  The ambitious scientific goals of SKA require a matching capability for
calibration of instrumental and atmospheric propagation contributions as
functions of time, frequency and position. The development of novel calibration
algorithms to meet these requirements is an active field of research. In this
work {we aim to characterize} these, focusing on the spatial and temporal
structure scales of the ionospheric effects; ultimately, these provide the
guidelines for designing the optimum calibration strategy. We used empirical
ionospheric measurements at the site where the SKA-Low will be built, using MWA
Phase-2 Extended baseline observations and the station-based Low-frequency
Excision of Atmosphere in Parallel (LEAP) calibration algorithm. We have done
this via direct regression analysis of the ionospheric screens and by forming
the full and detrended structure functions. We found that 50% of the screens
show significant non-linear structures at scales >0.6km that dominate at >2km,
and 1% show significant sub-minute temporal changes, providing that there is
sufficient sensitivity. Even at the moderate sensitivity and baseline lengths
of MWA, non-linear corrections are required at 88 MHz during moderate-weather
and at 154 MHz during poor weather, or for high SNR measurements. Therefore we
predict that improvements will come from correcting for higher-order defocusing
effects in observations with MWA Phase-2, and further with new developments in
MWA Phase-3. Because of the giant leap in sensitivity, the correction for
complex ionospheric structures will be mandatory on SKA-Low, for both imaging
and tied-array beam formation.
