Hadley Cell Section

What is modelled

An axisymmetric, pedagogical model of the overturning tropical circulation. Solar declination sets the daily-mean sunlight and a proxy for the ITCZ latitude; a stream function gives a closed overturning cell with rising air at the ITCZ, poleward flow aloft and equatorward flow below, and angular-momentum conservation gives the upper-level westerlies. The page uses the 3D page's science module unchanged and adds the cross-section and the checks.

Equations

• Declination delta = 23.44 sin(2 pi (day - 80) / 365.24).
• Daily-mean insolation Q = S0/pi (h0 sin(phi) sin(delta) + cos(phi) cos(delta) sin(h0)), cos h0 = -tan(phi) tan(delta).
• Stream function psi ~ sin(pi x) sin(pi z): v = d psi / dz, w = -d psi / dy.
• Angular momentum (u + Omega R cos phi) R cos phi = const, so u = Omega R (cos^2 phi0 / cos phi - cos phi).
• ITCZ proxy: 0.45 of the declination, scaled by sqrt(heating), limited to 14 degrees.

Checks run in the page

• Declination extremes of plus and minus 23.44 degrees and the equinox zero.
• Global mean insolation equals S0/4 on any day.
• Zero divergence of the stream-function wind by central differences.
• Conservation of absolute angular momentum along the poleward branch.

Honest simplifications

A phenomenological model, not a general circulation model: no eddies, no moisture or latent heating, no friction closure, a fixed cell width, the ITCZ shift is a proxy and not a forecast, the height is exaggerated in the picture and the vertical arrows are scaled up for visibility. The 3D page's disclaimer applies.

• Press June solstice and watch the ITCZ move into the northern hemisphere.
• Press Strong heating: the winds and the rising speed grow with the square root of the heating.
• Move the probe latitude and read the day length and insolation, then compare the polar summer with the equinox.