Entrainment and Decoupling Relations for Cloudy Boundary Layers

Abstract

An idealized model of the relationship between entrainment in cloud-topped boundary layers, circulation structure, and the degree of decoupling between the cloud and subcloud layers is developed based on simple turbulent flux distributions and the premise that the entrainment rate, both at cloud top and across cloud base when some stability exists there, is controlled by the large-eddy structure for quasi-steady buoyantly driven conditions. Layers are classified in three regimes depending on whether the cloud-top entrainment rate is ultimately limited by the transport of eddies spanning the full boundary layer (I), the cloud layer (II), or the subcloud layer (III). Algebraic relations are derived for the boundaries between, and entrainment fluxes in, each regime as a function of a convenient set of physical input parameters. The transition from regime II into III, representing the decoupling transition leading to a cumulus coupled layer, is emphasized. The model predicts that decoupling 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 cloud-top radiative cooling or an increase in cloud depth. In spite of the complex cloud-layer dynamics involving cumulus plumes, a simple prediction is given for the quasi-steady cloud-top entrainment rate in regime III based on the subcloud dynamics. 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, and relative cloud depth. Good agreement is found with the predicted entrainment rates, the qualitative layer structure, and location of the decoupling boundary in the parameter space varied.