Simulations of the atmospheric dispersion of radionuclides involve large uncertainties originating from the limited knowledge of meteorological input data, composition, amount and timing of emissions, and some model parameters. The estimation of these uncertainties is an essential complement to modeling for decision making in case of an accidental release. We have studied the relative influence of a set of uncertain inputs on several outputs from the Eulerian model Polyphemus/Polair3D on the Fukushima case. We chose to use the variance-based sensitivity analysis method of Sobol'. This method requires a large number of model evaluations which was not achievable directly due to the high computational cost of Polyphemus/Polair3D. To circumvent this issue, we built a mathematical approximation of the model using Gaussian process emulation. We observed that aggregated outputs are mainly driven by the amount of emitted radionuclides, while local outputs are mostly sensitive to wind perturbations. The release height is notably influential, but only in the vicinity of the source. Finally, averaging either spatially or temporally tends to cancel out interactions between uncertain inputs.