Highly Accurate Scrambled Stochastic Approaches for Multidimensional Sensitivity Analysis in Air Pollution Modeling

Abstract

A thorough experimental investigation of Monte Carlo algorithms based on Halton and Sobol scrambling algorithms has been performed for the first time for the model under consideration. For scrambling Halton sequence, we use a permutation of the radical inverse coefficients derived by applying a reverse-radix operation to all of the possible coefficient values. For scrambling Sobol sequence, we use random linear scramble combined with a random digital shift. These methods have never been applied and compared before for the Unified Danish Eulerian model and this motivates our study. The novelty of the proposed approaches is that Halton scrambling algorithm has been applied for the first time to sensitivity studies of the particular air pollution model. The computational experiments demonstrate that the proposed stochastic approaches are efficient for the considered multidimensional integrals evaluation and especially for computing small by value sensitivity indices which are very important for the reliability of the mathematical model.