Sensitivity analysis is the study of how uncertainty in model predictions is determined by uncertainty in model inputs. A global sensitivity analysis considers the potential effects from the simultaneous variation of model inputs over their finite range of uncertainty. A number of techniques are available to carry out global sensitivity analysis from a set of Monte Carlo simulations; some techniques are more efficient than others, depending on the strategy used to sample the uncertainty of model inputs and on the formulae employed for estimating sensitivity measures. The most common approaches are summarised in this paper by focusing on the limitations of each in the context of a sensitivity analysis of a spatial model. A novel approach for undertaking a spatial sensitivity analysis (based on the method of Sobol' and its related improvements) is proposed and tested. This method makes no assumptions about the model and enables the analysis of spatially distributed, uncertain inputs. The proposed approach is illustrated with a simple test model and a groundwater contaminant model.