Potential vorticity modeling of the ITCZ and the Hadley circulation

A simple zonally symmetric balanced model of the Hadley circulation is presented. The model is based on potential vorticity arguments and consists of a predictive equation for the potential pseudodensity and an invertibility principle to diagnose the associated balanced wind and mass fields. When the theory is formulated in the potential latitude coordinate, the meridional advection is implicit in the coordinate transformation, which makes the prediction equation for potential pseudodensity analytically solvable. For convective heating patterns that simulate the ITCZ, the model produces upper and lower tropospheric potential vorticity anomalies of opposite sign. The associated winds are easterly at low levels and westerly aloft, except between the equator and the ITCZ, where there are low-level westerlies and upper-level easterlies. Since the potential vorticity anomalies develop within a background state that has potential vorticity increasing to the north, reversed poleward gradients of potential vorticity are produced, just as has been observed in the west African region. For typical convective heating rates, significant potential vorticity gradient reversals occur quickly--on the order of a couple of days. According to the Charney-Stern theorem, such zonal flows are expected to be unstable. In this sense the ITCZ is self-destructive and should not be viewed as a strictly steady state feature of the tropical circulation. In addition, according to this scenario, the potential vorticity dynamics of the west African region are not unique, and we should expect a similar ITCZ formation-breakdown cycle to occur in other tropical regions such as the tropical east Pacific and northern Australia.