Starting from hydrostatic non-adiabatic equations for atmospheric flows, we use a matched asymptotic expansion technique, with the Kibel, Ekman and Mach numbers as small parameters, the last two of them being related in a definite way to the first one. We derive, as a first approximation, the quasi-geostrophic equation and in a second approximation the ageostrophic equation which is consistent with the scheme of expansion. A brief account is given of the various initial and boundary layers.