A quantitative model of the magnetic field from the large-scale system I of Birkeland currents in the Earth's magnetosphere is proposed. In the near-Earth space the electric current flow lines follow the dipolar magnetic field lines, while at larger distances they enter the high-latitude magnetosheath near midday, the low-latitude boundary layer along the magnetospheric flanks, and the plasma sheet boundary layer at the nightside. The model takes into account the local time dependence of the latitude of Birkeland current zone at the topside ionospheric level reported by Iijima and Potemra (1976, J. geophys. Res. 81, 2165.) The effects of the geodipole tilt in the overall geometry of the field-aligned current system are also incorporated. The model is sufficiently flexible; in particular, it permits an arbitrary choice of the current sheet thickness as well as of the M.L.T. distribution of the current intensity by using an appropriate combination of model coefficients in the corresponding Fourier expansion. One more possibility is to take into account the asymmetry in the net intensity and M.L.T. distribution of Birkeland currents between Northern and Southern Hemispheres which arises due to diurnal and seasonal variations of the geodipole tilt angle. The proposed analytical representation is relatively simple, which allows it to be incorporated in semi-empirical statistical magnetospheric models with parameters to be determined from spacecraft databases.

Two other approaches to the modeling of warped current sheets aimed at quantitative approximation of the magnetic field of Birkeland and tail current systems are considered.