• Deep convective clouds;
  • Shallow cumulus;
  • Third-order turbulence closure


The abilities of a cloud-resolving model (CRM) with double-Gaussian based and quasi-Gaussian based third-order closures (TOCs) to simulate shallow cumuli and their transition to deep convective clouds are compared in this study. The quasi-Gaussian based TOC is fully prognostic (FP), while the double-Gaussian based TOC is intermediately prognostic (IP). The latter only predicts three important third-order moments while the former predicts all the third-order moments. A shallow cumulus case is simulated by single-column versions of the FP and IP TOC models and a large-eddy simulation (LES). The IP TOC improves the simulation of shallow cumulus greatly over the FP TOC by producing more realistic cloud structures, when both are compared to LES. Large differences of the second- and third-order moments between the FP and IP TOC simulations appear in the cloud layer, because the cloud top height is underestimated by the FP TOC simulation. Sensitivity experiments and analysis of probability density functions (pdfs) used in the TOCs show that both the turbulence-scale condensation and higher-order moments are important to realistic simulations of the boundary-layer shallow cumuli.

A shallow to deep convective cloud transition case is also simulated by the two-dimensional (2-D) version of the CRM with FP and IP TOCs. Both simulations can capture the transition from the shallow cumuli to deep convective clouds. The IP simulations produce more and deeper shallow cumuli than the FP simulations, but the FP simulations produce larger and wider convective clouds than the IP simulations. The temporal evolutions of cloud and precipitation are closely related to the turbulent transport, the cold pool and the cloud-scale circulation. The large amount of turbulent mixing associated with the shallow cumuli slows down the increase of the convective available potential energy and inhibits the early transition to deep convective clouds in the IP simulation. When the deep convective clouds fully develop and the precipitation is produced, the cold pools produced by the evaporation of the precipitation are not favourable to the formation of shallow cumuli. As a whole, the IP simulations are able to more realistically capture the transition processes than the FP simulations, when both are compared to an LES-resolution 3-D simulation of the same case. Copyright © 2006 Royal Meteorological Society