Abstract
A semi-empirical one-dimensional model for non-adiabatic thermal convection in moist air is studied. The fundamental equations to be solved are those of the heat flux moisture balance and the motion of rising air parcels (thermals) with variable mass due to mixing with environmental air. A simple solution is found and a number of characteristic levels of the convection are determined for the case of a linear decrease of the environmental temperature and specific humidity with height. In contrast to previous studies, the entrainment rate, α(z)=Mi−1(dMi/dz), is taken as an explicit function of z, such that α(z)=3/(α1+z), where a1 is a constant. The predictions of the model are quite realistic and could be used in studying the initial stage of the formation of cumulus clouds.
