Development of a Scale-Aware Cumulus Parameterization from Analysis of Cloud-Resolving Model Simulations

Cumulus convection plays a key role in atmospheric circulation. The results of global climate models, which have been widely used in climate research, are highly sensitive to cumulus parameterizations used for modeling cumulus clouds. Existing parameterization schemes have relied upon a number of assumptions whose validity is questionable at high spatial resolutions. In this study, we examine the scale-dependence of eddy transport of water vapor, evaluate different eddy transport formulations, and develop a scale-aware eddy transport formulation for mesoscale and climate models. We show that the top-hat approach significantly underestimates updraft eddy transport of water vapor, although the top-hat approach represents the downdraft eddy transport of water vapor well. The three-draft approach evidently improves the parameterized updraft eddy transport because it accounts for the internal variability of updrafts. Based on the results from CRM simulations, we propose and recommend a simplified three-draft formulation that considers three updrafts and one downdraft for eddy transport and it has the following three advantages: (1) no assumption of cloud fractional area, σ, far less than 1, (2) a simple formulation, and (3) accurate representation of CRM-simulated eddy flux across scales. Our results also show that inclusion of finite σ in the eddy transport formulation as proposed by Arakawa et al. does not significantly improve the parameterized eddy transport of water vapor across scales, compared to the conventional formulation in which σ <<1 is assumed. We find that it is the internal variability of updrafts that contributes to the poor performance of the top-hat approach at the gray-zone scales for the full σ range, and using the three-updraft approach much improves the representation of eddy transport of moisture.