On Thermally Direct Circulations in Moist Atmospheres

An expression is derived for the critical horizontal gradient of subcloud-layer θe in radiative-convective equilibrium, sufficient for the onset of thermally direct, zonally symmetric circulations. This corresponds to zero absolute vorticity at the tropopause. The expression is then generalized to nonsymmetric flows under the approximation that the corresponding radiative-convective equilibrium state is in geostrophic balance. Scale analysis shows that actual moist entropy distributions cannot be far from critical in large-scale Hadley, Walker, and monsoon circulations. The balanced component of the surface winds can be calculated from the supercriticality of the surface θe distribution, and the secondary circulation can then be estimated from the surface stress.