A numerical study of convection in easterly waves using the "Relax to Balance" approximation

The interaction of convection with the large-scale circulation is an important but difficult problem in the study of atmospheric dynamics. One example of this interaction is the interplay of convection with easterly waves. Though observations have provided some insight into the structure and energetics of easterly waves, there is no real understanding of the effect of these waves on convection. For example, easterly waves can exert a forcing on the system in the form of quasi-geostrophic lifting, surfaces fluxes, and advection of dry or moist air. Which of these forcing mechanisms has the biggest effect on modulating convection is presently unknown. Understanding this aspect of easterly waves requires a numerical model capable of capturing the effects of the interaction of convection with the larger atmospheric scales.

Recently, a numerical technique has been developed for the purpose of investigating the interaction of convection with the large-scale tropical environment. This technique employs a cumulus ensemble model in the context of the weak temperature gradient approximation. The basic idea is that the local vertical profiles of virtual temperature tend to relax to a large-scale mean by redistributing buoyancy anomalies over a large area in the tropics. In the model, this is accomplished by the production of vertical motions which are just sufficient to counteract the effects of local heating associated with convection and radiation.

An extension of the weak temperature gradient approximation in the cumulus ensemble model comes from the overall tendency for the atmosphere to relax to a balanced state; Rather than relaxing to a static, homogeneous virtual temperature profile representative of the deep tropics, the system will in general relax to a time-dependent balanced profile. In this context, the effects of synoptic scale disturbances such as easterly waves can be investigated by imposing small perturbations in the reference profiles which are consistent with propagating easterly waves. Examining the response of convection to various perturbations can sort out the relative importance of the different forcing mechanisms, and thus provide insight into the interaction of convection with easterly waves. Results from this numerical investigation will be presented.