A mass-weighted isentropic coordinate for mapping chemical tracers and computing atmospheric inventories

We introduce a transformed isentropic coordinate Mθ_e, defined as the dry air mass under a given equivalent potential temperature surface (θ_e) within a hemisphere. Like θ_e, the coordinate Mθ_efollows the synoptic distortions of the atmosphere but, unlike θ_e, has a nearly fixed relationship with latitude and altitude over the seasonal cycle. Calculation of Mθ_eis straightforward from meteorological fields. Using observations from the recent HIAPER Pole-to-Pole Observations (HIPPO) and Atmospheric Tomography Mission (ATom) airborne campaigns, we map the CO₂seasonal cycle as a function of pressure and Mθ_e, where Mθ_eis thereby effectively used as an alternative to latitude. We show that the CO₂seasonal cycles are more constant as a function of pressure using Mθ_eas the horizontal coordinate compared to latitude. Furthermore, short-term variability in CO₂relative to the mean seasonal cycle is also smaller when the data are organized by Mθ_eand pressure than when organized by latitude and pressure. We also present a method using Mθ_eto compute mass-weighted averages of CO₂on a hemispheric scale. Using this method with the same airborne data and applying corrections for limited coverage, we resolve the average CO₂seasonal cycle in the Northern Hemisphere (mass-weighted tropospheric climatological average for 2009-2018), yielding an amplitude of 7.8±0.14 ppm and a downward zerocrossing on Julian day 173±6.1 (i.e., late June).Mθ_emay be similarly useful for mapping the distribution and computing inventories of any long-lived chemical tracer.