Mean-state convective circulations over large-scale tropical SST gradients

The dynamical balance of the mean tropical atmospheric circulation maintained over large-scale SST gradients is analyzed. To first order, the strength of the circulation is determined by the subsidence rate in the dry descent region that balances the radiative cooling. The divergent component of the horizontal wind is then proportional to the domain size. The convective intensity is determined by the balance between convective heating and the sum of the radiative cooling and adiabatic cooling by large-scale vertical ascent. A key result is that the amplitude of the SST gradients does not directly determine the strength of the large-scale circulation. A second-order analysis shows that the tropospheric temperature responds to SST only through the residual convective heating, which is the deviation of convective heating from the first-order estimate. This decreases the temperature gradient that drives the observed Walker circulation to only a small fraction of the SST gradient across the Pacific. This argument is analogous to Lindzen and Nigam's "back pressure.'' The suppression of the SST gradients by the residual convective heating further increases with decreasing horizontal extent of the large-scale circulation, as well as with increasing SST contrast. Therefore, the horizontal air temperature gradient required to drive the large-scale circulation is consistent with the first-order estimate. Analyses of cloud-resolving numerical simulations suggest that when the domain size is small, the suppression of SST gradients by residual convective heating is strong enough to generate a secondary convergence in the middle troposphere. This generates a mean circulation consisting of two shallow cells (third baroclinic mode). This shallower circulation maintains a horizontal flow strength comparable to that in a large domain. Two variables remain undetermined: the ratio between the ascending and the descending areas, and a closed expression for the residual heating rate.