Modified Ertel’s Potential Vorticity as a Climate Variable

Abstract Fundamental freedom existing in Ertel’s general definition of potential vorticity (PV) is used to construct an essential invariant measure in (q, χ) space, where q is an “optimal” modified PV and χ is a monotonic increasing function of potential temperature, which enters q. This novel measure is preserved in idealized climate processes, when external diabatic heating and frictional forcing, being applied to zonally oriented infinitely thin (q, χ) tubes (formed at the expense of intersection between isoscalar surfaces q = constant and χ = constant), annihilate each other. A reference stationary airmass distribution on (q, χ) values is introduced for both hemispheres, separately, which corresponds to a hypothetical atmospheric climate equilibrium state. This reference distribution, with no dependence on χ, is characterized by exponentially decaying function of the absolute value of q and has the same total amount of “PV substance” (atmospheric vorticity charge) as the actual atmospheric state. Comp...