We describe a technique that uses relatively sparse observations from aircraft of vertical column amounts together with a quasi-conserved parameter, potential vorticity (PV), to reconstruct column abundances on a near-global scale. Stratospheric column amounts for a number of gases (including HF, NO, NO2, HNO3, ClONO2, O3, and HCl) were measured during airborne field deployments to both polar regions in four separate years. Functions are determined that relate vertical column amounts to the isentropic potential vorticity at two potential temperature levels (440 K and 520 K) at the observation points. Gridded PV values, derived from National Center for Environmental Prediction temperature and heights, are used to reconstruct column distributions for an entire polar region. Reconstructed fields are used to explore the usefulness of column observations to describe vertically averaged properties of the polar vortex and to compare one year and hemisphere with another. ¿ 1999 American Geophysical Union