This paper presents an optimization method based on a particular polynomial lattice rule with interlaced factor two for estimating sensitivity indices in global sensitivity analysis, focusing on total, first-order and second-order Sobol indices.A comparison with one of the best available methods the Modified Sobol Sequence and component by component construction polynomial lattice rule have been done.Relative errors for key output quantities are analyzed and compared.Our results show that the proposed optimization method consistently outperforms other methods in accurately estimating both first-order and total-order sensitivity indices, especially for parameters with smaller effects.These findings highlight the strengths and limitations of each method, providing guidance for selecting appropriate stochastic sampling strategies in computational sensitivity analysis.

This paper introduces a sophisticated multidimensional sensitivity analysis, incorporating cutting-edge stochastic methods for air pollution modeling.The study focuses on a large-scale long-distance transportation model of air pollutants, specifically the Unified Danish Eulerian Model (UNI-DEM).This mathematical model plays a pivotal role in understanding the detrimental impacts of heightened levels of air pollution.With this research, our intent is to employ it to tackle crucial questions related to environmental protection.We suggest advanced Monte Carlo and quasi-Monte Carlo methods, leveraging specific lattice and digital sequences to enhance the computational effectiveness of multi-dimensional numerical integration.Moreover, we further refine the existing stochastic methodologies for digital ecosystem modeling.The main aspect of our investigation is to analyze the sensitivity of the UNI-DEM model output to changes in the input emissions of human-induced pollutants and the rates of a number of chemical reactions.The developed algorithms are utilized to calculate global Sobol sensitivity measures for various input parameters.We also assess their influence on key air pollutant concentrations in different European cities, considering the diverse geographical locations.The overarching goal of this research is to broaden our understanding of the elements influencing air pollution and inform potent strategies to alleviate its negative impacts on the environment.The work is supported by the Project BG05M2OP001-1.001-0004UNITe,