An electric circuit model of the Earth’s polar electrojets and field-aligned currents for the estimation of magnetospheric magnetic field from along-track Swarm magnetic data

Abstract

This study deals with the analysis of Swarm vector magnetic data in order to create a circuit model of electric currents flowing in the Earth’s polar ionosphere and the inner magnetosphere. The model is composed of a system of two-dimensional electric currents representing the magnetic fields of three-dimensional ionospheric polar electrojets (PEJs), the field-aligned currents (FACs), magnetospheric ring currents (MRCs) and magnetospherically induced electric currents inside the Earth (MICs) for each Swarm track. The aim of this paper is to model PEJ and FAC magnetic fields in terms of electric currents on a track-by-track base, subtract those magnetic fields from along-track Swarm magnetic data and estimate the magnetospheric magnetic field (MMF) in discrete time bins. The proposed method is primarily intended to apply to Swarm signals recorded during magnetic storms. The electric circuit model is set up in three steps. After subtracting the main, lithospheric, Sq ionospheric and oceanic tidal magnetic fields from along-track Swarm magnetic signals, the residuals are grouped in 1-h time bins and adjusted by the magnetic field of a two-circular loop model of MRCs and MICs represented by $$3\times 2$$ 3 × 2 parameters of the electric circular loops in the magnetosphere and the Earth. The adjustment is carried out for the X and Z magnetic field components only because the Y component contains a large signal due to FACs. In the second step, the modelled MRC–MIC magnetic field is removed from the original residuals and the reduced residuals are adjusted by the magnetic field of a system of two-dimensional electric circuits in the polar ionosphere and FACs. The circuit model is set up according to known geometry of PEJs and FACs. In the final step, the modelled magnetic fields of PEJs and FACs are subtracted from the original residuals and all three magnetic field components are adjusted by the MRC–MIC model, named MMC, in a similar way as in the first step. Reliability of the approach is demonstrated by the scatter plots of model MMC showing a significantly better agreement with Swarm magnetic field residuals than the existing MMFs. Graphical Abstract