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Understanding changes in UTLS ozone is exceptionally challenging because of large spatial and temporal variability and because of the difficulty of satellite measurements in the UTLS. It is also exceptionally important: for example, to understand climate impacts of radiatively active substances and to understand physical and biological effects of pollution transport and stratosphere-troposphere exchange (STE). Multi-decadal global observations of UTLS ozone are now available from numerous satellite platforms, as well as local and regional observations from aircraft, balloons, and lidar. The upper tropospheric (UT) jets and tropopauses are important drivers of composition variability in the UTLS, acting as transport barriers and controlling STE and long-range transport. We report here on investigations of relationships between extratropical UTLS ozone variability and dynamical diagnostics of mixing / transport barriers, Rossby Wave breaking, and stratosphere-troposphere exchange. We will view these relationships in the context of ozone mapped into dynamical coordinates with respect to the UTLS jets and / or the tropopause. This work will help provide direction for analyses within the Stratosphere-troposphere Processes And their Role in Climate (SPARC) Observed Composition Trends and Variability in the UTLS (OCTAV-UTLS) activity, which aims to use dynamical coordinate mapping to help detect and attribute observed UTLS composition trends, and to project future data needs to better quantify those trends. The work we report on here will focus on satellite ozone observations (primarily from the Aura Microwave Limb Sounder, additionally from ACE-FTS and OSIRIS) and assimilated ozone and dynamical fields (from multiple reanalyses); we will also provide some examples of comparisons with aircraft and balloon observations.