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

We introduce a transformed isentropic coordinate Mθe, defined as the dry air mass under a given equivalent potential temperature surface (θe) within a hemisphere. Like θe, the coordinate Mθe follows the synoptic distortions of the atmosphere but, unlike θe, has a nearly fixed relationship with latitude and altitude over the seasonal cycle. Calculation of Mθe 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 Mθe, where Mθe 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 Mθe 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 Mθe and pressure than when organized by latitude and pressure. We also present a method using Mθe 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 zero-crossing on Julian day 173 ± 6.1 (i.e., late June). Mθe may be similarly useful for mapping the distribution and computing inventories of any long-lived chemical tracer.