The weak temperature gradient approximation and balanced tropical moisturewaves

Horizontal temperature gradients are small in the tropical atmosphere, as a consequence of the smallness of the Coriolis parameter near the equator. T his provides a strong constraint on both large-scale fluid dynamics and dia batic processes. This work is a step toward the construction of a balanced dynamical theory for the tropical circulation that is based on this constra int, and in which the diabatic processes are explicit and interactive. The authors first derive the basic fluid-dynamical scaling under the weak t emperature gradient (WTG) approximation in a shallow water system with a fi xed mass source representing an externally imposed heating. This derivation follows an earlier similar one by Held and Hoskins, but extends the analys is to the nonlinear case (though on an f plane), examines the resulting sys tem in more detail, and presents a solution for an axisymmetric "top-hat'' forcing. The system is truly balanced, having no gravity waves, but is diff erent from other balance models in that the heating is included a priori in the scaling. The WTG scaling is then applied to a linear moist model in which the convec tive heating is controlled by a moisture variable that is advected by the f low. This moist model is derived from the Quasi-equilibrium Tropical Circul ation Model (QTCM) equations of Neelin and Zeng but can be viewed as somewh at more general. A number of additional approximations are made in order to consider balanced dynamical modes, apparently not studied previously, whic h owe their existence to interactions of the moisture and flow fields. A pa rticularly interesting mode arises on an f plane with a constant background moisture gradient. In the limit of low frequency and zero meridional waven umber this mode has a dispersion relation mathematically identical to that of a barotropic Rossby wave, though the phase speed is eastward (for moistu re decreasing poleward in the background state) and the propagation mechani sm is quite different. This mode also has significant positive growth rate for low wavenumbers. The addition of the beta effect complicates matters. F or typical parameters, when beta is included the direction of phase propaga tion is ambiguous, and the growth rate reduced, as the effects of the backg round gradients in moisture and planetary vorticity appear to cancel to a l arge degree. Possible relevance to intraseasonal variability and easterly w ave dynamics is briefly discussed.