely accepted that the solar and geomagnetic activities act as the main drivers of the Ionospheric variability, although meteorological causes transmitted from below may also contribute significantly (cf. Prolss, 2004). For instance, Ionospheric disturbances and storms often follow geomag- netic disturbances. Therefore, numerous attempts were conducted to assess correlation between geomagnetic and/or solar indices and Ionospheric variability (cf. Wu and Wilkinson, 1995; Kutiev et al., 1999; Francis et al., 2000; Richards, 2001; Mendillo et al., 2002, amongst many others) and to derive models for ionospheric fluctua- tion predictions (cf. Mikhailov, 1999 for a review of such models and limitations). Comparative studies tried to assess the solar wind impact on magnetospheric variability (cf. e.g., Consolini et al., 1996; Consolini and de Michelis, 2005). Despite those efforts, it is commonly admitted that Ionosphere fluctuation forecasting remains in an unsatisfactory state and that there is still a lot to achieve to refine correlation characterization and prediction models. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jastp Journal of Atmospheric and Solar-Terrestrial Physics 1364-6826/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jastp.2012.03.014 n Corresponding author. Tel.: þ33 4 72 72 83 78; fax: þ33 4 72 72 89 50. E-mail addresses: stephane.roux@ens-lyon.fr (S.G. Roux), pkn@ufa.cas.cz (P. Koucka´ Knı´zˇova´ ), patrice.abry@ens-lyon.fr (P. Abry). Journal of Atmospheric and Solar-Terrestrial Physics 90–91 (2012) 186–197