Measurements from the Halogen Occultation Experiment, together with assimilated winds, temperatures, and diabatic heating rates from the NASA Goddard data assimilation office, are used in the NASA Langley Research Center trajectory-photochemical model to compute photochemistry along three-dimensional air parcel trajectories for the Northern Hemisphere for the period March through September 1997. These calculations provide a global perspective for the interpretation of constituent measurements made from the ER-2 platform during the Photochemistry of Ozone Loss in the Arctic Region in Summer aircraft campaign. An important component of the model is a parameterization of sub-grid-scale diffusive mixing. The parameterization uses an n-member mixing approach which includes an efficiency factor that enhances the mixing in regions where strain dominates the large-scale flow. Model predictions of O3 and CH4 are compared with in situ measurements made from the ER-2. Comparison of the in situ data with model predictions, conducted with and without diffusive mixing, illustrates the contribution that irreversible mixing makes in establishing observed tracer-tracer correlations. Comparisons made for an ER-2 flight in late April 1997 show that irreversible mixing was important in establishing observed tracer-tracer correlations during spring 1997. Comparisons made in late June 1997, when filaments of very low N2O and CH4 were observed, indicate that remnants of air from the polar vortex survived unmixed in the low stratosphere 6 weeks after the breakup of the polar vortex in May. The results demonstrate that the sub-grid-scale mixing parameterization used in the model is effective not only for strong mixing conditions in late winter and early spring, but also for relatively weak mixing conditions that prevail in summer. ¿ 1999 American Geophysical Union