Jump-Diffusion Modeling of the Auroral Electrojet AL Index: Unveiling Complexity and Criticality

The Earth’s magnetosphere displays complex and nonlinear dynamics in response to solar wind changes. In the past, some attempts to model the magnetospheric global dynamics as monitored by geomagnetic indices, in terms of stochastic differential equations (SDEs) have been carried out. These studies are important to assess the role of stochastic fluctuations and burstiness in the dynamics of the magnetosphere-iononosphere system.

Here, we present a jump-diffusion model to describe the auroral electrojet AL index, which constitutes a key geomagnetic measure of polar ionospheric currents during substorms. The proposed model employs a jump-diffusion stochastic differential equation (SDE) to capture the nonlinear, intermittent, and scale-invariant behavior of the AL index. Comparison with observations highlights the model capability to reproduce key statistical features of the AL index, such as scaling exponents and burst distributions. However, since the stochastic process involved in our model is Markovian, the model does not have information about the external driving (solar wind) and further efforts are therefore required to include long-range correlations. The relevance and limitations of these approaches in modeling the magnetospheric response are finally discussed.