  We investigate the climatic effects of volcanic eruptions spanning from Mt.\
Pinatubo-sized events to super-volcanoes. The study is based on ensemble
simulations in the Community Earth System Model Version 2 (CESM2) climate model
using the Whole Atmosphere Community Climate Model Version 6 (WACCM6)
atmosphere model. Our analysis focuses on the impact of different
\ce{SO2}-amount injections on stratospheric aerosol optical depth (AOD),
effective radiative forcing (RF), and global temperature anomalies. Unlike the
traditional linear models used for smaller eruptions, our results reveal a
non-linear relationship between RF and AOD for larger eruptions. We also
uncover a notable time-dependent decrease in aerosol forcing efficiency across
all eruption magnitudes during the first post-eruption year. In addition, the
study reveals that larger as compared to medium-sized eruption events produce a
delayed and sharper peak in AOD, and a longer-lasting temperature response
while the time evolution of RF remains similar between the two eruption types.
When including the results of previous studies, we find that relating \ce{SO2}
to any other parameter is inconsistent across models compared to the
relationships between AOD, RF, and temperature anomaly. Thus, we expect the
largest uncertainty in model codes to relate to the chemistry and physics of
\ce{SO2} evolution. Finally, we find that the peak RF approaches a limiting
value, and that the peak temperature response follows linearly, effectively
bounding the temperature anomaly to at most (\sim\SI{-12}{\kelvin}).
