A Scheme for Representing Cumulus Convection in Large-Scale Models

Observations of individual convective clouds reveal an extraordinary degree of inhomogeneity, with much of the vertical transport accomplished by subcloud-scale drafts. In view of these observations, a representation of moist convective transports for use in large-scale models is constructed, in which the fundamental entities are these subcloud-scale drafts rather than the clouds themselves. The transport by these small-scale drafts is idealized as follows. Air from the subcloud layer is lifted to each level i between cloud base and the level of neutral buoyancy for undilute air. A fraction (εi) of the condensed water is then converted to precipitation, which falls and partially or completely evaporates in an unsaturated downdraft. The remaining cloudy air is then assumed to form a uniform spectrum of mixtures with environmental air at level i; these mixtures ascend or descend according to their buoyancy. The updraft mass fluxes Mi are represented as vertical velocities determined by the amount of convective available potential energy for undilute ascent to level i, multiplied by fractional areas σi, which are in turn determined in such a way as to drive the mass fluxes toward a state of quasi-equilibrium with the large-scale forcing. The downdraft mass fluxes are unique functions of the Mi, so that determination of the Mi closes the System. The main closure parameters in this scheme are the parcel precipitation efficiencies, εi, which determine the fraction of condensed water in a parcel lifted to level i that is converted to precipitation, and the fraction σis of precipitation that falls through unsaturated air. These may be specified as functions of altitude, temperature, adiabatic water content, and so on, and are regarded as explicitly determined by cloud microphysical processes. Specification of these parameters determines the vertical profiles of heating and moistening by cloud processes, given the large-scale (explicitly resolved) forcing. It is argued here that accurate calculation of the moistening by cumulus clouds cannot proceed without addressing the microphysics of precipitation formation, fallout, and reevaporation. One-dimensional radiative-convective equilibrium experiment with this scheme produce reasonable profiles of buoyancy and relative humidity. When large-scale descent is imposed, a trade-cumulus regime is produced, including a trade inversion and mixing-line structure in the cloud layer.