A Jump‐Diffusion Model of the Auroral Electrojet AL Index: Complexity and Criticality

Abstract This study presents a jump‐diffusion model to describe the dynamics of the auroral electrojet AL index, a geomagnetic measure frequently used to monitor polar ionospheric currents during substorms. The AL index captures the westward electrojet current's intensity, which responds to both solar wind‐driven disturbances and the magnetosphere's internal dynamics. These AL index fluctuations display “crackling noise” features, a statistical signature of scale‐invariant, burst‐like energy releases, suggesting the magnetosphere may operate near a critical point. Our model aims at reproducing these scaling laws and burst characteristics by means of a stochastic jump‐diffusion dynamics, that mirror the intermittent, non‐linear behavior seen in AL index data. In this framework, we can associate the Poisson‐distributed jump component with the onset of activity bursts in the AL index, which are commonly linked to substorm expansion phases. Through comparison of the model's output with actual AL index observations, we assess the model's ability to replicate key statistical properties, including scaling exponents and burst distributions, that define the AL index's response to magnetospheric substorms. Results indicate that while the model successfully captures the primary statistical features, refinements are needed to replicate observed long‐range correlation structures. This work provides new insights into the potential of stochastic models to simulate magnetospheric dynamics, emphasizing the AL index's role in understanding critical processes in space weather events.