Transformed eddy-PV flux and positive synoptic eddy feedback onto low-frequency flow

Interaction between synoptic eddy and lowfrequency flow (SELF) has been the subject of many studies. In this study, we further examine the interaction by introducing a transformed eddy-potential-vorticity (TEPV) flux that is obtained from eddy-potential-vorticity flux through a quasi-geostrophic potential-vorticity inversion. The main advantage of using the TEPV flux is that it combines the effects of the eddy-vorticity and heat fluxes into the net acceleration of the low-frequency flow in such a way that the TEPV flux tends to be analogous to the eddy-vorticity fluxes in the barotropic framework. We show that the anomalous TEPV fluxes are preferentially directed to the left-hand side of the low-frequency flow in all vertical levels throughout the troposphere for monthly flow anomalies and for climate modes such as the Arctic Oscillation (AO). Furthermore, this left-hand preference of the TEPV flux direction is a convenient three-dimensional indicator of the positive reinforcement of the lowfrequency flow by net eddy-induced acceleration. By projecting the eddy-induced net accelerations onto the lowfrequency flow anomalies, we estimate the eddy-induced growth rates for the low frequency flow anomalies. This positive eddy-induced growth rate is larger (smaller) in the lower (upper) troposphere. The stronger positive eddy feedback in the lower troposphere may play an important role in maintaining an equivalent barotropic structure of the low-frequency atmospheric flow by balancing some of the strong damping effect of surface friction.