Diagnostics based on the spatial moments of isopleths of a long-lived
tracer, or of potential vorticity, are presented that enable the struc
ture and evolution of stratospheric polar vortices to be concisely sum
marized and quantified. The area, centre, aspect ratio and orientation
of the 'equivalent ellipse' of the vortex, on an isentropic surface,
are defined using the second-and lower-order spatial moments of contou
rs within the vortex-edge region. By examining the variations of these
'elliptical' diagnostics with time and altitude, the temporal evoluti
on and vertical structure of the polar vortices can be quantified. The
usefulness of the diagnostics is assessed by examining nitrous oxide
data from the Geophysical Fluid Dynamics Laboratory 'SKYHI' general-ci
rculation model. The diagnostics show, and quantify, several differenc
es between the Arctic and Antarctic vortices in the SKYHI model. The A
rctic vortex moves further off the pole, is generally more elongated,
and has a more complicated vertical structure than the Antarctic vorte
x (with larger variations of both the vortex centre and elongation wit
h height). The elliptical diagnostics also identify the occurrence of
large-scale Rossby-wave breaking events, both at the vortex edge and i
n the subtropics, in the model.