Volterra network modeling of the nonlinear finite-impulse reponse of the radiation belt flux

We show how a general class of spatio-temporal nonlinear impulse-response forecast networks (Volterra networks) can be constructed from a taxonomy of nonlinear autoregressive integrated moving average with exogenous inputs (NAR-MAX) input-output equations, and used to model the evolution of energetic particle f uxes in the Van Allen radiation belts. We present initial results for the nonlinear response of the radiation belts to conditions a month earlier. The essential features of spatio-temporal observations are recovered with the model echoing the results of state space models and linear f nite impulse-response models whereby the strongest coupling peak occurs in the preceding 1-2 days. It appears that such networks hold promise for the development of accurate and fully data-driven space weather modelling, monitoring and forecast tools.