Can cloud-top entrainment promote cloud growth?

The primary significance of Cloud Deepening through Entrainment (CDE) is that it can prevent the cloud top entrainment instability from destroying a cloud deck. Without suppressing the instability, CDE transforms it from a cloud destroyer to a cloud builder. The analysis does not depend on an entrainment hypothesis. Moreover, it is not restricted to PBL stratocumulus sheets. Stratiform clouds in the free atmosphere can be subject to CDE we need only reinterpret Ps as the pressure at the base of an elevated turbulent mixed layer. Modest departures from well mixedness will alter the results quantitatively but not qualitatively. Processes other than entrainment, such as surface evaporation, radiative cooling, and advection will often work with CDE to build a cloud layer; but of course they can also oppose CDE by reducing the relative humidity. If we make the weak assumption that the deepening of a cloud layer favors an increase in the cloud top entrainment rate (without specifying any particular functional relationship) we are led to speculate that CDE can cause runaway cloud growth, even in the absence of cloud top entrainment instability. through CDE entrainment leads to a deeper cloud, which leads to stronger entrainment.