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

We introduce a transformed isentropic coordinate M theta(e), defined as the dry air mass under a given equivalent potential temperature surface (theta(e)) within a hemisphere. Like theta(e), the coordinate M-theta e follows the synoptic distortions of the atmosphere but, unlike theta(e), has a nearly fixed relationship with latitude and altitude over the seasonal cycle. Calculation of M-theta e is 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 CO2 seasonal cycle as a function of pressure and M-theta e, where M-theta e is thereby effectively used as an alternative to latitude. We show that the CO2 seasonal cycles are more constant as a function of pressure using Moe as the horizontal coordinate compared to latitude. Furthermore, short-term variability in CO2 relative to the mean seasonal cycle is also smaller when the data are organized by M-theta e and pressure than when organized by latitude and pressure. We also present a method using M-theta e to compute mass-weighted averages of CO2 on a hemispheric scale. Using this method with the same airborne data and applying corrections for limited coverage, we resolve the average CO2 seasonal 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). M-theta e may be similarly useful for mapping the distribution and computing inventories of any long-lived chemical tracer.