= Solution
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,
$$
\boxed{\delta\zeta\simeq\frac{f+\zeta}{h}\,\delta h,}
$$
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.
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