Three-dimensional structure of mass-weighted isentropic time-mean meridional circulations

The present study develops a diagnostic framework for investigating the three-dimensional (3D) structure of mass-weighted isentropic time-mean (T-MIM) meridional circulations and conducts a preliminary analysis of the winter hemispheres. The T-MIM meridional velocity can unfold, in the zonal direction, time-averaged two-dimensional (2D) mass-weighted isentropic zonal means. Furthermore, the T-MIM velocity can be decomposed into the unweighted isentropic time-mean (uTM) velocity and the temporal eddy-correlated transport velocity, the so-called bolus velocity. The bolus velocity greatly contributes to the 2D extratropical direct circulation in the troposphere and to the Brewer-Dobson circulation in the stratosphere. The 3D bolus velocity seems to reflect the geographical distributions of baroclinic instability wave activity. In the boreal winter, both low-level equatorward flows and upper-level poleward flows are located around the North Pacific and North Atlantic storm tracks. In the austral winter, low-level equatorward flows extend zonally across the midlatitudes. In the subtropics, the 3D bolus velocity is found to be significant in the upper branch of the Hadley circulation. A zonal momentum equation is formulated to examine the 3D momentum balance of the meridional circulation in the T-MIM framework. In the extratropics, the uTM and bolus meridional velocities are in geostrophic balance with the stationary and transient components of the 3D Eliassen-Palm (EP) flux divergence, respectively. The pressure gradient force of transient baroclinic instability waves balances with the low-level equatorward flows of the bolus velocity in the storm tracks.