Lipps, F. B., and R. S. Hemler, 1980: Another look at the thermodynamic equation for deep convection. Monthly Weather Review, 108 (1), 78-84.

Abstract: The study considers deep moist convection involving only a liquid-vapor phase change. An alternative form of the classical thermodynamic equation for reversible saturated flow is derived. Four approximate forms of this equation are obtained and their relative errors compared to the full equation are evaluated by using parcel theory. The best approximation is found to be an adequate respresentation of the full equation throughout the total depth of the convection.
The two best approximations are compared with some forms of the thermodynamic equation used by other investigators.