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

Abstract

he 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 ?u is further partitioned into the direct eddy drag ?A and the residual impulse ?uR 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 ?u is mainly due to the direct eddy drag (?u ≈ ?A) in the winter polar stratosphere and can reach approximately ?60 m s?1 in the Northern Hemisphere. In the extratropical troposphere ?u is a small residual (?uR ≈ 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.