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In this paper, we consider a computational modelling approach to gain some insight into the factors that strongly influence atmospheric pollution concentration and how uncertainties associated with these factors contribute to the uncertainties in pollution estimates. We consider a parametric advection-diffusion pollution dispersion model to estimate pollutant concentration over a spatial domain, given values for a set of model parameters and hyper-parameters. A global sensitivity analysis (GSA) is conducted to assess how the variability in the pollutant concentration can be attributed to the variability in the model parameters. We use a variance-based GSA technique based on the estimation of first order and total Sobol indices across the spatial domain using Quasi-Monte Carlo sampling. A possible use for the resulting spatial sensitivity maps is in the design of an optimal placement strategy for sensors.