Machine Learning Interpretability of Outer Radiation Belt Enhancement and Depletion Events

Abstract

We investigate the response of outer radiation belt electron fluxes to different solar wind and geomagnetic indices using an interpretable machine learning method. We reconstruct the electron flux variation during 19 enhancement and 7 depletion events and demonstrate the feature attribution analysis called SHAP (SHapley Additive exPlanations) on the superposed epoch results for the first time. We find that the intensity and duration of the substorm sequence following an initial dropout determine the overall enhancement or depletion of electron fluxes, while the solar wind pressure drives the initial dropout in both types of events. Further statistical results from a data set with 71 events confirm this and show a significant correlation between the resulting flux levels and the average AL index, indicating that the observed “depletion” event can be more accurately described as a “non‐enhancement” event. Our novel SHAP‐Enhanced Superposed Epoch Analysis (SHESEA) method can offer insight in various physical systems.

Simulating the Earth's Outer Radiation Belt Electron Fluxes and Their Upper Limit: A Unified Physics‐Based Model Driven by the AL Index

“…where f is the phase space density (PSD), t is the time, and S(α eq ) represents the bounce period approximated by S(α eq ) = 1.38 0.32 sin(α eq ) 0.32 ̅̅̅̅̅̅̅ ̅ sin √ (α eq ) (Lenchek et al, 1961). The lower energy boundary is set as the electron PSD at 235 keV provided by our ML model (D. Ma et al, 2022), which is primarily driven by the AL index during the post-storm period (D. Ma et al, , 2024, as shown in the solid line in Figure 1e. The lower boundary is set to be higher than in previous simulations as we focus on the relativistic electrons.…”

“…Hua, Bortnik, Chu, et al (2022), andHua et al (2023) show the maximum electron flux at different energy levels is strongly correlated to the cumulative effects of substorms instead of storms. Our previous ML models were driven only by geomagnetic indices and solar wind parameters, and with interpretable ML methods, we automatically discovered the integrated AL is a key parameter in the acceleration mechanism for relativistic and sub-relativistic electrons (D. Ma et al, , 2024. These studies indicate that we can use the AL index to model the time-varying physical parameters needed for traditional Fokker-Planck simulations, thereby obtaining a general model driven by the auroral index.…”

Machine‐Learning Based Identification of the Critical Driving Factors Controlling Storm‐Time Outer Radiation Belt Electron Flux Dropouts

“…Although these studies, based on traditional statistical analysis of satellite data, have comprehensively analyzed the dependence of dropouts on various driving factors, the traditional way has important limitations in that it is difficult to isolate the impact of different driving factors. These different driving factors are intrinsically correlated with each other in a nonlinear way and may nonlinearly interact with each other to produce different effects at different locations and phases of the storm (Ma et al, 2024). The dominant driving factors and physical mechanisms that cause dropouts are still not fully understood.…”

“…Since these nonlinearly correlated driving factors and their nonlinear interactions produce dropouts, to unravel these nonlinear correlations between various driving factors and dropouts, we take advantage of machine-learning techniques that can associate inputs with outputs in a nonlinear way, which have been widely used in space weather modeling and forecasting (Bortnik et al, 2016(Bortnik et al, , 2018Chu et al, 2017;Ma et al, 2022;Wing et al, 2022), and in discovering the important underlying/missing physical processes (Camporeale et al, 2022;Ma et al, 2023Ma et al, , 2024. In this letter, we employ Support Vector Machines (SVMs) to construct storm-time electron dropout prediction models over L = 4.0-6.0 using dropout data set based on 5-year Van Allen Probes observations from our previous study (Hua et al, 2023).…”

Influences of Solar Wind Parameters on Energetic Electron Fluxes at Geosynchronous Orbit Revealed by the Deep SHAP Method

“…In this study, we adopt a state-of-the-art feature attribution method, Deep SHapley Additive exPlanations (Deep SHAP) (Lundberg & Lee, 2017;D. Ma et al, 2023D. Ma et al, , 2024, to quantify the contributions of each solar wind parameter to prediction results of the PGREFM.…”