We consider the relevance of known constraints from each of Hide’s theorem, the angular momentum–conserving (AMC) model, and the equalarea model on the extent of crossequatorial Hadley cells. These theories respectively posit that a Hadley circulation must span all latitudes where the radiative–convective equilibrium (RCE) absolute angular momentum [Formula: see text] satisfies [Formula: see text] or [Formula: see text] or where the RCE absolute vorticity [Formula: see text] satisfies [Formula: see text]; all latitudes where the RCE zonal wind exceeds the AMC zonal wind; and over a range such that depthaveraged potential temperature is continuous and that energy is conserved. The AMC model requires knowledge of the ascent latitude [Formula: see text], which needs not equal the RCE forcing maximum latitude [Formula: see text]. Whatever the value of [Formula: see text], we demonstrate that an AMC cell must extend at least as far into the winter hemisphere as the summer hemisphere. The equalarea model predicts [Formula: see text], always placing it poleward of [Formula: see text]. As [Formula: see text] is moved poleward (at a given thermal Rossby number), the equalareapredicted Hadley circulation becomes implausibly large, while both [Formula: see text] and [Formula: see text] 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, crossequatorial 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.
Axisymmetric Hadley cell theory has traditionally assumed that the tropopause height ( H_{t}) is uniform and unchanged from its radiative–convective equilibrium (RCE) value by the cells’ emergence. Recent studies suggest that the tropopause temperature ( T_{t}), not height, is nearly invariant in RCE, which would require appreciable meridional variations in H_{t}. Here, we derive modified expressions of axisymmetric theory by assuming a fixed T_{t}and compare the results to their fixed H_{t}counterparts. If T_{t}and the depthaveraged lapse rate are meridionally uniform, then at each latitude H_{t}varies linearly with the local surface temperature, altering the diagnosed gradientbalanced zonal wind at the tropopause appreciably (up to tens of meters per second) but the minimal Hadley cell extent predicted by Hide’s theorem only weakly (≲1°) under standard annualmean and solsticial forcings. A uniform T_{t}alters the thermal field required to generate an angularmomentumconserving Hadley circulation, but these changes and the resulting changes to the equalarea model solutions for the cell edges again are modest (<10%). In numerical simulations of latitudebylatitude RCE under annualmean forcing using a singlecolumn model, assuming a uniform T_{t}is reasonably accurate up to the midlatitudes, and the Hide’s theorem metrics are again qualitatively insensitive to the tropopause definition. However imperfectly axisymmetric theory portrays the Hadley cells in Earth’s macroturbulent atmosphere, evidently its treatment of the tropopause is not an important error source.
more » « less Award ID(s):
 1912673
 NSFPAR ID:
 10140601
 Publisher / Repository:
 American Meteorological Society
 Date Published:
 Journal Name:
 Journal of the Atmospheric Sciences
 Volume:
 77
 Issue:
 4
 ISSN:
 00224928
 Page Range / eLocation ID:
 p. 12791294
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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