Bivariate stochastic modeling of the magnetospheric dynamics driven by solar wind forcing

Geomagnetic storms represent a major manifestation of the magnetospheric response to transient solar wind forcing, that carries structures such as shock waves, interplanetary coronal mass ejections, stream interaction regions, and so on. Previous studies have shown that the magnetospheric response cannot be described by purely deterministic dynamics, and also consists of strong sudden fluctuations developing across multiple scales. Such dynamics have been extensively modeled using stochastic differential equations, which provide a natural framework to describe the combined effects of large-scale driving and stochastic fluctuations in physical systems. For univariate models, e.g., based on a single geomagnetic index, the fluctuating character of the internal magnetospheric dynamics represents the response to the unresolved external driving, whose influence manifests as stochastic variability. This work extends univariate descriptions by developing a bivariate stochastic model that explicitly accounts for the coupling between magnetospheric dynamics and interplanetary magnetic field. We use the geomagnetic index SYM-H, which is a proxy of the large-scale ring current state, and the Bz component of the magnetic field as representative of the external driver. The potential of this model in the context of space weather is discussed.