Variance-based global sensitivity analysis is used to study how the variability of the output of a numerical model can be apportioned to different sources of uncertainty in its inputs. It is an essential component of model building as it helps to identify model inputs that account for most of the model output variance. However, this approach is seldom applied in Earth and Environmental Sciences, partly because most of the numerical models developed in this field include spatially distributed inputs or outputs . Our research work aims to show how global sensitivity analysis can be adapted to such spatial models, and more precisely how to cope with the following two issues: i) the presence of spatial auto-correlation in the model inputs, and ii) the scaling issues. We base our research on the detailed study of the numerical code NOE, which is a spatial model for cost-benefit analysis of flood risk management plans. We first investigate how variance-based sensitivity indices can be computed for spatially distributed model inputs. We focus on the "map labelling" approach, which allows to handle any complex spatial structure of uncertainty in the model inputs and to assess its effect on the model output. Next, we offer to explore how scaling issues interact with the sensitivity analysis of a spatial model. We define "block sensitivity indices" and "site sensitivity indices" to account for the role of the spatial support of model output. We establish the properties of these sensitivity indices under some specific conditions. In particular, we show that the relative contribution of an uncertain spatially distributed model input to the variance of the model output increases with its correlation length and decreases with the size of the spatial support considered for model output aggregation. By applying our results to the NOE modelling chain, we also draw a number of lessons to better deal with uncertainties in flood damage modelling and cost-benefit analysis of flood risk management plans.
