Probabilistic modelling of substorm occurrences with an echo state network

Abstract. The relationship between solar-wind conditions and substorm activity is modelled with an approach based on an echo state network. Substorms are a fundamental physical phenomenon in the magnetosphere–ionosphere system, but the deterministic prediction of substorm onset is very difficult because the physical processes that underlie substorm occurrences are complex. To model the relationship between substorm activity and solar-wind conditions, we treat substorm onset as a stochastic phenomenon and represent the stochastic occurrences of substorms with a non-stationary Poisson process. The occurrence rate of substorms is then described with an echo state network model. We apply this approach to two kinds of substorm onset proxies. One is a sequence of substorm onsets identified from auroral electrojet intensity, and the other is onset events identified from activity of Pi2 pulsations, which are irregular geomagnetic oscillations often associated with substorm onsets. We then analyse the response of substorm activity to solar-wind conditions by feeding synthetic solar-wind data into the echo state network. The results indicate that the effect of the solar-wind speed is important, especially for Pi2 substorms. A Pi2 pulsation can often occur even if the interplanetary magnetic field (IMF) is northward, while the activity of auroral electrojets is depressed during northward IMF conditions. We also observe spiky enhancements in the occurrence rate of substorms when the solar-wind density abruptly increases, which might suggest an external triggering due to a sudden impulse of solar-wind dynamic pressure. It seems that northward turning of the IMF also contributes to substorm occurrences, though the effect is likely to be minor.