On the use and significance of isentropic potential vorticity maps

Abstract

The two main principles underlying the use of isentropic maps of potential vorticity to represent dynamical processes in the atmosphere are reviewed, including the extension of those principles to take the lower boundary condition into account. The first is the familiar Lagrangian conservation principle, for potential vorticity (PV) and potential temperature, which holds approximately when advective processes dominate frictional and diabatic ones. The second is the principle of ‘invertibility ’ of the PV distribution, which holds whether or not diabatic and frictional processes are important. The invertibility principle states that if the total mass under each isentropic surface is specified, then a knowledge of the global distribution of PV on each isentropic surface and of potential temperature at the lower boundary (which within certain limitations can be considered to be part of the PV distribution) is sufficient to deduce, diagnostically, all the other dynamical fields, such as winds, temperatures, geopotential heights, static stabilities, and vertical velocities, under a suitable balance condition. The statement that vertical velocities can be deduced is related to the well-known omega equation principle, and depends on having sufficient information about diabatic and frictional processes. Quasi-geostrophic, semigeostrophic, and ‘nonlinear normal mode initialization ’ realizations of the balance condition are discussed. An important constraint on the mass-weighted integral of PV over a material volume and on its possible diabatic and frictional change is noted.