Stratospheric photochemistry leads to anomalous oxygen isotope enrichments in CO2 (for which Δ17O = δ17O − 0.516 × δ18O ≠ 0). This isotope anomaly is not lost until air returns to the troposphere and CO2 undergoes isotope exchange with water primarily in the terrestrial biosphere and oceans. A two-box model is used to investigate the contribution of stratospheric production and contemporary surface carbon fluxes to tropospheric Δ17OCO2. The predicted magnitude of ∼0.15‰ is large enough that measurement of a globally averaged tropospheric Δ17OCO2 should provide a new constraint for gross carbon exchanges between the biosphere and atmosphere in terrestrial carbon cycle models. Importantly, Δ17OCO2 should be complementary to the primary isotopic tracer of gross carbon exchanges, δ18OCO2, but is not dependent on numerous hydrologic variables. Furthermore, with improved measurement precision, Δ17OCO2 could serve as a direct tracer of gross carbon exchanges and their variations.
 The terrestrial biosphere plays a dominant role in controlling atmospheric CO2 on annual and interannual timescales and is responsible for about half of the net global carbon sink for anthropogenic CO2. This net sink and its variability on short time scales are governed primarily by the gross fluxes of CO2 into and out of the atmosphere due to respiration and photosynthesis, respectively. Because the net sink is the small difference between these large fluxes and is more easily constrained by observations, large uncertainties remain in the global magnitudes and the temporal and spatial variability of these gross fluxes [e.g., Gurney et al., 2002]. Moreover, the climate sensitivities of these gross fluxes are a key uncertainty in climate change predictions since understanding the distinct responses of photosynthesis versus respiration to changing environmental conditions is critical to predicting how carbon storage by the terrestrial biosphere will respond to global change [e.g., Friedlingstein et al., 2003; Cox et al., 2000; Schimel et al., 2001].
 While net CO2 exchanges between the atmosphere, biosphere, and ocean are studied using observations of the concentrations and δ13C values of CO2 [e.g., Francey et al., 1995] or measuring the local net fluxes of CO2 directly [e.g., Goulden et al., 1998], observations and modeling of δ18O of tropospheric CO2 have received increasing attention as a means to constrain gross carbon exchanges since both the gross photosynthetic uptake of carbon and the total ecosystem respiration play dominant and often opposing roles in determining δ18OCO2 [e.g., Farquhar et al., 1993; Ciais et al., 1997]. Francey and Tans  first suggested that isotope exchange between CO2 and water in the chloroplasts of leaves during photosynthesis largely determines tropospheric δ18OCO2. While ∼1/3 of atmospheric CO2 entering leaves is assimilated, the remainder diffuses back out with a new δ18O value determined largely by δ18Oleaf-H2O. Farquhar et al.  related this isotope exchange process to gross primary productivity (GPP) in a model which included a large number of isotopic, physical, hydrologic, and biological variables. Subsequent modeling studies confirmed that land biota are the primary determinant of δ18OCO2 [e.g., Ciais et al., 1997; Cuntz et al., 2003a, 2003b]. Table 1 summarizes the isotope exchange processes in the global δ18OCO2 cycle. Among the current aims of modeling efforts is to use δ18O observations of CO2 and H2O to improve estimates of GPP and respiration, both globally and locally [e.g., Cuntz et al., 2003a, 2003b; Riley et al., 2003].
Table 1. Processes Controlling δ18O and δ17O of Tropospheric CO2
 Clearly, using δ18OCO2 as a constraint on terrestrial GPP requires estimates and/or detailed modeling of δ18O values for numerous water pools which can be difficult to ascertain. δ18O of leaf water, e.g., depends on plant anatomy, the vertical distribution of δ18OH2O in soils, the humidity in the canopy and its δ18O, and other factors such as precipitation and temperature. In contrast, the anomalous relationship between δ18O and δ17O of tropospheric CO2, or Δ17OCO2 defined below, does not depend directly on values for δ18O or δ17O of soil and leaf H2O and may therefore be easier to link directly to GPP and to deconvolve the response of GPP to interannual changes in, e.g., temperature and precipitation.
 Stratospheric CO2 is anomalously enriched in 17O and 18O [e.g., Lämmerzahl et al., 2002; Boering et al., 2004]. Most physical and chemical processes fractionate isotopes in a mass-dependent manner for which δ17O = λ × δ18O, with λ = 0.500 to 0.529 [e.g., Thiemens, 1999]. However, for stratospheric CO2, δ17O ∼ 1.7 × δ18O, and the magnitude of the CO2 isotope anomaly may be defined as
where λ = 0.516 [Boering et al., 2004]. This CO2 isotope anomaly likely arises from anomalous kinetic isotope effects in the formation of O3 [e.g., Mauersberger et al., 1999], which can be photochemically transferred to CO2 via O(1D) from O3 photolysis [e.g., Yung et al., 1997]. Since there is, in effect, no stratospheric sink for Δ17OCO2, anomalous CO2 produced in the stratosphere is transported to the troposphere where the isotope anomaly is destroyed by isotope exchange with water and diluted by inputs of non-anomalous CO2. Importantly, when CO2 equilibrates with mass-dependently fractionated H2O, Δ17OCO2 is reset to zero.
 Thus, modeling a global cycle for Δ17O in tropospheric CO2 to investigate gross fluxes to and from the terrestrial biosphere is analogous to that for δ18OCO2 but is considerably less complex. In particular, explicit values for δ18O and δ17O of leaf water are not required since Δ17O for CO2 retro-diffusing out of leaves during photosynthesis is reset to zero (if isotopic equilibration is complete) or some fraction of Δ17OCO2 (if equilibration is incomplete). Likewise, explicit values for δ18O of soil H2O are not required since respired CO2 and the CO2 associated with the invasion flux of atmospheric CO2 into the soil [e.g., Miller et al., 1999] are not anomalous. Therefore, tropospheric Δ17OCO2 may provide a tracer of gross carbon fluxes that is complementary to δ18OCO2 but which does not depend on explicit values of δ18O for numerous water pools and is decoupled from potential ambiguities due to correlated changes in δ18O of leaf and soil water with changing temperature or precipitation patterns. Moreover, while Δ17O of O2 has been proposed as a constraint on GPP on millennial time scales [Luz et al., 1999], tropospheric Δ17OCO2 may provide information on annual to decadal time scales. In this first study, a two-box model is used to investigate the feasibility of using Δ17OCO2 as a constraint on gross CO2 fluxes to and from the terrestrial biosphere.
2. Model Description
 A two-box model representing the northern and southern hemispheres (NH and SH) was chosen since there are several flux asymmetries between the hemispheres. Carbon mass balance requires that the rate of change in CO2 inventory in the NH troposphere (MN) is the sum of the sources and sinks (QjN) of CO2 within the hemisphere and the interhemispheric exchanges of CO2:
The carbon sources and sinks are expressed as the sum of fluxes into and out of the NH:
where FXY represents the flux from a donor reservoir X to receiver reservoir Y, with the subscript S denoting the stratosphere, A the troposphere, O the ocean, and L leaves. FAL and FLA are the CO2 fluxes between the troposphere and leaves of plants and are proportional to GPP. Fresp, Fff, and Flanduse are unidirectional CO2 fluxes from stem and soil respiration, fossil fuel combustion, and land use, respectively. Analogous equations were used to calculate MS and Δ17OS.
Table 2 lists the estimated magnitude of each Qj, its NH:SH ratio, and its Δ17Oj value used in the “base” model scenario, while Table 3 lists sensitivity tests. The carbon budget for (2) is chosen to be that for the 1990s, with dM/dt = 3.2 PgCyr−1, and [CO2]0A = 370 ppm. The annual stratosphere-troposphere carbon exchange fluxes for each hemisphere, FSAN,S and FASN,S, are the products of air mass fluxes from Appenzeller et al.  and the tropospheric CO2 concentration, [CO2]A, calculated from MN and MS. This prescribes a stratospheric CO2 mixing ratio, [CO2]S, equal to [CO2]A; a time lag between [CO2]S and [CO2]A of 1–2 years does not change the carbon budget nor Δ17ON,S significantly. The fossil fuel flux Fff is 6 PgCyr−1, with 96% in the NH [Marland et al., 2003]. Land use modification is assumed to occur mainly in the tropics, with Flanduse ∼ 1.6 PgCyr−1 split evenly between the NH and SH [Schimel et al., 2001]. The gross CO2 flux to the ocean is calculated at each timestep as FAO = 90 PgCyr−1 × [CO2]A(t)/[CO2]0A. A constant net ocean sink of 2 PgCyr−1 is assumed and therefore FOA(t) = FAO(t) − 2. FAO and FOA are divided between the hemispheres using the partitioning of net ocean fluxes from the mean of the TransCom3 models [Gurney et al., 2003].
Table 2. Carbon Sources and Sinks (Qj) Controlling Δ17OA
 The background equilibrium terrestrial biosphere is represented by net carbon assimilation during photosynthesis (A) balanced by stem and soil respiration (A0 + Fresp0 = 0). Here A is the difference between CO2 to and from leaves (A = FAL + FLA) with the fluxes given by:
(6) and (7) follow from Farquhar and Lloyd  and Ciais et al. ; Cc and Ca are the CO2 concentrations in the chloroplasts and the atmosphere. Typical values for the Cc/Ca ratio are 2/3 for C3 plants and 1/3 for C4 plants [Pearcy and Ehleringer, 1984], with the assumption that Cc ∼ Ci, the intracellular [CO2]. The leaf flux estimates in Table 2 assume a global annual magnitude for GPP of 100 PgCyr−1 [Cramer et al., 1999]. The hemispheric distribution of GPP is assumed to be the same as that for net primary production (NPP) calculated by the terrestrial biogeochemistry model CASA [Randerson et al., 1997]. We assume that plants use 12% of GPP as leaf respiration [Ciais et al., 1997] so that A0 is 88 PgCyr−1. The global distribution of C3:C4 plant coverage is from Still et al. . Furthermore, isotope equilibration between CO2 and H2O in chloroplasts is incomplete. We therefore partitioned FLA into equilibrated (FLA_eq = Θ × FLA) and non-equilibrated fluxes, with the degree of equilibration (Θ) for C3 and C4 plants of 0.93 and 0.38, respectively [Gillon and Yakir, 2000]. We assumed that the land sink of 2.4 PgCyr−1 required to balance the contemporary carbon budget is due to enhanced GPP, with A(t) = A0 × [CO2]A(t)/[CO2]0A, and Fresp(t) = A(t) − 2.4. As Δ17OA is influenced by gross fluxes, our calculations show that assigning the net land sink to retarded respiration has little impact on Δ17OA (not shown).
 Solving (4) requires values for Δ17Oj for each carbon flux. Fluxes leaving the troposphere (FAS, FAO, FAL) carry the isotopic value of the troposphere (Δ17O = Δ17OA) and therefore do not contribute to (4). For the stratosphere-to-troposphere flux, Δ17OS was estimated using Δ17OA and an initial net Δ17OCO2 flux of 42.9‰PgCyr−1 [Boering et al., 2004]. Δ17Oj for the surface fluxes to the atmosphere, FOA, FLA_eq, and Fresp, are assumed to be zero since the CO2 is equilibrated with mass-dependently fractionated water pools. The non-equilibrated CO2 flux, (1 − Θ) × FLA, exits the leaf with an unchanged tropospheric Δ17OA. Δ17O for fossil fuel CO2 is assumed to be that for atmospheric O2 (Δ17OO2 = −0.155‰ [Luz et al., 1999]), as in δ18O modeling [Ciais et al., 1997]. Finally, processes that contribute to Flanduse are assumed to produce CO2 with Δ17O = 0.
3. Results and Discussion
 The base scenario was run for 50 yrs. The magnitude of each CO2 isotope source term in (4), calculated as (Δ17Oj − Δ17OA) × Qj, is plotted in Figure 1a, showing the dominance of the stratospheric input and terrestrial biospheric exchange in determining Δ17OA. After a 20-year spin-up, the model yielded a small but measurable global average tropospheric value for Δ17OA = 0.50 × (Δ17ON + Δ17OS) of 0.14‰ with very small hemispheric differences (Figure 1b and Table 3). The modeled trend and Figure 1a indicate that the increasing isotope flux of Δ17OCO2 > 0 from the stratosphere due to increased CO2 mixing ratios (FSA) has a larger impact on tropospheric Δ17OCO2 than the fossil fuel isotope flux with Δ17OCO2 < 0. Also, FLA, Fresp, and FOA dilute tropospheric Δ17OCO2. Thus, any trend in tropospheric Δ17OCO2 could not be predicted from the Suess effect for 13C and 14C for which the addition of fossil fuel CO2 acts as a dilution.
 Results of sensitivity tests are given in Table 3. The sensitivity of Δ17OA to the strat-trop air mass flux and to uncertainty in the net strat-trop isotope flux resulted in changes in Δ17OA of <0.01‰ and ∼0.04‰, respectively. Assuming complete equilibration of retro-diffused CO2 for both C3 and C4 plants or including a soil invasion flux of 4.4 PgCyr−1 [Stern et al., 2001] both decreased Δ17OA by <0.01‰. Changing dM/dt from 2 and 4 PgCyr−1 had no significant effect. Finally, varying GPP by ±10% and ±50% yielded changes in Δ17OA of ±0.01‰ and −0.04/+0.08‰, respectively. For comparison, interannual variations in GPP over the past 40 years are predicted to be on the order of ±5% while uncertainty in the absolute magnitude of global GPP is as large as ±50% [Schaefer et al., 2002; K. Schaefer, personal communication, 2004].
 Based on these initial modeling results, we conclude the following. First, we predict that tropospheric Δ17OCO2 is small but measurable by current techniques (with precisions of ∼0.1‰ [e.g., Boering et al., 2004]). Second, we predict that any Δ17OCO2 trend in the troposphere is dominated by the increasing flux of Δ17OCO2 from the stratosphere and by the terrestrial biosphere, with a smaller contribution from the oceans, and not by fossil fuel burning. Therefore, the largest changes in a tropospheric time series for Δ17OCO2 should result from variations in the terrestrial gross fluxes. Third, measurements and modeling of a global average value for tropospheric Δ17OCO2 can serve as a new constraint for GPP and ecosystem respiration in carbon isotope models by providing an average value for Δ17OCO2 that should be consistent with δ18OCO2 yet is independent of δ18OH2O. Fourth, these model results provide motivation and a benchmark for challenging yet feasible improvements in measurement precision that will allow the full potential of Δ17OCO2 as an independent tracer of the magnitude and variability of gross carbon exchanges to be realized. Fifth, since tropospheric Δ17OCO2 is predicted to be small, future work should include small variations in the mass-dependent fractionation factors for isotope exchange with H2O since a difference between the value for λ used in (1) and a slightly different λ resulting from isotope exchange with water reservoirs [e.g., Angert et al., 2003] could lead to an apparent non-zero Δ17OCO2. Sixth, these modeling results may aid in the interpretation of the time series of Δ17OCO2 measurements from La Jolla, CA and the NOAA/CMDL flask network (M. Thiemens, personal communication, 2004).
 Support from NSF (ATM-0096504), the David and Lucile Packard Foundation, and a NASA Earth System Science Fellowship (KJH) and suggestions from an anonymous reviewer are gratefully acknowledged.