Advanced algorithms for multidimensional sensitivity studies of large-scale air pollution models based on Sobol sequences

In this paper advanced variance-based algorithms for global sensitivity analysis are studied. We consider efficient algorithms: Monte Carlo, quasi-Monte Carlo (QMC) and scrambled quasi-Monte Carlo algorithms based on Sobol sequences. Low discrepancy ΛΠτ Sobol sequences are considered as a basis. Two other approaches are also analyzed. The first one is an efficient Monte Carlo (MC) algorithm for multidimensional integration based on modified Sobol sequences (MCA-MSS) and proposed in an earlier work by some of the authors [6]. Each random point in d-dimensional domain of integration is generated in the following way. A Sobol vector of dimension s (ΛΠτ point) is considered as a centrum of a sphere with a radius ρ. Then a random point uniformly distributed on the sphere is taken and a random variable is defined as a value of the integrand at that random point. It is proved that the Monte Carlo algorithm based on Sobol sequences MCA-MSS has an optimal rate of convergence for functions with continuous and bounded first derivatives in terms of probability and mean square error. The second one is a randomized ∗Corresponding author Email addresses: [email protected] (I. Dimov), [email protected] (R. Georgieva), [email protected] (Tz. Ostromsky), [email protected] (Z. Zlatev) URL: http://parallel.bas.bg/dpa/BG/dimov/index.html (I. Dimov), http://parallel.bas.bg/~rayna/ (R. Georgieva), http://parallel.bas.bg/~ceco/ (Tz. Ostromsky), http://www.dmu.dk/AtmosphericEnvironment/staff/zlatev.htm (Z. Zlatev) Preprint submitted to Computers & Mathematics with Applications February 13, 2012 QMC algorithm proposed by Art Owen [19]. The procedure of randomization in the latter case is also known as Owen scrambling. The chosen algorithms are applied to sensitivity studies of air pollution levels calculated by the Unified Danish Eulerian Model (UNI-DEM) to some chemical rate reactions. UNI-DEM is chosen as a case-study since it is a typical large-scale mathematical model in which the chemical reactions are strongly and adequately presented. Large number of numerical experiments is performed. Conclusions about applicability and efficiency of the algorithms under consideration are drawn.