Under quasi-steady conditions, a convective, cloudy boundary layer's large eddy dynamics and the cloud-top entrainment rate have been shown by large eddy simulations to be intimately tied to one another. We have developed an idealized model that predicts both the cloud-top entrainment rate and the degree of coupling between the eddies in the cloud layer and those in the subcloud layer. Boundary layers are classified into three regimes depending upon whether the cloud-top entrainment rate is predicted to be limited by the transport of eddies spanning the full boundary layer (I), the cloud layer (II), or the subcloud layer (III). The boundaries between these regimes and the entrainment rate within each are determined as algebraic functions of a convenient set of physical input parameters depending on the surface heat and humidity fluxes, cloud-top radiational cooling, cloud-top humidity to temperature jump ratio, and cloud depth. The transition from regime II into III we associate with the decoupling transition leading to a cumulus coupled layer. The model predicts that this transition is promoted by a decrease in Bowen ratio or increase in cloud-top humidity to temperature jump ratio, and, depending on the point in parameter space, either promoted or inhibited by an increase in radiative cloud-top cooling or an increase in cloud depth.

The model is compared with results from an extensive set of large-eddy simulations varying surface heat and moisture fluxes, cloud-top humidity and temperature jumps, relative cloud depth, etc.. Good agreement is found with the predicted entrainment rates, qualitative layer structure, and location of the decoupling boundary in the parameter space varied. Many of these results are summarized in a paper we have recently submitted to JAS, available on our website (http://eiger.mae.wvu.edu/cloud.html). Extension of the model may prove useful in addressing the long standing problem of relating the mean buoyancy flux directly to the mean conserved fluxes of heat and humidity under partly cloudy, highly skewed conditions like those that prevail under shallow cumulus conditions; recent results in this direction may also be included in the presentation.