Modeling the Dynamic Variability of Sub‐Relativistic Outer Radiation Belt Electron Fluxes Using Machine Learning

Abstract

The Earth's energetic particle environment consists of electrons that range in energy from a few keV to multiple MeV (e.g., Baker et al., 2017;Thorne, 2010), and were discovered by Geiger counters flown on Explorer 1, launched in January 1958, which represents the first major discovery of the space age (Van Allen & Frank, 1959;Van Allen et al., 1958). The dynamics of the different electron energies that have been studied over several decades, but more recently in great detail facilitated by high quality data from the Van Allen Probes mission (Li & Hudson, 2019;Mauk et al., 2013). The exact response of the radiation belts to solar wind driving is difficult to predict due to various competing loss and acceleration processes, often giving vastly different responses to seemingly similar driving conditions (Reeves et al., 2003) but occasionally even being accelerated up to roughly 10 MeV. The generally accepted process of radiation belt flux enhancement is believed to proceed as follows: an increase in the strength of the convection electric field causes an enhanced drift of plasma-sheet electrons into the inner magnetosphere, where they gradient-drift eastwards, and become unstable to plasma wave excitation. A particular class of waves, called whistler-mode chorus waves is excited on the dawn side of the Earth by ∼10-100 keV "source" electrons, and these waves then transfer a portion of their energy to higher energy "seed" electrons (>100 keV), that are further accelerated to relativistic energies (∼MeV) facilitated by Ultra-Low Frequency waves (

Unraveling the Critical Geomagnetic Conditions Controlling the Upper Limit of Electron Fluxes in the Earth's Outer Radiation Belt

“…Nevertheless, the studies of Mourenas et al (2019Mourenas et al ( , 2022 only focused on the time-integrated 2-MeV electron fluxes, and did not separate the dependence of the fluxes on substorms from storms, nor investigate a range of energies. Furthermore, the time series of AL rather than AE were found to be the most critical parameter in the outer belt electron flux model using a neural network approach (Chu et al, 2021;Ma et al, 2022), possibly because the AL index is more relevant to injections. Therefore, the critical geomagnetic conditions that produce the upper limit fluxes are still understood in a limited way.…”

Three‐Dimensional Simulations of Ultra‐Relativistic Electron Acceleration During the 21 April 2017 Storm

“…Machine learning technique has been adopted to predict the global wave amplitude and plasma density, helping us evaluate the space weather dynamics with high accuracy (e.g., D. Guo, Fu, et al., 2021; Y. Guo et al., 2022; Zhelavskaya et al., 2021). The machine learning technique can be used in future simulation and forecast ultra‐relativistic electron fluxes in the Earth's radiation belts (Chu et al., 2021; D. Ma et al., 2022).…”

Opening the Black Box of the Radiation Belt Machine Learning Model

“…, we use the time history of geomagnetic indices and solar wind parameters as the features of the model. For the 909 keV channel, the length of the look-back window is 18 days long, obtained after hyperparameter tuning (D. Ma et al, 2022), and the time series are 2-hr averages of AL, SYM-H, P sw and V sw (Figure 1a). Those time series along with the position vector 𝐴𝐴 𝐴 𝐴𝐴 = (𝐿𝐿𝐿 sin(𝑀𝑀𝐿𝐿𝑀𝑀 )𝐿 cos(𝑀𝑀𝐿𝐿𝑀𝑀 )𝐿 𝑀𝑀𝐿𝐿𝐴𝐴𝑀𝑀 ) are then input into the neural network model (Figure 1b) and the…”

“…It is worth noting that in this study we are focusing on the equatorial flux values and because the electron flux at 909 keV has an MLT-symmetric distribution, we only consider L-dependence (setting MLAT and MLT to zero). The detailed description of the ORIENT-M model is given in D. Ma et al (2022). For the flux output at t 0 (e.g., F(L = 4, t 0 )), the SHAP value for each feature is estimated using DeepSHAP and the background data is provided by random samples of 20% of the training data set with ∼500,000 data points.…”