Simple modelling of large-scale steady tropical circulations coupled with deep moist convection and driven by SST gradients

Most simple theories of the mean tropical circulation (such as the Gill model for the Walker circulation, Held and Hou's theory of the Hadley circulation, and Lindzen and Nigam's theory of how SST forces the low-level wind field) have not explicitly treated the two-way coupling of deep convection with the overall circulation. In the Gill model, for instance, the latent heating from deep convection is specified, and the resulting circulation deduced, but there is no guarantee that the circulation would in fact support the specified pattern of convection.

The recently developed quasi-equilibrium tropical circulation model (QTCM) of Neelin and coworkers is an enlightening attempt to self-consistently link deep convection with the mean tropical circulation. We show how this type of framework can usefully be further simplified for some archetypical problems.

One simplification we explore is the weak temperature gradient (WTG) approximation discussed by Sobel and Bretherton (2000, J. Climate). Within the deep tropics, free-tropospheric temperature variations are slight due to the smallness of the Coriolis parameter. The overall temperature profile is collectively maintained by all tropospheric columns; in each column, the vertical motion(i.e. the divergent circulation) must balance any convective or radiative heating. The rotational circulation is then determined from the vorticity equation and the known divergent circulation. We show how use of the WTG approximation in the shallow water equations has little impact on the solution of the Gill model forced by equatorially centered heating. Then we also show how the same set of equations can be obtained in a convectively coupled atmosphere by specification of an SST anomaly instead of a heating anomaly, if convection is represented as adjustment to a moist adiabatic sounding with specified relative humidity.

Lastly, we introduce a representation of boundary-layer friction into our model, and show that the Gill-like solution is significantly modified, particularly for zonally extended heat sources. We find, as observed, that the low-level convergence in the Walker circulation extends through the mid-troposphere, but the low-level convergence in the Hadley circulation is localized mainly in the boundary layer.