On the distribution of cloud top heights based on stochastic forcing

Abstract

Irregular small-scale motions, which are introduced into a one-dimensional entraining jet lead to a random cloud with additive stochastic forcing. These clouds are characterized by probability distributions of the thermodynamic cloud properties. Applying a first-passage analysis, probability distributions for maximum cloud top heights can be deduced. In the disturbed tropical atmosphere, random clouds reveal a bimodal probability distribution of cloud top heights, which is essentially due to the mid-tropospheric minimum of the moist static energy. They represent deep and shallow convection. If separated, each scale may be approximated by a log-normal distribution. Some aspects of the competition between these two cloud scales are evaluated.