Some Bulk Properties of Cumulus Ensembles Simulated by a Cloud-Resolving Model. Part II: Entrainment Profiles

As a continuation of the effort to develop an improved cloud model of cumulus parameterization, this study investigates entrainment profiles of the cumulus ensembles simulated by a cloud-resolving model (CRM). The simulated saturated updrafts are separated into different categories according to their maximum heights. Entrainment characteristics of each category are then inferred from cloud mass flux and moist static energy profiles. It is found that all categories of saturated updrafts tend to have the most significant entrainment at lower levels and near cloud top. Moreover, the details of the entrainment characteristics are not sensitive to vertical wind shear but are primarily determined by large-scale thermodynamic fields. The dependence of entrainment characteristics on large-scale thermodynamic fields can be interpreted as a manifestation of a relationship between cloud buoyancy and entrainment rate. With these findings, a formula is proposed to describe entrainment profiles of the cloud spectrum in the Arakawa–Schubert cumulus parameterization, in which the fractional rate of entrainment is originally assumed constant in height for each cloud type. In addition, the cloud-base conditions are revised in a way as suggested in Part I of this paper, and the thermodynamic properties of entrained air are assumed to be the averages between large-scale values and in-cloud values. It is demonstrated that the spectral cumulus ensemble model, after these revisions, has the capability to reproduce cloud mass flux and in-cloud properties for each category of saturated updrafts simulated by the CRM.