Past exam of the atmospheric physics course of the University of Cambridge / 2012 / Paper 1 / 3 / c

In the usual lower-tropospheric seasonal land-heating vorticity tendency, summer land is warmer than the adjacent ocean: the heated layer deepens, favouring stretching and a cyclonic thermal-low tendency in the Northern Hemisphere. In winter, colder land favours a shallow stable layer and an anticyclonic thermal-high tendency. In a column model conserving $q=(f+\zeta )/h$ at fixed f,so deepening and shallowing give the stated signs.

This is a conditional layer picture, not an assertion that heating conserves dry isentropic PV. In the isentropic expression, replace h by ${\sigma }_{\theta }$; an isolated temperature contrast does not specify that mass thickness. Diabatic heating, changes in stratification and increased surface drag over land alter the PV budget. The coastal vorticity tendency from variable surface drag illustrates another complication: the curl of a horizontal drag $-r\mathbf{u}$ is $-r\zeta -(\nabla r\times \mathbf{u}{)}_z$, whose coastal contribution depends on wind and coastline orientation. Vorticity can also differ with height. Without those profiles one cannot assign a universal sign to the full circulation solely from the season; the summer-low/winter-high tendency is the standard idealization.