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The TRANSCAR ionospheric model was extended to account for the convection of the magnetic field lines in the auroral and polar ionosphere. A mixed Eulerian-Lagrangian 13-moment approach was used to describe the dynamics of an ionospheric plasma tube. In the present study, one focuses on large scale transports in the polar ionosphere. The model was used to simulate a 35-h period of EISCAT-UHF observations on 16-17 February 1993. The first day was magnetically quiet, and characterized by elevated electron concentrations: the diurnal F₂ layer reached as much as 10¹²m^-3, which is unusual for a winter and moderate solar activity (F_10.7=130) period. An intense geomagnetic event occurred on the second day, seen in the data as a strong intensification of the ionosphere convection velocities in the early afternoon (with the northward electric field reaching 150mVm^-1) and corresponding frictional heating of the ions up to 2500K. The simulation used time-dependent AMIE outputs to infer flux-tube transports in the polar region, and to provide magnetospheric particle and energy inputs to the ionosphere. The overall very good agreement, obtained between the model and the observations, demonstrates the high ability of the extended TRANSCAR model for quantitative modelling of the high-latitude ionosphere; however, some differences are found which are attributed to the precipitation of electrons with very low energy. All these results are finally discussed in the frame of modelling the auroral ionosphere with space weather applications in mind.