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Here, we present an empirical model of the equatorial electron pitch angle distributions, based on the Magnetic Electron Ion Spectrometer (MagEIS) instrument aboard the Van Allen Probes. The model was created for energies from 37 keV up to 2.65 MeV. The model uses the solar wind dynamic pressure as a driving parameter and has a continuous dependence on Lm, magnetic local time and activity. It works for L-shells from 3.05 up around 5.95. For each channel of the MagEIS instrument, there are two files with model coefficients, one for Pdyn

Data assimilation aims to blend incomplete and inaccurate data with physics-based dynamical models. In the Earth's radiation belts, it is used to reconstruct electron phase space density, and it has become an increasingly important tool for validating our current understanding of radiation belt dynamics, identifying new physical processes, and predicting the near-Earth hazardous radiation environment. The dataset presents the electron flux reconstructed by assimilating electron flux measurements of the following spacecraft into the 3D Versatile Electron Radiation Belt model (VERB; Shprits et al., 2008, Subbotin and Shprits, 2009): 1. Van Allen Probes Magnetic Electron Ion Spectrometer (MagEIS; Blake et al., 2013) and Relativistic Electron Proton Telescope (REPT; Baker et al., 2013), and 2. Geostationary Operational Environmental Satellites (GOES) Magnetospheric Electron Detector (MAGED; Hanser, 2011), and Energetic Proton, Electron, and Alpha Detector (EPEAD; Onsager et al., 1996, Hanser, 2011). The method employs a split-operator Kalman filter (Shprits et al., 2013). The dataset contains electron flux for the period from 01 October 2012 00:00 UT to 01 October 2016 00:00 UT, organized in monthly files for selected values of electron energies (0.5 MeV, 1 MeV, and 2 MeV) and equatorial pitch angles (20 degree, 50 degree, and 70 degree).

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 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., Plain Language Summary: The radiation belts of the Earth, which are the zones of charged energetic particles trapped by the geomagnetic field, comprise complex and dynamic systems posing a significant threat to a variety of commercial and military satellites. While the inner belt is relatively stable, the outer belt is highly variable and depends substantially on solar activity; therefore, accurate and improved models of electron flux in the outer radiation belt are essential to understand the underlying physical processes. Although many models have been developed for the geostationary orbit and relativistic energies, prediction of electron flux in the 120–600 keV energy range still remains challenging. We present a data‐driven model of the medium energies (120–600 keV) differentialelectron flux in the outer radiation belt based on machine learning. We use 17 years of electron observations by Global Positioning System (GPS) satellites. We set up a 3D model for flux prediction in terms of L‐values, MLT, and magnetic latitude. The model gives reliable predictions of the radiation environment in the outer radiation belt and has wide space weather applications., Key Points: A machine learning model is created to predict electron flux at MEO for energies 120–600 keV. The model requires solar wind parameters and geomagnetic indices as input and does not use persistence. MERLIN model yields high accuracy and high correlation with observations (0.8)., Horizon 2020 – The EU Research and Innovation programme

In recent years, feedforward neural networks (NNs) have been successfully applied to reconstruct global plasmasphere dynamics in the equatorial plane. These neural network‐based models capture the large‐scale dynamics of the plasmasphere, such as plume formation and erosion of the plasmasphere on the nightside. However, their performance depends strongly on the availability of training data. When the data coverage is limited or non‐existent, as occurs during geomagnetic storms, the performance of NNs significantly decreases, as networks inherently cannot learn from the limited number of examples. This limitation can be overcome by employing physics‐based modeling during strong geomagnetic storms. Physics‐based models show a stable performance during periods of disturbed geomagnetic activity if they are correctly initialized and configured. In this study, we illustrate how to combine the neural network‐ and physics‐based models of the plasmasphere in an optimal way by using data assimilation. The proposed approach utilizes advantages of both neural network‐ and physics‐based modeling and produces global plasma density reconstructions for both quiet and disturbed geomagnetic activity, including extreme geomagnetic storms. We validate the models quantitatively by comparing their output to the in‐situ density measurements from RBSP‐A for an 18‐month out‐of‐sample period from June 30, 2016 to January 01, 2018 and computing performance metrics. To validate the global density reconstructions qualitatively, we compare them to the IMAGE EUV images of the He+ particle distribution in the Earth's plasmasphere for a number of events in the past, including the Halloween storm in 2003., Key Points: We develop an approach to combine a neural network with a physics‐based model of the plasmasphere using data assimilation. The approach is extensively validated using in‐situ density measurements and observed plasmapause position derived from the Imager for Magnetopause‐to‐Aurora Global Exploration EUV. The developed model reproduces the plasmasphere dynamics during quiet, moderate, disturbed, and extreme geomagnetic events., Geo.X, EU Horizon 2020, Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659, Helmholtz Association (亥姆霍兹联合会致力) http://dx.doi.org/10.13039/501100009318

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., Plain Language Summary: The radiation belts of the Earth, which are the zones of charged energetic particles trapped by the geomagnetic field, comprise complex and dynamic systems posing a significant threat to a variety of commercial and military satellites. While the inner belt is relatively stable, the outer belt is highly variable and depends substantially on solar activity; therefore, accurate and improved models of electron flux in the outer radiation belt are essential to understand the underlying physical processes. Although many models have been developed for the geostationary orbit and relativistic energies, prediction of electron flux in the 120–600 keV energy range still remains challenging. We present a data‐driven model of the medium energies (120–600 keV) differentialelectron flux in the outer radiation belt based on machine learning. We use 17 years of electron observations by Global Positioning System (GPS) satellites. We set up a 3D model for flux prediction in terms of L‐values, MLT, and magnetic latitude. The model gives reliable predictions of the radiation environment in the outer radiation belt and has wide space weather applications., Key Points: A machine learning model is created to predict electron flux at MEO for energies 120–600 keV. The model requires solar wind parameters and geomagnetic indices as input and does not use persistence. MERLIN model yields high accuracy and high correlation with observations (0.8)., Horizon 2020 – The EU Research and Innovation programme

Radial diffusion is one of the dominant physical mechanisms driving acceleration and loss of radiation belt electrons. A number of parameterizations for radial diffusion coefficients have been developed, each differing in the data set used. Here, we investigate the performance of different parameterizations by Brautigam and Albert (2000), https://doi.org/10.1029/1999ja900344, Brautigam et al. (2005), https://doi.org/10.1029/2004ja010612, Ozeke et al. (2014), https://doi.org/10.1002/2013ja019204, Ali et al. (2015), https://doi.org/10.1002/2014ja020419; Ali et al. (2016), https://doi.org/10.1002/2016ja023002; Ali (2016), and Liu et al. (2016), https://doi.org/10.1002/2015gl067398 on long‐term radiation belt modeling using the Versatile Electron Radiation Belt (VERB) code, and compare the results to Van Allen Probes observations. First, 1‐D radial diffusion simulations are performed, isolating the contribution of solely radial diffusion. We then take into account effects of local acceleration and loss showing additional 3‐D simulations, including diffusion across pitch‐angle, energy, and mixed diffusion. For the L* range studied, the difference between simulations with Brautigam and Albert (2000), https://doi.org/10.1029/1999ja900344, Ozeke et al. (2014), https://doi.org/10.1002/2013ja019204, and Liu et al. (2016), https://doi.org/10.1002/2015gl067398 parameterizations is shown to be small, with Brautigam and Albert (2000), https://doi.org/10.1029/1999ja900344 offering the smallest averaged (across multiple energies) absolute normalized difference with observations. Using the Ali et al. (2016), https://doi.org/10.1002/2016ja023002 parameterization tended to result in a lower flux than both the observations and the VERB simulations using the other coefficients. We find that the 3‐D simulations are less sensitive to the radial diffusion coefficient chosen than the 1‐D simulations, suggesting that for 3‐D radiation belt models, a similar result is likely to be achieved, regardless of whether Brautigam and Albert (2000), https://doi.org/10.1029/1999ja900344, Ozeke et al. (2014), https://doi.org/10.1002/2013ja019204, and Liu et al. (2016), https://doi.org/10.1002/2015gl067398 parameterizations are used., Key Points: 3‐D simulations using different radial diffusion coefficients, except Ali et al. (2016), produce similar results. Using Ali et al. (2016) DLL, simulated flux is significantly lower than observations. 3‐D modeling with Brautigam and Albert (2000) DLL results in a slightly smaller normalized difference (averaged over energies) to observations., National Aeronautics and Space Administration (NASA) http://dx.doi.org/10.13039/100000104, European Union's Horizon 2020, https://doi.org/10.25346/S6/U9WFPD