Aerosols from human emissions reside mainly in the Troposphere with some small percentage migrating to the Stratosphere. Aircraft emission of SO2 are included in this tropospheric loading though their impact is much less than that of the fossil fuel (coal mostly) industry.
Typical Tropospheric loading of SO2 only lasts in the atmosphere about 2 weeks since it settles out in precipitation. Stratospheric volcanoes cause a cooling effect but it lasts much longer since there is barely any water vapor at that altitude.
Also the cooling effect of stratospheric loading is much more dispersed globally (usually in the respective hemisphere if an upper or lower latitude volcano and globally if a tropical one). Stratospheric loading only operates on one component of the cooling process where it reflects the incoming solar energy through a fine haze. Tropospheric loading from human emissions also does this but also has interactions with clouds that, until very recently (and still with much uncertainty!) was not well known.
The interaction with clouds in the troposphere from SO2 causes lower cloud heights, slightly cools the regional troposphere, lowering the effective height of the atmosphere (a cooling effect on the GHG feedback impacting the lapse rate) and leads to shifts in wind and precipitation patterns regionally. It also causes finer water droplets at cloud tops, making them more white and reflective.
In the Arctic specifically, most models do not include the full impacts of SO2 but the ones that include these cloud interactions recognize quickly that the additional impacts at the very high latitudes are much greater than the global average. This is due to the lower angle of the sun at high latitudes.
Recent published studies (and historical evidence) indicates that the Arctic will warm between 2C and 4C without coal-produced SO2 emissions. This warming impact would begin within 2 weeks after the end of emissions and is basically instantaneous.
The long-term warming impacts could be much higher as these SO2 Tropospheric loading are seen in some studies to have a very strong effect on the prevalence of La Nina events (more SO2 more negative PDO) as well as tropical precipitation (more SO2 more tropical precipitation) as well as observed impacts on the AMO. These circulation changes are the biggest unknown in the climate models since the regional changes in winds and tropical humidity are expected to produce very large changes in the supremely complicated global atmospheric circulation patterns.
It is quite likely that the end of SO2 will greatly change the rate of upwelling tropical atmosphere, the driver the Hadley Cell, leading to increased expansion of the tropical rain belt from 20' latitude, expanding the 30' dry belt (where most of the global deserts are) and result in greatly increased pulses of water vapor into the upper latitudes and the Arctic.
The observation of these kinds of circulation changes contribute up to 60% of the total sea ice loss observed since 1979:
https://www.atmos.washington.edu/~david/Ding_etal_2017.pdfFWIW I was documenting the change in circulation and increase in water vapor pulses into the Arctic (as a result of the North East Pacific 'Ridiculously Resilient Ridge' beginning back in 2014:
https://forum.arctic-sea-ice.net/index.php/topic,784.0.htmlThe Hadley Cell has been observed to be already expanding, this will increase significantly with further reductions of aerosols as we end the fossil fuel era:
https://www.nature.com/articles/ngeo2091