Using geomagnetic data from the Ørsted satellite and observatories, two models of the Earth's magnetic field during 2001 have been produced. The two models differ in the time dependence of the spherical harmonic degree 1 magnetospheric field and its internally induced counterpart. The first model uses B-spline basis functions in time, with one node per day. The second uses a more common representation in which the hourly Dst index controls the rapid variations of the magnetospheric field. The solution of the first model shows that the amplitude of the magnetospheric field correlates well with the Dst index even for relatively active days. However, it shows much more variability in field direction than the magnetospheric field solution of the second model. In particular, this variability allows a better fit to the Y-components at magnetic observatories situated close to the meridian of the magnetic poles. For both models, the residuals of the fits to the observatory and satellite Y-component data have an unusual periodicity that is anticorrelated with the Y-component of the interplanetary magnetic field (IMF). This is possibly due to inter-hemispheric currents that flow in the upper ionosphere on the night-side of the Earth, but is more likely to be due to a direct penetration of the magnetosphere by the IMF.