Abstract. The continuum oscillation of a latitudinal range of closed geomagnetic field lines or shells appears to be a basic feature of the magnetosphere. Such oscillations are observed at the ground, and have been termed transient ULF pulsations. Earlier modelling showed that the apparent mean damping rate at the ground should be much greater than that in the magnetosphere. This modelling is extended to examine the time dependence of the magnetic field of transient pulsations as seen by a latitudinal chain of magnetometers. It is found that there should be significant temporal variation of both period and damping decrement observed at a given latitude, which could help to identify transient events even when the period variation with latitude is not obvious. Time-frequency analysis and analytical signal analysis do not seem to be effective in determining temporal parameter variation for the short, highly damped data segments typical of transient events. Least squares fitting of two decaying sinusoids gives surprisingly good results, but seems to have no physical basis, is difficult to interpret, and may be misleading. Least squares fitting of a single sinusoid with time-varying period and damping rate gives reasonably good fits. The resulting parameter variations with latitude may help to determine the structures of ionospheric current systems associated with transient ULF events. In particular, the time change of the period at a single station can determine where that station is relative to the ionospheric current maximum.