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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 [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 depth-averaged 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 equal-area 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 equal-area-predicted 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, 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.
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Axisymmetric Hadley Cell Theory with a Fixed Tropopause Temperature Rather than Height
Axisymmetric Hadley cell theory has traditionally assumed that the tropopause height ( Ht) is uniform and unchanged from its radiative–convective equilibrium (RCE) value by the cells’ emergence. Recent studies suggest that the tropopause temperature ( Tt), not height, is nearly invariant in RCE, which would require appreciable meridional variations in Ht. Here, we derive modified expressions of axisymmetric theory by assuming a fixed Ttand compare the results to their fixed- Htcounterparts. If Ttand the depth-averaged lapse rate are meridionally uniform, then at each latitude Htvaries linearly with the local surface temperature, altering the diagnosed gradient-balanced 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 annual-mean and solsticial forcings. A uniform Ttalters the thermal field required to generate an angular-momentum-conserving Hadley circulation, but these changes and the resulting changes to the equal-area model solutions for the cell edges again are modest (<10%). In numerical simulations of latitude-by-latitude RCE under annual-mean forcing using a single-column model, assuming a uniform Ttis 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.
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- Award ID(s):
- 1912673
- PAR ID:
- 10140601
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of the Atmospheric Sciences
- Volume:
- 77
- Issue:
- 4
- ISSN:
- 0022-4928
- Page Range / eLocation ID:
- p. 1279-1294
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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