The radiation belts of the Earth, filled with energetic electrons, comprise complex and dynamic systems that pose a significant threat to a variety of satellite systems. While various models of the relativistic electron flux have been developed for geostationary orbit (GEO), the behaviour of the medium energy (120-600 keV) electrons below GEO remains poorly quantified. In this paper we present a Medium Energy electRon flux In Earth’s outer radiatioN belt (MERLIN) model based on the Light Gradient Boosting (LightGBM) machine learning algorithm. The 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 and validated on $>$15 years of the GPS electron flux data, and tested on more than $1.5$ years of measurements. 10-fold cross validation (CV) yields that the model predicts the MEO radiation environment well, both in terms of dynamics and amplitudes of flux. Evaluation on the test set yields 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.

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 the data assimilation Kalman filtering. 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 30 June 2016 to 01 January 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.

Understanding the dynamic evolution of relativistic electrons in the Earth’s radiation belts during both storm and non-storm times is a challenging task. The U.S. National Science Foundation’s Geospace Environment Modeling (GEM) focus group “Quantitative Assessment of Radiation Belt Modeling” (QARBM) has selected two storm time and two non-storm time events that occurred during the second year of the Van Allen Probes mission for in-depth study. Here, we perform simulations for these GEM challenge events using the 3-Dimensional Versatile Electron Radiation Belt (VERB-3D) code. We set up the outer $L^*$ boundary using data from Geostationary Operational Environmental Satellites (GOES) and validate the simulation results against satellite observations from both the GOES and Van Allen Probe missions for 0.9 MeV electrons. Our results show that the position of the plasmapause plays a significant role in the dynamic evolution of relativistic electrons. The magnetopause shadowing effect is included by using last closed drift shell (LCDS), and it is shown to significantly contribute to the dropouts of relativistic electrons at high $L^*$.

Reconstruction and prediction of the state of the near-Earth space environment is important for anomaly analysis, development of empirical models and understanding of physical processes. Accurate reanalysis or predictions that account for uncertainties in the associated model and the observations, can be obtained by means of data assimilation. The ensemble Kalman filter (EnKF) is one of the most promising filtering tools for non-linear and high dimensional systems in the context of terrestrial weather prediction. In this study, we adapt traditional ensemble based filtering methods to perform data assimilation in the radiation belts. We use a one-dimensional radial diffusion model with a standard Kalman filter (KF) to assess the convergence of the EnKF. Furthermore, with the split-operator technique, we develop two new three-dimensional EnKF approaches for electron phase space density that account for radial and local processes, and allow for reconstruction of the full 3D radiation belt space. The capabilities and properties of the proposed filter approximations are verified using Van Allen Probe and GOES data. Additionally, we validate the two 3D split-operator Ensemble Kalman filters against the 3D split-operator KF. We show how the use of the split-operator technique allows us to include more physical processes in our simulations and offers computationally efficient data assimilation tools that deliver accurate approximations to the optimal solution of the KF and are suitable for real-time forecasting. Future applications of the EnKF to direct assimilation of fluxes and non-linear estimation of electron lifetimes are discussed.

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 dataset used. Here, we investigate the performance of different parameterizations by Brautigam and Albert (2000), Brautigam et al (2005), Ozeke et al. (2014), Ali et al. (2015, 2016); Ali (2016), and Liu et al. (2016) 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 and energy, as well as mixed diffusion. For the L* range studied, the difference between simulations with Brautigam and Albert (2000), Ozeke et al. (2014), and Liu et al. (2016) parameterizations is shown to be small, with Brautigam and Albert (2000) offering the best agreement with observations. Using Ali et al. (2016)’s parameterization tended to result in a lower flux at 1 MeV 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), Ozeke et al. (2014), and Liu et al. (2016) parameterizations are used.

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 μ ranging from 300 to 3000 MeV G. 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. Loss from L* = 4 to L* = 4.8 is dominated by EMIC wave scattering (μ ≥ 900 MeV G) and may amount to between 10%/hr to 30%/hr of the maximum value of phase space density (PSD) over all L shells for fixed first and second adiabatic invariants. Magnetopause shadowing is shown to deplete electrons across all energies, mostly between L* = 5 and L* = 6.6, resulting in loss from 50%/hr to 70%/hr of the maximum PSD. We also identify a boundary located between L* = 3.5 and L* = 5.2 clearly separating the regions where each mechanism dominates. Nevertheless, during times of enhanced geomagnetic activity, both processes can operate beyond such location and encompass the entire outer radiation belt.