Modified Lagrangian-Mean Diagnostics of the Stratospheric Polar Vortices. Part I. Formulation and Analysis of GFDL SKYHI GCM

Abstract

An exact, two-dimensional (height?latitude type) diagnostic model of tracer transport in the stratosphere is formulated. The model is a generalization of the area analysis method devised by Butchart and Remsberg but uses the mass element enclosed by the contours of a quasi-conservative tracer on a given isentropic surface as a ?meridional? coordinate. This modified Lagrangian-mean coordinate is transparent to the advective effects of the winds, and thus unambiguously extracts the nonconservative effects on the tracer distribution. The derived transport equation takes an equivalent advective form; that is, the tracer contours are ?advected? by the mean nonconservative mass flow while them are no ?eddy flux? contributions. Hence, the mass flux is implied in the motion of the tracer contours. Not only is this model conceptually simple, it is also computationally economical for analyzing large, high-resolution datasets since time averaging can be omitted to define a robust mean field of the tracer. The model is used to diagnose the N2O mixing ratio and potential vorticity simulated in the high-resolution, Geophysical Fluid Dynamics Laboratory SKYHI GCM. The analysis not only identifies the boundary of the polar vortex better than the Eulerian zonal-mean models but highlights how the nonconservative processes (diabatic heating and friction) contribute to the formation of the vortex edge. It also reveals the different kinematics for potential vorticity and chemical tracers.