Axisymmetric Hadley Cell Theory with a Fixed Tropopause Temperature Rather than Height

Abstract

Abstract 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 Tt and compare the results to their fixed-Ht counterparts. If Tt and the depth-averaged lapse rate are meridionally uniform, then at each latitude Ht varies 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 Tt alters 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 Tt 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.