Oxygen isotope anomaly in tropospheric CO₂ and implications for CO₂ residence time in the atmosphere and gross primary productivity

Abstract

The abundance variations of near surface atmospheric CO₂ isotopologues (primarily ¹⁶O¹²C¹⁶O, ¹⁶O¹³C¹⁶O, ¹⁷O¹²C¹⁶O, and ¹⁸O¹²C¹⁶O) represent an integrated signal from anthropogenic/biogeochemical processes, including fossil fuel burning, biospheric photosynthesis and respiration, hydrospheric isotope exchange with water, and stratospheric photochemistry. Oxygen isotopes, in particular, are affected by the carbon and water cycles. Being a useful tracer that directly probes governing processes in CO₂ biogeochemical cycles, Δ¹⁷O (=ln(1 + δ¹⁷O) − 0.516 × ln(1 + δ¹⁸O)) provides an alternative constraint on the strengths of the associated cycles involving CO₂. Here, we analyze Δ¹⁷O data from four places (Taipei, Taiwan; South China Sea; La Jolla, United States; Jerusalem, Israel) in the northern hemisphere (with a total of 455 measurements) and find a rather narrow range (0.326 ± 0.005‰). A conservative estimate places a lower limit of 345 ± 70 PgC year⁻¹ on the cycling flux between the terrestrial biosphere and atmosphere and infers a residence time of CO₂ of 1.9 ± 0.3 years (upper limit) in the atmosphere. A Monte Carlo simulation that takes various plant uptake scenarios into account yields a terrestrial gross primary productivity of 120 ± 30 PgC year⁻¹ and soil invasion of 110 ± 30 PgC year⁻¹, providing a quantitative assessment utilizing the oxygen isotope anomaly for quantifying CO₂ cycling.

Introduction

The net growth rate and level of CO₂ in the atmosphere represents a dynamic balance between anthropogenic activities and natural sources and sinks¹. The diurnal and seasonal cycles, however, are largely affected by terrestrial photosynthesis and respiration^2,3,4. The oxygen isotopic composition of atmospheric CO₂ has been shown to be a powerful tracer for improving understanding of carbon and water cycles involving CO₂ (ref.^{2,3,4,5,6,7,8,9}), providing a unique way to estimate terrestrial gross primary productivity^2,5,8,9. Oxygen has three stable isotopes (¹⁶O,¹⁷O, and¹⁸O). The¹⁸O/¹⁶O isotope ratio is used widely for studying aspects of the carbon and water cycles of natural systems^{2,3,5,6,7,8,9}, but¹⁷O/¹⁶O has rarely been used owing to added analytical difficulty. Here, we compare and analyze the results of the triple-oxygen isotope composition of surface air CO₂ from northern hemisphere sites in the western Pacific (South China Sea and Taipei, Taiwan)¹⁰ and available data from the middle east (Jerusalem, Israel)¹¹ and western North America (La Jolla, United States)¹², to provide deeper insight into the global CO₂ cycle of the atmosphere, biosphere, and hydrosphere (The data from Göttingen, Germany¹³ are not included because of the presence of unknown drift in their two-year ¹⁷O data, though their first year of data agree well with the data reported in this work. Our approach is discussed in detail in a following section). We derive the residence time of CO₂ in the atmosphere and gross primary production (GPP) from the integrated data set and discuss how interhemispheric transport affects these quantities. Given that the tropospheric mixing time in each hemisphere is much shorter than the interhemispheric mixing time^14,15 and the latter shorter than the CO₂ residence time derived here (see below), the compiled data should be a valid approximation of the global average.

We show that the terrestrial flux (the CO₂ cycling flux between the atmosphere and terrestrial biosphere) can be quantified using the Δ¹⁷O values of CO₂, where

$${{\rm{\Delta }}}^{17}{\rm{O}}=\,\mathrm{ln}(1+{{\rm{\delta }}}^{17}{\rm{O}})-{\rm{\lambda }}\times \,\mathrm{ln}(1+{{\rm{\delta }}}^{18}{\rm{O}}),$$

(1)

and we set λ = 0.516 (a value commonly used in the literature^16,17,18) and δ’s are referenced with respect to a commonly used scale, V-SMOW. Here, we follow typical notation (equation 1) to report the values of Δ¹⁷O. However, for the budget calculation that involves multiple-component mixing, Δ¹⁷O is not a conserved quantity¹⁹, and instead, the linear form of Δ¹⁷O, Δ, is used:

$${\Delta }={{\rm{\delta }}}^{17}{\rm{O}}-{\rm{\lambda }}\times {{\rm{\delta }}}^{18}{\rm{O}}.$$

(2)

The budget formulation is then identical to that using δ’s. We note that for describing sources in the budget calculation, Δ¹⁷O and Δ are equally valid. For example, global meteoric water²⁰ obeys the relation λ = 0.528, and the reported Δ¹⁷O value for δ¹⁸O greater than −10‰ is 0.032 ± 0.017‰. In contrast, Δ = 0.026 ± 0.017‰. The means are different but the standard deviations are the same, demonstrating that over the range of the δ¹⁸O values considered, there is no advantage of utilization of either equation (1) or (2) for source representation.

The advantage of using Δ¹⁷O (orΔ) over δ¹⁸O measurements is that Δ¹⁷O directly probes the associated processes in the carbon and water cycles^{11,20,21,22,23,24,25}, as discussed in the next section. Moreover, λ, unlike δ, is insensitive to temperature, and both δ¹⁷O and δ¹⁸O are affected following the canonical mass-dependent relation^23,26. Exchanging oxygen isotopes with water is the major process that we consider in determining CO₂ fluxes between the atmosphere and biosphere/hydrosphere; the associated λ is well defined experimentally^11,23, and the fluxes (e.g., the terrestrial flux - the cycling flux between the terrestrial biosphere and atmosphere, inferred from the oxygen isotopic composition of CO₂) are robustly constrained (cf. ref.⁸).

A classic application of the triple isotope approach is the measurement of Δ¹⁷O in dissolved O₂ in waters^25,27,28. The biologically produced Δ¹⁷O value of O₂ is balanced by the anomaly produced in the middle atmosphere as a consequence of O₂-O₃-CO₂ photochemistry. Since the signal has a millennium time scale, it can be used to study biospheric changes during the past thousand years. In addition, there is a potentially analogous application for CO₂, provided processes that affect Δ¹⁷O in CO₂ are quantified. Similar to O₂, the atmospheric Δ¹⁷O of CO₂ is controlled by CO₂-O₂-O₃ photochemistry and various anthropogenic, biospheric, and hydrospheric processes, including fossil fuel burning, photosynthesis, respiration, and exchange with leaf and soil water, oceans and other bodies of water^{11,16,18,19,29,30,31,32,33}. The primary enhancing source of the oxygen isotopic anomaly resides in the middle atmosphere, as a consequence of the exchange reaction between CO₂ and O₃ via the excited state oxygen atom O(¹D) (ref.^29,30,31,32). Along with various sources¹⁹ and processes^5,9,11,23,33 that determine the “net” Δ¹⁷O of CO₂ emitted from the Earth’s surface, Hoag and co-authors¹⁶ investigated the contribution of stratospheric CO₂ to the tropospheric CO₂ mass-independent isotopic composition and predicted an anomaly of Δ¹⁷O ≈ 0.15‰, above the mean value of emissions/fluxes from the surface.

Sources and processes defining Δ¹⁷O values

The size of the anomaly is dependent upon the choice of λ and the reference scale. Here, we choose 0.516 for the slope and the most commonly used scale for oxygen, V-SMOW. We note that the selection of reference scale does not affect interpretation, provided the variation and partitioning among the three oxygen isotopes are properly accounted for. Given that the carbon flux estimation presented in this paper is based on the deviations of the oxygen anomalies of reservoirs/processes from that measured in atmospheric CO₂, it is natural to take the λ value describing the variation of the triple-oxygen isotopic partitioning in tropospheric CO₂. Processes that affect CO₂ isotopologues in the troposphere are terrestrial, oceanic and anthropogenic, with the first being dominant. In the terrestrial biosphere, leaf water transpiration governs the variation of oxygen isotopes in CO₂; the mean, however, is largely determined by water-CO₂ equilibration catalyzed by carbonic anhydrase^{2,3,5,6,7,9,33}. It has been found previously that the transpiration λ value is a function of air relative humidity²¹, whereas dependence on other meteorological variables such as temperature and soil water isotopic composition has not been observed. We set λ = 0.516, as it represents the transpiration λ at 75% relative humidity, a globally averaged humidity near the surface³⁴. This λ value is essentially the same as that of CO₂ we obtained (0.518 ± 0.004, see below) for the western Pacific, which had an average relative humidity of 76 ± 4% during 2010–2015 (data obtained from the Center for Weather Bureau, Taiwan; site code: 466920; the value changes slightly to 72 ± 11% if considering only day time between 6 AM to 6 PM). However, given the sparse spatiotemporal coverage of the data, the governing slope cannot be firmly decided. More data taken under a variety of environmental conditions are needed to set a better constraint. From the current understanding of the processes occurring, we consider plant transpiration the most important process affecting the variation of atmopsheric CO₂ (e.g., see Landais et al.²¹ and Cuntz et al.³ and references contained therein). We stress that the value of λ does not affect the flux interpretation shown below, as long as equation (2) is used, but the selection must best represent the variation of atmospheric CO₂.

A schematic diagram (not to scale) that describes various sources and processes modifying CO₂ isotopologues is shown in Fig. 1, which summarizes the oxygen isotope transport at steady state. On a global scale, equilibrium processes are the major controllers in oxygen isotope dynamics; we show below in the Box model section that kinetic fractionations are insignificant. (Previous work¹³ utilized a time-dependent model showing a measurable seasonal cycle of Δ¹⁷O at an amplitude of ~0.05‰. The present work assesses the global carbon budget at steady state, leaving the assessment of spatiotemporal variability, including seasonality, to a latter paper when data covering a variety of spatial and temporal scales are available). Three sources/processes are considered: terrestrial (meteoric) water, ocean water, and anthropogenic CO₂, with the last inheriting the atmospheric O₂ isotopic composition. The variation of the triple oxygen isotopic composition of meteoric water follows a slope of 0.528 (ref.²⁰). Subsequent isotopic exchange between water and atmospheric CO₂ modifies the oxygen isotopic composition of CO₂ following a slope of 0.5229 (ref.¹¹). In addition, in the terrestrial biosphere, plant transpiration changes the source water following a slope of 0.516, a value chosen to represent the average slope at the globally averaged relative humidity of 75% (ref.^21,34), as discussed above. These three values (0.528, 0.5229, and 0.516) determine the Δ¹⁷O value of CO₂ mediated by processes involving water. We use the scheme in Fig. 1 to follow changes in oxygen isotopic composition, starting with meteoric water (point A). Transpiration that affects leaf water changes source meteoric water from A to B; the line AB follows the slope of 0.516. Subsequent water-CO₂ isotopic exchange determines the composition of oxygen in leaf CO₂, following the slope of 0.5229 to point C. For exchange with ocean water, only water-CO₂ equilibration is involved, that changes CO₂ to the blue “X.” When the CO₂ enters the stratosphere, the coupled CO₂-O₂-O₃ photochemistry moves the tropospheric CO₂ to D; this path goes through mean tropospheric CO₂ (diamond) and has slope of >1 (ref.^29,30,31,32). Large-scale circulation and synoptic eddy mixing bring the modified CO₂ back to the troposphere. The tropospheric CO₂ (diamond) represents a balance among stratospheric (grey), terrestrial (yellow), oceanic (blue “X”), and the final component - anthropogenic CO₂ (red symbol). Figure 1B, plotting Δ¹⁷O versus ln(1 + δ¹⁸O), shows that our reference λ is chosen (0.516) so that plant transpiration does not change the Δ¹⁷O value of terrestrial water. This is a rotation of Fig. 1A such that a slope of 0.516 becomes 0, and this removes the dominant variation along the correlation in Fig. 2A, as shown in Fig. 2B.

Figure 1

Schematic diagram (not to scale) of the sources and transport of CO₂ considered in this paper. (A) ln(1 + δ¹⁷O) vs. ln(1 + δ¹⁸O) plot for meteoric water (blue), transpiration water (green), plant equilibrated CO₂ (yellow), and stratospheric modified CO₂ (grey). Ocean water equilibrated CO₂ is shown by the blue “X” and averaged tropospheric CO₂ value by the diamond. Anthropogenic CO₂ is denoted by the explosive red starburst symbol. Arrows indicate transport. The slopes (m) for the lines AB, BC, and diamond-D are 0.516, 0.5229, and > 1, respectively. See text for details. (B) Similar to (A) but for Δ¹⁷O vs. ln(1 + δ¹⁸O). The corresponding slopes have been decreased by 0.516. Δ¹⁷O_mw is the meteoric Δ¹⁷O, the y-intercept of the line AB. α¹⁸O_water-CO2 represents the fractionation in δ¹⁸O of water and CO₂.

Figure 2

(A) ln(1 + δ¹⁷O) vs. ln(1 + δ¹⁸O) plot for atmospheric CO₂ collected from Taipei (Taiwan), South China Sea, La Jolla (United States), and Jerusalem (Israel). Values in ‰ are referenced to V-SMOW. The geometric mean regression of the Taipei data gives ln(1 + δ¹⁷O) = (0.519 ± 0.005)× ln(1 + δ¹⁸O) + (0.2 ± 0.2‰). (B) The reported Δ¹⁷O values vs. ln(1 + δ¹⁸O). Note that the Δ¹⁷O values for the last two datasets have been re-scaled following equation (1). The error bars are smaller than the symbol size, with an error of ~0.05‰ for δ¹⁸O and ~0.01‰ for Δ¹⁷O. The two points (give values or reference to table where the data are given) from La Jolla beyond the plotting range of Δ¹⁷O are not shown.

Δ¹⁷O values of source CO₂

In addition to well-quantified photochemical processes in the middle atmosphere, there are two known processes that modify Δ¹⁷O: combustion and isotope exchange with water. The former produces CO₂ with Δ¹⁷O = −0.21‰, the same as air O₂ (ref.¹⁹), used for the anthropogenic component below.

Isotopic exchange with water can be estimated using water-CO₂ equilibrium^11,23. Under the assumed definition of λ derived from equation (1), Δ¹⁷O of CO₂ emitted from sources involving water-CO₂ equilibration processes like respiration and soil invasion, following the slope of 0.5229 (ref.¹¹), is (0.5229 − 0.516) × ln $({{\alpha }^{18}}_{{\rm{w}}{\rm{a}}{\rm{t}}{\rm{e}}{\rm{r}}-{{\rm{C}}{\rm{O}}}_{2}})\,+\,{{\rm{\Delta }}}^{17}{O}_{{\rm{m}}{\rm{w}}}$ (see the previous section and Fig. 1), where ${{\alpha }^{18}}_{{\rm{w}}{\rm{a}}{\rm{t}}{\rm{e}}{\rm{r}}-{{\rm{C}}{\rm{O}}}_{2}}$ and Δ¹⁷O_mw are, respectively, the fractionation factor for water equilibrated ¹⁸O in CO₂ and Δ¹⁷O of water. See Fig. 1B for the schematics. We adopt ${{\alpha }^{18}}_{{\rm{w}}{\rm{a}}{\rm{t}}{\rm{e}}{\rm{r}}-{{\rm{C}}{\rm{O}}}_{2}}\,=\,1.043$ at a globally averaged land temperature of 15 °C (taken over 60° south to 75° north, where most biological activities occur; ref.³⁴). Globally averaged meteoric water has Δ¹⁷O_mw = −0.046 ± 0.005‰ (1 standard error; or 0.032 ± 0.003‰ at λ = 0.528; ref.²⁰), excluding highly depleted waters having δ¹⁸O less than −10‰ in high latitude regions covered by snow and/or ice. (Here, standard error represents the error of a sample mean; standard deviation describes the error of a single measurement, the spread of replicate analyses of a single sample, or the spread of an ensemble). Figure 3 shows that the values of Δ¹⁷O_mw from various regions are comparable.

Figure 3

The Δ¹⁷O value (Δ¹⁷O_mw) of global meteoric water²⁰ adopted in this work. For comparison, the values in Taiwan²⁸, mainland USA⁴⁸, and three tropical countries (Niger⁴⁹, Indonesia²⁰, and India²⁰) are also shown.

The Δ¹⁷O value for terrestrial CO₂ (Δ¹⁷O_land) is calculated to be 0.244 ± 0.005‰ ((0.5229 − 0.516) × ln(1.043) − 0.046‰ = 0.000244 = 0.244‰). We note that since water transpiration in plants follows λ = 0.516 at 75% relative humidity²¹, this process does not change Δ¹⁷O values of waters originating from meteoric water. This equivalence is a major advantage of choosing λ = 0.516 in equation (1). (We note that 5% variation in relative humidity results in ~0.015‰ change in the Δ¹⁷O of leaf water-equilibrated CO₂, through water transpiration²¹).

The other largest water reservoir is the oceans. The globally averaged Δ¹⁷O of ocean waters (Δ¹⁷O_ow) is 0.000 ± 0.001‰ (or −0.005 ± 0.001‰ at λ = 0.528; ref.²⁰), and the resulting Δ¹⁷O of oceanic CO₂ at 20 °C (ref.³⁵) is 0.284 ± 0.001‰. The observation that Δ¹⁷O of meteoric water is lower than that of oceanic water suggests that the Δ¹⁷O approach has greater sensitivity to terrestrial processes than to oceanic ones.

Below we combine the values calculated above with data from several locations around the world (La Jolla, CA, USA; Jerusalem, Israel; Taipei, Taiwan; and the South China Sea) to put constraints on GPP and the oxygen isotope residence time of CO₂ in the atmosphere. The oxygen isotope residence time is defined by the ratio of the atmospheric CO₂ mass loading (M) and the CO₂ mass flux between the atmosphere and biosphere/hydrosphere (F_sur). The flux is inferred from the mass balance calculation obtained using the triple oxygen isotopic composition of tropospheric CO₂ shown below.

Methods

In addition to using data available in the literature from Jerusalem¹¹, La Jolla¹², and western Pacific regions¹⁰, we have continuously collected air for isotopic analysis of CO₂ in three locations: (1) Academia Sinica campus (abbreviated AS; 121°36′51″ E, 25°02′27″ N; ~10 m above ground level or 60 m above sea level) in Taipei, Taiwan and (2) the campus of National Taiwan University (NTU; 121°32′21″ E, 25°00′53″ N; ~10 m above ground level or 20 m above sea level; ~10 km southwest of Academia Sinica). To check the reported Δ¹⁷O values in the eastern Pacific¹², we have also collected and analyzed CO₂ from Los Angeles, California at a latitude slightly higher than La Jolla, along the coast on Palos Verdes peninsula (118°10.9′ W, 33° 44.7′ N; PVD). Data reported in this work and analyzed in Taiwan are provided in full in the supplementary material.

Analytical methods are described in detail elsewhere^{10,18,36,37,38} and summarized here. Air from western Pacific regions for isotope analysis was collected in pre-conditioned 1-liter 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-liter) analyses were connected in series. Samples were collected and compressed to 2-bar after flushing the bottles for 5 minutes with ambient air at a flow rate of ~2 liter per min. Moisture was removed during sampling using magnesium perchlorate to minimize subsequent isotope exchange between CO₂ and water³⁹. Concentration of CO₂ is measured using a LI-COR infrared gas analyzer (model 840A, LI-COR, USA), with reproducibility better than 1 ppmv. The PVD samples were collected on Saturday afternoons at about 14:00 PST, into 2-liter evacuated Pyrex flasks after passing through Mg(ClO₄)₂. Carbon dioxide was separated from the air samples cryogenically and measured, following the method described in Newman et al.³⁸. The CO₂-O₂ oxygen isotope exchange method developed previously^36,37 was used to measure the Δ¹⁷O of CO₂ samples. Isotopic analyses were done using a FINNIGAN MAT 253 mass spectrometer in the 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).

Results

The concentrations of the isotopologues of CO₂ at South China Sea (SCS) are close to those reported at Mauna Loa measured by the National Oceanic and Atmospheric Administration - Earth System Research Laboratory (data available online at http://www.esrl.noaa.gov/gmd/dv/iadv/), with [CO₂] 395.4 ± 7.3 ppmv and δ¹³C −8.47 ± 0.22‰ (1-σ standard deviation). In Taipei (AS + NTU), the averaged [CO₂] is 416.2 ± 18.3 ppmv, δ¹³C is −9.22 ± 0.83‰, and δ¹⁸O is 40.65 ± 0.82‰. [CO₂] varies between ~350 and 475 ppmv, with low values during the day and high at night, representing the combined effect of natural biogeochemical cycle (photosynthesis and respiration), anthropogenic emissions, and boundary mixed layer height diurnal variation³⁸. During day time hours, photosynthesis dominates, resulting in reduction of CO₂ concentration and less negative δ¹³C and δ¹⁸O values. The CO₂ content is lower during the day than night also due to dilution as the boundary layer deepens. The mean values obtained for [CO₂] and δ¹³C, as compared to SCS, show that in Taipei a clear contribution from anthropogenic emissions is seen. Given the proximity of the AS and NTU stations (~10 km apart), air transport time is shorter than the CO₂ oxygen isotope residence time shown below, resulting in, on a yearly basis, similar levels of CO₂ isotopologues, including Δ¹⁷O.

Figure 2A compiles tropospheric CO₂ data in a plot of ln(1 + δ¹⁷O) vs. ln(1 + δ¹⁸O). The least square linear regression analysis of the data obtained in Taipei yields a slope of 0.518 ± 0.004 (excluding some outliers at δ¹⁸O < 38.5‰) and intercept of 0.3 ± 0.2‰ (1 standard error, R² = 0.99). The observation that the same slope is obtained as for transpiration at ~75% relative humidity (close to the value at the sampling sites in western Pacific, 76 ± 4% averaged between 2010 and 2015) suggests that transpiration is likely a controlling process affecting the variation of the triple oxygen isotopic composition of near surface CO₂. As the variation of oxygen isotopic compositions in CO₂ at the two Taipei sampling sites is biogeochemically mediated, one may use Δ¹⁷O to estimate the actual “flux” between the atmosphere and soil/leaf, which in turn gives the value for GPP. The overall ratio of ln(1 + δ¹⁷O)/ln(1 + δ¹⁸O) for Taipei is 0.524 ± 0.001, consistent with that of a water-CO₂ equilibrium value of 0.5229 ± 0.0001 (ref.^11,23), further verifying that the oxygen of near-surface CO₂ in this region is primarily affected by biogeochemistry with minor influences from the stratosphere and human activities. The Δ¹⁷O values in Taipei vary from 0.216 to 0.415‰ (Fig. 2B) with an average of 0.335 ± 0.039‰ (1-σ standard deviation of the range), a value similar to 0.31 ± 0.06‰ obtained in La Jolla¹² and 0.321 ± 0.007‰ in Jerusalem¹¹. (Note that the values for the last two have been re-scaled with respect to λ = 0.516, for the sake of consistency among the data sets). The value at SCS is 0.335 ± 0.033‰. The value reported at La Jolla is the lowest among the four. We then check the possibility that the difference between La Jolla and Taiwan is caused by the difference in Δ¹⁷O scale between the two labs. By taking CO₂ samples collected also in the eastern Pacific region but at a higher latitude near a southwest facing beach on the Palos Verdes peninsula (PVD). The obtained values for 2015 are 0.317 ± 0.032‰, essentially the same as the decadal mean from La Jolla. The average of the mean Δ¹⁷O values from La Jolla, Jerusalem, Taipei, and the South China Sea (0.326 ± 0.005‰) is used below in the box model calculation of GPP and oxygen isotope residence time. The averaged Δ¹⁷O value decreases by only 0.004‰ if just the two largest datasets, from Taiwan and La Jolla, are averaged. Therefore, we note that whether the SCS, Jerusalem, and PVD data are included does not change the conclusion presented below. For example, a 0.01‰ reduction in Δ¹⁷O results in ~0.2-year decrease in the oxygen isotope residence time. Moreover, given that the oxygen isotope residence time is on the order of one year only and sources and processes that change the isotopologues of the tropospheric CO₂ are variable spatially and temporally, spatiotemporal inhomogeneity in Δ¹⁷O is expected. The average of the mean values from more locations should be more representative for the global Δ¹⁷O.

Box model

A box model is employed to assess various contributing processes for Δ¹⁷O. At steady state, the mass balance equation for δ (where δ is either δ¹⁷O or δ¹⁸O), following Cuntz et al.³, can be written as follows:

$$\begin{array}{c}{C}_{{\rm{a}}}{M}_{{\rm{a}}}\frac{{{\rm{d}}\delta }_{{\rm{a}}}}{{\rm{d}}{\rm{t}}}=0={\varepsilon }_{{\rm{l}}}({{\rm{F}}}_{{\rm{l}}{\rm{a}}}-{{\rm{F}}}_{{\rm{a}}{\rm{l}}})+{{\rm{F}}}_{{\rm{l}}{\rm{a}}}({\delta }_{{\rm{l}}}-{\delta }_{{\rm{a}}})+{{\rm{F}}}_{{\rm{r}}}\,({\delta }_{{\rm{r}}}-{\delta }_{{\rm{a}}}+{\varepsilon }_{{\rm{s}}})+{{\rm{F}}}_{{\rm{s}}}\,({\delta }_{{\rm{s}}}-{\delta }_{{\rm{a}}})\\ \quad \quad \quad \quad \quad +{{\rm{F}}}_{{\rm{a}}{\rm{o}}}({\delta }_{{\rm{o}}}-{\delta }_{{\rm{a}}}+{\varepsilon }_{{\rm{o}}})+{{\rm{F}}}_{{\rm{a}}{\rm{n}}{\rm{t}}{\rm{h}}}({\delta }_{{\rm{a}}{\rm{n}}{\rm{t}}{\rm{h}}}-{\delta }_{{\rm{a}}})+{{\rm{F}}}_{{\rm{s}}{\rm{t}}}({\delta }_{{\rm{s}}{\rm{t}}}-{\delta }_{{\rm{a}}})\end{array}$$

(3)

where C is the volume mixing ratio of CO₂, M is the mass of the atmosphere, subscripts “a”, “st”, “anth”, “l”, “r”, “s”, and “o” of δ’s represent the δ values of the sampled air, the stratosphere, anthropogenic emissions, and leaf, respiration, soil, and ocean water, respectively, ε’s are the associated kinetic fractionation factors, and F is the flux in and out of a reservoir such that the subscript “la” refers to leaf-to-air, “al” air-to-leaf, and “ao” air-to-ocean. We then rewrite the equation (3) in terms of Δ in steady state as follows.

$$\begin{array}{c}{{\rm{F}}}_{{\rm{l}}{\rm{a}}}({{\rm{\Delta }}}_{{\rm{l}}}-{{\rm{\Delta }}}_{{\rm{a}}})+{{\rm{F}}}_{{\rm{r}}}\,({{\rm{\Delta }}}_{{\rm{r}}}-{{\rm{\Delta }}}_{{\rm{a}}})+{{\rm{F}}}_{{\rm{s}}}\,({{\rm{\Delta }}}_{{\rm{s}}}-{{\rm{\Delta }}}_{{\rm{a}}})+{{\rm{F}}}_{{\rm{a}}{\rm{o}}}({{\rm{\Delta }}}_{{\rm{o}}}-{{\rm{\Delta }}}_{{\rm{a}}})\\ \quad \quad \quad \quad \quad +{{\rm{F}}}_{{\rm{a}}{\rm{n}}{\rm{t}}{\rm{h}}}({{\rm{\Delta }}}_{{\rm{a}}{\rm{n}}{\rm{t}}{\rm{h}}}-{{\rm{\Delta }}}_{{\rm{a}}})+{{\rm{F}}}_{{\rm{s}}{\rm{t}}}({{\rm{\Delta }}}_{{\rm{s}}{\rm{t}}}-{{\rm{\Delta }}}_{{\rm{a}}})=\,0,\end{array}$$

(4)

where the kinetic terms ((F_la − F_al) × ε_l × (λ_l − λ₀) + F_r × ε_s × (λ_s − λ₀) + F_ao × ε_o × (λ_o − λ₀)) become negligible (even with extreme values for F at 500 PgC year⁻¹ or λ_l,s,o at 0.529, the value for equilibrium water between condensed and vapor phases, the isoflux is found to be less than 1‰ PgC year⁻¹). We note that Δ in the linear definition in equation (4) obeys mass conservation whereas Δ¹⁷O in the logarithmic definition does not. The use of Δ¹⁷O in equation (4) results in an error about 10% in each term derived, i.e., ~40 PgC year⁻¹ biased too high in F_la + F_r + F_s and ~0.2 year too short in the resident time of CO₂ in the atmosphere (though still within the error of the estimation). Parameters and values used in the box modeling are summarized in Table 1.

Table 1 Summary of the parameters and values considered in the box modeling. The quoted error refers to 1 standard error, representing the error of a sample mean.

Finally, we have Δ _l = −0.009 ± 0.006‰, Δ _r = Δ _s = 0.019 ± 0.006‰, Δ _o = 0.075 ± 0.001‰, and Δ _anth = −0.286 ± 0.001‰ (or Δ¹⁷O_l = Δ¹⁷O_r = Δ¹⁷O_s = Δ¹⁷O_land = 0.244 ± 0.005‰, Δ¹⁷O_o = 0.284 ± 0.001‰, and Δ¹⁷O_anth = −0.213 ± 0.001‰). The oceanic flux F_oa is 90 ± 6 PgC year⁻¹ (an average of IPCC 2001, 2007, and 2013; ref.^1,2,3,40), F_anth is 9.4 ± 0.8 PgC year⁻¹ for year 2011 (ref.^1,41). We further take F_la ≈ 2F_r ≈ 2F_s (from the fact that global net productivity is much less than the gross productivity, and the assumption of catalyzed soil invasion⁷), and with this, the terrestrial flux F_land equal to F_la + F_r + F_s. Then equation (4) can be reduced to

$${{\rm{F}}}_{{\rm{land}}}\times ({{\Delta }}_{{\rm{l}}}\,-\,{{\Delta }}_{{\rm{a}}}+{{\Delta }}_{{\rm{s}}}\,-\,{{\Delta }}_{{\rm{a}}})/2+{{\rm{F}}}_{{\rm{ao}}}\times ({{\Delta }}_{{\rm{o}}}\,-\,{{\Delta }}_{{\rm{a}}})+{{\rm{F}}}_{{\rm{anth}}}\times ({{\Delta }}_{{\rm{anth}}}\,-\,{{\Delta }}_{{\rm{a}}})+{{\rm{F}}}_{{\rm{st}}}\times ({{\Delta }}_{{\rm{st}}}\,-\,{{\Delta }}_{{\rm{a}}})=0.$$

(5)

For stratospheric flux, global model simulations¹⁷ that consider various atmospheric transports yield an averaged isoflux from the stratosphere, F_st × (Δ _st − Δ _a), of 50 ± 3‰ PgC year⁻¹, consistent with that obtained and used previously (~43‰ PgC year⁻¹; ref.^16,42). Figure 4 summarizes the derived terrestrial CO₂ flux and residence time in the atmosphere; in this particular model, the cross-hemispheric transport and mixing are not included, as the hemispheric difference in Δ¹⁷O was predicted to be small (<0.01‰; ref.¹⁶). Sensitivities of the derived quantities with respect to the variations of the relative importance of ocean flux, cross-tropopause exchange flux, soil invasion, and Δ¹⁷O value in the southern hemisphere are presented in Fig. 5. See below for the detail on the error assessment.

Figure 4

(A) CO₂ recycling time (pink) as a function of Δ¹⁷O in atmospheric CO₂ measured near the surface, calculated using equation (5), the box model. The corresponding oceanic (blue) and terrestrial (green) fluxes (the cycling flux between the atmosphere and terrestrial biosphere) are also shown (right-hand axis). The vertical dashed line represents the measured Δ¹⁷O in the tropospheric CO₂. Shaded zones represent 1-σ error. (B) The isoflux of Δ¹⁷O from anthropogenic (gold), terrestrial (green), oceanic (blue), and stratospheric (black) sources, as a function of Δ¹⁷O in atmospheric CO₂, with 1-σ error shown by the shaded areas. At Δ¹⁷O = 0.326‰, the terrestrial isoflux (42‰ PgC year⁻¹) is a factor of 10 higher than the oceanic isoflux (5‰ PgC year⁻¹), suggesting that the Δ¹⁷O approach has greater sensitivity to terrestrial processes than oceanic processes. For easier comparison, we have multiplied the oceanic and terrestrial isofluxes by −1.

Figure 5

(A) The calculated recycling time of CO₂ (pink line), as a function of F_land/F_sur. Stratospheric isoflux is adopted to be 50‰ PgC year⁻¹; anthropogenic flux is 9.4 PgC year⁻¹. The required fluxes from the land and ocean to reproduce the observed Δ¹⁷O = 0.326‰ in air CO₂ are also shown, in green and blue, respectively. The vertical dashed line is drawn through the generally adopted oceanic flux of 90 PgC year⁻¹. (B) The calculated recycling time of CO₂, as a function of the stratospheric isoflux, assuming an oceanic flux of 90 PgC year⁻¹ and Δ¹⁷O = 0.325‰ in air CO₂. The nominal flux adopted in (A) is indicated by the vertical dashed line. The associated terrestrial flux is also shown. (C) Estimated GPP as a function of soil invasion flux, for two photosynthetic scenarios (θ _eq represents the degree of hydration of CO₂ in stomata and κ _c is a measure of stomatal conductance). The stratospheric isoflux is set to be 50‰ PgC year⁻¹, anthropogenic flux is 9.4 PgC year⁻¹, and air CO₂ Δ¹⁷O = 0.326‰. (D) Estimated GPP as a function of southern hemisphere (SH) CO₂ Δ¹⁷O. The stratospheric isoflux is set to be 50‰ PgC year⁻¹, anthropogenic flux is 9.4 PgC year⁻¹, and northern hemisphere air CO₂ Δ¹⁷O = 0.326‰ (marked by the vertical dashed line).

The current steady state box model is an updated version of Hoag et al.¹⁶; the major surface resetting processes are included explicitly to distinguish the terrestrial (re-)cycling fluxes from the oceanic. Previous works (Cuntz et al.³ and Hofmann et al.¹³) solve time-dependent equations (equation 3). In this case, kinetic fractionations becomes important, and spatiotemporal variabilities in all components of carbon/oxygen cycling and recycling fluxes are significant. As a result, spatial and temporal inhomogeneity in sampling has to be considered and evaluated critically. When more data are available, natural variability in carbon fluxes can be assessed. Therefore, for examining the global carbon flux at steady state, we take measurements spanning as much space and time as possible. For error analysis, a standard error from each component of measurements is adopted, leaving standard deviation for representing spatiotemporal variability assessment in time-dependent models.

Assessing gross primary productivity

Plant uptake scenarios affect the estimates of GPP and soil invasion. GPP can be estimated as follows:

$$0.88\times {\rm{GPP}}={{\rm{F}}}_{al}-{{\rm{F}}}_{la}=\frac{{{\rm{F}}}_{{\rm{land}}}-{{\rm{F}}}_{{\rm{s}}}}{{\theta }_{eq}{\kappa }_{c}+1},$$

(6)

where θ _eq represents the degree of hydration of CO₂ in stomata and κ _c is a measure of stomatal conductance which can be expressed by

$${k}_{c}={C}_{c}/({C}_{a}-{C}_{c}),$$

(7)

where C _c is the CO₂ concentration in chloroplasts at the site of CO₂ hydration and C _a is the atmospheric concentration. The factor 0.88 is used to account for leaf respiration⁴³. For C₃ plants, C _c /C _a  = 2/3; for C₄ plants, C _c /C _a  = 1/3, assuming that C _c is equal to intracellular CO₂ concentration⁴⁴. A generally averaged C _c /C _a is 0.57 or κ _c  = 1.33 (ref.^8,9). Overall, the value of κ _c varies between 1.33 and 2.93 (ref.^3,9). θ _eq is also variable^33,45. Careful error assessment is made to quantify the effect of this variation on the value of GPP (Fig. 5C). See Table 1 for the summary of the parameters and the associated errors and variations used in this work.

Errors resulted from incomplete understanding of sources and the Δ¹⁷O values in various water bodies (meteoric, soil, and oceanic waters) and global atmospheric CO₂ (i.e., tropospheric and stratosphere-to-troposphere stream Δ¹⁷O). The corresponding errors are summarized in Table 1. There are, however, other related processes whose λ values remain poorly known, of which transpiration and plant uptake scenarios (i.e., chloroplast CO₂ concentration and enzyme catalyzed oxygen exchange efficiency) are the most uncertain. Transpiration is sensitive to plant species and ambient air relative humidity²¹. If we assume an average considered in Landais et al.²¹, the variation in λ results in a variation of 0.017‰ for Δ¹⁷O for a 0.05 change in relative humidity; this term contributes ~30% of the error (~1/3 from atmospheric CO₂ measurements and the remaining from the cross-tropopause exchange Δ¹⁷O flux) in estimating the global oxygen isotope residence time and terrestrial carbon flux. Proper error propagation is made to assess the error in the terrestrial flux (F_land) derived in equation (5), followed by a Monte Carlo approach to evaluate the errors from κ _c and θ _eq in equation (6) for GPP estimate.

A function f with n independent variables is expressed as:

$$f=f({x}_{1},{x}_{2},{x}_{3},\ldots ,{x}_{n})$$

(8)

The error of each quantity x _i is given by the standard deviation (σ _i ) or standard error $(\overline{{\sigma }_{i}})$. The former refers to the error of a single measurement while the latter is used to represent the error of a sample mean. With a large set of measurements, we use $\overline{{\sigma }_{i}}$ to represent the error of the sample mean $\overline{{x}_{i}}$. The errors in equation (4) refer to such an error. Following standard error propagation, the error of the function f is

$${\overline{{\sigma }_{f}}}^{2}=\,\sum _{i=1}^{i=n}{(\frac{\partial f}{\partial {x}_{i}})}^{2}{\overline{{\sigma }_{i}}}^{2}$$

(9)

For a single measurement, i.e., one measurement only for each of the variable x _i , the final error σ _f is the square root of $\sum _{i=1}^{i=n}{(\frac{\partial f}{\partial {x}_{i}})}^{2}{\sigma }_{i}^{2}.\,$ Therefore, for a set of many measurements reported in this work, the estimated terrestrial flux F_land is 345 PgC year⁻¹, with 1 standard error being 70 PgC year⁻¹. However, for each of the variables in equation (4) (Δ¹⁷ _a, Δ¹⁷ _l or Δ¹⁷O_mw, F_oa, F_anth, and F_st × (Δ¹⁷ _st − Δ¹⁷ _a)), if we measure them once, the error, or sample inhomogeneity due to inhomogeneity in sources and processes, increases to 600 PgC year⁻¹. For errors resulting from global carbon cycling scenarios, a Monte Carlo simulation is employed. The final error is estimated from 500 × 500 × 500 = 125 M (500 samplings for the terrestrial flux and 500 each for two variables in the carbon model in equation (6); the errors are converged with >300 random samplings) calculations of the model using repeated random sampling of each of the three variables. From the literature, κ _c ranges from 1.33 to 2.97 (depending critically on C _c ; ref.^3,9) and θ _eq from 0.7 to 0.78 (affected by enzyme carbonic anhydrase activity in C₄ plants; ref.^9,33,44). To consider final total errors in GPP and F_s, we perform Monte Carlo simulations to randomly determine values for κ _c and θ _eq over the aforementioned ranges. The distribution of these two parameters is assumed to be uniform, with the measurement error of Δ¹⁷O assumed to be following normal distribution.

Oxygen isotope residence time and gross primary productivity

Figure 4 summarizes the model results calculated using equation (5) and a value for Δ¹⁷O of 0.326 ± 0.005‰ for the troposphere, the average for the four locations discussed above. The current mass loading of atmospheric CO₂ (M) is 828 ± 10 PgC (ref.^1,45). The CO₂ oxygen isotope residence time τ is given by M/F_sur, where F_sur = F_land + F_ao. Taking into account the aforementioned uncertainties of the parameters in equation (5), the terrestrial flux F_land is determined to be 345 ± 70 PgC year⁻¹, and τ is 1.9 ± 0.3 years, consistent with previous estimates^2,3,8,9. The estimate is insensitive to the partitioning between ocean and terrestrial fluxes because of the sensitivity of the Δ¹⁷O approach to the terrestrial processes (Fig. 4). However, we show below that we cannot constrain the value for GPP better than other methods, because of unknown quantities for soil invasion and degree of isotopic equilibrium between leaf water and stomatal CO₂.

No significant advancement toward quantifying soil invasion has been made since Wingate et al.⁷. The reported flux can be as low as <10 PgC year⁻¹ (ref.⁶) to as high as 450 PgC year⁻¹ (ref.⁷), depending on the catalyzed hydration activity (via enzyme carbonic anhydrase). Recently, the hydration activity has been found to likely be high, resulting in an invasion flux as high as respiration⁷, and we choose this as our best estimate, i.e., F_s = F_r. By definition, GPP is the sum of respiration F_r and NEP (net ecosystem productivity). So equation (6) can be expressed by

$${\rm{GPP}}\,={0.88}^{-1}\times \frac{{{\rm{F}}}_{{\rm{land}}}-{{\rm{F}}}_{{\rm{s}}}}{{\theta }_{eq}{\kappa }_{c}+1}={\rm{NEP}}+{{\rm{F}}}_{{\rm{r}}}={\rm{NEP}}+{{\rm{F}}}_{{\rm{s}}}.$$

(10)

The globally estimated NEP is 10 PgC year⁻¹ (ref.⁴⁶). Once the values of κ _c and θ _eq are chosen, along with the value of F_land reported above, GPP and F_s can be derived.

With a previously suggested plant uptake scenario (κ _c  = 1.33 and θ _eq  = 0.78; ref.⁸) and an independent constraint for net ecosystem productivity^46,47, we derive an estimate of 130 ± 25 PgC year⁻¹ for GPP, with a best guess for soil invasion of 120 ± 20 PgC year⁻¹ (calculated from equation (10)). A Monte Carlo simulation that considers various carbon cycling models^3,8,9,33,44, including plant types and degree of oxygen equilibrium with various water bodies in the biosphere and hydrosphere, gives the estimates of GPP and soil invasion to 120 ± 30 and 110 ± 30 PgC year⁻¹, respectively. The estimated GPP is toward the lower end of Welp et al.⁸ but close to that of Beer et al.⁴. Given that the value of Δ¹⁷O is sensitive to the isofluxes between atmospheric CO₂ and water bodies, we expect that extended studies with multiple CO₂ isotopologues into C₃-dominated regions such as the Amazonian rainforest, C₄-dominated lands such as grasslands in North America, and vegetation-sparse areas such as the Canadian arctic could have great potential to refine the partitioning between photosynthesis, respiration and soil invasion, and thus to provide a better estimate of the terrestrial GPP.

Figure 5 shows the sensitivities of the derived quantities with respect to the variations of the ocean flux (expressed as variations in the fraction of flux from land to flux from the total surface) (A), cross-tropopause exchange flux (B), soil invasion (C), and Δ¹⁷O value in the southern hemisphere (D). Because of the low value of the oceanic isoflux shown in Fig. 4B, the ocean affects the derived terrestrial flux and CO₂ residence time weakly; changing the oceanic flux by 50% changes the residence time by 0.1 year. The stratospheric flux, however, is more sensitive. 10% changes in the stratospheric flux result in ~0.2 year changes in the residence time. The sensitivity to soil invasion (Fig. 5C) is calculated by varying the variable with F_land fixed at 345 PgC year⁻¹. Depending on soil invasion and plant uptake scenarios (the values of κ _c and θ _eq ), the value of GPP could vary between 0 and 200 PgC year⁻¹. Another important value that remains undetermined is the value of Δ¹⁷O of tropospheric CO₂ in the southern hemisphere. Figure 5D shows that the GPP and residence time are sensitive to the Δ¹⁷O value in the southern hemisphere; the sensitivity is obtained by assuming F_s = 110 PgC year⁻¹, F_land = 345 PgC year⁻¹, κ _c  = 1.33, and θ _eq  = 0.78. If Δ¹⁷O in the southern hemisphere is 0.01‰ (0.02‰) higher than that in the northern hemisphere, the GPP value increases to 170 (200) PgC year⁻¹; the residence time then reduces to 1.7 (1.5) years. As soon as the value of Δ¹⁷O in the southern hemisphere is measured, the global residence time can be determined and GPP can be better quantified.

In summary, the triple-oxygen isotopic composition of CO₂ constrains the global oxygen isotopic residence time in the atmosphere to 1.9 ± 0.3 years, compared to 0.9–1.7 years (ref.⁸) or longer^2,3,9 reported previously. The terrestrial flux is quantified to be 345 ± 70 PgC year⁻¹, falling in the range reported in the literature, 200–660 PgC year⁻¹ (ref.^2,3,8,9). 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. CO₂ sampling campaigns in the remote Pacific and southern hemisphere oceans can better remove interference from terrestrial processes, to quantify the oceanic flux. High-resolution global and regional models assimilating CO₂ isotopologues (Δ¹⁷O in particular) with online carbon and water cycle modules can potentially strengthen our understanding of the associated processes at molecular scales. We expect that existing models³ coupled with a cross-tropopause exchange module extending surface biogeochemical models to include stratospheric processes will greatly improve our estimates and provide extraordinary precision to probe the associated fluxes in the global carbon and water cycles involving CO₂.