Extent of Hadley circulations in dry atmospheres

The subtropical terminus of the Hadley circulation is interpreted as the latitude poleward of which vertical wave activity fluxes (meridional eddy entropy fluxes) become sufficiently deep to reach the upper troposphere. This leads to a sign change of the upper-tropospheric divergence of meridional wave activity fluxes (convergence of meridional eddy angular momentum fluxes) and marks the transition from the tropical Hadley cell to the extratropical Ferrel cell. A quantitative formulation for determining the depth of vertical wave activity fluxes and thus the terminus of the Hadley circulation is proposed based on the supercriticality, a measure of the slope of isentropes. The supercriticality assumes an approximately constant value at the terminus of the Hadley circulation in a series of simulations with an idealized dry general circulation model. However, it is unclear how to generalize this supercriticality-based formulation to moist atmospheres.