Past exam of the atmospheric physics course of the University of Cambridge / 2014 / Paper 1 / 3 / c

For an approximately conserved isentropic potential vorticity, ${\zeta }_{\theta }+f=q{\sigma }_{\theta }$: increased isentropic layer mass implies more cyclonic vorticity, and decreased layer mass more anticyclonic vorticity at fixed latitude. Equivalently, in the thin-layer analogy, stretching increases and compression decreases absolute vorticity.

The usual summer land-heating picture has a deeper, less stably stratified lower atmosphere and favours a cyclonic thermal low; winter land cooling gives a shallow stable layer and favours an anticyclonic thermal high. These are conditional lower-tropospheric tendencies, not a season-only conservation law. Heating is diabatic and the rougher land surface introduces friction and convergence, so parcel PV need not remain fixed. The sign at every altitude cannot be deduced from “ocean to land” alone without the heating/stability profile and background wind.