## Introduction

Imbalance between CO2 sources and sinks results in increasing atmospheric CO2 levels1,2,3. The increase is due mainly to fossil fuel burning, emitting at an average rate of 9.4 ± 0.5 PgC/year2. As a consequence, the average global temperature has increased by 1.1 °C3. The combined effect of elevated atmospheric CO2 levels and temperature leads to observable changes in the global carbon cycle4,5. A number of efforts have been used to quantify the changes of the carbon cycles in response to changing environments1,3,4,6,7,8. Climate models coupled with biogeochemical modules are frequently used to assess changing ecosystems in the context of changing climate1,3,8,9. However, it has been noted that current knowledge is insufficient to simulate and project the ecosystem responses6,7, owing to the boundaries of our knowledge of the gross processes. Reviewing the input components and processes considered9,10,11, terrestrial net ecosystem exchange (NEE) is better studied but gross primary production (GPP) processes (such as photosynthesis) comprising > 3/4 of the total carbon fluxes in the carbon cycling budget remain least well-constrained8,10,11,12,13,14,15,16,17,18. The incomplete knowledge of the gross processes is largely due to rapid hydration and dehydration of CO2 occurring in chloroplasts; it is also because of this fast reaction that regional and global assessments of the gross components are possible11,15,17,19. The carbonic anhydrase catalyzed process is, however, modulated by the impact of hydrological cycles and evapotranspiration, creating spatiotemporal inhomogeneities and variability. These complexities restrict carbon cycle quantification. Although regional and local carbon cycling fluxes have been extensively evaluated13, the magnitudes of the gross fluxes, including the global assessment extrapolated from regional/local measurements, remain inconclusive8,10,11,12,13,15,16,17,18,20.

In addition to applying a commonly utilized eddy-covariance method to terrestrial net ecosystem production13 for approximating gross components in carbon cycle models10,11,21,22 at local and regional scales, global assessment has extensively relied on oxygen isotopic analysis, which, however, is often complicated by source water isotopic inhomogeneity and meteorological dynamics23. Examining all the components in biogeochemical models, water isotopic composition in the hydration/dehydration reaction center, where carbonic anhydrase resides, is by far the least well understood, due primarily to water evaporation. As a result, differing interpretations for the biological carbon cycling vary and remain controversial11,13,15,16,17,18,20. Triple-oxygen isotopic analysis tackles the gross processes from a different vantage point, because of its sensitivity to and conservation in the canonical terrestrial processes, including the aforementioned evaporation17,24,25,26,27,28. Oxygen has three stable isotopes (16O, 17O, and 18O). In the present study, we use a linear form for the excess, Δ17O, for the carbon cycling flux calculation, because the excess in a typical log definition is not a conserved quantity:

$$\Delta^{{{17}}} {\text{O }} = {\updelta }^{{{17}}} {\text{O }} - {\uplambda } \times {\updelta }^{{{18}}} {\text{O}}$$
(1)

where the δs are the isotopic compositions of the species of interest, referenced to the VSMOW standard. The core reason for choosing triple oxygen isotopic analysis is that typical biogeochemical processes that modify δ17O and δ18O follow well-defined mass fractionation slopes in a three-isotope plot, with values close to 0.529,30,31. The formulation of the carbon flux budget using Δ17O is thus simplified, compared to that of δ18O, because the non-zero values are not affected by uptake and the uncertainties from water isotopic variability are removed. Multi-isotope measurements have proven valuable in global studies. This work enhances these efforts with new integrative interpretation and modeling focusing on unification of the multiple isotopic systems, in order to provide constraints on narrowing the range of terrestrial gross primary production, tGPP (~ 110–150 PgC/year) from climate models1,6,8,9 and allow better resolution of the previously poorly known oceanic production, oGPP32,33.

The value of λ, independent of source water isotopic composition, unlike δ, is process-specific and insensitive to temperature30. To our knowledge, λ depends on ambient air relative humidity only34,35, that largely removes the complexities from water evapotranspiration and equilibrium and kinetics processes associated with water-mediated gross processes. The adopted linear definition follows the same budget formulation as δ18O11,17 and has been used widely for dissolved O2 for assessing aquatic GPP24,25,26. It is recommended that a λ value of 0.516 is best for describing the O2 system25, same as our preferred choice for the CO2 system described below; we also show in the Supplementary Information that the choice only weakly affects the gross fluxes derived in this paper. For atmospheric CO2 in the terrestrial biosphere, leaf and soil water is responsible for the oxygen isotopic composition of CO2, readily affected by frequent isotope exchange between CO2 and water. The oxygen isotopic variation of leaf and soil water is controlled by evapotranspiration35, influenced by atmospheric relative humidity. At the globally averaged relative humidity of 75 ± 5%36, the value of λ is 0.5160 ± 0.000435. We thus adopt the value of 0.516 for λ for CO2, unifying the selection for the O2 and CO2 systems. (We stress that the selection of the λ value does not change the results (within error) presented in this work. For example, the recycling time derived at λ = 0.516 is 1.5 ± 0.2 year (see below) and it remains at 1.5 year for λ = 0.528 but with a larger error of 0.4 year. This is because the selection does not best represent the variation of tropospheric CO2). The co-variation and closure of CO2 and O226,32,33,37, specifically their triple-oxygen isotope compositions, thus, allow us to constrain the global carbon cycles (gross components) from a new and independent perspective, the basis for this new work.

Two recent attempts were made to provide new insight into the assessment of carbon cycling fluxes from a global perspective. These two approaches are the impact of hydrological cycles affected by ENSO using the δ18O values of atmospheric CO2 and the extension of single delta values to triple oxygen isotopic analysis. The values of tGPP from the two methods are ~ 150–17515 and 120 ± 3017 PgC/year, respectively. The merits of the two are different. The former utilizes the changing isotopic signal in precipitation and the quasi-equilibrium isotopic exchange between CO2 and rainwater; a global and extensive dataset of surface water is needed to account for spatiotemporal inhomogeneity of precipitation in response to ENSO. The second approach largely reduces the complexity of the analysis, because most of the known biogeochemical processes follow well-defined relations with the change in δ17O being about one-half of δ18O. Here, we examine the reported GPP values using the latter approach making use of the Δ17O values in atmospheric CO2 and O2, using data with by far the widest spatial and temporal coverage. In comparing and interpreting O2 gross production and CO2 photosynthetic uptake, we apply a steady state approximation where production of one O2 molecule consumes one CO2 molecule. The data used in this work are shown in Fig. 1 and summarized in Table 1.

## Materials and methods

### Air sampling

In addition to using data available in the literature from the middle East31, Pacific16,17, and South China Sea17 regions, we have extended and collected air for isotopic analysis of CO2 in four locations: (1) Academia Sinica campus (abbreviated AS; 121°36′51ʺE, 25°02′27ʺN; ~ 10 m above ground level or 60 m above sea level) in Taipei, Taiwan, (2) the campus of National Taiwan University (NTU; 121°32′21ʺE, 25°00′53ʺN; ~ 10 m above ground level or 20 m above sea level; ~ 10 km southwest of Academia Sinica), (3) the southern California coast on Palos Verdes peninsula (118°10.9′W, 33° 44.7′N; PVD), and (4) on the roof of the building of the Institute of Earth Sciences at the Edmond J. Safra campus of Hebrew University in Jerusalem, Israel (35°11′60.00ʺE, 31°46′19.79ʺN; ~ 18 m above ground level or 770 m above sea level).

Air from western Pacific regions was collected for isotopic analysis in pre-conditioned 1-L Pyrex bottles, achieved by passing dry, high purity nitrogen through the bottles overnight. The sampling bottles used for concentration (~ 350-mL bottle) and isotope (1-L) analyses were connected in series. Samples were collected and compressed to 2-bar after flushing the bottles for 5 min with ambient air at a flow rate of ~ 2 L per min. Moisture was removed during sampling using magnesium perchlorate to minimize secondary isotopic exchange between CO2 and water. The PVD samples were collected on Saturday afternoons at about 14:00 PST, into 2-L evacuated Pyrex flasks after passing through Mg(ClO4)2. Carbon dioxide was separated from the air samples cryogenically and measured, following the method described previously17. In brief, for samples collected in Taiwan, CO2 was extracted by pumping the air at a flow rate of ~ 90 mL/min from the flasks through a series of four coil traps, with first two kept in dry ice-ethyl alcohol slush (− 78 °C) for moisture removal and the others in liquid nitrogen (− 196 °C). For CO2 from PVD, it was extracted from the air samples on a glass vacuum line by freezing in liquid nitrogen U-traps containing glass beads, followed by drying in ethanol-dry ice trap.

In Israel, atmospheric air samples were collected in evacuated 5 L flasks, followed by CO2 extraction using Russian doll traps according to Brenninkmeijer and Röckmann38. See Barkan and Luz31 for details.

### Laboratory measurements

Full analytical procedures are described in detail elsewhere17 and summarized here. The concentration of CO2 is measured using a LI-COR infrared gas analyzer (model 840A, LI-COR, USA), with reproducibility better than 1 ppmv. The CO2–O2 oxygen isotope exchange method was used to measure the Δ17O of CO2 samples. Isotopic analyses were done using a FINNIGAN MAT 253 mass spectrometer in dual inlet mode. The analytical precision obtained for a single measurement of the Δ17O value of CO2 is better than 0.01‰ (1 − σ standard deviation).

In Israel, the measurements of three oxygen isotopes in CO2 were carried out by CO2 isotopic exchange with O2 of known isotopic composition over hot platinum39. After isotopic exchange, δ17O and δ18O of O2 were measured in dual-inlet mode by a multi-collector mass spectrometer (Delta Plus, ThermoFisher Scientific, Bremen, Germany). The analytical errors in δ17O and δ18O are 0.008 and 0.004‰, respectively. All measurements were performed against an in-house CO2 standard analyzed daily to determine the performance of the CO2–O2 isotopic exchange line and the mass spectrometer. See Barkan et al.39 for details.

In total, 123 new measurements of the triple oxygen isotope compositions in atmospheric CO2 were obtained. Along with the available data from our previous work16,17, there are 578 used for deriving the CO2 oxygen isotope turnover time and gross primary production of the terrestrial biosphere.

### Inter-calibration of the CO2 Δ17O scale

New calibrations presented below show that the Δ17O values reported by Liang et al.17 were biased too high by ~ 0.03–0.04‰. This conclusion results from comparing exchanged aliquots of working CO2 gas with water-equilibrated CO2. The latter is a process largely controlling the oxygen delta values of CO2 (both Δ17O and δ18O) in the biosphere, providing a robust approach (in contrast to the previous graphite method40 for Δ17O standardization) to consolidating the scale of Δ17O in CO2. As a result of the reduced Δ17O values in atmospheric CO2, the new calibration is expected to yield a shorter CO2 recycling time and larger terrestrial carbon cycling flux than those derived previously17, as obtained in the main text (1.5 ± 0.2 years here as opposed to 1.9 ± 0.3 years in Liang et al.17).

For water-equilibrated CO2, we followed the same procedure as earlier41 for equilibrating CO2 with VSMOW water on a shaking stage at an oscillation frequency of 1 s−1 in a thermostatic water bath maintained at 25 °C. About 150-µL of water were introduced to a quarter-inch diameter, 15-cm long Pyrex tube, followed by freezing at acetone-dry ice slush temperature for air evacuation. After evacuation, about 100–150 µmoles of CO2 were injected, and the tube was then flamed-sealed. This procedure resulted in the H2O:CO2 molar ratio being ~ 70. The CO2 used was taken from our high purity (> 99.9999%; Air Products, Inc.) CO2 cylinder (AS-2) with nominal values of − 32.62‰ (VPDB) and 36.64‰ (VSMOW) for δ13C and δ18O42, respectively. One may question whether this H2O:CO2 molar ratio introduces noticeable errors in the final determination of the delta values of CO2. A mass-balance calculation shows that the ratio affects the δ18O values of CO2 by as much as ~ 0.2‰. So, for example, a 0.001 shift in λ results in offsetting Δ17O by 0.0002‰, negligible compared to the nominal precision of 0.01‰.

The equilibrated CO2 was measured for its triple oxygen isotopic composition, following our standard procedure utilizing the technique of CO2–O2 isotopic exchange over hot platinum17,40. The δ17O scale was maintained using our working CO2 (AS-2) with a nominal value of 17Δ = 0.161‰, calibrated against well calibrated AS-117,43. With the established scale for δ18O and δ17O, we measured VSMOW–equilibrated CO2 at 25 °C and the results are summarized in Table S1. The resulting fractionation factors, 17α and 18α, are 1.02139 ± 0.00001 and 1.04122 ± 0.00002 (standard errors with n = 9), respectively, for 17O and 18O. The value of 18α is about 0.0002 different from Barkan and Luz31 or ~ 0.2‰ in the δ18O value that, if attributable to temperature, is 1 °C error of the thermostat (our nominal precision). With this, the calculated ln(17α)/ln(18α) value is 0.52393 ± 0.00009, 0.001 ± 0.0001 higher than that (0.5229 ± 0.0001) from Barkan and Luz31. Calculation shows that this shift in the λ value introduces a difference of 0.042 ± 0.006‰ (= (0.52393–0.5229) × 41.2‰, where 41.2‰ is the value of 18α − 1 at 25 °C) in Δ17O values between the two labs.

Additionally, aliquots of AS-2 CO2 were shared with and measured by co-author Barkan in Israel; the measured values are summarized in Table S2. There is a difference of 0.032 ± 0.001‰ in Δ17O, consistent with the value noted above from the measurements of water-equilibrated CO2. There are two ways to circumvent the issues of Δ17O scale. One is to normalize and rescale the measured Δ17O values of samples and report the values with respect to the VSMOW-equilibrated CO2. The other is to take the value of water-CO2 λ from Barkan and Luz31 and rescale our measured Δ17O values for samples using the two AS-2 values (AS-2 and VSMOW-water-equilibrated AS-2) reported by the two labs. We take the latter approach and rescale the Δ17O values with the mean value of 0.037‰ (mean of 0.032‰ and 0.042‰). The tropospheric CO2 Δ17O values reported in the main text and Supplementary table (Table S3) reflect this scale recalibration.

### Box modeling and gross primary production assessment

For global gross production assessments, we ensured that the length of the sampling for each location is at least one year, to best remove seasonal variations. PVD at the eastern border of the Pacific, the site with the shortest time span of sampling (1 year), though sampling rather clean marine air during the 2014–2016 El Nino, on average, does not show a significant difference (Table 1) in CO2 Δ17O values relative to the data from the other localities with multi-year data records averaged. Though the mean is the same as the others, the site, however, exhibit statistically significant intra-annual variabilities, shown also from the data at the western side of the Pacific at AS (see below). This new finding poses a new challenge to the current carbon cycling framework, and we will discuss this new issue.

To utilize Δ17O for a gross flux study, one requires at least one source of Δ17O that is well-understood and distinct from that of the biosphere and hydrosphere. Stratospheric O2–O3–CO2 photochemistry is the only process that is known to produce large non-zero Δ17O values in O2 and CO2 different from those originating at the surface. Reactions with ozone, as the intermediate, repartition the oxygen isotopes between O2 and CO2. As a result of the coupled photochemistry, Δ17O in stratospheric CO2 is enhanced, materially balanced by its depletion in O244. When the CO2 and O2 molecules return to the troposphere, the excess is diluted by various biological and hydrospheric processes, reflected in the value of Δ17O in the tropospheric CO2 and O216,17,26. See Fig. 2 for a schematic diagram of these processes.

The global carbon cycling budget, at steady state, can be formulated, with respect to CO2 and O2 in the troposphere (Δ17O), as follows:

$$\sum_{\mathrm{i}}{\mathrm{F}}_{\mathrm{i}}\times ({\Delta }^{17}{\mathrm{O}}_{\mathrm{i}}-{\Delta }^{17}\mathrm{O})=0$$
(2)

where Fi is the flux for each reservoir “i" considered, with its characteristic Δ17Oi. For CO2, the reservoirs include water equilibrated CO2 coming from leaf stomata, soil respiration, soil invasion, and oceans, and CO2 from anthropogenic emissions and the stratosphere. Given the sensitivity of the isoflux to the terrestrial CO2 processes (Fig. 3; see also Fig. 4 of Liang et al.17), the approach would successfully give the flux from the terrestrial biosphere, a poorly constrained quantity in current carbon cycle models8. The tGPP may then be determined. Because of its long lifetime in the atmosphere, we use atmospheric O2 for the globally averaged GPP, obtained in steady state by balancing the stratospheric O2 flux having a negative 17O-excess (i.e., Δ17Ost–Δ17O < 0) with the positive biospheric O2. That is,

$${\text{tGPP}} \times (\Delta^{{{17}}} {\text{O}}_{{\text{t}}} - \Delta^{{{17}}} {\text{O}}) \, + {\text{ oGPP}} \times (\Delta^{{{17}}} {\text{O}}_{{\text{o}}} - \Delta^{{{17}}} {\text{O}}) \, + {\text{ F}}_{{{\text{st}}}} \times (\Delta^{{{17}}} {\text{O}}_{{{\text{st}}}} - \Delta^{{{17}}} {\text{O}}) \, = \, 0,$$
(3)

following the approach of Luz et al.26, with the values of Δ17O for atmospheric O2, Δ17Ot for terrestrial photosynthetic O2, and Δ17Oo for oceanic given in Table 1. With the values of GPP and tGPP determined, the oGPP can be calculated (Supplementary Information). We describe below first the tGPP, followed by GPP and oGPP.

## Results and discussion

We analyze data (see Supplementary Information for details) of the triple-oxygen isotopic compositions of surface air CO2 (Fig. 1 and Table 1) from six northern hemisphere sites (South China Sea and Taipei, Taiwan; Jerusalem, Israel; La Jolla, California, United States; Palos Verdes, California, United States). We derive the oxygen isotopic recycling time (τ) of CO2 in the atmosphere and tGPP from the integrated data set and discuss how inter/intra-hemispheric transport affects these quantities. Given that the tropospheric mixing time within each hemisphere is much shorter than the interhemispheric mixing time45,46 and the latter is also shorter than the CO2 residence time derived here (see below), the compiled data should be a valid approximation for the global average. Table 2 summarizes the model results calculated using Eqs. (2) and (3), with the errors obtained following the standard error propagation. For the current mass loading of atmospheric CO2 (M) of 828 ± 10 PgC1,47, the globally averaged τ given by M/Fsur (where the surface flux Fsur is the sum of terrestrial and oceanic gross fluxes; the former is 465 ± 60 PgC/year and the latter is 90 ± 6 PgC/year17) is 1.5 ± 0.2 years, assuming that the Δ17O value in tropospheric CO2 in the southern hemisphere (Δ17OS) is the same as that reported in the northern hemisphere (Δ17ON). Our sensitivity calculation finds ∂τ/∂(Δ17OS – Δ17ON) to be 6.4 years/‰. See Supplementary Information for discussion of the evenness of intra- and inter-hemispheric Δ17O values. At Δ17OS = Δ17ON, the northern hemispheric recycling time τN is 1.2 year and the southern hemispheric τS is 1.8 year. At a maximum interhemispheric difference of 0.025‰ (obtained by assuming absence of inter-hemispheric mixing; see Supplementary Information), the value of τ increases to 1.6 ± 0.2 years, with τN = 1.4 and τS = 2.0 years, consistent with those values (0.4–0.8 year and > 2 years, respectively) estimated earlier15; this level of interhemispheric difference was reported earlier from a global model simulation (~ 0.02‰)20.

With the derived terrestrial flux from Eq. (2), we can estimate the value of tGPP following Liang et al.17. Our best estimate for tGPP is ~ 170–200 PgC/year. The global GPP is evaluated using Eq. (3), with the values of 0.149‰ and 0.202‰ (referenced to tropospheric O2) for terrestrial and oceanic photosynthetic O2, respectively. Following the photosynthetic O2 scenario of Luz and Barkan25, we derived a global GPP of 290 ± 30 PgC/year at tGPP of ~ 170–200 PgC/year obtained above from CO2, in excellent agreement with the most recent value (292 ± 20 PgC/year) from the atmospheric O2 Dole effect33. The derived global GPP from O2 is insensitive to the partitioning between the terrestrial and oceanic components. For example, assuming an equal flux of tGPP and oGPP, global GPP changes to 283 ± 30 PgC/year, within error of the value estimated above (see Supplementary Information). The global carbon budget obtained from this work is summarized in Fig. 2 and Table 2.

The interplay of climate and biogeochemical cycles is yet to be fully understood1,8. Several lines of evidence have shown that the global carbon cycle has changed noticeably4,5,48. For example, an unexpected reversal of C3 versus C4 grass response to elevated CO2 noted recently from a 20-year field experiment posed a great challenge to the community and modelers that the current knowledge of carbon cycles remains insufficient in assessing the changing ecosystem7. Despite the progress made in attempting to model the carbon cycles, caveats remain1,6,8,15. Central components that need more study include gross fluxes of CO2 between reservoirs such as terrestrial and oceanic gross primary productivities. This work provides a lengthy data set from a new perspective with wide geographical coverage and resolution. The triple-oxygen isotopic composition of CO2 constrains the global oxygen isotopic residence time of CO2 in the atmosphere to 1.5 ± 0.2 years, compared to 0.9–1.7 years15,17 or longer10,11. The terrestrial gross flux is quantified to be 550 ± 60 PgC/year, falling in the range reported in the literature, 200–660 PgC/year10,11,15. Our best estimate of tGPP is ~ 170–200 PgC/year, compared to the current models of tGPP of ~ 110–150 PgC/year8, suggesting that the models should be revisited to achieve a full understanding of ecosystem changes due to the changing climate and environmental factors4,5,6,7,49. The inferred oGPP is ~ 90–120 PgC/year, verifying those reported previously32,33 but from an independent perspective. Because of the isotope recycling time of CO2, the spatial inhomogeneity of Δ17O obtained between localities shows that the commonly used δ values can be applied to Δ17O to refine knowledge of the flux partitioned between respiration/soil invasion, photosynthesis, and air-sea exchange.

In short, with constraints from the triple oxygen isotopic compositions in atmospheric CO2 and O2, we robustly derive the terrestrial and oceanic gross fluxes of oxygen on the global scale, done by averaging the CO2 data (because of its lifetime in the atmosphere, O2 is well-mixed) over the various localities and time. We note that the El Nino-modulated changes in the global carbon cycle reported by Thiemens et al.16 are, however, not seen in the new dataset during the 2014–2016 event (the strength of this El Nino event was slightly weaker than the 1997–1998 one), inferring a hitherto unidentified response in the global carbon cycle to climatic effects. Indeed, from a recent analysis of CO2 concentrations in western Pacific regions50, the amplitude of inter-annual climatic modulations of ENSO and Pacific Decadal Oscillation-like variabilities is ~ 5 ppm in the lower troposphere and reduces to ~ 0.5 ppm in the mid-troposphere. How this is translated into gross fluxes, reflected in the Δ17O of CO2, is yet to be quantified. However, further analysis of the data presented in Fig. 1 shows significant and systematic spatial and temporal variations of Δ17O in CO2 (Fig. 4). The maximum seasonal changes are found to be similar to the reduction of Δ17O reported earlier during the 1997–1998 El Nino period16, though no apparent seasonal variation in Δ17O was seen during 1997–199816. Comparing AS and PVD, the values during the second half of 2015 (July–November) are drastically different, being enhanced by as much as ~ 0.04‰ for the former and depleted by ~ 0.05‰ for the latter. The features and magnitudes are inconsistent with a current global model simulation20 where, for both locations, the model predicted the Δ17O values would be higher by ~ 0.02‰ during March–August than during January–February and September–December. More astonishingly, AS and NTU do not vary coherently, despite their close proximity. Overall, AS and Israel each show a seasonal maximum in summer, in contrast to the winter high at PVD. The analysis suggests that the CO2 recycling time in the northern hemisphere is not much longer than one year because of the rather short hemispheric mixing time of less than ~ 4 months46, verifying the result of ~ 1 year recycling time derived above. However, we defer detailed analysis of the inter-annual and intra-annual variations to a later study, when longer data sets are available. Finally, we note that the Δ17O approach, with proper model assimilation20, can be used in the future to quantify and refine the gross fluxes, which were not available, including on local and regional scales51.