Spatiotemporal variations of radiation belt relativistic electron fluxes analyzed by a machine learning tool

Relativistic electrons (>1 MeV) in the Earth's radiation belt, known as “killer electrons,” are primarily influenced by solar wind disturbances and geomagnetic activities. This study proposes a popular explainable machine learning tool, the Deep SHapley Additive exPlanations (Deep SHAP), for studying the spatiotemporal variations of radiation belt relativistic electron fluxes during realistic geomagnetic storm events. The fundamental machine learning framework is derived from the artificial neural networks proposed by Yuan et al. [“Predicting radiation belt relativistic electron flux from sub-relativistic electron fluxes using machine learning,” Phys. Fluids 37(2), 026618 (2025)], utilizing sub-relativistic electron fluxes (a few hundred kiloelectronvolts) as inputs. Analysis of the estimated SHAP values for all input parameters revealed that the lower envelopes of the auroral electrojet index positively contribute to the relativistic electron enhancement during the main and recovery phases of a geomagnetic storm on 17 March 2013, while the Symmetric Horizontal Component of the Geomagnetic Field and Nsw (solar wind density) index negatively influence them at higher L shells (the distance from Earth's center to the equatorial crossing point of a magnetic field line). In addition, spatial location and sub-relativistic electrons also significantly influence the relativistic electron dynamics. From the perspective of the explainable machine learning method, it is confirmed that the relativistic electrons are significantly influenced by the sub-relativistic electrons, the impinging of solar winds, and the occurrence of geomagnetic storms and substorms. The current work helps reveal the underlying physical mechanisms of radiation belt electron dynamics and facilitates the optimization of space weather prediction models.