Finite-Amplitude Wave Activity and Mean Flow Adjustments in the Atmospheric General Circulation. Part I: Quasigeostrophic Theory and Analysis

Abstract

A diagnostic relationship between finite-amplitude wave activity and the associated adiabatic adjustments to the zonal-mean zonal wind and temperature is developed in the quasigeostrophic (QG) framework and is applied to a 23-yr segment (1979?2001) of the 40-yr ECMWF Re-Analysis (ERA-40) data. Wave activity is defined in terms of an instantaneous areal displacement of QG potential vorticity (PV) from zonal symmetry. Unlike previous forms, the tendency of wave activity equals exactly the negative of the eddy PV flux (Eliassen?Palm flux divergence) in the conservative limit, even at finite amplitude. This allows one to integrate the transformed Eulerian mean (TEM) theory in time and quantify the departure (adiabatic adjustment) of the zonal-mean state from an eddy-free reference state in terms of the observed wave activity. The structure of wave activity identifies synoptic eddies in the extratropics and planetary waves in the high latitudes of winter-to-spring stratosphere. In addition, a thin layer of high wave activity is found at the top of the lowermost stratosphere (?17 km) in the summer extratropics. The reference state is constructed by ?zonalizing? the PV contours conservatively (preserving area) on the isobaric surface and by inverting the resultant PV gradient for the mean flow. The adjustment associated with wave activity depends on the assumed surface boundary condition for the reference state. With a no-slip condition, the observed zonal-mean temperature is on average ?33 (90) K higher than the reference state in the troposphere (stratosphere) of the Arctic winter, while the zonal-mean zonal wind is ?30 m s?1 slower in the upper stratosphere. Since the reference state filters out the advective eddy?mean flow interaction, it fluctuates less than the zonal-mean state, potentially improving the signal-to-noise ratio for climate diagnosis.