Change of support effects in spatial variance-based sensitivity analysis
Résumé
Variance-based global sensitivity analysis (GSA) aims at studying how uncertainty in the output of a model can be apportioned to different sources of uncertainty in its inputs. GSA is an essential ingredient in model building: it helps to identify model inputs that account for most of model output variability. Yet this approach is not really appropriate for spatial models, as it cannot describe how uncertainty interacts with another key issue in spatial modeling: the issue of model upscaling and change of spatial support. In many environmental models, the end-user is interested in the spatial average or sum of model output over a given spatial unit (e.g. the average porosity of a geological block). Under a change of spatial support, the relative contribution of uncertain model inputs to the variance of aggregated model output may change. We propose in this paper a simple formalism to discuss this question within GSA framework by defining point and block sensitivity indices. We show that the relative contribution of an uncertain spatially distributed model input increases with its covariance range and decreases with the size of the spatial unit considered for model output aggregation. Results are briefly illustrated by a simple example.
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