Predicting the Multifractal Geomagnetic Field

The geomagnetic field at the Earth’s surface is determined by a large number of current sources, internal and external, which vary at overlapping time scales. As a result, the time variation of the field, ranging from nHz to tens of Hz, can be modeled as a multifractal whose properties depend on frequency and activity level, with the latter being largely determined by the external driving due to the interplanetary medium. Multifractal properties are apparent in all measures, conventional or modern, of magnetic activity: the magnitude and individual components; regional and global nonlinear averages known as magnetic indices; and nonstationary oscillations due to wave excitation and damping. In recent years, we have developed predictive models of the three types of measures which are representations of the field’s modes of response to interplanetary magnetic and plasma variables. Thus, although the field’s time variation appears multifractal, many of its features are predictable since they are related to nonlinear modes in response to the turbulent interplanetary medium. We present two examples: the predictive modeling of the high-latitude field disturbances as a response to the interplanetary electric field, and that of its derivative, / t ∂ ∂ B , at midand high latitudes as a response to the solar wind plasma moments. We discuss the merits and disadvantages of the “modal” versus the “multifractal” approach.