A 2.5-Layer Diabatic Long-Wave Balance Model for the Equatorial β-Plane

Some of the most serious effects of climate change are expected to be felt in the tropics. Yet climate models exhibit a wide divergence of predicted responses to climate change in the tropics, especially in terms of atmospheric circulation, and also struggle with accurately representing tropical variability. It is widely believed that the two problems are related, and that both stem from systematic model errors in diabatic heating associated with convection. Unfortunately, observational estimates of diabatic heating are highly uncertain, and there is no accepted framework for relating circulation and diabatic heating on large scales. Both factors limit progress in this area. An asymptotic expansion is used to derive a diabatic balance model for the Boussinesq equations on the equatorial β-plane. The approach is based on the anisotropy of planetary-scale flows and implies a semi-geostrophic balance between the zonal wind and the meridional pressure gradient at leading order. The balance model is a fully non-linear vertically layered model including a boundary layer, which will be extended to include a moisture budget. It provides a complete description of the low-frequency planetary-scale structures in the tropics and thereby offers a theoretical framework to study the coupling between diabatic heating and the tropical circulation, including the relationship between different model errors. The balance relations can be used to calculate the wind field directly from temperature observations and to obtain better constrained observational estimates of diabatic heating. A number of numerical examples are presented to demonstrate the performance of the balance model.