The ambitious scientific goals of the square kilometre array (SKA) require a matching capability for calibration of instrumental and atmospheric propagation contributions as functions of time, frequency, and position. The development of calibration algorithms to meet these requirements is an active field of research. 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 Murchison widefield array (MWA) phase-2 extended baseline observations and the station-based low-frequency excision of atmosphere in parallel (LEAP) calibration algorithm. We did 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 nonlinear structures at scales >0.6  km that dominate at >2  km and 1% show significant subminute temporal changes, providing that there is sufficient sensitivity. Even at the moderate sensitivity and baseline lengths of MWA, nonlinear corrections are required at 88 MHz during moderate weather and at 154 MHz during poor weather or for high signal-to-noise ratio 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 the tied-array beam formation.