Multi-scale models for cumulus cloud dynamics

Cumulus clouds involve processes on a vast range of scales -- including cloud droplets, turbulent mixing, and updrafts and downdrafts -- and it is often difficult to determine how processes on different scales interact with each other. In this talk, several multi-scale asymptotic models are presented for multi-scale interactions between cumulus cloud phenomena: updrafts, pulses, parcels, and sub-parcel turbulent mixing. The purpose for these models is twofold: (i) to help guide theoretical understanding of multi-scale interactions, and (ii) to provide frameworks for multi-scale numerical cloud models.

The models provide two types of results simultaneously: (i) scale analysis on each scale of interest, and (ii) dominant interactions between scales of interest. As an example of the scale analysis results, it is shown that cumulus updrafts can be described by balanced dynamics with balance between source terms and ascent/descent; these are cloud-scale versions of so-called weak-temperature-gradient models. As an example of the multi-scale interactions results, a model is derived that connects these balanced updrafts to the fluctuations within the balanced updraft envelope. These fluctuations describe parcels and updraft pulses, and this model encompasses some of the multi-scale aspects of entrainment.

Models are derived for both shallow cumulus and deep cumulus, and the results for the two cases are compared and contrasted. It is shown that, in some sense, shallow cumuli are parcel-dominated and deep cumuli are updraft-dominated. The differences between the two cases are largely due to the difference in the apparent magnitude of the background temperature stratification.

Finally, the authors are using these models to design multi-scale numerical cloud models, and the setup of such a model will be described.