A comparison of the probability distribution of observed substorm magnitude with that predicted by a minimal substorm model

We compare the probability distributions of substorm magnetic bay magnitudes from observations and a minimal substorm model. The observed distribution was derived previously and independently using the IL index from the IMAGE magnetometer network. The model distribution is derived from a synthetic AL index time series created using real solar wind data and a minimal substorm model, which was previously shown to reproduce observed substorm waiting times. There are two free parameters in the model which scale the contributions to AL from the directly-driven DP2 electrojet and loading-unloading DP1 electrojet, respectively. In a limited region of the 2-D parameter space of the model, the probability distribution of modelled substorm bay magnitudes is not significantly different to the observed distribution. The ranges of the two parameters giving acceptable (95% confidence level) agreement are consistent with expectations using results from other studies. The approximately linear relationship between the two free parameters over these ranges implies that the substorm magnitude simply scales linearly with the solar wind power input at the time of substorm onset.