Forecasting the geomagnetic activity of the Dst Index using radial basis function networks

The Dst index is a key parameter which characterises the disturbance of the geomagnetic field in magnetic storms. Modelling of the Dst index is thus very important for the analysis of the geomagnetic field. A data-based modelling approach, aimed at obtaining efficient models based on limited input-output observational data, provides a powerful tool for analysing and forecasting geomagnetic activities including the prediction of the Dst index. Radial basis function (RBF) networks are an important and popular network model for nonlinear system identification and dynamical modelling. A novel generalised multiscale RBF (MSRBF) network is introduced for Dst index modelling. The proposed MSRBF network can easily be converted into a linear-in-the-parameters form and the training of the linear network model can easily be implemented using an orthogonal least squares (OLS) type algorithm. One advantage of the new MSRBF network, compared with traditional single scale RBF networks, is that the new network is more flexible for describing complex nonlinear dynamical systems

Whistler Mode Waves Below Lower Hybrid Resonance Frequency: Generation and Spectral Features

Equatorial noise in the frequency range below the lower hybrid resonance frequency, whose structure is shaped by high proton cyclotron harmonics, has been observed by the Cluster spacecraft. We develop a model of this wave phenomenon which assumes (as, in general, has been suggested long ago) that the observed spectrum is excited due to loss-cone instability of energetic ions in the equatorial region of the magnetosphere. The wave field is represented as a sum of constant frequency wave packets which cross a number of cyclotron resonances while propagating in a highly oblique mode along quite specific trajectories. The growth (damping) rate of these wave packets varies both in sign and magnitude along the ray path, making the wave net amplification, but not the growth rate, the main characteristic of the wave generation process. The growth rates and the wave amplitudes along the ray paths, determined by the equations of geometrical optics, have been calculated for a 3D set of wave packets with various frequencies, initial L-shells, and initial wave normal angles at the equator. It is shown that the dynamical spectrum resulting from the proposed model qualitatively matches observations

Electron Flux Dropouts at L ∼ 4.2 From Global Positioning System Satellites: Occurrences, Magnitudes, and Main Driving Factors

Dropouts in electron fluxes at L ∼ 4.2 were investigated for a broad range of energies from 120 keV to 10 MeV, using 16 years of electron flux data from Combined X-ray Dosimeter on board Global Positioning System (GPS) satellites. Dropouts were defined as flux decreases by at least a factor 4 in 12 h, or 24 h during which a decrease by at least a factor of 1.5 must occur during each 12 h time bin. Such fast and strong dropouts were automatically identified from the GPS electron flux data and statistics of dropout magnitudes, and occurrences were compiled as a function of electron energy. Moreover, the Error Reduction Ratio analysis was employed to search for nonlinear relationships between electron flux dropouts and various solar wind and geomagnetic activity indices, in order to identify potential external causes of dropouts. At L ∼ 4.2, the main driving factor for the more numerous and stronger 1-10 MeV electron dropouts turns out to be the southward interplanetary magnetic field B s , suggesting an important effect from precipitation loss due to combined electromagnetic ion cyclotron and whistler mode waves in a significant fraction of these events, supplementing magnetopause shadowing and outward radial diffusion which are also effective at lower energies

Electron flux dropouts at GEO: occurrences, magnitudes, and main driving factors

Large decreases of daily average electron flux, or dropouts, were investigated for a range of energies from 24.1 keV to 2.7 MeV, on the basis of a large database of 20 years of measurements from Los Alamos National Laboratory (LANL) geosynchronous satellites. Dropouts were defined as flux decreases by at least a factor 4 in 1 day, or a factor 9 in 2 days during which a decrease by at least a factor of 2.5 must occur each day. Such decreases were automatically identified. As a first result, a comprehensive statistics of the mean waiting time between dropouts and of their mean magnitude has been provided as a function of electron energy. Moreover, the Error Reduction Ratio analysis was applied to explore the possible nonlinear relationships between electron dropouts and various exogenous factors, such as solar wind and geomagnetic indices. Different dropout occurrences and magnitudes were found in three distinct energy ranges, lower than 100 keV, 100–600 keV, and larger than 600 keV, corresponding to different groups of drivers and loss processes. Potential explanations have been outlined on the basis of the statistical results

Wavelet Based Nonparametric Additive Models for Nonlinear System Identification and Prediction

Wavelet based nonparametric additive models are considered for nonlinear system identification. Additive functional component representations are an important class of models for describing nonlinear input-output relationships and eavelets, which have excellent approximation capabilities, can be chosen as the functional components in the additive models. Wavelet based additive models, combined with model order determination and variable selection, are capable of handling problems of high dimensionality. Examples are given to demonstrate the efficiency of this new modelling approach

Wavelet Based Nonparametric NARX Models for Nonlinear Input-Output System Identification

Wavelet based nonparametric additive NARX models are proposed for nonlinear input-output system identification. By expanding each functional component of the nonparametic NARX model into wavelet multiresolution expansions, the nonparametric estimation problem becomes a linear-in-the-parameters problem and least-squares-based methods such as the orthogonal forward regression (OFR) approach can be used to select the model terms and estimate the parameters. Wavelet based additive models, combined with model order determination and variable selection approaches, are capable of handling problems of high dimensionality

Investigation of the Chirikov resonance overlap criteria for equatorial magnetosonic waves

Observations of equatorial magnetosonic waves made during the Cluster I nnerMagnetospheric Campaign clearly show discrete spectra consisting of emissions around harmonics of theproton gyrofrequency. Equatorial magnetosonic waves are important because of their ability to efficientlyscatter electrons in energy and pitch angle. This wave-particle interaction is numerically modeled throughthe use of diffusion coefficients, calculated based on a continuous spectrum such as that observed byspectrum analyzers. Using the Chirikov overlap resonance criterion, the calculation of the diffusioncoefficient will be assessed to determine whether they should be calculated based on the discrete spectralfeatures as opposed to a continuous spectrum. For the period studied, it is determined that the discretenature of the waves does fulfill the Chirikov overlap criterion and so the use of quasi-linear theory with theassumption of a continuous frequency spectrum is valid for the calculation of diffusion coefficients

Comparison of the Dynamic Processes in Plasma Turbulence Observed in the High and Low-B Regions of the Terrestrial Foreshock

This paper highlights the fact that the dynamical processes that characterise plasma turbulence observed in the high-B region of the terrestrial foreshock are significantly different from the dynamical processes identified in the low B-region. The study is based on a time-domain model identified from measurements taken by AMPTE-UKS and AMPTE-IRM satellites

Cluster observations of non-time-continuous magnetosonic waves

Equatorial magnetosonic waves are normally observed as temporally continuous sets of emissions lasting from minutes to hours. Recent observations, however, have shown that this is not always the case. Using Cluster data, this study identifies two distinct forms of these non-temporallycontinuous emissions. The first, referred to as rising tone emissions, are characterised by the systematic onset of wave activity at increasing proton gyroharmonic frequencies. Sets of harmonic emissions (emission elements) are observed to occur periodically in the region ±10◦ off the geomagnetic equator. The sweep rate of these emissions maximises at the geomagnetic equator. In addition, the ellipticity and propagation direction also change systematically as Cluster crosses the geomagnetic equator. It is shown that the observed frequency sweep rate is unlikely to result from the sideband instability related to nonlinear trapping of suprathermal protons in the wave field. The second form of emissions is characterised by the simultaneous onset of activity across a range of harmonic frequencies. These waves are observed at irregular intervals. Their occurrence correlates with changes in the spacecraft potential, a measurement that is used as a proxy for electron densit

Prediction of Kp Index Using NARMAX Models with A Robust Model Structure Selection Method

The severity of global magnetic disturbances in Near-Earth space can crucially affect human life. These geomagnetic disturbances are often indicated by a Kp index, which is derived from magnetic field data from ground stations, and is known to be correlated with solar wind observations. Forecasting of Kp index is important for understanding the dynamic relationship between the magnetosphere and solar wind. This study presents 3 hours ahead prediction for Kp index using the NARMAX model identified by a novel robust model structure detection method. The identified models are evaluated using 4 years of Kp data. Overall, the models with robust structure can produce very good Kp forecast results and provide transparent and compact representations of the relationship between Kp index and solar wind variables. The robustness and conciseness of the models can highly benefit the space weather forecast tasks