A semi-empirical model for magnetic storm dynamics

The near-Earth electromagnetic environment represents a far-from-equilibrium system characterized by sudden irregular energy relaxation events. For a broad class of complex systems, time series can be interpreted in terms of a superposition of stochastic and deterministic components occurring at different time scales. In this work we use the generalization of the SYM-H index provided by the SuperMAG collaboration (SMR), which is meant for monitoring the global variation of the horizontal component of the Earth's magnetic field in the near-equatorial regions. The aim of this work is to model the SMR dynamics via stochastic differential equations thus providing a semi-empirical model whose parameters are retained from data. As a first step we test the Markov condition on the SMR data sample, which represents the basic condition for our stochastic modeling, and we show that such a requirement is accurately satisfied by SMR time series. This allows us to infer the model parameters for the SMR index through the Kramers-Moyal analysis. Finally, we give evidence that a purely diffusive process is not representative of the observed dynamics and then a model based on jump-diffusion processes must be considered to correctly reproduce the dynamical features of the SMR index.