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Accurate quantification of the effects of volcanic eruptions on climate is a key requirement for better attribution of anthropogenic climate change. Here we use the UM-UKCA composition-climate model to simulate the atmospheric evolution of the volcanic aerosol clouds from the three largest eruptions of the 20th century: 1963 Agung, 1982 El Chichón and 1991 Pinatubo. The model has interactive stratospheric chemistry and aerosol microphysics, with coupled aerosol-radiation interactions for realistic composition-dynamics feedbacks. Our simulations align with the design of the Interactive Stratospheric Aerosol Model Intercomparison (ISA-MIP) "Historical Eruption SO2 Emissions Assessment". For each eruption, we perform 3-member ensemble model experiments with upper, mid-point and lower estimates for SO2 emission, each initialised to a meteorological state to match the observed phase of the quasi-biennial oscillation (QBO) at the times of the eruptions. We assess how each eruption's emitted SO2 evolves into a tropical reservoir of volcanic aerosol and analyse the subsequent dispersion to mid-latitudes. We compare the simulations to the three volcanic forcing datasets used in historical integrations for the two most recent Coupled Model Intercomparison Project (CMIP) assessments: the Global Space-based Stratospheric Aerosol Climatology (GloSSAC) for CMIP6, and the Sato et al. (1993) and Ammann et al. (2003) datasets used in CMIP5. We also assess the vertical extent of the volcanic aerosol clouds by comparing simulated extinction to Stratospheric Aerosol and Gas Experiment II (SAGE-II) v7.0 satellite aerosol data (1985-1995) for Pinatubo and El Chichón, and to 1964-65 northern hemisphere ground-based lidar measurements for Agung. As an independent test for the simulated volcanic forcing after Pinatubo, we also compare to the shortwave (SW) and longwave (LW) Top-of-the-Atmosphere flux anomalies measured by the Earth Radiation Budget Experiment (ERBE) satellite instrument. For the Pinatubo simulations, an injection of 10 to 14 Tg SO2 gives the best match to the High Resolution Infrared Sounder (HIRS) satellite-derived global stratospheric sulphur burden, with good agreement also to SAGE-II mid-visible and near-infrared extinction measurements. This 10-14 Tg range of emission also generates a heating of the tropical stratosphere that is comparable with the temperature anomaly seen in the ERA-Interim reanalyses. For El Chichón the simulations with 5 Tg and 7 Tg SO2 emission give best agreement with the observations. However, these runs predict a much deeper volcanic cloud than present in the CMIP6 data, with much higher aerosol extinction than the GloSSAC data up to October 1984, but better agreement during the later SAGE-II period. For 1963 Agung, the 9 Tg simulation compares best to the forcing datasets with the model capturing the lidar-observed signature of peak extinction descending from 20 km in 1964 to 16 km in 1965. Overall, our results indicate that the downward adjustment to previous SO2 emission estimates for Pinatubo as suggested by several interactive modelling studies is also needed for the Agung and El Chichón aerosol clouds. This strengthens the hypothesis that interactive stratospheric aerosol models may be missing an important removal or redistribution process (e.g. effects of co-emitted ash) which changes how the tropical reservoir of volcanic aerosol evolves in the initial months after an eruption. Our analysis identifies potentially important inhomogeneities in the CMIP6 dataset for all three periods that are hard to reconcile with variations predicted by the interactive stratospheric aerosol model. We also highlight large differences between the CMIP5 and CMIP6 volcanic aerosol datasets for the Agung and El Chichón periods. Future research should aim to reduce this uncertainty by reconciling the datasets with additional stratospheric aerosol observations. [ABSTRACT FROM AUTHOR]