A pseudo-incompressible model for moist atmospheric flows is presented. The equation set is derived from a fully compressible system by assuming that the pressure perturbations are small. Unlike the standard dry pseudo- incompressible approximation the hydrostatic background state is allowed to vary in time and a set of equations dictating the evolution of the background state are derived. Changes of the background state are the result of net accumulation of diabatic processes and latent heat conversion. Their governing equations emerge in the theory from a consistency condition for the velocity divergence constraint. The model is validated by comparing its results for a well-established benchmark test with those from a fully compressible model.
