A Rational Approach to Cumulus Parameterization

Traditionally, cumulus parameterizations in largescale atmospheric models are simpli ed treatments based on plausibility arguments and followed by extensive tuning to optimize overall model behavior. The results of this approach are not always satisfactory, and have stimulated the development of socalled superparameterizations, in which a cumulus ensemble model run in each gridbox takes the place of the cumulus parameterization. Though some of the early results of this approach are encouraging, it seems unlikely that computing power will increase su ciently in the near-term to make this approach generally feasible at spatial resolutions needed to resolve most tropical phenomena. Assuming that cumulus ensemble models can themselves be veri ed against observation to su cient accuracy, an alternative approach is to use such models to improve cumulus parameterizations. However, in order to do so, the cumulus models must be run in a realistic context, so that the full range of behaviors possible in the large-scale model is exercised. Sobel and Bretherton (2000), Derbyshire et al. (2004), and Raymond and Zeng (2000, 2005) have developed such a context, called the weak temperature gradient (WTG) approximation by Sobel and Bretherton. In this context the e ects of buoyancy redistribution by gravity waves in the tropics are mimicked by relaxing the average virtual temperature pro le of the model to some reference tropical pro le. This relaxation may be thought of as being due to the adiabatic cooling from some vertical velocity, called the WTG vertical velocity. Vertical advection and (optionally) lateral entrainment and detrainment from the surroundings follow from this vertical motion, and are used to modify the average humidity eld in the model as well. After determin-