Quasi-geostrophic dynamics in the presence of moisture gradients
  The derivation of a quasi-geostrophic (QG) system from the rotating shallow water equations on a midlatitude beta-plane coupled with moisture is presented. Condensation is prescribed to occur whenever the moisture at a point exceeds a prescribed saturation value. It is seen that a slow condensation time scale is required to obtain a consistent set of equations at leading order. Further, since the advecting wind fields are geostrophic, changes in moisture (and hence, precipitation) occur only via non-divergent mechanisms. Following observations, a saturation profile with gradients in the zonal and meridional directions is prescribed. A purely meridional gradient has the effect of slowing down the dry Rossby waves, through a reduction in the "equivalent gradient" of the background potential vorticity. A large scale unstable moist mode results on the inclusion of a zonal gradient by itself, or in conjunction with a meridional moisture gradient. For gradients that are are representative of the atmosphere, the most unstable moist mode propagates zonally in the direction of increasing moisture, matures over an intraseasonal timescale and has small phase speed. 
Joy M. Monteiro and Jai Sukhatme
physics.ao-ph physics.flu-dyn