We present a global model to infer past biosphere productivity using the record of triple isotopic composition of atmospheric oxygen. Our model incorporates recent determinations of the mass-dependent relationships between δ17O and δ18O associated with leaf transpiration and various O2 uptake processes. It also considers the spatial and seasonal variations of vegetation distribution, climatic conditions, and isotopic composition of meteoric water. On the basis of this model, we provide global estimates for the Last Glacial Maximum (LGM) and the present of (1) the triple isotopic composition of leaf water, (2) isotopic fractionation factors for terrestrial dark respiration in soils and in leaves as well as total terrestrial respiration, (3) relationships between δ17O and δ18O associated with terrestrial biological steady state, and (4) 17O anomalies issued from both the terrestrial and oceanic biospheres. Using these data and the vegetation distribution simulated by the ORCHIDEE model, we estimated that the rate of global biological productivity during the LGM was 60–75% of the present rate. Our value for the LGM is at the lower end of previous estimates and suggests that the rise in biosphere productivity since the last glacial is larger than previously thought.
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 Among the main processes that affect global climate changes are the interactions between the atmosphere and biosphere. Climatic conditions control biosphere production and, in turn, vegetation strongly influences climate through the emission and consumption of greenhouse gases and through the terrestrial albedo. The only way to understand these interactions is to depict the past climate changes and the related biosphere evolution. While many different proxies exist that allow for reconstruction of past climates, our knowledge about the past biosphere remains very sketchy.
 For the most part, past biosphere evolution is inferred from local studies of terrestrial and marine sediments. An important representative property of the past biosphere, which is extensively measured in the ocean, is paleoproductivity [e.g., Kohfeld et al., 2005]. These studies, however, give information only on local variations in biosphere productivity, and much effort in data compilation is needed to infer the evolution of biosphere productivity at the global scale.
 The triple isotopic composition of atmospheric oxygen is an additional tracer that reflects global oxygen biosphere productivity [Luz et al., 1999]. This is because oxygen in the lower atmosphere is exchanged with the terrestrial and oceanic biosphere through photosynthesis and respiration, and with the stratosphere through mixing of tropospheric and stratospheric air. While O2 fluxes associated with biosphere productivity modify the isotopic composition of atmospheric oxygen through mass-dependent fractionation (change in 17O/16O is about 0.52 of the change in 18O/16O), stratospheric oxygen is fractionated in a mass-independent way (change in 17O/16O roughly equals the change in 18O/16O) through photochemical reactions with ozone [Thiemens et al., 1991; Bender et al., 1994; Luz et al., 1999]. As a result, atmospheric O2 becomes depleted in 17O in comparison to O2 affected by biology alone. The magnitude of this depletion depends on the relative proportions of the oxygen fluxes associated with biosphere productivity and with the stratosphere exchange. In turn, records of past changes in the triple isotope ratios enable one to infer variations in past biosphere productivity.
 One of the major climatic changes documented in numerous studies is the last deglaciation, and thus this presents a highly important challenge to determine the productivity over this period. Luz et al.  and Blunier et al.  measured the triple isotopic composition of O2 in the past atmosphere from air trapped in ice cores. On the basis of these data, Luz et al.  presented a rough mass balance of three oxygen isotopes in the biosphere, stratosphere and lower atmosphere and provided a first estimate of the ratio between the Last Glacial Maximum (LGM) and the present-day oxygen biosphere productivities as 90%. Blunier et al.  refined the method and estimated LGM paleoproductivity as 76–83% of the present value.
 In their model, Blunier et al.  took into account the influence of every process associated with oxygen production and consumption on the oxygen fractionation. In the absence of precise determinations of the mass-dependent relationships between δ17O and δ18O associated with these processes, they assumed that the same relationship applies to all the different processes. However, recently developed analytical capabilities for precise measurements of the triple isotopic composition of oxygen in O2 and in H2O [Barkan and Luz, 2003, 2005] have made it possible to show significant differences in the relationships between δ17O and δ18O for the different mass-dependent processes affecting atmospheric O2 [Angert et al., 2003a; Helman et al., 2005; Landais et al., 2006]. These differences influence the triple isotopic composition of O2 and, as shown by Angert et al. [2003a], at least 15% of the changes in the triple isotopic composition of oxygen in the past atmosphere should be related to the variations in these relationships among different respiration mechanisms. Taking into account other processes involved in biosphere productivity, the influence on the triple isotopic composition of O2 can be even greater.
Blunier et al.  also used for their calculation spatial and temporal averages for climatic conditions, land vegetation cover and isotopic composition of meteoric water during the different climatic periods. However, Hoffmann et al.  showed that the spatial and seasonal variations of these parameters significantly affect the isotopic composition of atmospheric O2 produced by the biosphere, and should be also considered in correct estimations of past biosphere productivity. Therefore the estimate of the LGM oxygen biosphere productivity obtained by Blunier et al.  may not be adequate.
 In the present work we describe a complete three oxygen isotopes mass balance model for atmospheric oxygen that takes into account the recently determined mass-dependent relationships between δ17O and δ18O in the biosphere and in leaf water, as well as the spatial and seasonal variations of climatic conditions, land vegetation cover and isotopic composition of meteoric water. On the basis of this model we recalculated the ratio between the LGM and the present-day oxygen biosphere productivities.
where δ*O = (*R/*Rref − 1) (the factor 1000 is omitted but the δ*O values are reported in ‰) and λ is the slope of a line of mass-dependent fractionation on a ln(δ17O + 1) versus ln(δ18O + 1) plot.
 As in previous studies [Luz and Barkan, 2000, 2005; Angert et al., 2003a], we report the extent to which an O2 sample is enriched in 17O with respect to the present atmosphere (atm, PST). For the calculation of 17Δ we use the reference slope λ corresponding to ordinary respiration, the most widespread biological mass O2 consumption mechanism. In the present study we assume that atmospheric oxygen is at steady state; that is, photosynthesis equals respiration. In this case, λ equals 0.516 [Angert et al., 2003a; Luz and Barkan, 2005]. By definition, the anomaly of the present atmosphere (17Δatm,PST) equals 0.
3. Budget of the Triple Isotopic Composition of Atmospheric Oxygen
 The 17O anomaly of oxygen in the atmosphere, 17Δatm, results from an oxygen isotopic balance between two important global processes: mass-dependent biospheric O2 production and mass-independent stratospheric photochemistry involving O2, O3 and CO2 [Luz et al., 1999],
where 17Δstrat and 17Δbio are the 17O anomalies of the stratospheric O2 flux (Fstrat) and the biospheric O2 flux (Fbio), respectively.
 The ratio of the oxygen biosphere productivity between the LGM and the present is calculated from equation (2) as
where subscripts bio, strat, atm, PST and LGM stand for total biosphere, stratosphere, lower atmosphere, present day and LGM, respectively. By definition (section 2) 17Δatm,PST = 0, whereas 17Δatm,LGM was determined by Blunier et al.  as +43 permeg (note that the original value of Blunier et al. is +38 permeg since it was calculated with λ of 0.521, instead of 0.516 accepted in the present study as a reference slope). Following Luz et al. , we assumed that the ratio of the production rates of anomalously depleted O2 in the stratosphere, Fstrat × (17Δstrat − 17Δatm), between the LGM and the present is proportional to the ratio of atmospheric CO2 concentrations between the LGM and the pre-industrial Holocene. Then, using CO2 concentrations of 280 ppmv for the pre-industrial Holocene and 190 ppmv for the LGM [Barnola et al., 1987], equation (3) becomes
 The quantification of past biosphere productivity from the triple isotopic composition of oxygen in the atmosphere is therefore highly dependent on the change in atmospheric concentration of CO2 and on the precise knowledge of the triple isotopic composition of oxygen produced by the biosphere, 17Δbio, for the present and the LGM. Both ocean and land biospheres contribute to the global oxygen productivity so that 17Δbio is the weighted average of 17Δ issued from the oceanic biosphere, 17Δocean, and the terrestrial biosphere, 17Δterr,
where FO and FT are the oxygen fluxes associated with the oceanic and terrestrial productivities.
 In order to estimate 17Δocean for the LGM, we assumed that the fractionation during O2 uptake was the same during the LGM and the present. Therefore any change in 17Δocean between the LGM and the present is only due to the shift in the isotopic composition of the global ocean. The decrease of the ice sheet volume between the LGM and the present induced a decrease of 1‰ of the mean ocean δ18O [Waelbroeck et al., 2002]. The triple isotopic composition of ice and seawater falls on the meteoric water line of slope 0.528 in a ln(δ17O + 1) − ln(δ18O + 1) plot [Meijer and Li, 1998; Barkan and Luz, 2005]. Thus the change of δ18O by 1‰ is reflected by a change of 0.53‰ in δ17O of the mean global ocean. These changes in δ17O and δ18O of the ocean are directly transmitted to the δ17O and δ18O of O2 produced by oceanic photosynthesis.
5. Estimate of 17Δterr
 We estimated global 17Δterr for the present and for the LGM in the following way. According to equation (1), 17Δterr is defined as
where 18Rterr and 17Rterr are the isotopic ratios of O2 produced by the terrestrial biosphere. These ratios depend on the fractionation during oxygen uptake and on the isotopic composition of the substrate water for photosynthesis, i.e., leaf water. As in previous studies [Bender et al., 1994; Blunier et al., 2002; Hoffmann et al., 2004], we consider a steady state so that the flux during oxygen uptake is balanced by the corresponding O2 flux released during photosynthesis. In this case, Rterr can be calculated as
where “*” stands for 17 or 18, *Rlw is the global isotopic composition of leaf water, and *αterr stands for the global effective isotope fractionation factor associated with oxygen uptake. These two terms are estimated separately below.
5.1. Global Isotopic Composition of Leaf Water
 The most recent estimate of present global leaf water δ18O (6–8‰) was obtained by Gillon and Yakir . For the LGM, Blunier et al.  assumed that global δ18Olw has the same value as the present-day one. However, owing to the variations in climatic conditions and isotopic composition of the meteoric water consumed by plants between LGM and today, this assumption is not justified. Thus we redetermined global δ18Olw for the LGM. We estimated this value from the worldwide distributions of δ18Olw and photosynthetic O2 flux. We multiplied for each region the local δ18Olw by the local O2 flux, then summed the values for each region and normalized the final value by the global terrestrial photosynthetic O2 flux.
 The local δ18Olw were obtained using the Craig and Gordon  expression of evaporation applied to leaf water [Dongmann et al., 1974; Flanagan et al., 1991]. The Craig and Gordon approach states that δ18Olw depends on the isotopic composition of meteoric water, water vapor, relative humidity and temperature. From the latitudinal and seasonal variability of these input parameters (Appendix A), we produced monthly maps (2° × 2°) of δ18Olw. In Figures 1a and 1b we present the mean annual values of δ18Olw for the present and the LGM conditions. As can be seen, the spatial distribution of δ18Olw for both periods is roughly similar.
 The repartition of the photosynthesis fluxes was estimated as follows. Because vegetation is considered at steady state, the photosynthesis flux is equal to the sum of all O2 uptake fluxes, i.e., of dark respiration, photorespiration and the Mehler reaction. Then, as detailed by Hoffmann et al. , the worldwide repartition of the O2 fluxes can be calculated from the distribution of the terrestrial Gross Primary Production (GPP), expressed in terms of carbon flux, and the distribution of the different plant types on Earth. Indeed, the proportion of plant types (C3, C4) greatly influences the rate of photorespiration and therefore the relationship between carbon and O2 fluxes. As a rule, while C3 plants photorespire, C4 plants, under normal circumstances, do not. Moreover, the photorespiration flux varies among the different types of C3 plants. Thus, depending on the C3/C4 distribution, the repartition of O2 fluxes can be significantly different from the one of carbon fluxes.
 We obtained the worldwide repartition of the GPP per unit surface for different biomes using the new dynamic global vegetation model ORCHIDEE (Organizing Carbon and Hydrology in Dynamic Ecosystems) integrating the most recent parameterizations of vegetation dynamics [Krinner et al., 2005] (Appendix B). In this model, the variety of the biomes is expressed through 12 different plant functional types (PFT): two PFTs stand for the C4 plants and ten for the C3 plants. The competitive balance between C4 and C3 plants is driven by the growing season temperature and humidity as well as by CO2 level.
 In Figures 2a and 2b, we present the total GPP (i.e., integrating the contribution of the 12 plant species) for present day and the LGM. As can be seen, there is a considerable decrease of GPP over the high latitudes in the Northern Hemisphere during the LGM due to the presence of large ice sheets. Thus the global δ18Olw, which is transmitted to the atmospheric oxygen by photosynthesis, is less influenced by the high latitudes during the LGM than at present.
 In Figures 3a and 3b we show the distribution of the relative productivity of C4 plants for the present and the LGM, i.e., the distribution of the ratio between the GPP of C4 plants and the total GPP, obtained by the ORCHIDEE model. The high relative productivity of C4 plants in the LGM over Africa, Australia and South America implies a decrease of the O2 flux over these regions due to low photorespiration. As a result, these regions had a relatively small influence on the global δ18Olw. The distribution of the relative productivity of C3 plants can be directly derived from the maps on Figures 3a and 3b, since the sum of the relative productivities of both C3 and C4 plants equals one by definition.
 Lastly we calculated the global δ18Olw values as 7.0‰ and 8.0‰ for present day and LGM, respectively. The value for present day falls in the middle of the range proposed by Gillon and Yakir . The ∼1‰ difference between the two periods is mainly due to the increase of the oxygen flux in the high latitudes between the LGM and present day owing to the reduction of the ice sheets (Figures 2a and 2b). Indeed, the plants consume meteoric water with a relatively low δ18O in the high latitudes [Edwards et al., 2002] such that δ18Olw is accordingly depleted (Figures 1a and 1b). Therefore an increase of the O2 flux from the high latitudes vegetation results in a decrease of the global δ18Olw.
 Until now there was no determination of leaf water δ17O and the estimate of a global leaf water δ17O for present day and the LGM was not possible. However, a recent study [Landais et al., 2006] performed the first measurements of leaf water δ17O over a various range of environmental conditions. They showed that the local δ17O of leaf water may be calculated from the triple isotopic composition of oxygen in meteoric water and leaf water δ18O, as
where the subscripts “lw” and “mw” stand for leaf water and meteoric water, respectively, and λtranspi depends on the relative humidity, h, as [Landais et al., 2006]
when h is between 32 and 100%. For the very few regions with a relative humidity less than 32%, we assumed that λtranspi is equal to 0.519. The δ17Omw is deduced for the given δ18Omw using the slope of 0.528 for the meteoric water line [Meijer and Li, 1998; Barkan and Luz, 2005].
 Using equations (8) and (9), we derived monthly maps of δ17Olw for present day and the LGM as it was done for δ18Olw. Spatial and temporal integrations led to global δ17Olw values of 3.5‰ for present day and 4.1‰ for the LGM (Table 1).
Table 1. Estimates for the Present and the Last Glacial Maximum of the Different Parameters Involved in the Calculation of the Triple Isotopic Composition of Oxygen Issued From the Biospherea
PST, present; LGM, Last Glacial Maximum. Uncertainties are given for most of the parameters except for those derived from the ORCHIDEE model (see text).
Note that in work of Helman et al.  the slope is given as λ = (17α − 1)(18α − 1) for the one-way oxygen uptake processes. Here we deal with steady state (combination of O2 uptake and mixing with photosynthetic O2) so that λ = ln(17α)/ln(18α) (details given by Luz and Barkan ).
5.2. Global Terrestrial Isotope Fractionation Factor
 We define the global isotope fractionation factor during terrestrial oxygen uptake by vegetation, αterr, as the fractionation coefficients associated with the different O2 uptake pathways (photorespiration, Mehler reaction, dark respiration in soil and in leaves) and express it as
where “*” is 17 or 18; αphotor, αMehler, αdark_soil and αdark_leaves are the isotope fractionation factors associated with photorespiration, Mehler reaction and dark respiration in soil and in leaves, and fphotor, fMehler, fdark_soil and fdark_leaves are the corresponding fractions of the oxygen respiratory fluxes (fphotor + fMehler + fdark_soil + fdark_leaves = 1).
Blunier et al.  obtained values for 18αterr of 0.9811 and 0.9809 for the present and the LGM, respectively. For this calculation they used a value for 18αMehler of 0.9849 obtained by Guy et al.  while Helman et al.  recently estimated it to be 0.9892. They also assumed a constant value for discrimination associated with dark respiration both in the soil and in the leaves as 0.982. However, Angert et al. [2003b] showed that the in situ 18O discrimination associated with soil respiration is considerably weaker than in leaves and that the discrimination in soil varies between 10‰ and 22‰ among different vegetation types and, accordingly, among the different climatic regions. Thus we recalculated the values of 18αterr taking into account the recent results by Angert et al. [2003b] and Helman et al.  (Table 1; see details of calculations in Appendix C). The new values for the global 18αterr are 0.9826 and 0.98306 for present day and for the LGM, respectively.
The corresponding values of 18α and λ as well as the resulting 17αterr are given in Table 1.
 Finally, we obtained λterr as 0.5145 for present day and 0.5156 for the LGM. Sensitivity tests showed that the main uncertainty in λterr (0.0006–0.0007) is linked to the uncertainties in the slopes λ for the different processes [Helman et al., 2005]. The other parameters included in equations (10) and (11) would modify λterr by less than 0.0002. It should be mentioned that, at first glance, λterr for present day and the LGM are statistically identical. However, because in the calculation of λterr for present day and the LGM the same values of λ are used for different processes, any increase/decrease of their values leads to a parallel increase/decrease of λterr for both present day and the LGM. Therefore the calculated decrease of λterr by 0.001 over the deglaciation is a firm result. It is a direct consequence of the larger fraction of C4 plants during the LGM than the present (Figures 3a and 3b); with more C4 plants the fraction of photorespiration associated with a low triple isotope slope (0.509) decreases and the resulting mean slope, λterr, increases.
6. Input Parameters
 In Table 1 we summarize all model parameters used in the calculations. The values for some of the parameters were taken from the literature, while the others were obtained in the present study.
7. Results and Discussion
7.1. The 17O Anomalies for Present Day and LGM
 Using the model presented above, we calculated 17Δocean for the LGM and 17Δterr for the present and the LGM as 261, 110 and 140 permeg, respectively. The associated uncertainties are detailed below.
 For 17Δterr our most disputable parameterization choice was the relationship used to infer humidity and temperature during photosynthesis (Appendix A). A change in humidity by 5% leads to 18O enrichment of the global leaf water by 1‰ or more. Thus for the present day the calculated δ18Olw becomes higher than 8‰, which is in disagreement with the data of Gillon and Yakir . Therefore we consider 5% as the maximum uncertainty associated with humidity. Sensitivity tests have shown that such change in humidity affects 17Δterr only by 4 permeg. For temperature, modifications by 3°C, corresponding to the maximal uncertainties in classical temperature reconstructions (http://www.ncdc.noaa.gov/paleo/recons.html), lead to changes in 17Δterr that are less than 4 permeg.
 Another important assumption in our model concerns the fraction of the Mehler reaction in the total flux of oxygen into the biosphere. As the slope of the biological steady state associated with the Mehler reaction is relatively high, a change in the proportion of the Mehler reaction will increase/decrease the 17Δterr. We realize that the value of 0.1 given by Bader et al.  is not necessarily representative of the global terrestrial biosphere but, to the best of our knowledge, there are no other estimates of this parameter. Sensitivity tests showed that the variations up to 70% in fMehler lead to an uncertainty of 10 permeg in 17Δterr, which corresponds to the usual analytical precision [Barkan and Luz, 2003, 2005].
 Lastly, the accuracy of 17Δterr depends on the correctness of different slopes, λ, which are usually determined with a precision around 0.001 (Table 1). These uncertainties introduce a total error in 17Δterr of ∼20 permeg.
 We did sensitivity experiments modifying randomly the relationships used to obtain temperature and relative humidity, the proportion of the Mehler reaction and the slopes of the different processes involved in the terrestrial biosphere productivity (the other uncertainties presented on Table 1 have negligible effects on 17Δterr) and found that the maximal error for 17Δterr is 35 permeg. This uncertainty is relatively high, but it should be mentioned that when we modify any basic assumption in our model, we shift in a similar way both 17Δterr,LGM and 17Δterr,PST so that the difference between them, 30 permeg, remains constant.
 The uncertainty in 17Δocean,LGM results from the uncertainties in the LGM global sea level δ18O and 17Δocean,PST. The uncertainty associated with the first term is less than 0.1‰, and has a negligible effect on 17Δocean, LGM. Thus 17Δocean,LGM has the same uncertainty as 17Δocean,PST. This means that if 17Δocean,PST is over(under)estimated by 15 permeg, the same applies to 17Δocean,LGM, and the difference between 17Δocean,PST and 17Δocean,LGM remains constant as 12 permeg.
 Our discussion does not include the uncertainties associated with the ORCHIDEE model, which are very difficult to estimate as with every biosphere model. However, outputs of this model show a good agreement with the present vegetation [Krinner et al., 2005]. Furthermore, Lathiere  did a detailed comparison between available vegetation paleodata [Ray and Adams, 2001] and ORCHIDEE outputs for the LGM. It was shown that although the PFT of ORCHIDEE are based on present-day vegetation, there is a good agreement between maps of LGM vegetation obtained from the model and from paleodata.
 As stated in section 3.1 (equation (5)), 17Δbio varies with the relative proportions of oceanic to terrestrial oxygen productivities. For present day, FO/FT was given within the range of 0.45 to 0.59 by several authors [Bender et al., 1994; Blunier et al., 2002; Hoffmann et al., 2004]. For the LGM we used the ORCHIDEE model and found that FT was 54% of the present-day value. From two other terrestrial biosphere models (CARAIB [Francois et al., 1998] and BIOME [Haxeltine and Prentice, 1996]), Blunier et al.  found that FT during the LGM was 50–80% of the present value. On the basis of these results, we accepted 50–80% as the maximum range of FT variations between the LGM and the present day. To evaluate the oceanic fluxes FO, we assumed that FO varied proportionally to oceanic productivity. While Bopp et al.  found no change in oceanic productivity between the LGM and the present, G. Hoffmann and E. Maier-Reimer (personal communication, 2006) modeled oceanic productivity that was 20% higher in the LGM than the present. The latter result is in agreement with the reviews by Bender et al.  and Kohfeld et al. , suggesting a worldwide decrease of the oceanic productivity and export production between the LGM and present day. Because the accuracy of each estimate is subject to discussion, we used both of them as extreme values in our study. Finally, on the basis of different values of FT,LGM/FT,PST and FO,LGM/FO,PST, we obtained the ratio FO/FT for the LGM as a function of the ratio FO/FT for the present. FO,LGM/FT,LGM varies between 0.56 and 1.41 (Table 2).
Table 2. The 17Δbio for the LGM and Present Day (PST) and the Resulting Ratios Fbio,LGM/Fbio,PSTa
 It should be mentioned that it is tempting to use the Dole effect approach for estimating the change in FO/FT between the present and the LGM [e.g., Bender et al., 1994; Hoffmann et al., 2004]. According to this approach the magnitude of the Dole effect should decrease as FO/FT increases. However, the magnitude of the Dole effect during the LGM was similar to the present value [Bender et al., 1994; Malaizé et al., 1999], despite ample evidence for considerable change in terrestrial primary productivity. As discussed by Hoffmann et al.  the magnitude of the Dole effect depends, in addition to FO/FT, also on other factors such as latitudinal shifts in precipitation that resulted in different δ18O of meteoric water used by the terrestrial vegetation in the temperate zone. Therefore we cannot use the change in the Dole effect as a measure of the FO/FT difference between the present and the LGM.
 Values of 17Δbio for present day and the LGM were calculated using equation (5). As can be seen, the uncertainties in 17Δbio depend on uncertainties in the FO/FT ratio, 17Δterr and 17Δocean. In Table 2 we present estimates of 17Δbio obtained for the maximum and minimum values of FO/FT, taking into account the maximum uncertainties in 17Δterr and 17Δocean. It is important to note that the uncertainties in 17Δbio,LGM and 17Δbio,PST are not independent because, as discussed above, 17Δterr,LGM is always 30 permeg higher than 17Δterr,PST and 17Δocean,LGM is 12 permeg higher than 17Δocean,PST. We end up with a present-day estimate of 17Δbio of 124–189 permeg for present and 156–234 permeg for the LGM.
 As can be seen from Table 2, there is a general decrease of 17Δbio between the LGM and present day. With the aim of understanding the cause of this phenomenon, we present a scheme in Figure 4 that explains how the temporal variation of 17Δbio results from the difference in the relationships between δ17O and δ18O among the various processes, and from the spatial repartition of vegetation and isotopic composition of meteoric water.
 We first focus on the anomaly associated with the oceanic biosphere, 17Δocean. Point A accounts for the isotopic composition of the global ocean today. From this point, production of O2 by photosynthesis and marine respiration at the biological steady state leads to point B, representing the isotopic composition of oxygen issued from the ocean and characterized by a 17Δocean of 249 permeg [Luz and Barkan, 2000]. For the LGM, the larger ice sheets imply that δ18O of the global ocean at LGM is 1‰ higher than the present-day oceanic δ18O [Waelbroeck et al., 2002], and thus point A is shifted to point A′. This shift is driven along the meteoric water line of slope 0.528, i.e., larger than 0.516, so that 17Δ in point A' is greater than in point A. Since we assume no change in the slope of the oceanic biological steady state between the LGM and present day (section 4), the shift from A to A′ is reflected by a similar shift from B to B′, the point representing the isotopic composition of oxygen issued from the ocean at LGM. As a result, 17Δocean,LGM is larger than 17Δocean,PST by 12 permeg.
 We now concentrate on the anomaly associated with the terrestrial biosphere, 17Δterr. The mean annual meteoric water isotopic composition consumed by the plants is shown by point C. From this point, transpiration in leaves leads to the isotopic composition of leaf water represented by point D. We estimated the mean slope of this line (CD) for present-day conditions as 0.517. From point D, production of O2 by photosynthesis and oxygen uptake leads to point E, representing the isotopic composition of oxygen emanating from the terrestrial biosphere and characterized by a 17Δterr of 110 permeg today. The slope of the line (DE) is influenced by the relative proportions of the different respiration processes (section 5.2 and Table 1). For present-day conditions we calculated the mean slope associated with terrestrial biological steady state, λterr, as 0.514.
 During the LGM, the ice sheets extent reduces the biosphere productivity in the high latitudes (Figures 2a and 2b). These regions are associated with low δ18O of the meteoric water [Edwards et al., 2002] and therefore the ice sheet extent leads to an increase of the mean δ18O of meteoric water consumed during photosynthesis for the LGM as compared to present day. Using the spatial and seasonal repartition of oxygen fluxes associated with photosynthesis (section 5.1) and of the meteoric water δ18O for both the LGM and present day, we calculated this increase as 1.2‰. By definition, C lies on the meteoric water line with the slope 0.528 [Meijer and Li, 1998]. Thus the corresponding change of δ17O shifts point C to C' along the line with a slope higher than 0.516, and this results in an increase of 17Δterr by ∼15 permeg.
 We then evaluated the mean relative humidity during photosynthesis through a spatial and annual weighted average by the oxygen biosphere productivity and found that this mean relative humidity was not considerably different in the LGM than at present. Therefore the slope of the line accounting for the leaf transpiration process is roughly the same for the LGM and present day, and the change in the leaf water isotopic composition from D to D′ mainly reflects the shift from C to C′. Finally, the contribution of C3 plants to the total biosphere productivity is far less important during the LGM than the present (Figures 3a and 3b) and, despite the higher photorespiration of these plants during the LGM compared to today, the total effect is that the photorespiration flux is lower during the LGM than today. Because photorespiration is associated with a relatively small slope (0.509), the slope of the line accounting for global terrestrial biological steady state during the LGM (D′E′) is larger than the one accounting for present-day conditions (DE). This leads to an additional increase of 17Δterr,LGM (point E′) with respect to 17Δterr,PST (point E) by another 15 permeg.
7.2. Increase in Global Plant Productivity Since the LGM
 On the basis of the obtained 17Δbio in the LGM and the present, we calculated using equation (4) the rate of global biological productivity during the LGM as 60–75% of the present rate (Table 2).
Blunier et al.  with their model for interpreting the triple isotopic composition of oxygen, obtained that Fbio,LGM is 80 ± 4% of Fbio,PST. Note that the given uncertainty only accounts for the uncertainty of FT,LGM/FT,PST. As discussed above, these authors used the same slope for the different relationships between δ17O and δ18O associated with biosphere productivity, and this assumption leads to a 4% overestimation of the ratio Fbio,PST/Fbio,LGM. In addition, Blunier et al. did not consider the seasonal and spatial distributions of vegetation and isotopic composition of meteoric water between the LGM and present day. Our calculations showed that this simplification can explain another part of the overestimation of Fbio,PST/Fbio,LGM obtained by these authors.
 The LGM productivity obtained in the present study is at the lowest end of the previous estimates from different oceanic [Bopp et al., 2003; G. Hoffmann and E. Maier-Reimer, personal communication, 2006] and terrestrial (BIOME, CARAIB, ORCHIDEE) biosphere models: 65–95%. It thus suggests that the change in the global biosphere over the last deglaciation was larger than previously thought.
 Finally, our constraint on the LGM biosphere productivity can be used as an additional and independent tool to test the numerous vegetation models recently developed [e.g., Francois et al., 1998; Friedlingstein et al., 1992; Kaduk and Heimann, 1996; Krinner et al., 2005]. Until now, such models were tested through a comparison between the simulated change of vegetation over the deglaciation and local paleodata of vegetation [e.g., Ray and Adams, 2001; Harrison and Prentice, 2003]. Here we propose comparing the changes in biosphere productivity over the deglaciation obtained from our budget of three oxygen isotopes and the one calculated by biosphere models. As an illustration, the ORCHIDEE, BIOME and CARAIB models give values for Fbio,LGM/Fbio,PST of 0.72 ± 0.05, 0.70 ± 0.05 and 0.90 ± 0.05, respectively, assuming a ratio Focean,LGM/Focean,PST of 1.10 ± 0.1 as in our study [Bopp et al., 2003; G. Hoffmann and E. Maier-Reimer, personal communication, 2006]. Our estimate, 0.60–0.75, supports the use of the BIOME and ORCHIDEE models to study the interaction between biosphere and climate over the deglaciation.
 We have presented a global model to infer the past biosphere productivity from the record of the triple isotopic composition of atmospheric oxygen. This model incorporates the recently determined relationships between δ17O and δ18O in the biological and hydrological cycles as well as the spatial and seasonal variations of vegetation distribution, climatic conditions and isotopic composition of meteoric water. On the basis of this model, we provide the best possible global estimates for LGM and present day of: leaf water triple isotopic composition, isotopic fractionation factors for terrestrial dark respiration in soils and in leaves and total terrestrial respiration, relationships between δ17O and δ18O associated with terrestrial biological steady state, and 17O anomalies issued from the both terrestrial and oceanic biospheres.
 Using three oxygen isotope budget calculations and the vegetation distribution simulated by the ORCHIDEE model, we evaluated the global oxygen biospheric productivity of the LGM as 60–75% of the present value. Our result is based on using the ORCHIDEE model, and it is possible that new and more powerful vegetation models might require us to reconsider our conclusion. However, the 30 permeg difference in 17O anomalies between the LGM and the present is explained mostly by the different ice sheet extensions and the C3/C4 distributions. These differences between the LGM and the present are confirmed by paleodata [Ray and Adams, 2001; Clark and Mix, 2002], and we therefore do not expect a considerable change in the given value.
 Our value is at the lower end of previous estimates and suggests that the difference in biosphere productivity between the LGM and the present is larger than previously thought. The obtained result has an important implication for evaluating the performances of biosphere models. Further studies on the long-term records of the triple isotopic composition of atmospheric oxygen are necessary to better understand the link between climate and biosphere productivity over different climatic transitions.
Appendix A:: Input Parameters for Calculation of Leaf Water δ18O
A1. Source Water and Water Vapor δ18O
 The current distribution of δ18O in meteoric water has been mapped from the GNIP network [Edwards et al., 2002]. For the LGM, estimates of the isotopic composition of meteoric water are very rare except over the Polar Regions. Sparse local reconstructions suggest that the δ18O of meteoric water during the LGM was 2–4‰ lower than today in temperate Europe [von Grafenstein et al., 1999; Navarro et al., 2004] and similar to today in tropical America [Mora and Pratt, 2001; Chowdhury et al., 2004]. Jouzel et al.  modeled a worldwide repartition of δ18O in meteoric water for the LGM that is in agreement with the aforementioned available local data. We therefore used, for our LGM calculations, the map of meteoric water δ18O from Jouzel et al. .
 We calculated the difference in δ18O between the water vapor and the meteoric water with the atmospheric general circulation model, ECHAM, including the isotopes in the hydrological cycle [Hoffmann et al., 1998] for the LGM and for the present.
A2. Climatic Conditions: Temperature and Relative Humidity
 The present-day climate conditions (monthly mean relative humidity and temperature at 2 m) are based on climate forcing from CRU (Climate Research Unit, UK) with relative humidity corrected using ECMWF (European Centre for Medium-Range Weather Forecasts, UK) data. Concerning the LGM, monthly mean relative humidity and temperature are based on the present forcing corrected by the corresponding anomalies simulated with the LMDz (Laboratoire de Météorologie Dynamique) general circulation model [Harzallah and Sadourny, 1995] considering LGM atmospheric CO2 concentration [Poutou et al., 2004]. Note that the climatic fields issued from the last version of LMDz, traditionally used to force the ORCHIDEE mode, are very close to those simulated by the ECHAM model even at high latitudes where general circulation models often disagree.
 The aforementioned spatial fields of temperature and humidity are monthly averages and integrate night and day values. However, photosynthesis occurs only during the day, i.e., with a higher temperature and a lower relative humidity than the monthly averages. The isotopic composition of leaf water transmitted to the atmospheric oxygen hence corresponds to day conditions and not to monthly averages. In order to calculate temperature and humidity corresponding to day conditions from monthly averages, we followed the approach by Lloyd and Farquhar  and Hoffmann et al. . Leaf temperature during photosynthesis, Tl, was related to the monthly mean air temperature, Tm (in °C), through Tl = 1.05 × (Tm + 2.5). The mean humidity was obtained by multiplying the monthly average humidity by a coefficient, Ch, less than 1. Ch was adjusted to 0.85 so that the global mean annual average for our modeled leaf water δ18O matches the determination by Gillon and Yakir  who obtained a global leaf water δ18O between 6 and 8‰ for the present.
Appendix B:: GPP Distributions for Different Plant Species—ORCHIDEE Model
 The ORCHIDEE model considers 12 different plant functional types (PFT) among which two are C4 plants and ten are C3 plants. For the present, the vegetation distribution was prescribed with global maps based on the work by Loveland et al. , corrected by Ramankutty and Foley  and by Goldewijk  for crops and grasses. The repartition of the vegetation for the LGM resulted from a model simulation: It starts with bare soil and runs 500 years using the corrected LGM climate, orbital parameters and atmospheric CO2 until equilibrium is reached. Emerged land due to the sea level decrease was taken into account. The resulting worldwide repartition of vegetation shows a good agreement with observations for the present [Krinner et al., 2005] and with the compilation of paleodata for the LGM by Ray and Adams .
 The GPP per unit surface was determined for each grid point and each of the 12 PFT, through a coupled photosynthesis and water balance directly included in the ORCHIDEE model [Krinner et al., 2005]. Combining these results with the vegetation distribution, we calculated the distribution of the GPP for the 12 plant species. The distribution of the GPP for the C4 plants is then directly obtained by adding the GPP distributions of the two PFT standings for C4 plants. Similarly, adding the GPP distributions of the ten remaining PFTs gives the distribution of GPP for the C3 plants. Adding up both C3 and C4 plants gives the distribution of the total GPP.
Appendix C:: Calculation of 18αterr
 The calculation of 18αterr is done using equation (10); we outline below how we estimated each parameter involved in equation (10).
 Because there is no information on variations of fMehler among different plant species, we assumed that fMehler is independent of the spatial and seasonal distributions of vegetation. In the present study we followed Bader et al.  and took a constant fMehler of 0.1. In contrast, fphotor depends on the type of vegetation cover (especially on the ratio of C3/C4 plants). The worldwide distribution of fphotor was therefore derived from the distributions of the relative productivity of each group of plant species given by the ORCHIDEE model. A consequent integration gave the values for global fphotor of 0.3 and 0.15 for the present and the LGM, respectively. The difference in photorespiration fraction between the LGM and the present is linked to the substantial decrease of C4 plants since the last glacial because C4 plants do not photorespire under normal conditions. It should be pointed out that the shift from C4 to C3 domination masks the effect of increased photorespiration fraction in the remaining C3 plants due to lower CO2 concentration during the LGM.
Schlesinger and Andrews  have recently proposed that the modern global carbon flux of soil respiration is 63% of the global GPP. Using the present-day vegetation distribution from the ORCHIDEE model, we converted this estimate from carbon flux to oxygen flux, and obtained the present-day global O2 soil respiration flux as 44% of the global oxygen productivity. Then fdark_leaves was calculated as 0.16 (= 1-0.1-0.3-0.44). For the LGM, in the absence of any available estimate for the proportion of soil respiration, we used the same ratio fdark_leaves/fdark_soil of 0.16/0.44 and, given the fractions of photorespiration and Mehler reaction, we obtained values of 0.55 and 0.20, respectively, for fdark_soil and fdark_leaves.
 The fractionation factors, 18α, for photorespiration and Mehler reaction have recently been determined by Helman et al.  and are given in Table 1. For estimating the global 18αdark_soil, we first plotted its spatial variability. With this aim, we used the distribution of the vegetation types derived by the ORCHIDEE model and attributed to each vegetation type the appropriate value of soil isotope discrimination by respiration given by Angert et al. [2003b]. Then, to integrate this distribution, we took into account the different rates of soil respiration in climatic regions. This was calculated from the distribution of the global oxygen uptake flux (section 5.1), and from the distribution of fdark_soil (calculated from the vegetation distribution to have the proportion of photorespiration in the same way that we obtained the global fdark_soil). Finally, combining the distributions of the global oxygen uptake flux, fdark_soil and 18αdark_soil, we integrated over the vegetated areas and obtained the global values for 18αdark_soil as 0.9844 for present day and 0.9839 for the LGM. Our sensitivity tests showed that the maximum possible error in the global 18αdark_soil due to possible uncertainties in the relative proportions of dark respiration in soils and leaves is ±0.0005.
 For estimating 18αdark_leaves, we followed Angert et al. [2003a] assuming that 10% of the dark respiration is through the AOX (alternative oxidase pathway) and 90% through the COX (cytochrome oxidase pathway). Then, using the fractionation factors of AOX (18α = 0.97 [Ribas-Carbo et al., 2000]) and of COX (18α = 0.982 [Guy et al., 1989, 1993]), we obtained a constant value for 18αdark_leaves as 0.981. Using equation (10) we calculated the global 18αterr as 0.9826 for present day and 0.98306 for the LGM. The smaller fraction of photorespiration during the LGM than at present explains why 18αterr is larger for the LGM than now, while the evolution of 18αdark_soil was the opposite. Finally, taking into account the uncertainties in 18αdark_soil, 18αphotor, 18αMehler and in the proportion of COX and AOX, the maximum error on 18αterr is about ±0.001.
 We would like to acknowledge Georg Hoffmann, Gerhardt Krinner, and Pierre Friedlingstein for helpful discussions. We are very grateful to the associated editor Corinne Le Quere and one anonymous reviewer whose comments contributed to significantly improving this paper. B. L. thanks the Israel Science Foundation (grant 188/03-13.0) for supporting of this research. A. L. was also supported by fellowships from the Lady Davis Foundation and the European Marie Curie grant (MEIF-CT-2005-023822). The work of J. L. was supported by the European project ENSEMBLES (GOCE-CT-2003-505539).