Sensitivity analysis of atmospheric models is necessary to identify the processes that lead to uncertainty in model predictions, to help understand model diversity through comparison of driving processes, and to prioritise research. Assessing the effect of parameter uncertainty in complex models is challenging and often limited by CPU constraints. Here we present a cost-effective application of variance-based sensitivity analysis to quantify the sensitivity of a 3-D global aerosol model to uncertain parameters. A Gaussian process emulator is used to estimate the model output across multi-dimensional parameter space, using information from a small number of model runs at points chosen using a Latin hypercube space-filling design. Gaussian process emulation is a Bayesian approach that uses information from the model runs along with some prior assumptions about the model behaviour to predict model output everywhere in the uncertainty space. We use the Gaussian process emulator to calculate the percentage of expected output variance explained by uncertainty in global aerosol model parameters and their interactions. To demonstrate the technique, we show examples of cloud condensation nuclei (CCN) sensitivity to 8 model parameters in polluted and remote marine environments as a function of altitude. In the polluted environment 95 % of the variance of CCN concentration is described by uncertainty in the 8 parameters (excluding their interaction effects) and is dominated by the uncertainty in the sulphur emissions, which explains 80 % of the variance. However, in the remote region parameter interaction effects become important, accounting for up to 40 % of the total variance. Some parameters are shown to have a negligible individual effect but a substantial interaction effect. Such sensitivities would not be detected in the commonly used single parameter perturbation experiments, which would therefore underpredict total uncertainty. Gaussian process emulation is shown to be an efficient and useful technique for quantifying parameter sensitivity in complex global atmospheric models.