R. J. Boynton

Statistical study of chorus wave distributions in the inner magnetosphere using Ae and solar wind parameters

Energetic electrons within the Earths radiation belts represent a serious hazard to geostationary satellites. The interactions of electrons with chorus waves play an important role in both the acceleration and loss of radiation belt electrons. The common approach is to present model wave distributions in the inner magnetosphere under different values of geomagnetic activity as expressed by the geomagnetic indices. However, it has been shown that only around 50% of geomagnetic storms increase flux of relativistic electrons at geostationary orbit while 20% causes a decrease and the remaining 30% has relatively no effect. This emphasizes the importance of including solar wind parameters such as bulk velocity (V), density (n), flow pressure (P), and the vertical interplanetary magnetic field component (Bz) that are known to be predominately effective in the control of high energy fluxes at the geostationary orbit. Therefore, in the present study the set of parameters of the wave distributions is expanded to include the solar wind parameters in addition to the geomagnetic activity. The present study examines almost 4 years (1 January 2004 to 29 September 2007) of Spatio-Temporal Analysis of Field Fluctuation data from Double Star TC1 combined with geomagnetic indices and solar wind parameters from OMNI database in order to present a comprehensive model of wave magnetic field intensities for the chorus waves as a function of magnetic local time, L shell (L), magnetic latitude (λm), geomagnetic activity, and solar wind parameters. Generally, the results indicate that the intensity of chorus emission is not only dependent upon geomagnetic activity but also dependent on solar wind parameters with velocity and southward interplanetary magnetic field Bs (Bz < 0), evidently the most influential solar wind parameters. The largest peak chorus intensities in the order of 50 pT are observed during active conditions, high solar wind velocities, low solar wind densities, high pressures, and high Bs. The average chorus intensities are more extensive and stronger for lower band chorus than the corresponding upper band chorus.

Electron flux dropouts at Geostationary Earth Orbit: 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.

Modeling and prediction of global magnetic disturbance in near‐Earth space: A case study for Kp index using NARX models

Severe geomagnetic disturbances can be hazardous for modern technological systems. The reliable forecast of parameters related to the state of the magnetosphere can facilitate the mitigation of adverse effects of space weather. This study is devoted to the modeling and forecasting of the evolution of the Kp index related to global geomagnetic disturbances. Throughout this work the Nonlinear AutoRegressive with eXogenous inputs (NARX) methodology is applied. Two approaches are presented: i) a recursive sliding window approach, and ii) a direct approach. These two approaches are studied separately and are then compared to evaluate their performances. It is shown that the direct approach outperforms the recursive approach, but both tend to produce predictions slightly biased from the true values for low and high disturbances.

Nonlinear Model Identification From Multiple Data Sets Using an Orthogonal Forward Search Algorithm

A basic assumption on the data used for nonlinear dynamic model identification is that the data points are continuously collected in chronological order. However, there are situations in practice where this assumption does not hold and we end up with an identification problem from multiple data sets. The problem is addressed in this paper and a new cross-validation-based orthogonal search algorithm for NARMAX model identification from multiple data sets is proposed. The algorithm aims at identifying a single model from multiple data sets so as to extend the applicability of the standard method in the cases, such as the data sets for identification are obtained from multiple tests or a series of experiments, or the data set is discontinuous because of missing data points. The proposed method can also be viewed as a way to improve the performance of the standard orthogonal search method for model identification by making full use of all the available data segments in hand. Simulated and real data are used in this paper to illustrate the operation and to demonstrate the effectiveness of the proposed method.

Statistical analysis of electron lifetimes at GEO: Comparisons with chorus-driven losses

The population of electrons in the Earths outer radiation belt increases when the magnetosphere is exposed to high-speed streams of solar wind, coronal mass ejections, magnetic clouds, or other disturbances. After this increase, the number of electrons decays back to approximately the initial population. This study statistically analyzes the lifetimes of the electron at Geostationary Earth Orbit (GEO) from Los Alamos National Laboratory electron flux data. The decay rate of the electron fluxes are calculated for 14 energies ranging from 24 keV to 3.5 MeV to identify a relationship between the lifetime and energy of the electrons. The statistical data show that electron lifetimes increase with energy. Also, the statistical results show a good agreement up to ∼1 MeV with an analytical model of lifetimes, where electron losses are caused by their resonant interaction with oblique chorus waves, using average wave intensities obtained from Cluster statistics. However, above 500 keV, the measured lifetimes increase with energy becomes less steep, almost stopping. This could partly stem from the difficultly of identifying lifetimes larger than 10 days, for high energy, with the methods and instruments of the present study at GEO. It could also result from the departure of the actual geomagnetic field from a dipolar shape, since a compressed field on the dayside should preferentially increase chorus-induced losses at high energies. However, during nearly quiet geomagnetic conditions corresponding to lifetime measurement periods, it is more probably an indication that outward radial diffusion imposes some kind of upper limit on lifetimes of high-energy electrons near geostationary orbit.

Comparative analysis of NOAA REFM and SNB3GEO tools for the forecast of the fluxes of high‐energy electrons at GEO

Abstract Reliable forecasts of relativistic electrons at geostationary orbit (GEO) are important for the mitigation of their hazardous effects on spacecraft at GEO. For a number of years the Space Weather Prediction Center at NOAA has provided advanced online forecasts of the fluence of electrons with energy >2 MeV at GEO using the Relativistic Electron Forecast Model (REFM). The REFM forecasts are based on real‐time solar wind speed observations at L1. The high reliability of this forecasting tool serves as a benchmark for the assessment of other forecasting tools. Since 2012 the Sheffield SNB3GEO model has been operating online, providing a 24 h ahead forecast of the same fluxes. In addition to solar wind speed, the SNB3GEO forecasts use solar wind density and interplanetary magnetic field B z observations at L1.The period of joint operation of both of these forecasts has been used to compare their accuracy. Daily averaged measurements of electron fluxes by GOES 13 have been used to estimate the prediction efficiency of both forecasting tools. To assess the reliability of both models to forecast infrequent events of very high fluxes, the Heidke skill score was employed. The results obtained indicate that SNB3GEO provides a more accurate 1 day ahead forecast when compared to REFM. It is shown that the correction methodology utilized by REFM potentially can improve the SNB3GEO forecast.

Simulation of high‐energy radiation belt electron fluxes using NARMAX‐VERB coupled codes

This study presents a fusion of data-driven and physics-driven methodologies of energetic electron flux forecasting in the outer radiation belt. Data-driven NARMAX (Nonlinear AutoRegressive Moving Averages with eXogenous inputs) model predictions for geosynchronous orbit fluxes have been used as an outer boundary condition to drive the physics-based Versatile Electron Radiation Belt (VERB) code, to simulate energetic electron fluxes in the outer radiation belt environment. The coupled system has been tested for three extended time periods totalling several weeks of observations. The time periods involved periods of quiet, moderate, and strong geomagnetic activity and captured a range of dynamics typical of the radiation belts. The model has successfully simulated energetic electron fluxes for various magnetospheric conditions. Physical mechanisms that may be responsible for the discrepancies between the model results and observations are discussed.

Applications of NARMAX in Space Weather

Abstract The methodology based on Nonlinear AutoRegressive Moving Average eXogenous (NARMAX) models is one of the most robust techniques for studying complex dynamical systems. NARMAX was initially employed to deduce models for engineering systems, which could be used in conjunction with control engineering techniques. However, the power of such a technique was quickly realized, and it has been successfully applied to investigate many diverse systems, such as stem cells dynamics, neuroimaging, finance, and the solar-terrestrial system. This chapter reviews the application of the NARMAX methodology to problems in space weather, such as forecasting the geomagnetic indices and fluxes of the high-energy particles in the radiation belts. As NARMAX provides physically interpretable models, this chapter also discusses how the application of the NARMAX methodology can advance physical understanding of space weather processes.

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.

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.