An approximate system of equations for deep and shallow atmospheric convection. The equations are derived under the assumptions that the percentage range in potential temperature is small and that the timescale is set by the Brunt–Väisälä frequency. Acoustic waves are thereby filtered - hence the term anelastic, meaning elastic energy is not allowed. If the vertical scale of motion is small compared to the depth of an adiabatic atmosphere, the anelastic equations reduce to the Boussinesq equations for shallow convection.