Axisymmetric constraints on cross-equatorial Hadley cell extent

TL;DR

This paper examines theoretical constraints on the extent of cross-equatorial Hadley cells, comparing models and demonstrating how forcing and ascent latitude influence their size and symmetry in idealized simulations.

Contribution

It analyzes and compares three key theoretical models constraining Hadley cell extent, revealing their implications and limitations in idealized circulation simulations.

Findings

AMC model requires ascent latitude knowledge and extends at least as far into winter as summer hemisphere.

Equal-area model predicts poleward placement of ascent latitude, leading to implausibly large cells at high forcing.

Idealized models show nearly pole-to-pole Hadley cells with extent controlled by supercritical forcing.

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 ($M_\mathrm{rce}$) satisfies $M_\mathrm{rce}>\Omega a^2$ or $M_\mathrm{rce}<0$ or where the RCE absolute vorticity ($\eta_\mathrm{rce}$) satisfies $f\eta_\mathrm{rce}<0$; 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 $\varphi_\mathrm{a}$, which need not equal the RCE forcing maximum latitude $\varphi_\mathrm{m}$. Whatever the value of $\varphi_\mathrm{a}$, 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 $\varphi_\mathrm{a}$, always placing it poleward of $\varphi_\mathrm{m}$. As $\varphi_\mathrm{m}$ is moved poleward (at a given thermal Rossby number), the equal-area predicted Hadley circulation becomes implausibly large, while both $\varphi_\mathrm{m}$ and $\varphi_\mathrm{a}$ 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.