Georgios Balasis

Introducing POMME, the POtsdam Magnetic Model of the Earth

Models of the main and external field play a key role in the analysis and interpretation of satellite, airborne, marine and ground magnetic data. Here, we introduce a series of main field models with several new features: (1) External fields are parametrised in SM and GSM coordinate systems, accounting for the geometry of the ring current, the magnetosphere and the solar wind. (2) We use vector data globally, instead of the usual approach of using vector data at low latitudes and scalar data at high latitudes. (3) The angles between CHAMPs star camera and its vector magnetometer are co-estimated in a joint inversion with Orsted data. (4) The model includes 2nd time derivatives of the magnetic field to account for the non-negligible secular acceleration in the current period of new magnetic satellite data. As inferred from the degree spectrum of the current version POMME-1.4, the secular variation is stable to degree 11 and the secular acceleration to degree 6.

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

Empirical orthogonal function analysis of magnetic observatory data : further evidence for non-axisymmetric magnetospheric sources for satellite induction studies

comprehensive model, has a substantial Y2 1 quadrupole component and is highly correlated with Dst. This pattern of temporal variability, which implies enhanced ring current densities in the dusk sector, persists even when peak stormtime data are omitted. The observed asymmetry agrees with that inferred previously by Balasis et al. (2004), from the local time dependence of biases in satellite induction transfer functions. Temporal correlation of the leading mode with Dst, and consistency of its spatial structure with recent empirical ring current models, suggest a magnetospheric origin. Citation: Balasis, G., and G. D. Egbert (2006), Empirical orthogonal function analysis of magnetic observatory data: Further evidence for nonaxisymmetric magnetospheric sources for satellite induction studies, Geophys. Res. Lett., 33, L11311, doi:10.1029/ 2006GL025721.

THE MAJOR GEOEFFECTIVE SOLAR ERUPTIONS OF 2012 MARCH 7: COMPREHENSIVE SUN-TO-EARTH ANALYSIS

During the interval 2012 March 7–11 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultra-low-frequency wave enhancements and relativistic-electron dropouts in the radiation belts, as well as strong energetic-electron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultra-fast (>2000 km s) coronal mass ejections (CMEs), linked to two X-class flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic Sun-to-Earth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earth-directed. Using a novel method, we estimated its near-Sun magnetic field at 13 Re to be in the range [0.01, 0.16] G. Steep radial fall-offs of the near-Sun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solar-wind conditions, as resulting from the shock associated with the Earth-directed CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiation-belt dynamics.

Magnetospheric ULF wave studies in the frame of Swarm mission: a time-frequency analysis tool for automated detection of pulsations in magnetic and electric field observations

We combine the advantages of multi-spacecraft and ground-based monitoring of the geospace environment in order to analyze and study magnetospheric ultra low frequency (ULF) waves. In line with this aim, we also develop and deliver relevant analysis tools based on wavelet transforms and tailored to the Swarm mission. In the preparation phase as well as the lifetime of the Swarm mission, the analysis of isolated ULF wave events— especially those detected in the Pc3 frequency range (20–100 mHz) that a topside ionosphere mission efficiently resolves—can help to elucidate the processes that play a crucial role in the generation of waves and their most defining propagation characteristics. Additionally, we offer a useful platform to monitor the wave evolution from the outer boundaries of Earth’s magnetosphere through the topside ionosphere down to the surface. Data from a single Low Earth Orbit (LEO) satellite (CHAMP), a multi-satellite LEO mission (ST5) and the ongoing multi-satellite magnetospheric mission (Cluster) along with a ground-based magnetic network (CARISMA) are used to demonstrate the potential of our analysis technique in studying wave evolution in detail. A better understanding of the generation and propagation of waves will also allow to geophysically validate some of Swarm’s data products, especially those related to the magnetic and electric fields in geospace. With a carefully selected case study focusing on the recovery phase of a moderate magnetic storm (9 April 2006 with a minimum Dst value of −82 nT) as a starting point, we clearly demonstrate the capabilities offered by our wavelet analysis tools and highlight the options opened to treat various categories of multipoint multi-instrument measurements (both spaceborne and ground-based) for signatures of ULF wave signals as well as the effects of various other sources.

Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Over the last couple of decades nonextensive Tsallis entropy has shown remarkable applicability to describe nonequilibrium physical systems with large variability and multifractal structure. Herein, we review recent results from the application of Tsallis statistical mechanics to the detection of dynamical changes related with the occurrence of magnetic storms. We extend our review to describe attempts to approach the dynamics of magnetic storms and solar flares by means of universality through Tsallis statistics. We also include a discussion of possible implications on space weather forecasting efforts arising from the verification of Tsallis entropy in the complex system of the magnetosphere.

Dynamical analogy between epileptic seizures and seismogenic electromagnetic emissions by means of nonextensive statistical mechanics

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and neurodynamics can be analyzed within similar mathematical frameworks. Recently, authors have shown that a dynamical analogy supported by scale-free statistics exists between seizures and earthquakes, analyzing populations of different seizures and earthquakes, respectively. The purpose of this paper is to suggest a shift in emphasis from the large to the small scale: our analyses focus on a single epileptic seizure generation and the activation of a single fault (earthquake) and not on the statistics of sequences of different seizures and earthquakes. We apply the concepts of the nonextensive statistical physics to support the suggestion that a dynamical analogy exists between the two different extreme events, seizures and earthquakes. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes and the distribution of the waiting time until the next event). The performed analysis confirms the existence of a dynamic analogy between earthquakes and seizures, which moreover follow the dynamics of magnetic storms and solar flares.

Detection of Dynamical Complexity Changes in Dst Time Series Using Entropy Concepts and Rescaled Range Analysis

Using an array of diagnostic tools including entropy concepts and rescaled range analysis, we establish that the Dst index time series exhibits long-range correlations, and that the underlying stochastic process can be modeled as fractional Brownian motion. We show the emergence of two distinct patterns in the geomagnetic variability of the terrestrial magnetosphere: (1) a pattern associated with intense magnetic storms, which is characterized by a higher degree of organization (i.e., lower complexity or higher predictability for the system) and persistent behavior, and (2) a pattern associated with normal periods, which is characterized by a lower degree of organization (i.e., higher complexity or lower predictability for the system) and anti-persistent behavior.

Investigating magnetospheric dynamics using various complexity measures

Dynamical complexity detection for output time series of complex systems is one of the foremost problems in physics, biology, engineering, and economic sciences. Especially in magnetospheric physics, accurate detection of the dissimilarity of complexity between normal and abnormal states (e.g. pre‐storm activity and magnetic storms) can vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. A variety of complexity measures based on linear and nonlinear analysis techniques (i.e., wavelet transforms and entropies, respectively) is applied to the Dst index time variations in order to detect changes that can play the role of warnings for future magnetic storm occurrence.

Observation of Intermittency‐Induced Critical Dynamics in Geomagnetic Field Time Series Prior to the Intense Magnetic Storms of March, June, and December 2015

Criticality has been proposed as a suitable framework to study the nonlinear system of the Earth’s magnetosphere. The magnetic field variations observed by the midlatitude HellENIc GeoMagnetic Array with respect to the most intense magnetic storms (Dst < −150 nT) of the current solar cycle (i.e., 17 March, 23 June, and 20 December 2015) are analyzed using the method of critical fluctuations. We show that the application of method of critical fluctuation to the HellENIc GeoMagnetic Array time series reveals the existence of intermittency-induced criticality in the range of 6 to 45 hr prior to the onset of these events. The results suggest that the underlying dynamical processes in the magnetosphere prior to intense magnetic storms present dynamics analogous to those of thermal systems undergoing second-order phase transition. Our findings demonstrate that the proposed method can be very relevant for the analysis of critical fluctuations in the framework of space systems.