Solar Wind–Magnetosphere Coupling Functions as Proxies for Energetic Electron Precipitation: Evidence for Timescale Dependence and Internal Modulation

Abstract Solar wind/magnetosphere coupling functions are widely used to quantify geoeffective energy transfer. However, their effectiveness as proxies for energetic electron precipitation (EEP) has not been adequately characterized. This study evaluates the performance of the Kan‐Lee (KL) electric field coupling function and the Akasofu ε parameter using >30, >100, and >300 keV precipitating electron fluxes. Correlation, multivariate regression, and superposed epoch analyses were performed using instantaneous, optimally lagged, and temporally integrated forcing representations. Both coupling functions exhibited significant correlations with EEP, with peak correlations occurring when the forcing led to precipitation by approximately 1–3 h. Regression analyses showed that explained variance increased systematically from instantaneous to lagged forcing and improved further when temporally integrated forcing was employed. For >30 keV precipitation, coefficients of determination increased from 0.136 (instantaneous) to 0.172 (lagged) and 0.420 (integrated) for KL, with corresponding values of 0.079, 0.201, and 0.408 for ε, respectively. Although KL generally exhibits stronger statistical associations with EEP, differences between the coupling functions were smaller than the improvements associated with incorporating response delays and cumulative forcing histories. Additional analyses using the auroral electrojet index showed that internal magnetospheric activity accounts for much of the variance associated with instantaneous solar wind coupling, while integrated coupling retained additional explanatory power. These results indicate that EEP is best represented as a temporally integrated response to coupled external solar wind forcing and internal magnetospheric dynamics operating across multiple timescales.