Explosive volcanic eruptions can inject sulfur dioxide (SO2) into the stratosphere, which forms stratospheric sulfate aerosol that can significantly impact the climate. The radiative forcing of an eruption depends on several eruption source parameters: the mass of SO2 emitted, the latitude and the emission height. However, the combined effects of these parameters are not well understood. Reconstructions of historic volcanic radiative forcing, which are essential for understanding the role of volcanism on climate variability, are derived from ice core sulfate records, but rely on relationships between ice sheet deposition, stratospheric aerosol burdens and radiative forcing from limited observations. The aim of this thesis is to understand the impact of explosive volcanic eruptions on radiative forcing and volcanic sulfate deposition. The role of individual and combined eruption source parameters are comprehensively investigated using interactive stratospheric aerosol models, perturbed parameter ensembles and statistical emulation. The results demonstrate that radiative forcing is primarily determined by the SO2 emission magnitude, is stronger for tropical eruptions and has a greater dependency on the injection height if the eruption is tropical. The ice sheet deposition is relatively independent of the injection height. The results reveal complex combined effects of the eruption parameters and illustrate the importance of explicitly simulating aerosol microphysical processes to determine aerosol mass, size and lifetime. A wide range of eruption-realisations is found that produce ice sheet deposition that is consistent with ice-core-derived estimates for historic eruptions in the last 2500 years. These eruptions have a range in time-integrated radiative forcing (> ~300 MJ m-2) that is not considered in reconstructions. Sulfate deposition differs considerably between models for the 1815 eruption of Mt. Tambora. The results suggest there is a large uncertainty in radiative forcing derived from ice cores. Consequently, the efficacy of volcanic radiative forcing derived from previous reconstructions may be incorrect