This chapter delves into advanced statistical and mathematical methodologies for atmospheric pollution source identification, focusing on optimizing efficiency and accuracy in air quality monitoring. It draws a comparative analysis between software tools, each with distinct features tailored to different modeling needs, ranging from simple terrain atmospheric dispersion to complex explosion and chemical release scenarios. A state-of-the-art statistical approach is employed to compare sample correlation coefficients using Fisher’s Z-transformation, enabling the determination of whether different samples originate from the same population. Additionally, the research implements Principle Component Analysis (PCA) and Positive Matrix Factorization (PMF), sophisticated estimation methods, to decompose data variability and accurately apportion sources contributing to fine particulate emissions. In addressing PMF’s computational challenges, the chapter describes two approaches for scaling coefficient calculations, thus enhancing precision in the construction of source profiles and contributions. The integration of the polyline method, predictor–corrector technique, and steepest descent optimization surpasses the classical Newton method, speeding up the source identification process by 3 times. The findings of this chapter hold significant implications for environmental agencies and policymakers in strengthening air pollution management strategies.