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.

Automated summary

In this study, a new transformed isentropic coordinate M-theta e is introduced and effectively used to study the seasonal cycle of CO2, serving as an alternative to latitude in related research. The findings suggest that when calculating the CO2 seasonal cycle using M-theta e, the relationship with pressure is more stable and short-term variability is smaller compared to organizing by latitude and pressure.