Entrainment-mixing parameterization in shallow cumuli and effects of secondary mixing events

Parameterization of entrainment-mixing processes in cumulus clouds is critical to improve cloud parameterization in models, but is still at its infancy. For this purpose, we have lately developed a formulation to represent a microphysical measure defined as homogeneous mixing degree in terms of a dynamical measure defined as transition scale numbers, and demonstrated the formulation with measurements from stratocumulus clouds. Here, we extend the previous work by examining data from observed cumulus clouds and find positive correlations between the homogeneous mixing degree and transition scale numbers. These results are similar to those in the stratocumulus clouds, but proved valid for the first time in observed cumulus clouds. The empirical relationships can be used to parameterize entrainment-mixing processes in two-moment microphysical schemes. Further examined are the effects of secondary mixing events on the relationships between homogeneous mixing degree and transition scale numbers with the explicit mixing parcel model. The secondary mixing events are found to be at least partially responsible for the larger scatter in the above positive correlations based on observations than that in the previous results based on numerical simulations without considering secondary mixing events.