Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model

Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.