  Refraction and diffraction of incoming radio waves by the ionosphere induce
time variability in the angular positions, peak amplitudes and shapes of radio
sources, potentially complicating the automated cross-matching and
identification of transient and variable radio sources. In this work, we
empirically assess the effects of the ionosphere on data taken by the Murchison
Widefield Array (MWA) radio telescope. We directly examine 51 hours of data
observed over 10 nights under quiet geomagnetic conditions (global storm index
Kp < 2), analysing the behaviour of short-timescale angular position and peak
flux density variations of around ten thousand unresolved sources. We find that
while much of the variation in angular position can be attributed to
ionospheric refraction, the characteristic displacements (10-20 arcsec) at 154
MHz are small enough that search radii of 1-2 arcmin should be sufficient for
cross-matching under typical conditions. By examining bulk trends in amplitude
variability, we place upper limits on the modulation index associated with
ionospheric scintillation of 1-3% for the various nights. For sources fainter
than ~1 Jy, this variation is below the image noise at typical MWA
sensitivities. Our results demonstrate that the ionosphere is not a significant
impediment to the goals of time-domain science with the MWA at 154 MHz.
