The Efficiency of Upward Wave Propagation Near the Tropopause

Extreme states of the polar stratospheric vortex are typically followed by anomalous surface circulation. These extreme stratospheric vortex states are in turn often associated with extreme heat flux between the tropopause and 100 hPa. 

The goal of this work is to better understand upward wave propagation between the tropopause and the bottom of the vortex near 100 hPa using both theory and reanalysis data.

Following Charney and Drazin (1961) we analytically solve a quasi-geostrophic planetary-scale model with three different layers: troposphere, tropopause inversion layer (TIL) and stratosphere. We allow for different buoyancy frequencies in each layer and show the dependence of transmission and reflection coefficients on the buoyancy frequencies, TIL depth and mean-state zonal wind. The dependence of heat flux in the TIL and stratosphere, as well as phase-lines for the wave solution, are presented. This analysis highlights the key role that the TIL and jumps in buoyancy frequency play for upward wave propagation.

We then use reanalysis data to consider the importance of this effect in observations. Four different specifications of the index of refraction are compared: that derived by Charney and Drazin in 1961, that derived by Matsuno in 1970, and two that relax some of the assumptions used in the derivations of the first two. The Charney and Drazin index of refraction includes terms ignored by Matsuno that are critical for understanding upward wave propagation just above the tropopause in both the climatology and associated with extreme heat flux events. By adding these ignored terms to the Matsuno index of refraction, it is possible to construct a useful tool that describes wave flux immediately above the tropopause and at the same time also describes the role of meridional gradients within the stratosphere. Specifically, a stronger tropopause inversion layer (TIL) tends to restrict upward wave propagation. It is also shown that while only 38% of extreme wave-1 Eliassen-Palm flux vertical component (F_z) at 100hPa events are preceded by extreme F_z at 300hPa, there are almost no extreme events at 100hPa in which the anomaly at 300hPa is of opposite sign or very weak.