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 \(\sim\SI{-12}{\kelvin}\).

A new algorithm is proposed for estimating time-evolving global forcing in climate models. The method is a further development of the work of Forster et al. (2013), taking into account the non-constancy of the global feedbacks. We assume that the non-constancy of this global feedback can be explained as a time-scale dependence, associated with linear temperature responses to the forcing on different time scales. With this method we obtain stronger forcing estimates than previously assumed for the representative concentration pathway experiments in the Coupled Model Intercomparison Project Phase 5 (CMIP5). The reason for the higher future forcing is that the global feedback parameter is more negative at shorter time scales than at longer time scales, consistent with the equilibrium climate sensitivity increasing with equilibration time. Our definition of forcing provides a clean separation of forcing and response, and we find that linear temperature response functions estimated from experiments with abrupt quadrupling of CO$_2$ can be used to predict responses also for future scenarios. In particular, we demonstrate that for most models, the response to our new forcing estimate applied on the 21st century scenarios provides a global surface temperature up to year 2100 consistent with the output of coupled model versions of the respective model.