Abstract. 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.

Abstract. 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 HIPPO and 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 cycles are more constant as a function of pressure using Mθe as the horizontal coordinate compared to latitude. Furthermore, short-term variability of 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 at 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.

The air‐sea exchange of oxygen (O2) is driven by changes in solubility, biological activity, and circulation. The total air‐sea exchange of O2 has been shown to be closely related to the air‐sea exchange of heat on seasonal timescales, with the ratio of the seasonal flux of O2 to heat varying with latitude, being higher in the extratropics and lower in the subtropics. This O2/heat ratio is both a fundamental biogeochemical property of air‐sea exchange and a convenient metric for testing earth system models. Current estimates of the O2/heat flux ratio rely on sparse observations of dissolved O2, leaving it fairly unconstrained. From a model ensemble we show that the ratio of the seasonal amplitude of two atmospheric tracers, atmospheric potential oxygen (APO) and the argon‐to‐nitrogen ratio (Ar/O2), exhibits a close relationship to the O2/heat ratio of the extratropics (40–normal70°). The amplitude ratio, AAPO/AArN2, is relatively constant within the extratropics of each hemisphere due to the zonal mixing of the atmosphere. AAPO/AArN2 is not sensitive to atmospheric transport, as most of the observed spatial variability in the seasonal amplitude of δAPO is compensated by similar variations in δ(Ar/N2). From the relationship between O2/heat and AAPO/AArN2 in the model ensemble, we determine that the atmospheric observations suggest hemispherically distinct O2/heat flux ratios of 3.3 ± 0.3 and 4.7 ± 0.8 nmol J−1 between 40 and normal70° in the Northern and Southern Hemispheres respectively, providing a useful constraint for O2 and heat air‐sea fluxes in earth system models and observation‐based data products.

Interactive comment on "A mass-weighted atmospheric isentropic coordinate for mapping chemical tracers and computing inventories" by Yuming Jin et al.Yuming Jin et al.