Decomposing solar and geomagnetic activity and seasonal dependencies to examine the relationship between GPS loss of lock and ionospheric turbulence.

Ionospheric irregularities are plasma density variations that occur at various altitudes and latitudes and whose size ranges from a few meters to a few hundred kilometers. They can have a negative impact on the Global Navigation Satellite Systems (GNSS), on their positioning accuracy and even cause a signal loss of lock (LoL), a phenomenon for which GNSS receivers can no longer track the satellites' signal. Nowadays, the study of plasma density irregularities is important because many of the crucial infrastructures of our society rely on the efficient operation of these positioning systems. It was recently discovered that, of all possible ionospheric plasma density fluctuations, those in a turbulent state and characterized by extremely high values of the Rate Of change of the electron Density Index appear to be associated with the occurrence of LoL events. The spatial distributions of this class of fluctuations at mid and high latitudes are reconstructed for the first time using data collected on Swarm satellites between July 15th, 2014 and December 31st, 2021, emphasizing their dependence on solar activity, geomagnetic conditions, and season. The results unequivocally show that the identified class of plasma fluctuations exhibits spatio-temporal behaviours similar to those of LoL events.

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 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 K2-1 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'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.

Dissipation of field-aligned currents in the topside ionosphere.

Field-aligned currents (FACs) are electric currents parallel to the geomagnetic field and connecting the Earth's magnetosphere to the high-latitude ionosphere. Part of the energy injected into the ionosphere by FACs is converted into kinetic energy of the surrounding plasma. Such a current dissipation is poorly investigated, mainly due to the high electrical conductivity and the small electric field strength expected in direction parallel to the geomagnetic field. However, previous results in literature have shown that parallel electric field is not null (and may be locally not negligible), and that parallel electrical conductivity is high but finite. Thus, dissipation of FACs may occur. In this work, for the first time, we show maps of power density dissipation features associated with FACs in the topside ionosphere of the Northern hemisphere. To this aim, we use a 6-year time series of data at one second cadence acquired by the European Space Agency's "Swarm A" satellite flying at an altitude of about 460 km. In particular, we use data from the Langmuir probe together with the FAC product provided by the Swarm team. The results obtained point out that dissipation of FACs, even if small when compared to that associated with horizontal currents flowing about 350 km lower, is not null and shows evident features co-located with electron temperature at the same altitude. In particular, power density dissipation features are enhanced mainly in the ionospheric regions where intense energy injection from the magnetosphere occurs. In addition, these features depend on geomagnetic activity, which quantifies the response of the Earth's environment to energetic forcing from magnetized plasma of solar origin.

Local dimensionality and inverse persistence analysis of atmospheric turbulence in the stable boundary layer.

The dynamics across different scales in the stable atmospheric boundary layer has been investigated by means of two metrics, based on instantaneous fractal dimensions and grounded in dynamical systems theory. The wind velocity fluctuations obtained from data collected during the Cooperative Atmosphere-Surface Exchange Study-1999 experiment were analyzed to provide a local (in terms of scales) and an instantaneous (in terms of time) description of the fractal properties and predictability of the system. By analyzing the phase-space projections of the continuous turbulent, intermittent, and radiative regimes, a progressive transformation, characterized by the emergence of multiple low-dimensional clusters embedded in a high-dimensional shell and a two-lobe mirror symmetrical structure of the inverse persistence, have been found. The phase space becomes increasingly complex and anisotropic as the turbulent fluctuations become uncorrelated. The phase space is characterized by a three-dimensional structure for the continuous turbulent samples in a range of scales compatible with the inertial subrange, where the phase-space-filling turbulent fluctuations dominate the dynamics, and is low dimensional in the other regimes. Moreover, lower-dimensional structures present a stronger persistence than the higher-dimensional structures. Eventually, all samples recover a three-dimensional structure and higher persistence level at large scales, far from the inertial subrange. The two metrics obtained in the analysis can be considered as proxies for the decorrelation time and the local anisotropy in the turbulent flow.

Analysis of Pseudo-Lyapunov Exponents of Solar Convection Using State-of-the-Art Observations.

The solar photosphere and the outer layer of the Sun's interior are characterized by convective motions, which display a chaotic and turbulent character. In this work, we evaluated the pseudo-Lyapunov exponents of the overshooting convective motions observed on the Sun's surface by using a method employed in the literature to estimate those exponents, as well as another technique deduced from their definition. We analyzed observations taken with state-of-the-art instruments at ground- and space-based telescopes, and we particularly benefited from the spectro-polarimetric data acquired with the Interferometric Bidimensional Spectrometer, the Crisp Imaging SpectroPolarimeter, and the Helioseismic and Magnetic Imager. Following previous studies in the literature, we computed maps of four quantities which were representative of the physical properties of solar plasma in each observation, and estimated the pseudo-Lyapunov exponents from the residuals between the values of the quantities computed at any point in the map and the mean of values over the whole map. In contrast to previous results reported in the literature, we found that the computed exponents hold negative values, which are typical of a dissipative regime, for all the quantities derived from our observations. The values of the estimated exponents increase with the spatial resolution of the data and are almost unaffected by small concentrations of magnetic field. Finally, we showed that similar results were also achieved by estimating the exponents from residuals between the values at each point in maps derived from observations taken at different times. The latter estimation technique better accounts for the definition of these exponents than the method employed in previous studies.

Causality and Information Transfer Between the Solar Wind and the Magnetosphere-Ionosphere System.

An information-theoretic approach for detecting causality and information transfer is used to identify interactions of solar activity and interplanetary medium conditions with the Earth's magnetosphere-ionosphere systems. A causal information transfer from the solar wind parameters to geomagnetic indices is detected. The vertical component of the interplanetary magnetic field (Bz) influences the auroral electrojet (AE) index with an information transfer delay of 10 min and the geomagnetic disturbances at mid-latitudes measured by the symmetric field in the H component (SYM-H) index with a delay of about 30 min. Using a properly conditioned causality measure, no causal link between AE and SYM-H, or between magnetospheric substorms and magnetic storms can be detected. The observed causal relations can be described as linear time-delayed information transfer.

Looking for a proxy of the ionospheric turbulence with Swarm data.

The present work focuses on the analysis of the scaling features of electron density fluctuations in the mid- and high-latitude topside ionosphere under different conditions of geomagnetic activity. The aim is to understand whether it is possible to identify a proxy that may provide information on the properties of electron density fluctuations and on the possible physical mechanisms at their origin, as for instance, turbulence phenomena. So, we selected about 4 years (April 2014-February 2018) of 1 Hz electron density measurements recorded on-board ESA Swarm A satellite. Using the Auroral Electrojet (AE) index, we identified two different geomagnetic conditions: quiet (AE < 50 nT) and active (AE > 300 nT). For both datasets, we evaluated the first- and second-order scaling exponents and an intermittency coefficient associated with the electron density fluctuations. Then, the joint probability distribution between each of these quantities and the rate of change of electron density index was also evaluated. We identified two families of plasma density fluctuations characterized by different mean values of both the scaling exponents and the considered ionospheric index, suggesting that different mechanisms (instabilities/turbulent processes) can be responsible for the observed scaling features. Furthermore, a clear different localization of the two families in the magnetic latitude-magnetic local time plane is found and its dependence on geomagnetic activity levels is analyzed. These results may well have a bearing about the capability of recognizing the turbulent character of irregularities using a typical ionospheric plasma irregularity index as a proxy.

On Yaglom's Law for the Interplanetary Proton Density and Temperature Fluctuations in Solar Wind Turbulence.

In the past decades, there has been an increasing literature on the presence of an inertial energy cascade in interplanetary space plasma, being interpreted as the signature of Magnetohydrodynamic turbulence (MHD) for both fields and passive scalars. Here, we investigate the passive scalar nature of the solar wind proton density and temperature by looking for scaling features in the mixed-scalar third-order structure functions using measurements on-board the Ulysses spacecraft during two different periods, i.e., an equatorial slow solar wind and a high-latitude fast solar wind, respectively. We find a linear scaling of the mixed third-order structure function as predicted by Yaglom's law for passive scalars in the case of slow solar wind, while the results for fast solar wind suggest that the mixed fourth-order structure function displays a linear scaling. A simple empirical explanation of the observed difference is proposed and discussed.

Multiscale measures of phase-space trajectories.

Characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series is one of the most intensively studied contemporary problems in nonlinear sciences. In this work, we address this problem by combining two established concepts-empirical mode decomposition (EMD) and generalized fractal dimensions-into a unified analysis framework. Specifically, we demonstrate that the intrinsic mode functions derived by EMD can be used as a source of local (in terms of scales) information about the properties of the phase-space trajectory of the system under study, allowing us to derive multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three well-known low-dimensional deterministic dynamical systems (the Hénon map, the Lorenz '63 system, and the standard map), three realizations of fractional Brownian motion with different Hurst exponents, and two somewhat higher-dimensional deterministic dynamical systems (the Lorenz '96 model and the on-off intermittency model). These examples allow us to assess the performance of our formalism with respect to practically relevant aspects like additive noise, different initial conditions, the length of the time series under study, low- vs high-dimensional dynamics, and bursting effects. Finally, by taking advantage of two real-world systems whose multiscale features have been widely investigated (a marine stack record providing a proxy of the global ice volume variability of the past 5×106 years and the SYM-H geomagnetic index), we also illustrate the applicability of this formalism to real-world time series.

Measuring Information Coupling between the Solar Wind and the Magnetosphere-Ionosphere System.

The interaction between the solar wind and the Earth's magnetosphere-ionosphere system is very complex, being essentially the result of the interplay between an external driver, the solar wind, and internal processes to the magnetosphere-ionosphere system. In this framework, modelling the Earth's magnetosphere-ionosphere 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-magnetosphere-ionosphere system. We show that a time delay of about 30-60 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.

Dynamical Complexity of the 2015 St. Patrick's Day Magnetic Storm at Swarm Altitudes Using Entropy Measures.

The continuously expanding toolbox of nonlinear time series analysis techniques has recently highlighted the importance of dynamical complexity to understand the behavior of the complex solar wind-magnetosphere-ionosphere-thermosphere coupling system and its components. Here, we apply new such approaches, mainly a series of entropy methods to the time series of the Earth's magnetic field measured by the Swarm constellation. We show successful applications of methods, originated from information theory, to quantitatively study complexity in the dynamical response of the topside ionosphere, at Swarm altitudes, focusing on the most intense magnetic storm of solar cycle 24, that is, the St. Patrick's Day storm, which occurred in March 2015. These entropy measures are utilized for the first time to analyze data from a low-Earth orbit (LEO) satellite mission flying in the topside ionosphere. These approaches may hold great potential for improved space weather nowcasts and forecasts.

Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection.

The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions at different timescales, are investigated and compared with the symmetry conjecture of the steady-state fluctuation theorem by Gallavotti and Cohen. Our results show that solar turbulent convection satisfies the symmetries predicted by the fluctuation relation of the Gallavotti and Cohen theorem at a local level.

A stretched logistic equation for pandemic spreading.

In this brief work we present a novel approach to the logistic dynamics of populations and epidemic spreading that can take into account of the complex nature of such a process in several real situations, where due to different agents the dynamics is no longer characterized by a single characteristic timescale, but conversely by a distribution of time scales, rendered via a time-dependent growth rate. In detail, a differential equation containing a power-law time dependent growth rate is proposed, whose solution, named Stretched Logistic Function, provides a modified version of the usual logistic function. The model equation is inspired by and applied to the recent spreading on COVID-19 disease in Italy, showing how the real dynamics of infection spreading is characterized by a time dependent dynamics. A speculative discussion of the Stretched Logistic Function in relation to diffusion processes is attempted.

Multifractal and Chaotic Properties of Solar Wind at MHD and Kinetic Domains: An Empirical Mode Decomposition Approach.

Turbulence, intermittency, and self-organized structures in space plasmas can be investigated by using a multifractal formalism mostly based on the canonical structure function analysis with fixed constraints about stationarity, linearity, and scales. Here, the Empirical Mode Decomposition (EMD) method is firstly used to investigate timescale fluctuations of the solar wind magnetic field components; then, by exploiting the local properties of fluctuations, the structure function analysis is used to gain insights into the scaling properties of both inertial and kinetic/dissipative ranges. Results show that while the inertial range dynamics can be described in a multifractal framework, characterizing an unstable fixed point of the system, the kinetic/dissipative range dynamics is well described by using a monofractal approach, because it is a stable fixed point of the system, unless it has a higher degree of complexity and chaos.

Magnetic reconnection rate in space plasmas: a fractal approach.

Magnetic reconnection is generally discussed via a fluid description. Here, we evaluate the reconnection rate assuming a fractal topology of the reconnection region. The central idea is that the fluid hypothesis may be violated at the scales where reconnection takes place. The reconnection rate, expressed as the Alfvén Mach number of the plasma moving toward the diffusion region, is shown to depend on the fractal dimension and on the sizes of the reconnection or diffusion region. This mechanism is more efficient than prediction of the Sweet-Parker model and even Petschek's model for finite magnetic Reynolds number. A good agreement also with rates given by Hall MHD models is found. A discussion of the fractal assumption on the diffusion region in terms of current microstructures is proposed. The comparison with in-situ satellite observations suggests the reconnection region to be a filamentary domain.

Generalized dimensions for fluctuations in the solar wind.

We analyze time series of velocities of the solar wind plasma including the outward-directed component of Alfvénic turbulence within slow wind observed by the Helios 2 spacecraft in the inner heliosphere. We demonstrate that the influence of noise in the data can be efficiently reduced by a singular-value decomposition filter. The resulting generalized dimensions show a multifractal structure of the solar wind attractor in the inner heliosphere. The obtained multifractal spectrum is consistent with that for the multifractal measure on the self-similar weighted baker's map with two parameters describing uniform compression and natural invariant measure on the attractor of the system.

Stochastic resonance in geomagnetic polarity reversals.

Among noise-induced cooperative phenomena a peculiar relevance is played by stochastic resonance. In this paper we offer evidence that geomagnetic polarity reversals may be due to a stochastic resonance process. In detail, analyzing the distribution function P(tau) of polarity residence times (chrons), we found the evidence of a stochastic synchronization process, i.e., a series of peaks in the P(tau) at T(n) approximately (2n+1)T(Omega)/2 with n=0,1,...,j and T(omega) approximately 0.1 Myr. This result is discussed in connection with both the typical time scale of Earth's orbit eccentricity variation and the recent results on the typical time scale of climatic long-term variation.

Fluid motions in the Earth's core inferred from time spectral features of the geomagnetic field.

The aim of this work is to investigate the time spectral features of the main geomagnetic field fluctuations as measured on the Earth's surface in connection with a nontraditional turbulent dynamics of the fluid motions in the outer layers of the Earth's liquid core. The average geomagnetic field spectrum is found to be a power law, characterized by a spectral exponent alpha approximately -11/3, on time scales longer than 5 yr. We discuss the spectral exponent in connection with an intense magnetic field in the Earth's core and with a vortex coalescence process in a regime of drift-wave turbulence.