**Abstract**

A novel analytical solution has been developed for the three-dimensional dispersion of atmospheric pollutants, providing a new approach to understanding and addressing this important environmental issue. The central concept of the study is to divide the planetary boundary layer into multiple vertical sub-layers, each characterized by its own average wind speed and eddy diffusivity. This allows for a more comprehensive and nuanced examination of atmospheric processes within the boundary layer. The validity of the model is thoroughly evaluated through a comparison of its predictions with data collected from the Copenhagen Diffusion and Prairie Grass experiments. This approach ensures that the model accurately reflects the complexities of atmospheric dispersion in real-world scenarios. The results of the study demonstrate a strong correlation between the predicted and measured crosswind-integrated concentrations. Furthermore, the statistical indices computed for the model fall within an acceptable range, indicating a high level of accuracy in the model's predictions. These findings reinforce the validity of the analytical solution for modeling atmospheric pollutant dispersion.

**Keywords:** analytical solution, atmospheric dispersion, atmospheric boundary layer sub-layers, Fourier transform, Sturm-Liouville eigenvalue problem
