Stochastic modeling of the AE index and its relation to fluctuations in Bz of the IMF on time scales shorter than substorm duration

Abstract

We perform a detailed analysis of the auroral electrojet (AE) index on the typical substorm time scales from one minute up to a few hours. Through a systematic test against a model for selfsimilar motion in the form of fractional Lévy flights, and against a model for fractional Brownian motion in multifractal time, it is demonstrated that the AE index is better approximated by a multifractal model than by a fractional Lévy flight. Standard structure function analysis of the z‐component Bz of the interplanetary magnetic field indicates that it is neither selfsimilar nor multifractal, but approximately satisfies a version of extended selfsimilarity. A method to discern an underlying multifractality also in Bz is pointed out.