Triple oxygen isotope composition of CO₂ in the upper troposphere and stratosphere

High-precision measurements of the triple oxygen isotope composition of CO₂ (Δ^′17O) can be used to estimate biosphere–atmosphere exchange of CO₂, the residence time of tropospheric CO₂, and stratosphere–troposphere exchange. In this study, we report measurements of the Δ^′17O(CO₂) from air samples collected during two aircraft-based programmes, CARIBIC and StratoClim. CARIBIC (Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container) provided air samples from numerous transcontinental flights in the upper troposphere–lower stratosphere region. StratoClim (Stratospheric and upper tropospheric processes for better climate predictions) conducted intensive campaigns with the high-altitude aircraft M55 Geophysica during the Asian summer monsoon anticyclone (ASMA), providing air samples from altitudes up to 21 km.

Using high-precision Δ^′17O measurements of the CARIBIC samples, we show that the N₂O–Δ^′17O correlation, previously observed in the stratosphere, extends to the upper troposphere. Moreover, we found no significant spatial or hemispheric differences in Δ^′17O(CO₂) for the upper-tropospheric samples collected during the CARIBIC programme. However, in many of the StratoClim samples, with significant stratospheric contributions, we observed a much lower N₂O–Δ^′17O slope compared to CARIBIC samples and previous publications. This deviation is attributed to change in eddy diffusion above the tropopause within the ASMA, confirming previously published model calculations. These samples provide the first experimental evidence that differences in vertical mixing/transport can lead to significantly different N₂O–Δ^′17O slopes. High-precision Δ^′17O measurements can identify ejections of tropospheric air into the stratosphere based on the slope of the N₂O–Δ^′17O correlation, as both tracers have chemical lifetimes longer than their transport times.

Furthermore, we use the Δ^′17O measurements from the lower stratosphere and the upper troposphere to estimate global stratospheric production and surface removal of the isotope tracer Δ^′17O. The removal estimate is then used to derive an independent estimate of global vegetation exchange of CO₂, confirming earlier estimates based on surface level Δ^′17O measurements.

1 Introduction

Measurements of the isotope composition of CO₂ (δ¹³C and δ¹⁸O; see definition below) are used in many ways to understand sources and sinks of CO₂ in the global carbon cycle (Farquhar et al., 1993; Welp et al., 2011; Cuntz et al., 2003b; Ciais et al., 1997a, 1995). The flux estimates of CO₂ from the terrestrial biosphere are poorly constrained in current carbon cycle models (Piao et al., 2013). By using δ¹³C it is possible to differentiate between the ocean sink and biosphere activity. However, distinguishing respiration, photosynthesis, and combustion signals using δ¹³C of CO₂ is impossible (Ciais et al., 1995). To address this challenge, δ¹⁸O of CO₂ is a valuable tool for distinguishing respiration from photosynthesis. The δ¹⁸O value of CO₂ is higher during photosynthesis than during respiration due to isotope exchange of CO₂ with isotopically different leaf water and soil water pools, as leaf water typically has a higher δ¹⁸O value than soil water (Ciais et al., 1997a, b; Welp et al., 2011; Farquhar et al., 1993; Cuntz et al., 2003a, b; Francey and Tans, 1987; Yakir, 2020).

One of the limitations of using δ¹⁸O of CO₂ to distinguish photosynthesis and respiration is the oxygen isotope exchange of CO₂ with liquid water in surface water bodies or vegetation, since this isotope exchange affects δ¹⁸O of CO₂, without contributing to a net flux. Numerous equilibrium and kinetic effects can alter the δ¹⁸O value of water and other molecules (Cuntz et al., 2003a, b; Peylin et al., 1999). Importantly, the isotopic composition of leaf water at the CO₂–H₂O exchange site in the mesophyll is not well understood, primarily due to fractionation associated with evaporation, transport, and diffusion (Adnew et al., 2020, 2021, 2023; Gan et al., 2002; Cousins et al., 2006; Song et al., 2015; Landais et al., 2006; Cernusak et al., 2016; Helliker and Ehleringer, 2000). These unknown physico-chemical fractionation processes introduce large uncertainty into estimates of gross fluxes of CO₂ when using δ¹⁸O as quantitative tracer. This uncertainty can potentially be reduced using the triple oxygen isotopic composition of CO₂, Δ^′17O (see Eq. 4), which is a combination of the δ¹⁷O and δ¹⁸O isotopic composition (Hoag et al., 2005; Koren et al., 2019; Adnew et al., 2020).

Stratospheric CO₂ has a high Δ^′17O value, i.e. Δ^′17O ≫ 0, due to isotope exchange with O(¹D) produced from O₃ photolysis (Thiemens et al., 1991, 1995a; Lyons, 2001; Lämmerzahl et al., 2002; Thiemens, 2006; Kawagucci et al., 2008; Wiegel et al., 2013; Yung et al., 1991, 1997; Shaheen et al., 2007). The main sink for this higher Δ^′17O signal of CO₂ is isotope exchange with leaf, soil, and ocean water at the Earth's surface, after Δ^′17O-enriched CO₂ has re-entered the troposphere via the large-scale Brewer–Dobson circulation and synoptic eddy diffusion (Boering et al., 2004; Thiemens et al., 2014; Liang and Mahata, 2015; Francey and Tans, 1987). With the exception of stratospheric CO₂, Δ^′17O variations in nature are much smaller compared to δ¹⁸O variations and are better defined, as conventional biogeochemical processes follow a well-defined three-isotope fractionation slope (Barkan and Luz, 2005, 2007, 2012; Landais et al., 2006; Angert et al., 2004, 2003). Furthermore, the triple oxygen isotope fractionation slopes for specific processes are independent of the source water isotope composition, insensitive to temperature, and process-specific (Landais et al., 2006; Hofmann et al., 2012). As a result, Δ^′17O is less affected by the numerous physico-chemical fractionation processes mentioned above and may provide an additional constraint for quantifying the gross fluxes of the terrestrial carbon cycle than measuring δ¹⁸O alone (Koren et al., 2019; Hoag et al., 2005; Liang et al., 2017a, 2023; Hofmann et al., 2017; Adnew et al., 2020; Thiemens et al., 2014).

In addition to quantifying the gross fluxes of the terrestrial carbon cycle, Δ^′17O can provide useful information concerning stratospheric intrusions (Liang and Mahata, 2015; Steur et al., 2024), stratosphere–troposphere exchange (Boering et al., 2004; Luz et al., 1999), atmospheric transport and chemistry in the mesosphere and stratosphere (Liang et al., 2007, 2008), and combustion processes (Laskar et al., 2016; Horváth et al., 2012) and for estimating the residence time of CO₂ in the troposphere (Liang et al., 2017b; Laskar et al., 2019; Hoag et al., 2005).

High-precision measurements of Δ^′17O(CO₂) are particularly interesting in the tropical upper troposphere–lowermost stratosphere region, which is remote from the sources and sinks. Therefore, Δ^′17O(CO₂) can be used to study the influence of the stratosphere–troposphere exchange on the variations and dynamics of Δ^′17O and its correlation with other long- and short-lived trace gases. Additionally, these measurements may be valuable for using Δ^′17O as a tracer to quantify gross fluxes of CO₂, as this region links the stratosphere, where Δ^′17O of CO₂ is produced, to the troposphere, where Δ^′17O of CO₂ is “washed out”. Furthermore, it is interesting to investigate whether Δ^′17O varies spatially in the upper troposphere and whether it is possible to detect large-scale dynamic phenomena that happen in the Asian summer monsoon anticyclone (ASMA). The monsoon circulation system has a large variability in its spatial extent, and the ASMA can reach the Mediterranean, north-east Africa, and east Asia (Annamalai and Slingo, 2001; Garny and Randel, 2013; Pan et al., 2016; Vogel et al., 2019).

Here we present high-precision measurements of Δ^′17O(CO₂) from a total of 85 air samples collected in the upper troposphere and stratosphere as part of the CARIBIC and StratoClim aircraft air sampling projects. We investigate the spatial distribution (horizontal and vertical) of Δ^′17O(CO₂) signals associated with the ASMA and refine previous estimates of the net stratosphere–troposphere flux of Δ^′17O(CO₂) and constraints on surface CO₂ emissions.

2 Materials and method

2.1 Definitions and notation

Variations in isotopic abundance are reported as deviations of a heavy-to-light isotope ratio in a sample relative to a reference material (Eq. 1). For oxygen the reference material is Vienna Standard Mean Ocean Water (VSMOW), whereas for carbon the reference material is Vienna Pee Dee Belemnite (VPDB). Since isotope variations are small, they are usually reported in per mill (‰) in δ notation.

$$\begin{array}{}\text{(1)}& {\mathit{\delta }}^x={\displaystyle \frac{{}^x{R}_{\mathrm{sam}}}{{}^x{R}_{\mathrm{std}}}}-\mathrm{1},\end{array}$$

where x can be 13, 17, and 18 (for ¹³C, ¹⁷O, and ¹⁸O, respectively). The indices sam and std stand for sample and standard, respectively, and R is the ratio between the heavy isotope and the light isotope of the respective element, for instance for ¹³C and ¹⁸O and ¹³R = $\frac{{}^{\mathrm{13}}\mathrm{C}}{{}^{\mathrm{12}}\mathrm{C}}$ and ¹⁸R = $\frac{{}^{\mathrm{18}}\mathrm{O}}{{}^{\mathrm{16}}\mathrm{O}}$, respectively. The variations in δ¹⁷O and δ¹⁸O are closely related during most physico-chemical fractionation processes according to Eq. (2) (Matsuhisa et al., 1978; Young et al., 2002).

$$\begin{array}{}\text{(2)}& {\left({\displaystyle \frac{{}^{\mathrm{18}}{R}_{\mathrm{sam}}}{{}^{\mathrm{18}}{R}_{\mathrm{std}}}}\right)}^{{\mathit{\theta }}_{\mathrm{p}}}={\displaystyle \frac{{}^{\mathrm{17}}{R}_{\mathrm{sam}}}{{}^{\mathrm{17}}{R}_{\mathrm{std}}}}\end{array}$$

The exponent θ_p denotes a three-isotope slope that occurs from a single process. Equation (2) can be expressed in δ notation as

$$\begin{array}{}\text{(3)}& \ln \left({\mathit{\delta }}^{\mathrm{17}}\mathrm{O}+\mathrm{1}\right)-{\mathit{\theta }}_{\mathrm{p}}\times \ln \left({\mathit{\delta }}^{\mathrm{18}}\mathrm{O}+\mathrm{1}\right)=\mathrm{0}.\end{array}$$

The deviation of the left-hand side of Eq. (3) from zero is defined as Δ^′17O:

$$\begin{array}{}\text{(4)}& {\mathrm{\Delta }}^{\prime \mathrm{17}}\mathrm{O}=\ln \left({\mathit{\delta }}^{\mathrm{17}}+\mathrm{1}\right)-{\mathit{\lambda }}_{\mathrm{ref}}\times \ln \left({\mathit{\delta }}^{\mathrm{18}}\mathrm{O}+\mathrm{1}\right),\end{array}$$

where the process-dependent exponent θ_p has been replaced by a three-isotope reference slope λ_ref. Note that the choice of λ_ref is arbitrary since in nature isotopic compositions rarely reflect fractionation from a single process but instead integrate multiple fractionating processes and several three-isotope values (Adnew, 2020; Barkan and Luz, 2005, 2007, 2012; Angert et al., 2004). For most natural processes, λ_ref ranges from 0.5 to 0.5305 (Thiemens, 2006; Matsuhisa et al., 1978; Young et al., 2002; Cao and Liu, 2011; Thiemens et al., 1991; Kaiser, 2008) with some exceptions (Adnew et al., 2022; Hayles et al., 2017; Hayles and Killingsworth, 2022). In this study we use a λ_ref value of 0.528, the value associated with meteoric water (Meijer and Li, 1998; Luz and Barkan, 2010).

2.2 Sampling

Air samples were collected from the upper troposphere and stratosphere during two different international projects, CARIBIC and StratoClim, which are shortly described below. Figure 1 shows the geographical coordinates of the sampling locations for the samples measured in this study.

Figure 1 Geographical location of the CARIBIC (black markers), StratoClim2016 (blue circles), and StratoClim2017 (blue stars) air samples measured in this study. Upper-tropospheric CARIBIC samples are categorized based on the geographical location where they are collected. These categories include Southern Hemisphere samples, Northern Hemisphere samples, African samples (longitude between 7 and 45°), Asian samples (longitude > 45°), and American samples (longitude < 0°).

2.2.1 CARIBIC samples

In the CARIBIC project (Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container, CARIBIC, https://www.caribic-atmospheric.com/, last access: 20 September 2024), samples were collected using a Boeing 767 aircraft (LTU, Germany). The flights operated at typical commercial cruising altitude between 9 and 12 km, i.e. which is the upper troposphere–lower stratosphere region at higher latitudes and the upper-troposphere region in the mid-latitudes and tropics (Assonov et al., 2010). The details of the CARIBIC instrument container are described in Brenninkmeijer et al. (1999). The payload of the flights before 2003 included large stainless steel canisters for collecting whole-air samples (WAS) (sample size ≈ 340 L STP) at several locations along the flight path. On a single flight 12 discrete samples were collected. Each sample collection took about 20 min, which corresponds to a horizontal distance of 250 km (Brenninkmeijer et al., 1999). The samples collected are relatively dry since the ambient temperature was always below −30 °C, and the relative humidity was about 0.44 % at 20 °C (Assonov et al., 2009b). The air samples were processed soon after they returned to the Division of Atmospheric Chemistry, Max Planck Institute for Chemistry, Mainz, Germany (Pupek et al., 2005). The processing included the extraction of CO₂ and CO for isotope analysis, including radiocarbon (Brenninkmeijer, 1993; Assonov et al., 2009b), as well as measurement of several other trace gases including N₂O, CH₄, and SF₆ (Brenninkmeijer et al., 1999). The CARIBIC container was also equipped with an automated in situ analyser for O₃ (UV absorption), CO (gas chromatography, GC), and other parameters (Brenninkmeijer et al., 1999). In this study we measured the Δ^′17O value of 50 CARIBIC samples.

2.2.2  StratoClim samples

A total of 35 additional air samples were collected on the high-altitude M55 Geophysica aircraft during two campaigns of the StratoClim project (https://www.stratoclim.org/, last access: 10 September 2024) (Stefanutti et al., 1999; Cairo et al., 2010) in 2016 and 2017. In 2016, three flights were conducted over the Mediterranean region from Kalamata, Greece (37°2^′ N, 22°7^′ E), between 30 August and 6 September, and eight flights were conducted in 2017 over the Indian subcontinent from Kathmandu, Nepal (27°46^′ N, 85°16^′ E), between 27 July and 10 August. The whole-air sampler of the Institute for Marine and Atmospheric research Utrecht (IMAU), Utrecht University, was used to compress air into 2 L pre-evacuated stainless-steel canisters (Kaiser et al., 2006). We analysed 16 samples from the 2016 flights and 19 samples from the 2017 flights (Table S3 in the Supplement). Further details on sample collection using the Geophysica aircraft can be found in Kaiser et al. (2006) and Stefanutti et al. (1999).

2.3 Extraction of CO₂

For the StratoClim samples, the CO₂ was extracted from the whole-air samples using a cryogenic extraction system developed at Utrecht University (Adnew et al., 2020, 2023). The extraction system was made of electropolished stainless steel and has four traps. The first two traps remove moisture and condensable organics at dry ice temperature, whereas the third and fourth traps were used to collect CO₂ at liquid nitrogen temperature. The extraction was performed at a flow rate of 55 mL min⁻¹.

For the CARIBIC samples, the CO₂ had previously been extracted at the Max Planck Institute for Chemistry, Mainz, as described in Assonov et al. (2009b) and Pupek et al. (2005). Two “Russian doll” cryogenic traps (Brenninkmeijer and Röckmann, 1996; Brenninkmeijer, 1991) immersed in liquid nitrogen trapped all condensable gases including CO₂, N₂O, H₂O, and most organics. After pumping out non-condensables, the traps were slowly heated, and the evolving CO₂ and N₂O were trapped in a U trap cooled with liquid nitrogen, while the H₂O remained trapped in the Russian doll traps. The collected CO₂ was further dried using P₂O₅ and flame-sealed in clean vials made of borosilicate glass (Assonov et al., 2009b; Pupek et al., 2005).

2.4 Measurement of δ¹³C, δ¹⁸O, and Δ^′17O of CO₂

The δ¹⁸O and δ¹³C values presented below were measured using a Delta V PLUS isotope ratio mass spectrometer (ThermoFisher Scientific, Germany) in dual-inlet mode at Utrecht University. The interference of N₂O was corrected using δ¹⁸O = δ¹⁸O${}_{\mathrm{measured}}+\frac{\left[{\mathrm{N}}_{\mathrm{2}}\mathrm{O}\right]}{\left[{\mathrm{CO}}_{\mathrm{2}}\right]}\left(\frac{\mathrm{347}}{\mathrm{1000}}\right)$ and δ¹³C = δ¹³C${}_{\mathrm{measured}}+\frac{\left[{\mathrm{N}}_{\mathrm{2}}\mathrm{O}\right]}{\left[{\mathrm{CO}}_{\mathrm{2}}\right]}\left(\frac{\mathrm{250}}{\mathrm{1000}}\right)$ (Friedli and Siegenthaler, 1988; Sirignano et al., 2004). Figure 2 shows a comparison of the δ¹⁸O and δ¹³C of CO₂ of CARIBIC samples measured in this study with those previously measured at the Max Planck Institute for Chemistry and reported in Assonov et al. (2009b, a, 2010).

Figure 2 The δ¹⁸O and δ¹³C of CARIBIC samples and comparison with values published in Assonov et al. (2009b, a, 2010).

The δ¹⁸O values measured in this study are systematically higher compared to the measurement by Assonov et al. (2010) by 0.096 ± 0.008 ‰. For δ¹³C values, our measurement is also higher by 0.089 ± 0.011 ‰. The reported error is the 95 % confidence limit (standard error of the mean multiplied by Student's t factor). The tight distribution of differences is of the order of the measurement precision, which suggests that the isotopic composition of the samples remained stable during long-term storage in borosilicate glass vials and that the mean offset is due to scale differences. These observed offsets are consistent with the scale uncertainty reported by Assonov et al. (2009a) and better than typical inter-laboratory uncertainties (Levin et al., 2009).

The Δ^′17O of the CO₂ was determined using the CO₂–O₂ exchange method (Adnew et al., 2019, 2022, 2023; Barkan et al., 2015) at Utrecht University. Equal amounts of CO₂ sample and the laboratory reference O₂ (with known isotopic composition) were allowed to exchange isotopes for 2 h in a quartz reactor at 750 °C in the presence of platinum sponge at the bottom of the reactor. After the reaction, the mixture was passed through a liquid-nitrogen-cooled trap to condense the CO₂, and the O₂ was collected in a separate trap on three pellets of 5Å molecular sieve (1.6 mm, Sigma-Aldrich, USA) at liquid nitrogen temperature. The O₂ was then transferred to the bellows of the dual-inlet system of a Delta V PLUS isotope ratio mass spectrometer (ThermoFisher Scientific, Germany) and measured for its isotope composition. The Δ^′17O value of the original CO₂ was calculated from the change in the isotopic composition of the non-reacted and reacted O₂, and knowledge of the precise steady-state O₂–CO₂ isotope fractionations (Adnew et al., 2019; Barkan et al., 2015). The precision of the CO₂ isotope measurements was 0.007 ‰, 0.03 ‰, and 0.008 ‰ for δ¹³C, δ¹⁸O, and Δ^′17O, respectively (Adnew et al., 2019, 2020, 2023).

2.5 Calculation of net isotope flux from stratosphere to troposphere

The isotopic composition of CO₂ in the upper stratosphere and mesosphere provides a unique tool to study atmospheric transport and chemistry (Boering et al., 2004; Liang et al., 2007, 2008). The Δ^′17O(CO₂) is primarily modified by O(¹D), which is produced photochemically by O₃ photolysis. However, the relevant isotope effects occurring in the stratosphere are still not yet good enough (Wiegel et al., 2013; Liang et al., 2007, 2008). Nevertheless, an empirical estimate of the isotope flux from the stratosphere can be derived from measurements near the tropopause, like the ones presented here. As described in detail by Plumb and Ko (1992) and Plumb (2007), gases that are chemically long-lived relative to vertical and quasi-horizontal transport timescales exhibit compact correlations in the stratosphere, and the slope of the observed correlation between the two tracers is equal to the ratio of their net vertical fluxes. Following this approach, Luz et al. (1999) and Boering et al. (2004) determined the global annual mean net isotope flux (NIF) from the stratosphere (ST) to the troposphere (T) for Δ^′17O of CO₂ using the Δ^′17O(CO₂)–N₂O correlation as described in detail by Garofalo et al. (2019).

$$\begin{array}{}\text{(5)}& \begin{array}{rl}& {\mathrm{\Delta }}^{\prime \mathrm{17}}\mathrm{O}\left({\mathrm{CO}}_{\mathrm{2}}\right)-\text{NIF}\\ & =\text{MF}\times {\left[{\mathrm{CO}}_{\mathrm{2}}\right]}_{\mathrm{ST}}\times \left[m\times {\displaystyle \frac{-L_{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}}{\text{MF}}}+{\mathrm{\Delta }}^{\prime \mathrm{17}}\mathrm{O}({\mathrm{CO}}_{\mathrm{2}}{)}_{\mathrm{T}}\right]\\ & -\text{MF}\times {\left[{\mathrm{CO}}_{\mathrm{2}}\right]}_{\mathrm{T}}\times {\mathrm{\Delta }}^{\prime \mathrm{17}}\mathrm{O}({\mathrm{CO}}_{\mathrm{2}}{)}_{\mathrm{T}}\end{array}\end{array}$$

The terms MF, $L_{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}$, and m stand for the total air mass flux from the stratosphere to the troposphere, the global N₂O loss rate, and the correlation slope between Δ^′17O and N₂O, respectively. In our analysis, this correlation slope is determined using a Williamson–York bivariate fit, accounting for uncertainties in both the Δ^′17O(CO₂) and N₂O data (Mikkonen et al., 2019). There is a significant variation in estimates for the air mass flux from the stratosphere to the troposphere. For instance, the estimates by Holton et al. (1995) and Appenzeller et al. (1996) differ by a factor of 3 in their calculated cross-tropopause air mass fluxes, but note that the troposphere definitions are also different. As described in Garofalo et al. (2019), the net isotope flux is not strongly sensitive to the actual air mass fluxes. Since the mole fraction of CO₂ in the lower stratosphere and troposphere is the same within about 1 %, Eq. (5) can be simplified to

$$\begin{array}{}\text{(6)}& {\mathrm{\Delta }}^{\prime \mathrm{17}}\mathrm{O}\left({\mathrm{CO}}_{\mathrm{2}}\right)-\text{NIF}=-m\times L_{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}\times \left[{\mathrm{CO}}_{\mathrm{2}}\right].\end{array}$$

The uncertainty in the estimated net annual mean flux of Δ^′17O(CO₂) depends on the uncertainty of m and $L_{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}$. In our calculation, we used 370 ppm for [CO₂], the average value for CARIBIC samples, most of them collected in the year 2001.

In the stratosphere the CO₂ and N₂O isotopes are influenced by different processes. N₂O is mainly destroyed by N₂O photolysis, but it is also affected by O(¹D) in the lower stratosphere and upper troposphere. Since N₂O photolysis and O₃ photolysis occur at different wavelengths, the relationship between Δ^′17O(CO₂) and N₂O contains valuable information about atmospheric chemistry and transport. The lifetime of N₂O varies with altitude. In the upper stratosphere and mesosphere, the N₂O lifetime decreases, leading to greater scatter. This scatter remains small until transport time becomes shorter than the N₂O lifetime. The scatter in Δ^′17O(CO₂) vs. N₂O mixing ratio plots of Δ^′17O (CO₂) vs. N₂O is mainly caused by latitudinal variations in the age of the air in the stratosphere. Δ^′17O(CO₂) values increase with altitude as N₂O mixing ratios decrease below ≈ 70 km. However, above 70 km, Δ^′17O(CO₂) begins to decrease with further decreases in N₂O mixing ratios. However, in the lower stratosphere and upper troposphere, where the lifetime of N₂O against photolysis is longer than the transport time, the scatter in N₂O values remains low (Liang et al., 2007, 2008). The Δ^′17O(CO₂)–N₂O correlation remains consistent both spatially and temporally in the lower stratosphere and the upper troposphere (Liang et al., 2007, 2008). Since the net isotope flux of Δ^′17O(CO₂) is derived from samples from the lower stratosphere and upper troposphere, the observed variability (scatter) in the stratosphere does not affect the global average Δ^′17O(CO₂)–N₂O slope used to estimate the flux of Δ^′17O(CO₂) from the stratosphere to the troposphere.

2.6 Estimating gross surface flux using Δ^′17O(CO₂)

The CARIBIC samples analysed in this study cover latitudes from 30° south to 54° north (see Fig. 1). We used these samples to estimate surface emissions using a mass balance box model calculation. The box model used in this study is not suitable for simulating the spatial and temporal variability of Δ^′17O(CO₂) (Koren et al., 2019). Our box model is an extended version of those used by Hoag et al. (2005) and Liang et al. (2017b). Hoag et al. (2005) used a two-box model to explore the relative contributions to the production of Δ^′17O(CO₂) in the stratosphere, its flux to the troposphere, and its destruction or dilution by various surface carbon fluxes in the troposphere. Liang et al. (2017b) used a one-box model, in which the major surface resetting processes were explicitly included to distinguish terrestrial fluxes from oceanic fluxes. In our model, we incorporated an intermediate upper-troposphere (UT) box. Furthermore, our study includes measurements of Δ^′17O from both hemispheres and different seasons. The Δ^′17O(CO₂) value in the UT depends on the Δ^′17O(CO₂) value of stratosphere (ST) and surface processes (assimilation/photosynthesis (A), respiration (R), soil invasion (SI), ocean (o), and anthropogenic emission (anth)) and the corresponding fluxes (F). In steady state, the mass balance equation for Δ^′17O(CO₂) in the upper troposphere is

$$\begin{array}{}\text{(7)}& \begin{array}{rl}& F_{\mathrm{A}}\times {\mathrm{\Delta }}_{\mathrm{A}}{\mathrm{\Delta }}^{\prime \mathrm{17}}\mathrm{O}+F_{\mathrm{anth}}\times {\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{anth}}\\ & +F_{\mathrm{ST}}\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{ST}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)\\ & +F_{\mathrm{o}}\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{o}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)\\ & +F_{\mathrm{R}}\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{R}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)\\ & +F_{\mathrm{SI}}\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{SI}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)=\mathrm{0},\end{array}\end{array}$$

where F_A = F_al−F_la = 0.88×GPP (Ciais et al., 1997a), with al, la, and GPP being atmosphere-to-leaf flux, leaf-to-atmosphere flux, and gross primary production, respectively. Δ_AΔ^′17O is the discrimination against Δ^′17O during assimilation and is calculated as Δ_AΔ^′17O = $\left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{M}}\right)\times \left(-\mathrm{0.150}\times e^{\mathrm{3.707}\times \frac{c_{\mathrm{m}}}{c_{\mathrm{a}}}}+\mathrm{0.028}\right)$, as described by Adnew et al. (2020) (see the Supplement for more detail). This parameterization was derived from leaf cuvette studies using both C₃ and C₄ plants under different light conditions. c_m and c_a represent the CO₂ mole fraction in the mesophyll and the atmosphere, respectively. Δ^′17O_M is the Δ^′17O of CO₂ in the mesophyll, calculated from the Δ^′17O value of meteoric water (MW) (Landais et al., 2007; Barkan and Luz, 2012; Bottinga and Craig, 1968; Brenninkmeijer et al., 1983); see also the Supplement.

The estimates of soil invasion fluxes are highly uncertain; the reported values in the literature vary from < 10 PgC yr⁻¹ (Stern et al., 2001) to 450 PgC yr⁻¹ (Wingate et al., 2009). For this study, we assume that F_SI and F_R are equal, and F_A = 0.88×GPP = $\mathrm{0.88}\times \left(\text{NEP}-F_{\mathrm{R}}\right)$ (Liang et al., 2017b). Substituting this term in Eq. (7),

$$\begin{array}{}\text{(8)}& \begin{array}{rl}& F_{\mathrm{A}}\times {\mathrm{\Delta }}_{\mathrm{A}}{\mathrm{\Delta }}^{\prime \mathrm{17}}\mathrm{O}+F_{\mathrm{anth}}\times {\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{anth}}\\ & +F_{\mathrm{ST}}\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{ST}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)\\ & +F_{\mathrm{o}}\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{o}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)\\ & +\left({\displaystyle \frac{F_{\mathrm{A}}}{\mathrm{0.88}}}-\text{NEP}\right)\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{R}}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)\\ & +\left({\displaystyle \frac{F_{\mathrm{A}}}{\mathrm{0.88}}}-\text{NEP}\right)\times \left({\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{SI}-{\mathrm{\Delta }}^{\prime \mathrm{17}}{\mathrm{O}}_{\mathrm{UT}}\right)=\mathrm{0}.\end{array}\end{array}$$

The Δ^′17O_anth value is −0.446 ± 0.077 ‰ (Horváth et al., 2012; Laskar et al., 2016). The Δ^′17O_o value is calculated from the Δ^′17O value of ocean water (OW) (Table 1). Similarly, the Δ^′17O values for soil invasion and respiration are derived from the Δ^′17O value of meteoric water (Liang et al., 2023; Koren et al., 2019; Hofmann et al., 2017). For the calculations, we used a surface temperature of 15 °C and a relative humidity of 75 % (Dai, 2006). The sensitivity of Δ_AΔ^′17O to temperature and relative humidity is shown in Fig. S1 of the Supplement. The value of Δ_AΔ^′17O increases with an increase in relative humidity but decreases with increasing temperature. Using the parameters described above and provided in Table 1 and Eq. (8), we estimated the gross primary production (GPP), surface flux (including land and ocean), and the oxygen isotope residence time (turnover time) of CO₂ in the atmosphere. The oxygen isotope residence time of CO₂ in the atmosphere is defined by the ratio of the atmospheric CO₂ mass loading (M_a) and the CO₂ surface flux (Welp et al., 2011). The error for all estimated values is determined using a Monte Carlo simulation with 10⁶ runs, where values of the input parameters are randomly picked from a normal distribution defined by their uncertainty.

Bottinga and Craig (1968)Brenninkmeijer et al. (1983)Farquhar and Lloyd (1993)Miller et al. (1999)Landais et al. (2007)Barkan and Luz (2012)Young et al. (2002)Ciais et al. (1997b)Farquhar et al. (1993)Farquhar et al. (1993)Farquhar et al. (1993)Stocker et al. (2013)Stocker et al. (2013)Stocker et al. (2013)Saugier et al. (2001)Barkan and Luz (2012)Barkan and Luz (2012)

Table 1 Summary of parameters used for the box model mass balance calculation in Eq. (8). T and RH represents temperature in kelvin and relative humidity near the Earth's surface, respectively.

The sensitivity of GPP to relative humidity, temperature, the Δ^′17O value of the upper troposphere, and the net flux of Δ^′17O from the stratosphere to the troposphere is shown in Figs. S2 and S3. A higher net flux of Δ^′17O to the troposphere leads to an increase in GPP to fulfil the isotope balance of Eq. (8). An increase in relative humidity leads to a decrease in GPP due to an increase in Δ_AΔ^′17O. Conversely, an increase in temperature results in an increase in GPP, as higher temperatures cause a decrease in Δ_AΔ^′17O, as described above. The parameters used in the mass balance calculations and their errors are provided in Table 1.

2.7 De-trending and classification of samples into the upper troposphere and stratosphere

To ensure comparability of previously published data and the CARIBIC and StratoClim samples measured in this study, all N₂O measurements were trend-corrected to the year 2001 following a similar approach described in Koren et al. (2019).

$$\begin{array}{}\text{(9)}& {{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{\det }={{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{\mathrm{obs}}\times {\left[\mathrm{1}-{\displaystyle \frac{{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{\mathrm{growth}\mathrm{rate}}}{{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{\mathrm{ref}}}}\times \left(t_{\mathrm{ref}}-t_{\mathrm{obs}}\right)\right]}^{-\mathrm{1}}\end{array}$$

Here, N₂O_obs, N₂O_det, N₂O_ref, and N₂O_growthrate refer to the observed and detrended mole fractions of N₂O, the mole fraction of N₂O at the reference time, and the growth rate of N₂O in the troposphere, respectively. The variables t_obs and t_ref represent the time of observation and the reference time (1 July 2001). The growth rate of N₂O in the troposphere, used in this study, is 0.75 ppb yr⁻¹ (Stocker et al., 2013). The mole fraction of N₂O at the reference time (1 July 2001) is 316.24 ppb (Lan et al., 2024).

The mole fraction of CH₄ in the StratoClim data was detrended to 2007 using an average growth rate of 12 ppb yr⁻¹ (Nisbet et al., 2019). The 2007 mole fraction of CH₄ is assumed to be the same as the CH₄ mole fraction in 2001, since the atmospheric CH₄ mole fraction was stable between 2000 and 2007 (Nisbet et al., 2019).

We used the N₂O–CO correlation to classify air samples into upper-tropospheric and upper-stratospheric samples, as described in detail by Assonov et al. (2013). N₂O maintains a nearly constant tropospheric concentration, as it is minimally affected by chemical processes and has no significant atmospheric sources. This stability allows stratospheric influence to be more easily identified. The correlation between N₂O and CO forms an L-shaped curve, similar to O₃–CO correlations observed during stratosphere–troposphere air mass mixing events (Assonov et al., 2013). As a result, the troposphere corresponds to the horizontal branch (high N₂O, variable CO), while the stratosphere, free from tropospheric influence, corresponds to the vertical branch (low CO, variable N₂O). The CARIBIC samples are mostly from the upper troposphere (UT) and include a few from the lower stratosphere (see Fig. S4). Based on the mole fraction of N₂O, we grouped the Δ^′17O values into two categories: upper-troposphere (UT) samples (N₂O ≥ 313.5 ppb) and lower-stratosphere (LS) samples (N₂O < 313.5 ppb). We further divided the lower stratosphere into two subgroups: 313.5 > N₂O > 306 ppb and N₂O < 306 ppb. Furthermore, we used a zonal average tropopause pressure simulated using the TM5 model as outlined in Krol et al. (2018) and the age of air tracer, to support the classification of samples into upper tropospheric and upper stratospheric. The age of air was calculated using SF₆ measurements, as described in Krol et al. (2018). Most of the samples classified as upper tropospheric based on the mole fraction of N₂O were collected far below the tropopause, whereas the samples classified as stratospheric were collected above or close to the tropopause with a few exceptions (see Fig. S5).

3 Results

Figure 3a shows Δ^′17O(CO₂) as a function of latitude for the CARIBIC samples. The samples classified as upper-tropospheric Δ^′17O(CO₂) do not show geographic variations between large regions referred to as America, Asia, and Africa, respectively (see Fig. 1), and no statistically significant difference in Δ^′17O(CO₂) between the hemispheres (see Fig. 3b). Table S2 presents the mole fraction of CO₂, O₃, CO, N₂O, and CH₄, along with the isotopic composition of CO₂ (δ¹³C, δ¹⁸O and Δ^′17O) for the analysed CARIBIC samples. Similarly, the mole fraction of CO₂ and other trace gases (O₃, CO, N₂O, and CH₄), along with the isotopic composition of CO₂ for StratoClim samples, is shown in Table S3.

Figure 3 (a) Δ^′17O(CO₂) values of CARIBIC samples as a function of latitude. The Δ^′17O values are grouped into three categories based on the mole fraction of N₂O as described in the text. (b) Average Δ^′17O value of all upper-tropospheric CARIBIC air samples and larger geographical regions. The errors are the standard error of the mean multiplied by Student's t factor for the 95 % confidence limit. n, SH, and NH stands for the number of samples, Southern Hemisphere, and Northern Hemisphere, respectively.

Figure 4 shows the correlation of Δ^′17O(CO₂) measurements with the mole fractions of CH₄ and N₂O. For both sets of samples (CARIBIC and StratoClim), N₂O and Δ^′17O(CO₂) are clearly correlated, with R² values of ≥ 0.9, as shown in Fig. 4. Similar tight correlations between N₂O and Δ^′17O(CO₂) were reported in the previous studies, as shown in Fig. 6. Interestingly, StratoClim samples plot in two distinct groups of N₂O–Δ^′17O(CO₂) correlations. Most of the StratoClim samples with Δ^′17O < 0.2 ‰ have a similar N₂O–Δ^′17O slope as the CARIBIC samples as shown in Fig. 4a. However, unexpectedly the N₂O–Δ^′17O correlation slope for most of StratoClim samples with Δ^′17O > 0.2 ‰ is much lower (−0.017 ‰ ppb⁻¹) (see Fig. 4a).

Figure 4 Correlation of Δ^′17O(CO₂) with (a) N₂O for StratoClim samples (StratoClim-2016 is Kathmandu (KT; blue stars) and StratoClim-2017 is Kalamata (KL; blue circles)) and CARIBIC samples (black circles) and (b) CH₄. The errors of the linear regression slopes are the 95 % confidence interval. The data points marked in red indicate StratoClim samples with a low N₂O–Δ¹⁷O correlation slope.

As shown in Fig. 4b, there is a strong inverse correlation between CH₄ and Δ^′17O. For the StratoClim samples, the correlation is higher compared to the CARIBIC samples, with R² values of ≥ 0.9 and 0.79, respectively. For both CARIBIC and StratoClim samples with Δ^′17O < −0.2 ‰, no clear correlation between CH₄ and Δ^′17O can be established (see Fig. 4b).

Figure 5 shows the three-isotope plot for both CARIBIC and StratoClim samples. The three-isotope plot of upper-tropospheric samples shows a tight correlation for both CARIBIC and StratoClim samples with slopes of 0.540 ± 0.005 and 0.556 ± 0.012, respectively (Fig. 5). For the StratoClim samples with higher stratospheric influence, the ln (δ¹⁷O+1) vs. ln (δ¹⁸O+1) is poorly correlated. It is apparent in Fig. 5a that the vertical offsets from the fit line defined by the upper-tropospheric samples get larger for larger stratospheric age, which is shown as colour coding. Figure 5b shows the correlation between the age of the air and Δ^′17O(CO₂). An increase in the age of the air correlates well with a progressive enrichment of Δ^′17O(CO₂).

Figure 5 (a) Three-isotope plot for StratoClim (stars) and CARIBIC (open circles) samples. The linear regression is a fit to the samples identified as upper tropospheric based on the N₂O mole fraction. The colour bar indicates the age of the air mass for the StratoClim samples reported in Adcock et al. (2021). The stated errors for the linear regression parameters are the 95 % confidence intervals. (b) Relationship between the age of the air and Δ^′17O(CO₂) for StratoClim samples. The data points marked in red indicate samples with a low N₂O–Δ¹⁷O correlation slope.

Figure 6 shows a comparison of our CARIBIC and StratoClim samples measured in this study with previously published Δ^′17O measurements of upper-tropospheric and stratospheric CO₂ (Thiemens et al., 1995a, b; Alexander et al., 2001; Lämmerzahl et al., 2002; Boering et al., 2004; Wiegel et al., 2013; Kawagucci et al., 2005; Yeung et al., 2009). Four different characteristics are shown: the three-isotope plot (Fig. 6a), Δ^′17O as a function of altitude (only for StratoClim samples) (Fig. 6b), the N₂O–Δ^′17O correlation (Fig. 6c), and the CH₄–Δ^′17O correlation (Fig. 6d). In these overview plots of N₂O–Δ^′17O and CH₄–Δ^′17O plots, the new CARIBIC and StratoClim measurements are almost indistinguishable from the measurements reported in the literature. However, when we zoom in and compare the correlation slopes, clear differences for some of the measurements become apparent, such as those shown in Fig. 4a for the variation in the N₂O–Δ^′17O correlation between CARIBIC and StratoClim samples.

Figure 6 Comparison of results from CARIBIC samples (black circles) and StratoClim samples (blue circles) to previous publications (open circles). (a) Three-isotope plot and (b) correlation of Δ^′17O(CO₂) with N₂O. The data points marked in red indicate StratoClim samples with a low N₂O–Δ¹⁷O correlation slope. (c) Correlation of Δ^′17O(CO₂) with altitude and (d) correlation of Δ^′17O(CO₂) with CH₄. Previous stratospheric samples are from Thiemens et al. (1995a, b), Alexander et al. (2001), Lämmerzahl et al. (2002), Boering et al. (2004), Wiegel et al. (2013), Kawagucci et al. (2005), and Yeung et al. (2009).

4 Discussion

When the CARIBIC and StratoClim samples presented here are separated into upper tropospheric and upper stratospheric based on N₂O levels, these two groups exhibit distinct characteristics. The upper-tropospheric samples show a tight correlation on the three-isotope plot, whereas the stratospheric samples display significant variability without a clear correlation. Interestingly, the three-isotope slopes (from a linear fit to the data) for the upper-tropospheric samples are higher than the expected canonical range for tropospheric samples (λ > 0.5309). This indicates that upper-tropospheric air already has a stratospheric influence. The contribution of stratospheric air in the CARIBIC samples is evident from an excellent correlation between Δ^′17O(CO₂) and both ¹⁴C(CO) and O₃, as illustrated in Fig. 7. Both ¹⁴CO and O₃ are reliable tracers for stratospheric air (Brenninkmeijer et al., 1995). Similar correlations between ¹⁴CO and Δ^′17O(CO₂) have been previously reported for stratospheric CO₂ (Thiemens et al., 1995b; Brenninkmeijer et al., 1995).

Figure 7 Correlation of Δ^′17O with stratospheric air tracers ¹⁴CO and O₃ for CARIBIC samples.

The observed scatter in the three-isotope plot for the stratospheric samples is conceptually similar to the scatter reported in previous studies (Boering et al., 2004; Wiegel et al., 2013; Mrozek, 2017; Thiemens et al., 1995a). In these publications it was mostly assumed to be due to the low precision of the measurement method. However, in this study, with high-precision measurements, a similar scatter in the three-isotope plot is observed, demonstrating that the scatter observed in the three-isotope plot for stratospheric samples is a real signal of mixing, transport and production of Δ^′17O(CO₂) (i.e. exchange between O(¹D) and CO₂). The tight correlation with the age of air provides a clear clue to explain this lack of correlation. The longer CO₂ has been exposed to the stratospheric CO₂–O(¹D) exchange, the higher the Δ^′17O(CO₂) signal is (Yung et al., 1997; Gamo et al., 1995; Yung et al., 1991). The fact that the different samples do not line up on a single three-isotope correlation line shows that we have sampled stratospheric air originating from different upper-tropospheric “entry values” before entering the stratosphere. These differences in entry values are likely driven by the seasonality of δ¹⁷O(CO₂) and δ¹⁸O(CO₂). Thus, different tropospheric air masses have entered the stratosphere from various points along the correlation line established by the upper-tropospheric samples. Once in the stratosphere, photochemical isotope exchange with O¹D occurs, and the samples progressively acquire a higher Δ^′17O(CO₂) signature as the sampled air resided longer in the stratosphere. This is clearly demonstrated by the strong correlation between Δ^′17O(CO₂) and the age of air, and it was not clearly visible in previous studies because of the higher measurement uncertainty.

Interestingly, despite our high measurement precision, we did not observe significant geographic variations in Δ^′17O(CO₂) of CARIBIC air samples classified as upper troposphere (see Fig. 3b), which could potentially arise from varying stratospheric and tropospheric air mass influences in different geographical regions. The lack of geographic variability contrasts with the reported regional Δ^′17O(CO₂) variability at the surface (Liang et al., 2017a, 2023). Apparently, the variability at the surface, caused by sources and sinks of CO₂, including isotope exchange with surface water reservoirs and anthropogenic emissions, is no longer visible in the upper troposphere, where the reservoir seems to be relatively well mixed in terms of Δ^′17O(CO₂). Air masses in the upper troposphere experience rapid horizontal mixing, which could explain the uniform stratospheric influence in the CARIBIC samples.

The slope of two tracers near the tropopause is a measure of their relative net fluxes between the troposphere and stratosphere (Plumb and Ko, 1992; Plumb, 2007). The slope of N₂O–Δ^′17O(CO₂) was first used by Luz et al. (1999) and Boering et al. (2004) to quantify the so-called isoflux of Δ^′17O(CO₂) from the stratosphere into the troposphere. Previous measurements had a lower precision and could not define the slope close to the tropopause but only for older stratospheric air. Our high-precision measurements of Δ^′17O(CO₂) allow us to determine the N₂O–Δ^′17O(CO₂) slope right down to the tropopause. Figure 8 shows that the slope for CARIBIC samples is indistinguishable from the correlations reported in the previous studies for stratospheric samples (−0.024 ‰ ppb⁻¹) (Kawagucci et al., 2008; Wiegel et al., 2013; Boering et al., 2004). However, the regression lines have an offset. This offset likely arises from variations in the Δ^′17O(CO₂) measurement scales among different laboratories. Recently, Liang et al. (2023) reported a scale offset in Δ^′17O(CO₂) of 0.037 ‰ to 0.042 ‰ between two laboratories (Institute of Earth Sciences, Academia Sinica, and Institute of Earth Sciences, Hebrew University of Jerusalem). To optimize the application of Δ^′17O(CO₂) measurements, the implementation of interlaboratory calibration is crucial (Adnew and Röckmann, 2023). A recent study by Laskar et al. (2019) reported a higher slope (0.036 ‰ ppb⁻¹) for the N₂O–Δ^′17O correlation of CARIBIC samples collected during two flights. The samples they analysed mostly represent upper-troposphere air, evident from a lower O₃ mole fraction compared to the CARIBIC samples measured in this study. This is supported by the relatively low three-isotope slope of 0.48 reported by Laskar et al. (2019) compared to the samples measured in this study (> 0.54). Furthermore, their samples cover only a very small range of N₂O (only 3.5 ppb difference, i.e. between 311.5 and 315 ppb), which likely leads to a high error in the determination of the N₂O–Δ^′17O(CO₂) correlation slope.

Figure 8 Δ^′17O–N₂O correlation for CARIBIC samples and measurements of Kawagucci et al. (2008) and Boering et al. (2004). The inset shows the zoomed-in view of the data close to the tropopause. For the CARIBIC samples measured in this study, the error bars are smaller than the data markers. For the linear regression slopes, the errors are the 95 % confidence interval.

In contrast, for the StratoClim samples, the N₂O–Δ^′17O(CO₂) correlation shows an unexpectedly low slope of −0.017 ‰ ppb⁻¹, which is about 1.5 times lower than for the CARIBIC and other stratospheric samples (Fig. 4). All our samples were measured in the same laboratory and on the same analytical system. We suggest that the lower N₂O–Δ^′17O correlation slope for StratoClim samples is due to enhanced vertical mixing during the Asian summer monsoon anticyclone (ASMA), as these samples were collected during mid-June to early September. The ASMA causes deep convection and anticyclonic flow in the upper troposphere and lower stratosphere (UTLS) where tropospheric air masses are uplifted into the UTLS (Park et al., 2009; Vogel et al., 2015, 2016; Brunamonti et al., 2018). The lifetime for CO₂ isotopic exchange is much slower than the transport time at all altitudes, whereas the photochemical production and quenching rates for O¹(D) are much faster than transport processes. Therefore, the isotopic composition of stratospheric CO₂ should reflect both the variety of transport histories of air parcels and the sources of O¹(D) (Liang et al., 2007; Boering et al., 2004). Furthermore, throughout the entire atmosphere, the CO₂ isotopic exchange time is longer than the transport time. However, the lifetime of N₂O varies with altitude. In the lower stratosphere, the lifetime of N₂O against photolysis is longer than the transport time, resulting in less variability in the region. In contrast, in the middle stratosphere the N₂O lifetime decreases, resulting a different N₂O–Δ^′17O correlation slope (Liang et al., 2008). The influence of vertical mixing on N₂O–Δ^′17O correlations was investigated in a model study by Liang et al. (2007). Indeed, they found that an increase in the vertical eddy diffusion coefficient – thus more vigorous vertical mixing – leads to a lower slope of the N₂O–Δ^′17O correlation. This supports our hypothesis that the low correlation for the StratoClim samples is caused by intense vertical mixing in the ASMA. An independent indication for the enhanced mixing is the scatter observed in the three-isotope plot and air age variability for the samples classified as stratospheric (Fig. 5). Enhanced mixing, probably caused by deep convection and anticyclone flow in the upper troposphere and lower stratosphere, is consistent with the enhanced mole fraction of ozone-depleting substances in the samples collected in the same flight (Adcock et al., 2021).

A high-precision N₂O–Δ^′17O(CO₂) correlation can thus help identify enhanced mixing of tropospheric air into the stratosphere and may be a measurable tracer to quantify the intensity of eddy diffusion/transport (Liang et al., 2007; Boering et al., 2004). There are many other indicators for enhanced mixing above the tropopause due to the ASMA including a 25 % increase in long-lived ozone-depleting substances in the upper troposphere–lower stratosphere from the same samples (Adcock et al., 2021) and a contribution of about 30 % of young tropospheric air in the extratropical lower stratosphere in the Northern Hemisphere due to the ASMA (Vogel et al., 2016). Recently, Ma et al. (2022) reported that 30 % to 50 % of the air mass in the UTLS above the ASMA region is mixed, with the highest mixing occurring around 16.5 km altitude. Moreover, for StratoClim samples collected over the Indian subcontinent in Kathmandu (2017) in the tropopause region, the three major chlorinated very short-lived substances were enhanced up to 136 % compared to typical tropical tropopause values in 2013–2014. In contrast, only a 10 % increase was observed in ground-based measurements from 2014 to 2017 (Adcock et al., 2021; Engel et al., 2019).

For the StratoClim samples, the CO mole fraction reached a stratospheric background value at a potential temperature of 420 K, and the N₂O mole fraction remained similar to the tropospheric value up to 400 K, as described in detail by von Hobe et al. (2021) and Vogel et al. (2024). The deviation of the correlation between N₂O and Δ^′17O is observed for air samples where the potential temperature is higher, about 420 K and above (Fig. 9). At these potential temperatures, mixing processes become more significant, and the air inside the anticyclone is exported vertically and horizontally into the surrounding stratosphere (von Hobe et al., 2021; Ma et al., 2022). This enhanced mixing apparently causes the diminished slope for the N₂O and Δ^′17O correlation plot (Fig. 4) and also a very scattered three-isotope plot (Fig. 5). Up to a potential temperature of 400 to 415 K, the strong isolation of air inside the ASMA prevents significant mixing of the stratospheric air into the predominately tropospheric inner cyclone (von Hobe et al., 2021; Vogel et al., 2024). Mixing of air masses is evident from the correlation between CO and O₃, as well as from the Δ¹⁷O–CO plots shown in Fig. 10. Consequently, the N₂O–Δ¹⁷O correlation slope of the lowermost stratospheric StratoClim samples agrees with the slopes for CARIBIC samples and previously published measurements.

Figure 9 Correlation between Δ^′17O and potential temperature for StratoClim samples. The inset shows the N₂O–Δ^′17O correlation of StratoClim samples from Fig. 4. The colour bar for the inset is potential temperature. The data points marked in red indicate those with a low N₂O–Δ¹⁷O correlation slope.

Figure 10 (a) The correlation of two short-lived gases, ozone vs. CO for Kathmandu samples. (b) Correlation of Δ^′17O with CO for both Kalamata and Katmandu samples. The data points marked in red indicate those with a low N₂O–Δ¹⁷O correlation slope.

5 Implication for troposphere and stratosphere exchange and surface emissions of CO₂

Air samples from the upper troposphere and lower stratosphere are well suited for studying stratosphere–troposphere exchange (Olsen et al., 2001). We used CARIBIC samples with Δ^′17O(CO₂) > −0.2 ‰ because for this group Δ^′17O(CO₂) and N₂O have a very compact relationship with a slope of −0.024 ± 0.0002 ‰ ppb⁻¹, despite the air samples being collected at different latitudes, in different seasons, and in different years (see Table S1, Figs. 1 and 3). The Δ^′17O(CO₂)–N₂O correlation slope is similar to the values reported in the previous measurements (Boering et al., 2004; Wiegel et al., 2013; Kawagucci et al., 2008). However, the uncertainty of the correlation slope is 10 times smaller than in previous measurements (see Garofalo et al., 2019, for a detailed summary), and the new data confirm that the correlation actually extends down to the troposphere. Using the net vertical flux of N₂O (which is equal to the global N₂O loss rate, 13.43 TgN yr⁻¹ ± 3 % Prather et al., 2023; see also Tian et al., 2020), the global mean net flux of Δ^′17O(CO₂) is 51.3 ± 1.6 ‰ PgC yr⁻¹. This estimate aligns well with previous numerical model calculations (Liang et al., 2008) and falls within the range reported previously using a similar approach (Boering et al., 2004; Garofalo et al., 2019; Wiegel et al., 2013; Kawagucci et al., 2008), but the uncertainty in our estimate is much lower than the 10 to 20 ‰ PgC yr⁻¹ uncertainty reported in the previous studies (Garofalo et al., 2019). The relatively precise estimate of the net Δ^′17O(CO₂) flux from the stratosphere to the troposphere results from the improved precision of Δ^′17O(CO₂) measurements (see Fig. 8) and the reduced uncertainty in the global N₂O loss rate (3 % vs. 25 %).

Using the mass balance model described in Sect. 2.6 (see Eq. 8), we estimated a terrestrial flux of 749 ± 93 PgC yr⁻¹. This estimate falls within the range, near the upper range of values, reported by previous studies (200–817 PgC yr⁻¹) (Ciais et al., 1997a, b; Cuntz et al., 2003b, a; Farquhar et al., 1993; Liang et al., 2017b; Welp et al., 2011). The surface flux, which is the sum of terrestrial and ocean fluxes, is 829 ± 93 PgC yr⁻¹ (see Fig. 11). This value is consistent with the range reported by Welp et al. (2008) using δ¹⁸O of CO₂. The corresponding surface turnover time of CO₂ is 0.98 ± 0.1 years, also within the range of previous estimates (i.e. 0.4 to 2.8 years) (Liang et al., 2017b, 2023; Laskar et al., 2019; Welp et al., 2011; Farquhar et al., 1993; Ciais et al., 1997a; Cuntz et al., 2003b) (see Fig. 11). As shown in Fig. 11, the estimated surface flux and turnover time of CO₂ are sensitive to the Δ^′17O(CO₂) value in the upper troposphere. A higher Δ^′17O(CO₂) value in the upper troposphere results in a lower surface flux and a longer CO₂ turnover time. The GPP value is 211 ± 26 PgC yr⁻¹, which is in good agreement with the estimates (200 PgC yr⁻¹) by Liang et al. (2023) and Hofmann et al. (2017) using Δ^′17O(CO₂) and higher than the estimate (150–175 PgC yr⁻¹) by Welp et al. (2008) using δ¹⁸O of CO₂. These estimates are very sensitive to the assumed c_m $/$ c_a ratio, the degree of equilibration (Cuntz, 2011; Farquhar et al., 1993), and the soil invasion flux (Wingate et al., 2009). For example, increasing the c_m $/$ c_a ratio by 0.05 (c_m $/$ c_a = 0.7) decreases the GPP from 212 to 189 PgC yr⁻¹. Conversely, decreasing the c_m $/$ c_a ratio by 0.05 (c_m $/$ c_a = 0.6) will increase the GPP from 212 to 234 PgC yr⁻¹. A detailed sensitivity analysis is provided in the Supplement. Although the approach involves a number of assumptions as detailed in the “Materials and method” section, it has the potential to be a valuable tool for quantifying and refining gross fluxes (Hoag et al., 2005; Koren et al., 2019). This will be especially true when more measurements become available from the lower stratosphere–upper troposphere and troposphere/surface. Additionally, understanding the effects of various processes on Δ^′17O(CO₂), such as soil invasion, and taking into account inter-laboratory calibration-scale differences (Adnew and Röckmann, 2023; Liang et al., 2023) and proper model assimilation (Koren et al., 2019) will further enhance its effectiveness.

Figure 11 Surface flux of CO₂ (F_Surf; left axis) and the oxygen isotope turnover time of CO₂ (left axis) as a function of the Δ^′17O_UT value of upper-tropospheric CO₂. The solid line indicates our best estimates of F_Surf and the oxygen isotope turnover time of CO₂ and the shaded area is the corresponding uncertainty calculated using error propagation.

6 Conclusions

High-precision measurements of Δ^′17O(CO₂) enable the identification of mixing, transport, and chemical processes in the stratosphere. Through the analysis of CARIBIC samples, this study showed that the N₂O–Δ^′17O(CO₂) correlation reported previously from stratospheric samples extends down to the tropopause. Using the N₂O–Δ^′17O(CO₂) correlation slope of CARIBIC samples, we estimated the net mean Δ^′17O(CO₂) flux from the stratosphere to the troposphere to be 51.3 ± 1.6 ‰ PgC yr⁻¹. Notably, no significant spatial or hemispheric variability was observed in Δ^′17O(CO₂) values for the upper-tropospheric samples collected during the CARIBIC programme. The new measurements could be used in a mass balance approach to estimate that the surface turnover time of CO₂ is approximately 1 year, and the GPP is estimated to between 185 and 237 PgC yr⁻¹.

In contrast, StratoClim samples showed a much lower N₂O–Δ^′17O slope compared to CARIBIC samples and previous studies. This deviation is attributed to the increased mixing/eddy diffusion due to the ASMA. The N₂O–Δ^′17O slope may thus be a direct measurable tracer for the intensity of vertical mixing in the UTLS region.