Several approaches to parameterize the turbulent transport of momentum, heat, water vapour and cloud water for use in a general circulation model (GCM) have been tested in 1-dimensional and 3-dimensional model simulations. The schemes differ with respect to their closure assumptions (conventional eddy diffusivity model versus turbulent kinetic energy closure) and also regarding their treatment of cloud–turbulence interactions. The basic properties of these parameterizations are discussed first in relation to column simulations of a stratocumulus–topped atmospheric boundary layer (ABL) under a strong subsidence inversion during the KONTROL experiment in the North Sea. It is found that the K-models tend to decouple the cloud layer from adjacent layers above and below because the turbulent activity is calculated from local variables. The higher-order scheme performs better in this respect because internally generated turbulence can be transported up and down through the action of turbulent diffusion. Thus, the TKE-scheme provides not only a better link between the cloud and the sub-cloud layer but also between the cloud and the inversion as a result of cloud-top entrainment. In the stratocumulus case study, where the cloud is confined by a pronounced subsidence inversion, increased entrainment favours cloud dilution through enhanced evaporation of cloud droplets. In the GCM study, however, additional cloud-top entrainment supports cloud formation because indirect cloud generating processes are promoted through efficient ventilation of the ABL, such as the enhanced moisture supply by surface evaporation and the increased depth of the ABL. As a result, tropical convection is more vigorous, the hydrological cycle is intensified, the whole troposphere becomes warmer and moister in general and the cloudiness in the upper part of the ABL is increased.