Lipps, F. B. and R. S. Hemler, 1985: Another look at the scale analysis for deep moist convection. Journal of the Atmospheric Sciences, 42 (18), 1960-1964.

Abstract: In this note, a more rational approach is given to specify the parameters G and B in the scale analysis of Lipps and Hemler. The thermodynamic equation is written in a different form so that a closed expression for B can be derived. The present values of G and B are very similar to those in the previous scale analysis. A new result is that the time scale t is expressed in terms of moist convective instability rather than the inverse of the Brunt-Vaisala frequency.
The ratio of volume integrated kinetic energy to volume integrated first-order sensible heat is also discussed in more detail. It is found that for an accurate estimate of sensible heat the region of compensating downward motion between the active clouds must be taken into account. As indicated by earlier authors, the amount of sensible heat produced inside the clouds is relatively small.