Isentropic potential vorticity
= Isentropic potential vorticity
On potential-temperature surfaces, $q=(\zeta_\theta+f)/\sigma_\theta$, where $\sigma_\theta=-(1/g)\partial p/\partial\theta$ is isentropic mass density. In adiabatic frictionless flow it is materially conserved. Diagnosing a velocity field also requires balance and boundary data.