Axisymmetric constraints on cross-equatorial hadley cell extent

Abstract

We consider the relevance of known constraints from each of Hide's theorem, the angular momentum- conserving (AMC) model, and the equal-area model on the extent of cross-equatorial Hadley cells. These theories respectively posit that a Hadley circulation must span all latitudes where the radiative-convective equilibrium (RCE) absolute angular momentum Mrce satisfies Mrce > Ωa2 or Mrce < 0 or where the RCE absolute vorticity hrce satisfies fηrce < 0; all latitudes where the RCE zonal wind exceeds theAMCzonal wind; and over a range such that depth-averaged potential temperature is continuous and that energy is conserved. The AMC model requires knowledge of the ascent latitude ϕa, which needs not equal the RCE forcing maximum latitude ϕm.Whatever the value of ϕa, we demonstrate that anAMCcell must extend at least as far into the winter hemisphere as the summer hemisphere. The equal-area model predicts ϕa, always placing it poleward of ϕm. As ϕm is moved poleward (at a given thermal Rossby number), the equal-area-predicted Hadley circulation becomes implausibly large, while both ϕm and ϕa become increasingly displaced poleward of the minimal cell extent based on Hide's theorem (i.e., of supercritical forcing). In an idealized dry general circulation model, cross-equatorial Hadley cells are generated, some spanning nearly pole to pole. All homogenize angular momentum imperfectly, are roughly symmetric in extent about the equator, and appear in extent controlled by the span of supercritical forcing.