A Quasi-one-Dimensional Cumulus Cloud Model and Parameterization of Cumulus Heating and Mixing Effects

Abstract

The characteristic properties of cumulus convection are investigated using a semi-one-dimensional, axisymmetric, quasi-Lagrangian steady-state model which takes into consideration the influence of the pressure perturbation, density stratification and nearby moist downdraft under two different environmental situations: 1) a potentially more unstable tropical environment and 2) a less unstable middle-latitude environment with prominent stable layers in the middle troposphere. It is found that the compressional heating of the dry environment makes the cloud air warmer and reduces the updraft velocity slightly, and moist downdraft cools the cloud air and reduces both the updraft and the cloud depth, while the influence of pressure perturbation also reduces the updraft but it is effective only for clouds of radii >1000 m. The influence of density stratification is to reduce wc, slightly at low levels and augment wc, at high levels and to slightly increase the cloud depth. The calculated precipitation rates appear to be close to the representative values obtained from observations. One most interesting result given by the model is that, under the less unstable middle-latitude environment, the precipitation rate jumps from lower than 0.7 cm h?1 for cloud radii <1000 m to more than 5.4 cm h?1 for cloud radii >2000 m, reflecting the inhibiting effect of the midtropospheric stable layer on the penetrative power of the smaller clouds. Another interesting result revealed by the model is that with the pressure perturbation included, the maximum updraft velocity wmax achieves highest value when the cloud radius is ?8 km. The influences of cumulus convection on the average thermodynamic properties of the atmosphere also have been calculated and it was found that the main heating is from latent beat but compressional heating of environmental air is also of importance, especially close to the top of the cloud.