Abstract
This paper presents a single-column model of moist atmospheric convection. The problem is formulated in terms of conservation laws for mass, moist potential temperature and specific humidity of air parcels. A numerical adjustment algorithm is devised to model the convective adjustment of the column to a statically stable equilibrium state for a number of test cases. The algorithm is shown to converge to a weak solution with saturated and unsaturated parcels interleaved in the column as the vertical spatial grid size decreases. Such weak solutions would not be obtainable via discrete PDE methods, such as finite differences or finite volumes, from the governing Eulerian PDEs. An equivalent variational formulation of the problem is presented and numerical results show equivalence with those of the adjustment algorithm. Results are also presented for numerical simulations of an ascending atmospheric column as a series of steady states. The adjustment algorithm developed in this paper is advantageous over similar algorithms because first it includes the latent heating of parcels due to the condensation of water vapour, and secondly it is computationally efficient making it implementable into current weather and climate models.