 Solution

The isentropic potential vorticity is Ertel potential vorticity expressed on constant potential temperature surfaces:Here ${\zeta }_{\theta }$ is the vertical curl of horizontal velocity differentiated on an isentropic surface, and ${\sigma }_{\theta }$ is mass per unit area per unit potential-temperature interval. For smooth inviscid adiabatic motion, $Dq/Dt=0$. Conserved anomalies are advected and deformed, explaining much balanced large-scale weather variability. Diagnosing velocity from PV additionally needs balance, stratification and boundary information. Strong latent/radiative heating, friction and irreversible mixing generate or modify PV, limiting a purely conservative explanation.^[ref]