This study addresses the computational challenges of global sensitivity analysis (GSA) in high-dimensional environmental models by developing an advanced quasi-Monte Carlo methodology. The main objective is to improve the estimation of variance-based Sobol’ sensitivity indices through the application of an enhanced rank-1 lattice rule. This rule is constructed using component-by-component (CBC) techniques with order-dependent weights to optimize integration performance in models with smooth, multivariate output. The methodology is applied to the Unified Danish Eulerian Model (UNI-DEM), a hemispheric-scale air quality model used to simulate atmospheric chemical and physical processes. Despite its classical structure, UNI-DEM remains relevant for large-scale pollution transport studies and offers a realistic benchmark for numerical experimentation. Comparative numerical experiments are conducted using multiple stochastic techniques, including the modified Sobol’ sequence, Fibonacci-based and bijectional lattice rules. The results demonstrate that the proposed CBC-optimized lattice method consistently achieves lower relative errors and better convergence behavior, particularly in scenarios with higher dimensionality and smooth integrands. The findings also confirm that the enhanced method is computationally efficient and well-suited for quantifying the influence of anthropogenic emission levels on atmospheric pollutants such as ammonia, ozone, ammonium sulfate, and ammonium nitrate. This work contributes to the advancement of scalable GSA techniques and highlights the importance of integrating modern quasi-Monte Carlo approaches into legacy environmental models. The approach has broader applicability in scientific computing domains requiring high-dimensional numerical integration.