Modelling tropical atmospheric convection in the context of the weak temperature gradient approximation



A cumulus ensemble model is used to simulate the interaction between tropical atmospheric convection and the large-scale tropical environment in the context of Sobel and Bretherton's (2000) weak temperature gradient approximation. In this approximation, gravity waves are assumed to redistribute buoyancy anomalies over a broad area of the tropics, thus maintaining the local virtual-temperature profile close to the large-scale mean. This result is implemented in the model by imposing the advective effects of a hypothetical mean vertical velocity which is just sufficient to counteract the local heating induced by convection and radiation. The implied vertical advection in the moisture equation and entrainment of air from the surrounding environment have major effects on the evolution of convection in the model.

The precipitation produced by the model mimics the results of a very simple model of tropical precipitation introduced by Raymond (2000), in that the mean rainfall rate predicted by the cumulus ensemble model is, to a good approximation, a function only of the mean column precipitable water. The evolution of the precipitable water, and hence the precipitation rate, is a result of the imbalance between the surface flux of moist entropy into the domain and the radiative loss of entropy out of the top of the domain. This evolution leads to a statistically steady solution in which the resulting precipitation rate is a unique function of the entropy flux imbalance. These results support the hypothesis that tropical precipitation averaged over distance scales of a few hundred kilometres and time scales of a day is a consequence only of local thermodynamic factors. Copyright © 2005 Royal Meteorological Society