  A widely used approach to mathematically describe the atmosphere is to
consider it as a geophysical fluid in a shallow domain -- and thus to model it
using classical fluid dynamical equations combined with the explicit inclusion
of an {\epsilon} parameter representing the small aspect ratio of the physical
domain. In our previous paper [15] we proved a weak convergence theorem for the
polluted atmosphere described by the Navier-Stokes equations extended by an
advection-diffusion equation. We obtained a justification of the generalised
hydrostatic limit model including the pollution effect described for the case
of classical, east-north-upwards oriented local Cartesian coordinates. Here we
give a two-fold improvement of this statement. Firstly, we consider a
meteorologically more meaningful coordinate system, incorporate the analytical
consequences of this coordinate change into the governing equations, and verify
that the weak convergence still holds for this altered system. Secondly, still
considering this new, so-called downwind-matching coordinate system, we prove
an analogous strong convergence result, which we make complete by providing a
closely related existence theorem as well.
