Global Transport Calculations with an Equivalent Barotropic System

Abstract

Transport properties of the two-dimensional equations governing equivalent barotropic motion are investigated on the sphere. Because of its relationship to the primitive equations in isentropic coordinates, the equivalent barotropic system has explicit representation of forcing, equivalent depth, and diabatic effect, not easily identified in other barotropic representations of atmospheric motion. In addition, this two-dimensional system provides a natural framework for investigating the behavior of column abundances acted upon by deep atmospheric motions. Its column-integrated nature together with the separation of time scales for horizontal advection and mean meridional motions and vertical shear suggest the equivalent barotropic system should provide a reasonable description of column-averaged behavior over many horizontal advection times. Horizontal transport properties of this system are investigated under adiabatic and diabatic conditions, for different forms of dissipation, and over a range of resolutions. Integrated numerically on the sphere with a Hough spectral algorithm, the equivalent barotropic system conserves potential vorticity Q very accurately, even at low resolution. Isopleths of Q track closely a material contour, consisting of a large ensemble of fluid particles, which is integrated forward in a Lagrangian calculation in tandem with the Eulerian integration, The two tracers of fluid motion remain coincident through great distortions of the material field, diverging only after scales have collapsed down to the resolution where numerical dissipation is effective. Forcing representative of time-mean and amplified conditions at 10 mb leads to behavior typical of observations at this level. The familiar displacement of the polar night vortex and its distortion into a comma shape are evident, as is irreversible mixing under sufficiently strong forcing amplitude. Thermal dissipation influences the behavior importantly by inhibiting the amplification of unstable eddies and thereby the horizontal stirring of air. With forcing representative of time-mean conditions, irreversible mixing is confined to a narrow zone adjacent to the tropical zero wind line. However, amplified forcing leads to stirring across much of the winter hemisphere, at least under adiabatic conditions. The picture in this case is one of ?global-scale entrainment,? polar and tropical air being exchanged in the form of cyclonic and anticyclonic tongues. Injection of tropical air into the polar cap results in an anticyclonic circulation which spins up at high latitudes, mirroring the behavior during a stratospheric warming.