Finite-Amplitude Wave Activity and Mean Flow Adjustments in the Atmospheric General Circulation. Part II: Analysis in the Isentropic Coordinate

The finite-amplitude wave activity diagnostic developed for quasigeostrophic (QG) flows in Part I is extended to the global primitive equation system in the isentropic coordinate. The Rossby wave activity density A is proportional to Kelvin’s circulation around the wavy potential vorticity (PV) contour minus that around the zonal circle that encloses the same isentropic mass. A quasi-conservative, eddy-free reference state flow uREF is constructed from the observed Kelvin’s circulation by zonalizing the PV contours conservatively while enforcing gradient balance. The departure of the observed zonal-mean flow of the atmosphere from the reference state is defined as the net adjustment by the eddies. Then Δu is further partitioned into the direct eddy drag −A and the residual impulse ΔuR consistent with the time-integrated transformed Eulerian mean (TEM) zonal-wind equation. The analyzed climatological-mean wave activity in the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) is similar to that in Part I. The net adjustment Δu is mainly due to the direct eddy drag (Δu ≈ −A) in the winter polar stratosphere and can reach approximately −60 m s−1 in the Northern Hemisphere. In the extratropical troposphere Δu is a small residual (ΔuR ≈ A), yet it clearly reveals a 5–6 m s−1 eddy driving of the Southern Hemisphere jet as well as a 7–8 m s−1 eddy drag in the subtropical upper troposphere of both hemispheres. The local maxima in wave activity in the equatorial upper troposphere and the extratropical lower stratosphere found in Part I are undetected, while negative wave activity is found where the isentropes intersect the ground. As in the QG case, uREF exhibits significantly less transient and interannual variability than , implying a better signal-to-noise ratio as a climate variable.