Stochastic perturbations and dimension reduction for modelling uncertainty of atmospheric dispersion simulations

Abstract

Decision of emergency response to releases of hazardous material in the atmosphere increasingly rely on numerical simulations. This paper presents two contributions for accounting for the uncertainty inherent to those simulations. We first focused on one way of modelling these uncertainties, namely by applying stochastic perturbations to the inputs of the numerical dispersion model. We devised a generic mathematical formulation for time dependent perturbation of both amplitude and dynamics of the inputs. It allows a more thorough exploration of possible outcomes than simpler perturbations found in the literature. We then improved on the current state of the art on dimension reduction of atmospheric data. Indeed, most statistical methods cannot cope with high dimensional data such as the maps simulated with atmospheric dispersion models. Principal component analysis, the most widely used method for dimension reduction, relies on a linearity hypothesis that is not verified by these sets of maps. We conducted a very encouraging experiment with auto-associative models, a non-linear extension of this method.