The Mean Meridional Circulation of the Atmosphere Using the Mass above Isentropes as the Vertical Coordinate

The mean meridional circulation of the atmosphere is presented using the mass (more specifically, the pressure corresponding to the mass) above the isentrope of interest as the vertical coordinate. In this vertical coordinate, themass-weightedmean circulation is exactly balanced by entropy sources and sinks with no eddy flux contribution as in the isentropic coordinate, and the coordinate can be readily generalized to the mass abovemoist isentropes or other quasi-conservative tracers by construction. The corresponding Eliassen–Palm (EP) flux divergence for the zonal-mean angular momentum is formulated in a hybrid isobaric–isentropic form, extending the conventional transformed Eulerian-mean (TEM) formulation to finite-amplitude nongeostrophic eddies on the sphere. In the small-amplitude limit, the hybrid isobaric–isentropic formulation reduces to the TEM formulation. Applying to the NCEP–U.S. Department of Energy (DOE) Reanalysis 2, the new formulation resolves the deficiency of the conventional TEM formulation for the near-surface flow, where the isentropic surface intersects the ground, and the mean circulation agrees well with the TEM above the near-surface layer. In the small-amplitude limit, this improvement near the surface can be partially attributed to the isentropic static stability over the isobaric counterpart, as the mass density in the near-surface isentropic layers gradually approaches zero. Also, the meanmass streamfunction can be approximately obtained from the EP flux divergence except for the deep tropics or the near-surface flow, highlighting the dominant control of potential vorticity mixing for the subtropics-to-pole mean circulations. It is then expected to provide a valuable diagnostic framework not only for global circulation theory, but also for atmospheric transport in the troposphere.