The center ideas to modify hydrostatic primitive dynamical equations in atmospheric model to non-hydrostatic system, split the dynamical system equation into two parts. First part is corresponds to the hydrostatic system, except for higher order corrections due to the vertical acceleration. Second part is the system of equations that allows computation of the corrections appearing in the first system due to the vertical acceleration. We studied atmospheric model, that us hybrid vertical coordinate and let special notation “m”. The hybrid-coordinate density “m” is related to the hydrostatic pressure coordinate density. In order to cambering between to out put models forecast special sand, dust, thunder storm, and rain, so we put complete chapter in theoretical weather variables investigation.