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Accurately predicting total electron content (TEC) during geomagnetic storms is still a challenging task for ionospheric models. In this work, a neural-network (NN)-based model is proposed which predicts relative TEC with respect to the preceding 27-day median TEC, during storm time for the European region (with longitudes 30 degrees W-50 degrees E and latitudes 32.5 degrees N-70 degrees N). The 27-day median TEC (referred to as median TEC), latitude, longitude, universal time, storm time, solar radio flux index F10.7, global storm index SYM-H and geomagnetic activity index Hp30 are used as inputs and the output of the network is the relative TEC. The relative TEC can be converted to the actual TEC knowing the median TEC. The median TEC is calculated at each grid point over the European region considering data from the last 27 days before the storm using global ionosphere maps (GIMs) from international GNSS service (IGS) sources. A storm event is defined when the storm time disturbance index Dst drops below 50 nanotesla. The model was trained with storm-time relative TEC data from the time period of 1998 until 2019 (2015 is excluded) and contains 365 storms. Unseen storm data from 33 storm events during 2015 and 2020 were used to test the model. The UQRG GIMs were used because of their high temporal resolution (15 min) compared to other products from different analysis centers. The NN-based model predictions show the seasonal behavior of the storms including positive and negative storm phases during winter and summer, respectively, and show a mixture of both phases during equinoxes. The model's performance was also compared with the Neustrelitz TEC model (NTCM) and the NN-based quiet-time TEC model, both developed at the German Aerospace Agency (DLR). The storm model has a root mean squared error (RMSE) of 3.38 TEC units (TECU), which is an improvement by 1.87 TECU compared to the NTCM, where an RMSE of 5.25 TECU was found. This improvement corresponds to a performance increase by 35.6%. The storm-time model outperforms the quiet-time model by 1.34 TECU, which corresponds to a performance increase by 28.4% from 4.72 to 3.38 TECU. The quiet-time model was trained with Carrington averaged TEC and, therefore, is ideal to be used as an input instead of the GIM derived 27-day median. We found an improvement by 0.8 TECU which corresponds to a performance increase by 17% from 4.72 to 3.92 TECU for the storm-time model using the quiet-time-model predicted TEC as an input compared to solely using the quiet-time model.
Different modeling methodologies possess different strengths and weakness. For instance, data based models may provide superior accuracy but have a limited spatial coverage while physics based models may provide lower accuracy but provide greater spatial coverage. This study investigates the coupling of a data based model of the electron fluxes at geostationary orbit (GEO) with a numerical model of the radiation belt region to improve the resulting forecasts/pastcasts of electron fluxes over the whole radiation belt region. In particular, two coupling methods are investigated. The first assumes an average value for L* for GEO, namely LGEO* L-GEO* = 6.2. The second uses a value of L* that varies with geomagnetic activity, quantified using the Kp index. As the terrestrial magnetic field responds to variations in geomagnetic activity, the value of L* will vary for a specific location. In this coupling method, the value of L* is calculated using the Kp driven Tsyganenko 89c magnetic field model for field line tracing. It is shown that this addition can result in changes in the initialization of the parameters at the Versatile Electron Radiation Belt model outer boundary. Model outputs are compared to Van Allen Probes MagEIS measurements of the electron fluxes in the inner magnetosphere for the March 2015 geomagnetic storm. It is found that the fixed LGEO* L-GEO* coupling method produces a more realistic forecast.
Predicting the electron population of Earth's ring current during geomagnetic storms still remains a challenging task.
In this work, we investigate the sensitivity of 10 keV ring current electrons to different driving processes, parameterised by the Kp index, during several moderate and intense storms.
Results are validated against measurements from the Van Allen Probes satellites. Perturbing the Kp index allows us to identify the most dominant processes for moderate and intense storms respectively.
We find that during moderate storms (Kp < 6) the drift velocities mostly control the behaviour of low energy electrons, while loss from wave-particle interactions is the most critical parameter for quantifying the evolution of intense storms (Kp > 6). Perturbations of the Kp index used to drive the boundary conditions at GEO and set the plasmapause location only show a minimal effect on simulation results over a limited L range.
It is further shown that the flux at L & SIM; 3 is more sensitive to changes in the Kp index compared to higher L shells, making it a good proxy for validating the source-loss balance of a ring current model.
In this study we analyze the storm-time evolution of equatorial electron pitch angle distributions (PADs) in the outer radiation belt region using observations from the Magnetic Electron Ion Spectrometer (MagEIS) instrument aboard the Van Allen Probes in 2012-2019. The PADs are approximated using a sum of the first, third and fifth sine harmonics. Different combinations of the respective coefficients refer to the main PAD shapes within the outer radiation belt, namely the pancake, flat-top, butterfly and cap PADs. We conduct a superposed epoch analysis of 129 geomagnetic storms and analyze the PAD evolution for day and night MLT sectors. PAD shapes exhibit a strong energy-dependent response. At energies of tens of keV, the PADs exhibit little variation throughout geomagnetic storms. Cap PADs are mainly observed at energies < 300 keV, and their extent in L shrinks with increasing energy. The cap distributions transform into the pancake PADs around the main phase of the storm on the nightside, and then come back to their original shapes during the recovery phase. At higher energies on the dayside, the PADs are mainly pancake during pre-storm conditions and become more anisotropic during the main phase. The quiet-time butterfly PADs can be observed on the nightside at L> 5.6. During the main phase, butterfly PADs have stronger 90 degrees-minima and can be observed at lower L-shells (down to L = 5), then transitioning into flat-top PADs at L similar to 4.5 - 5 and pancake PADs at L < 4.5. The resulting PAD coefficients for different energies, locations and storm epochs can be used to test the wave models and physics-based radiation belt codes in terms of pitch angle distributions.
In this study, we present an empirical model of the equatorial electron pitch angle distributions (PADs) in the outer radiation belt based on the full data set collected by the Magnetic Electron Ion Spectrometer (MagEIS) instrument onboard the Van Allen Probes in 2012-2019. The PADs are fitted with a combination of the first, third and fifth sine harmonics. The resulting equation resolves all PAD types found in the outer radiation belt (pancake, flat-top, butterfly and cap PADs) and can be analytically integrated to derive omnidirectional flux. We introduce a two-step modeling procedure that for the first time ensures a continuous dependence on L, magnetic local time and activity, parametrized by the solar wind dynamic pressure. We propose two methods to reconstruct equatorial electron flux using the model. The first approach requires two uni-directional flux observations and is applicable to low-PA data. The second method can be used to reconstruct the full equatorial PADs from a single uni- or omnidirectional measurement at off-equatorial latitudes. The model can be used for converting the long-term data sets of electron fluxes to phase space density in terms of adiabatic invariants, for physics-based modeling in the form of boundary conditions, and for data assimilation purposes.
The investigation of heavy ions dynamics and properties in the Earth's magnetosphere is still an important field of research as they play an important role in several space weather aspects. We present a statistical survey of the average ion mass in the dayside magnetosphere made comparing plasma mass density with electron number density measurements and focusing on both spatial and geomagnetic activity dependence. Field line resonance frequency observations across the European quasi-Meridional Magnetometer Array, are used to infer the equatorial plasma mass density in the range of magnetic L-shells 1.6-6.2. The electron number density is derived from local electric field measurements made on Van Allen Probes using the Neural-network-based Upper-hybrid Resonance Determination algorithm. The analysis is conducted separately for the plasmasphere and the plasmatrough during favorable periods for which both the plasma parameters are observed simultaneously. We found that throughout the plasmasphere the average ion mass is similar or equal to 1 amu for a wide range of geomagnetic activity conditions, suggesting that the plasma mainly consist of hydrogen ions, without regard to the level of geomagnetic activity. Conversely, the plasmatrough is characterized by a variable composition, highlighting a heavy ion mass loading that increases with increasing levels of geomagnetic disturbance. During the most disturbed conditions, the average radial structure shows a broad maximum around 3-4 Earth radii, probably correlated with the accumulation of oxygen ions near the plasmapause. Those ions are mostly observed in the post-dawn and pre-dusk longitudinal sectors.
The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.
In this study we investigate two distinct loss mechanisms responsible for the rapid dropouts of radiation belt electrons by assimilating data from Van Allen Probes A and B and Geostationary Operational Environmental Satellites (GOES) 13 and 15 into a 3-D diffusion model. In particular, we examine the respective contribution of electromagnetic ion cyclotron (EMIC) wave scattering and magnetopause shadowing for values of the first adiabatic invariant mu ranging from 300 to 3,000 MeV G(-1). We inspect the innovation vector and perform a statistical analysis to quantitatively assess the effect of both processes as a function of various geomagnetic indices, solar wind parameters, and radial distance from the Earth. Our results are in agreement with previous studies that demonstrated the energy dependence of these two mechanisms. We show that EMIC wave scattering tends to dominate loss at lower L shells, and it may amount to between 10%/hr and 30%/hr of the maximum value of phase space density (PSD) over all L shells for fixed first and second adiabatic invariants. On the other hand, magnetopause shadowing is found to deplete electrons across all energies, mostly at higher L shells, resulting in loss from 50%/hr to 70%/hr of the maximum PSD. Nevertheless, during times of enhanced geomagnetic activity, both processes can operate beyond such location and encompass the entire outer radiation belt.
The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.
The radiation belts of the Earth, filled with energetic electrons, comprise complex and dynamic systems that pose a significant threat to satellite operation. While various models of electron flux both for low and relativistic energies have been developed, the behavior of medium energy (120-600 keV) electrons, especially in the MEO region, remains poorly quantified. At these energies, electrons are driven by both convective and diffusive transport, and their prediction usually requires sophisticated 4D modeling codes. In this paper, we present an alternative approach using the Light Gradient Boosting (LightGBM) machine learning algorithm. The Medium Energy electRon fLux In Earth's outer radiatioN belt (MERLIN) model takes as input the satellite position, a combination of geomagnetic indices and solar wind parameters including the time history of velocity, and does not use persistence. MERLIN is trained on >15 years of the GPS electron flux data and tested on more than 1.5 years of measurements. Tenfold cross validation yields that the model predicts the MEO radiation environment well, both in terms of dynamics and amplitudes o f flux. Evaluation on the test set shows high correlation between the predicted and observed electron flux (0.8) and low values of absolute error. The MERLIN model can have wide space weather applications, providing information for the scientific community in the form of radiation belts reconstructions, as well as industry for satellite mission design, nowcast of the MEO environment, and surface charging analysis.
Electromagnetic ion cyclotron waves have long been recognized to play a crucial role in the dynamic loss of ring current protons. While the field-aligned propagation approximation of electromagnetic ion cyclotron waves was widely used to quantify the scattering loss of ring current protons, in this study, we find that the wave normal distribution strongly affects the pitch angle scattering efficiency of protons. Increase of peak normal angle or angular width can considerably reduce the scattering rates of <= 10 keV protons. For >10 keV protons, the field-aligned propagation approximation results in a pronounced underestimate of the scattering of intermediate equatorial pitch angle protons and overestimates the scattering of high equatorial pitch angle protons by orders of magnitude. Our results suggest that the wave normal distribution of electromagnetic ion cyclotron waves plays an important role in the pitch angle evolution and scattering loss of ring current protons and should be incorporated in future global modeling of ring current dynamics.
Current algorithms for the real-time prediction of the Kp index use a combination of models empirically driven by solar wind measurements at the L1 Lagrange point and historical values of the index. In this study, we explore the limitations of this approach, examining the forecast for short and long lead times using measurements at L1 and Kp time series as input to artificial neural networks. We explore the relative efficiency of the solar wind-based predictions, predictions based on recurrence, and predictions based on persistence. Our modeling results show that for short-term forecasts of approximately half a day, the addition of the historical values of Kp to the measured solar wind values provides a barely noticeable improvement. For a longer-term forecast of more than 2 days, predictions can be made using recurrence only, while solar wind measurements provide very little improvement for a forecast with long horizon times. We also examine predictions for disturbed and quiet geomagnetic activity conditions. Our results show that the paucity of historical measurements of the solar wind for high Kp results in a lower accuracy of predictions during disturbed conditions. Rebalancing of input data can help tailor the predictions for more disturbed conditions.
New wave frequency and amplitude models for the nightside and dayside chorus waves are built based on measurements from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument onboard the Van Allen Probes. The corresponding 3D diffusion coefficients are systematically obtained. Compared with previous commonly-used (typical) parameterizations, the new parameterizations result in differences in diffusion rates that depend on the energy and pitch angle. Furthermore, one-year 3D diffusive simulations are performed using the Versatile Electron Radiation Belt (VERB) code. Both typical and new wave parameterizations simulation results are in a good agreement with observations at 0.9 MeV. However, the new parameterizations for nightside chorus better reproduce the observed electron fluxes. These parameterizations will be incorporated into future modeling efforts.
Simulations of the inner magnetospheric energetic electrons using the IMPTAM-VERB coupled model
(2019)
In this study, we present initial results of the coupling between the Inner Magnetospheric Particle Transport and Acceleration Model (IMPTAM) and the Versatile Electron Radiation Belt (VERB-3D) code. IMPTAM traces electrons of 10-100 keV energies from the plasma sheet (L = 9 Re) to inner L-shell regions. The flux evolution modeled by IMPTAM is used at the low energy and outer L* computational boundaries of the VERB code (assuming a dipole approximation) to perform radiation belt simulations of energetic electrons. The model was tested on the March 17th, 2013 storm, for a six-day period. Four different simulations were performed and their results compared to satellites observations from Van Allen probes and GOES. The coupled IMPTAM-VERB model reproduces evolution and storm-time features of electron fluxes throughout the studied storm in agreement with the satellite data (within similar to 0.5 orders of magnitude). Including dynamics of the low energy population at L* = 6.6 increases fluxes closer to the heart of the belt and has a strong impact in the VERB simulations at all energies. However, inclusion of magnetopause losses leads to drastic flux decreases even below L* = 3. The dynamics of low energy electrons (max. 10s of keV) do not affect electron fluxes at energies >= 900 keV. Since the IMPTAM-VERB coupled model is only driven by solar wind parameters and the Dst and Kp indexes, it is suitable as a forecasting tool. In this study, we demonstrate that the estimation of electron dynamics with satellite-data-independent models is possible and very accurate.
The Kp index is a measure of the midlatitude global geomagnetic activity and represents short-term magnetic variations driven by solar wind plasma and interplanetary magnetic field. The Kp index is one of the most widely used indicators for space weather alerts and serves as input to various models, such as for the thermosphere and the radiation belts. It is therefore crucial to predict the Kp index accurately. Previous work in this area has mostly employed artificial neural networks to nowcast Kp, based their inferences on the recent history of Kp and on solar wind measurements at L1. In this study, we systematically test how different machine learning techniques perform on the task of nowcasting and forecasting Kp for prediction horizons of up to 12 hr. Additionally, we investigate different methods of machine learning and information theory for selecting the optimal inputs to a predictive model. We illustrate how these methods can be applied to select the most important inputs to a predictive model of Kp and to significantly reduce input dimensionality. We compare our best performing models based on a reduced set of optimal inputs with the existing models of Kp, using different test intervals, and show how this selection can affect model performance.
Plain Language Summary Radiation belts of the Earth, which are the zones of charged energetic particles trapped by the geomagnetic field, comprise enormous and dynamic systems. While the inner radiation belt, composed mainly of high-energy protons, is relatively stable, the outer belt, filled with energetic electrons, is highly variable and depends substantially on solar activity. Hence, extended reliable observations and the improved models of the electron intensities in the outer belt depending on solar wind parameters are necessary for prediction of their dynamics. The Cluster mission has been measuring electron flux intensities in the radiation belts since its launch in 2000, thus providing a huge dataset that can be used for radiation belts analysis. Using 16 years of electron measurements by the Cluster mission corrected for background contamination, we derived a uniform linear-logarithmic dependence of electron fluxes in the outer belt on the solar wind dynamic pressure.
Space radiation is one of the main concerns for human space flights. The prediction of the radiation dose for the actual spacecraft geometry is very important for the planning of long-duration missions. We present a numerical method for the fast calculation of the radiation dose rate during a space flight. We demonstrate its application for dose calculations during the first and the second sessions of the MATROSHKA-R space experiment with a spherical tissue-equivalent phantom. The main advantage of the method is the short simulation time, so it can be applied for urgent radiation dose calculations for low-Earth orbit space missions. The method uses depth-dose curve and shield-and-composition distribution functions to calculate a radiation dose at the point of interest. The spacecraft geometry is processed into a shield-and-composition distribution function using a ray-tracing method. Depth-dose curves are calculated using the GEANT4 Monte-Carlo code (version 10.00.P02) for a double-layer aluminum-water shielding. Aluminum-water shielding is a good approximation of the real geometry, as water is a good equivalent for biological tissues, and aluminum is the major material of spacecraft bodies.
In this paper we report a rare and fortunate event of fast magnetosonic (MS, also called equatorial noise) waves modulated by compressional ultralow frequency (ULF) waves measured by Van Allen Probes. The characteristics of MS waves, ULF waves, proton distribution, and their potential correlations are analyzed. The results show that ULF waves can modulate the energetic ring proton distribution and in turn modulate the MS generation. Furthermore, the variation of MS intensities is attributed to not only ULF wave activities but also the variation of background parameters, for example, number density. The results confirm the opinion that MS waves are generated by proton ring distribution and propose a new modulation phenomenon.
Models of ring current electron dynamics unavoidably contain uncertainties in boundary conditions, electric and magnetic fields, electron scattering rates, and plasmapause location. Model errors can accumulate with time and result in significant deviations of model predictions from observations. Data assimilation offers useful tools which can combine physics-based models and measurements to improve model predictions. In this study, we systematically analyze performance of the Kalman filter applied to a log-transformed convection model of ring current electrons and Van Allen Probe data. We consider long-term dynamics of mu = 2.3 MeV/G and K = 0.3 G(1/2) R-E electrons from 1 February 2013 to 16 June 2013. By using synthetic data, we show that the Kalman filter is capable of correcting errors in model predictions associated with uncertainties in electron lifetimes, boundary conditions, and convection electric fields. We demonstrate that reanalysis retains features which cannot be fully reproduced by the convection model such as storm-time earthward propagation of the electrons down to 2.5 R-E. The Kalman filter can adjust model predictions to satellite measurements even in regions where data are not available. We show that the Kalman filter can adjust model predictions in accordance with observations for mu = 0.1, 2.3, and 9.9 MeV/G and constant K = 0.3 G(1/2) R-E electrons. The results of this study demonstrate that data assimilation can improve performance of ring current models, better quantify model uncertainties, and help deeper understand the physics of the ring current particles.
In this study, rapid loss of relativistic radiation belt electrons at low L* values (2.4-3.2) during a strong geomagnetic storm on 22 June 2015 is investigated along with five possible loss mechanisms. Both the particle and wave data are obtained from the Van Allen Probes. Duskside H+ band electromagnetic ion cyclotron (EMIC) waves were observed during a rapid decrease of relativistic electrons with energy above 5.2 MeV occurring outside the plasma sphere during extreme magnetopause compression. Lower He+ composition and enriched O+ composition are found compared to typical values assumed in other studies of cyclotron resonant scattering of relativistic electrons by EMIC waves. Quantitative analysis demonstrates that even with the existence of He+ band EMIC waves, it is the H+ band EMIC waves that are likely to cause the depletion at small pitch angles and strong gradients in pitch angle distributions of relativistic electrons with energy above 5.2 MeV at low L values for this event. Very low frequency wave activity at other magnetic local time can be favorable for the loss of relativistic electrons at higher pitch angles. An illustrative calculation that combines the nominal pitch angle scattering rate due to whistler mode chorus at high pitch angles with the H+ band EMIC wave loss rate at low pitch angles produces loss on time scale observed at L = 2.4-3.2. At high L values and lower energies, radial loss to the magnetopause is a viable explanation.