Stratospheric Warmings Diagnosed Using the Transformed Eulerian-Mean Equations and the Effect of the Mean State on Wave Propagation

Abstract

Terms in the transformed Eulerian mean equations are computed for the stratospheric warmings of December and January, 1976?77, together with cross sections showing the directions of the Eliassen-Palm (EP) fluxes and residual mean meridional circulations. The picture of warmings that emerges from them transformed diagnostics is compared and contrasted with that presented for the same events by O'Neill and Taylor (1979), whose analysis was based on the traditional momentum and heat budgets. The transformed equations lead to a simpler interpretation of warmings mainly because one term, the convergence of the EP flux, embodies to good approximation the total effect of the waves in forcing the mean flow. Zonal mean temperature changes occur essentially as an adiabatic response to the wave-induced, residual mean meridional circulation. Some evidence that critical lines may act to absorb rather than to reflect planetary waves an a short time-scale is presented. One aspect of these and other warmings of dynamical importance is the switching of the EP fluxes which occurs from an upward and equatorward direction to an upward and poleward direction. It is proposed that this represents a feedback effect on wave propagation of an evolving mean flow. Some support for this idea comes from an analysis of ray paths in the meridional plane. They are computed for different mean wind fields which arise during a warming, and give the direction of wave propagation according to a linear theory based on the WKB approximation. Within the approximations of the theory, the mean state determines how the planetary waves propagate meridionally and vertically through a quantity Q which may be termed a refractive index. Rays are refracted poleward or equatorward according to whether Q increases poleward or equatorward. After a minor warming when the stratospheric jet has been replaced by weak westerlies, a local minimum in Q occurs in the stratosphere and rays reaching upper levels are refracted equatorward. They are refracted poleward when a strong jet is established at high latitudes, which implies that subsequent wave disturbances are focused into the polar cap, leading there to a deceleration of the mean wind. The ray paths are compared with the directions of wave propagation as given by the observed EP fluxes. Good qualitative agreement is found.