Episodic mixing and buoyancy-sorting representations of shallow cumulus convection

This dissertation combines a diagnostic study, a numerical simulation and a theory of cumulus mixing to investigate shallow cumulus convection and its representation in large-scale models. The objective is to facilitate the development of a cumulus parameterization scheme and also to improve our understanding of the mixing dynamics, transport and life-cycle of shallow cumulus clouds.; Applying an episodic mixing and buoyancy sorting (EMBS) model to shallow clouds requires specification of the undilute eroding/mixing rate (UER), a cloud detrainment criterion and the cloud-environment mixing distribution. A diagnostic equation is formulated for the UER based on a convective equilibrium constraint. A particular UER profile is retrieved by applying the diagnostic equation to an observed trade cumulus boundary layer. Based on this framework, a study of the UER retrieval sensitivity to variations in the mixing distribution and the detrainment criterion is carried out. The retrieved UER decreases exponentially with height above cloud-base, suggesting a strong modulation by the cloud size distribution. The EMBS-diagnosed vertical mass flux is downward within the inversion layer and upward within the cloud layer, indicating the important role of cloud evaporation in cloud detrainment.; A large eddy simulation (LES) is conducted to provide a further evaluation of the EMBS model and the diagnostic results. Numerical tracers are used to identify the cloud-mixed region. Six clouds with a range of heights are isolated from the LES field. The results reveal that the lifetime-averaged vertical mass-flux profile decreases with height and becomes negative within the upper cloud layers. The simulated clouds produce cooling/moistening in their upper portion of the penetration depth and warming/drying in the lower portion of their penetration depth. The success of the EMBS approach is found to be primarily due to its correct representation of the growing and dissipating phase of a cloud life-cycle. Unsaturated downdrafts are evaporatively driven and dominate the overall mass and buoyancy fluxes at upper cloud layers for all simulated clouds. The explicit simulation also strengthens a conclusion made in the diagnostic study that an equilibrium cloud size distribution can be seen as the product of the large scale forcing and dynamics of individual convective clouds.