A state-space model of radiation belt electron flux dynamics

A state-space model was optimized from data and used to characterize the linear dynamics governing variations observed in 2–6 MeV electron flux across a range of magnetic L shells. A correction term exploits correlated structure in previous one-step prediction errors, or innovations, to improve the current forecast. More importantly, this correction term helps reduce parameter estimation bias that arises when relevant inputs are ignored, or higher-order linear and nonlinear dynamical terms are left out of the model while it is being trained. Analyses of the L-dependent response functions, one-step predictions, and prediction error statistics, lead to several conclusions: (1) the direct effects of first-order solar wind perturbations only penetrate to L∼4RE, while linear feedback, which dominates flux dynamics throughout the radiation belts, accounts for over 80% of the observed variability below this location; (2) electron flux diffuses upward above L∼5RE, and downward below L∼5RE, except below L∼1.75RE, where the estimated model parameters are considered suboptimal anyway; (3) corrections to model output required above L∼4RE suggest that modified or additional solar wind drivers may be required for a more complete physical description of solar wind-radiation belt coupling; while (4) corrections to model output required below L∼4RE indicate episodic reconfigurations of the global electron radiation belt state, a type of variation that will never be captured with linear dynamics alone.