This paper presents an advanced stochastic method based on a lattice rule with an optimized generating vector, which has been developed and thoroughly analyzed. A central component of the study is the Unified Danish Eulerian Model (UNI-DEM), a large-scale mathematical model that accurately represents complex physical and chemical processes in the atmosphere. The research compares the proposed lattice rule with the one of the best available methods for the problem under consideration - the modified Sobol sequence, and also the bijectional lattice rule and the Fibonacci-based lattice rule, demonstrating its advantageous in estimating multidimensional integrals. The enhanced approach proves to be robust and computationally efficient, making it highly effective for computing sensitivity indices, a critical aspect of scientific computing. Additionally, variance-based sensitivity analysis techniques, particularly the Sobol’ method, have been employed to quantify the influence of input parameters on model outputs. A comprehensive experimental study has been conducted, integrating advanced Monte Carlo algorithms with scrambling stochastic techniques to improve computational efficiency. The study also investigates the impact of emission levels on key atmospheric pollutants such as ammonia, ozone, ammonium sulfate, and ammonium nitrate, focusing on major European cities with diverse geographical conditions. The results underscore the importance of sensitivity analysis in evaluating model reliability and understanding the intricate relationships between input parameters and environmental outcomes.