Sherwood et al. used the large eddy simulation of deep convection to estimate the Reynolds stresses on and the entrainment rate into a control volume centered on the peak upward velocity field in an ascending cloud parcel. Sherwood concluded that traditional assumptions about the entrainment and drag are overestimates as such estimations do not count for the detraining vortical circulations inside the ascending plumes, and postulated a one-dimensional plume model which assumes a high entrainment rate, but ignores the momentum sink due to entrainment as well as drag. This new model is consistent with the observations, but differs significantly with traditional cloud models. The discrepancies between different plume models have been investigated by analyzing the results produced using a cloud resolving simulation model named System for Atmospheric Modeling (SAM).
Through direct and explicit calculations of individual cloud momentum budget terms, it was possible to estimate individual terms in the vertical velocity equation. It is found that the effective entrainment term is negligible in determining the vertical velocity of the ascending plumes, and that it is largely determined by the buoyancy and the pressure perturbation. The results show that the sub-cloud scale effects from the Reynolds number and the pressure perturbation are dominant in the vertical velocity budget. This thesis will document the results from the fine-resolution large eddy simulation, compare different parameterization schemes for the shallow cumulus vertical velocity budget equation, and present the results of explicit calculations of simulated data and a simple parameterization scheme based on the new observations from the high-resolution large eddy simulation.