Abstract
A quasi-one-dimensional, lime-dependent and non-precipitating cumulus cloud model is presented. The model has a source and three regions—a core region, an immediate environmental annular region and a far-environmental region. These regions constitute a convective cell with the bottom open to the source layer below. The source layer is replaced by a circular source located directly beneath the core region, below the cloud base and above the ground. The source emits source air of specified properties at a constant rate. If the properties are good enough and the rate of emission is high, namely, a high source strength, clouds are expected to form. Through a sensitivity test composed of more than 100 different source strengths, we have discovered that there exist two critical values for the strength of the source in producing shallow and deep cumulus clouds in a given atmosphere. If the source strength is below the lower critical value, no cloud can form. Above the upper critical value, a deep cumulus cloud is produced. In between, a shallow plume cloud is produced. These two critical values are both small and close to each other. In a given atmosphere, whether a deep or a shallow cloud develops is extremely sensitive to the variation of the source strength, when the source strength is near its critical value. An important implication of our result is that a cloud can only be shallow or deep. None can be of intermediate height, unless other factors are present, such as an inversion. Applying these results, we have offered some plausible explanations to the bimodal distribution of the final heights of the cloud tops, with respect to time as observed over mountain peaks, and with respect to space as observed over tropical oceans. Also, we have attempted to clarify the conditions for the formation of shallow and deep cumulus clouds.
