Eulerian Mean, Contour Integral, and Finite-Amplitude Wave Activity Diagnostics Applied to a Single-Layer Model of the Winter Stratosphere

Abstract

A shallow water model is used to simulate a case of planetary wave breaking in the lower winter stratosphere. The simulation is diagnosed in terms of zonal mean mass and zonal momentum budgets, and also in terms of potential vorticity (PV) contour mass and circulation budgets. The time evolution of the PV contour diagnostics depends only on nonconservative processes such as diabatic heating, friction, and irreversible small-scale mixing;transient but essentially reversible events such as a temporary displacement of the vortex from the pole are effectively filtered out. The PV contour diagnostics show unambiguously and quantitatively aspects of the evolution such as shrinking of the vortex and sharpening of the vortex edge. The cross-contour mass flux gives a radically different view of meridional transport from that given by the mass-weighted Eulerian mean poleward velocity, both in terms of its qualitative behavior and in terms of the physical mechanisms that cause it. The PV contour diagnostics can be used to define a balanced, zonally symmetric state, whose evolution can be compared directly with that of the Eulerian zonal mean state. A new expression is presented for finite-amplitude wave activity in terms of the PV contour diagnostics. Wave activity diagnostics for the wave-breaking simulation are shown. There are large differences between the zonal mean wave activity flux and its small-amplitude approximation, the Eliassen?Palm (EP) flux; some of the implications for interpreting EP flux diagnostics in the stratosphere are discussed.