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

Abstract

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 depth-averaged lapse rate are meridionally uniform, then at each latitude H_t 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 T_t 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 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.