Development of a Scale-Aware Cumulus Parameterization – Part II: Analysis of Cloud-Resolving Model Simulations

Following Part I, in which 3-D cloud-resolving model (CRM) simulations of a squall line and mesoscale convective complex in the mid-latitude continent and the tropical regions are conducted and evaluated, 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 performance.