The minimum possible buoyancy of mixed parcels,
used by previous studies as a measure of CTEI, was
based on the virtual-potential-temperature difference between
the mixture and its environment, 
,
where 
and 
and 
are the vapor and liquid water mixing
ratios. A modification to this
measure was suggested by Duynkerke [1993].
He argued that when an amount 
of clear air is entrained and
mixed with an amount 
of cloudy air,
the measure of buoyancy for instability
should be the total buoyancy of the parcel per unit mass
of entrained air, i.e., 
.
A more generalized interpretation of CTEI is based on the sign of the feedback between the boundary-layer turbulent circulations and the entrainment rate, rather than just on the cloud-top jump conditions. When an increase in entrainment results in stronger boundary-layer circulations, the strengthened circulations can in turn increase entrainment, setting off runaway entrainment that can dissipate the cloud. This idea partly stems from many observational studies that showed no correlation between the jump conditions and the fractional cloudiness [e.g., Albrecht 1991]. Based on saturation point diagrams, Boers [1991] also pointed out the importance of boundary-layer circulation strength and entrainment speed in determining CTEI.
To study the CTEI mechanism, it is important to know how negatively buoyant downdrafts, which drive boundary-layer circulations, are modified by entrainment near the cloud top. For this purpose, Khalsa [1993] and Wang and Albrecht [1994] examined entrainment events by identifying the high ozone and low total water content events from the FIRE aircraft data. They separated the contributions of cloud-top radiative and evaporative cooling to the buoyancy of downdrafts. Based on their study, Wang and Albrecht further proposed a conceptual model that describes the interaction between entrainment and the boundary-layer circulations to explain why cloud can remain solid under the jump condition that satisfies the Deardorff-Randall CTEI criterion. Also, recognizing the importance of small-scale mixing in determining the amount of cloud-top evaporative cooling for CTEI, Krueger [1993] used the linear eddy model, in which molecular diffusion is implemented explicitly while small-scale turbulent eddies are represented through a sequence of statistically-independent rearrangement events on a one-dimensional domain. Krueger's study showed that entrained air usually takes a significant amount of time to become totally mixed with cloudy air, and during this period the mixture is likely to be carried away from the cloud top by a large-eddy downdraft. This supports the idea that cloud-top evaporative cooling enhances boundary-layer circulations, and thus indirectly enhances the entrainment rate.