  Considered as a geophysical fluid, the polluted atmosphere shares the shallow
domain characteristics with other natural large-scale fluids such as seas and
oceans. This means that its domain is excessively greater horizontally than in
the vertical dimension, leading to the classic hydrostatic approximation of the
Navier-Stokes equations. The authors of the \cite{azerad2001mathematical}
article have proved a convergence theorem for this model with respect to the
ocean, without considering pollution effects. The novelty of this present work
is to provide a generalisation of their result translated to the atmosphere,
extending the fluid velocity equations with an additional convection-diffusion
equation representing pollutants in the atmosphere.
