Interactive comment on “ Reply to Nicholson ’ s comment on “ Consistent calculation of aquatic gross production from oxygen triple isotope measurements ” by Kaiser ( 2011 )

Abstract. The comment by Nicholson (2011a) questions the "consistency" of the "definition" of the "biological end-member" used by Kaiser (2011a) in the calculation of oxygen gross production. "Biological end-member" refers to the relative oxygen isotope ratio difference between photosynthetic oxygen and Air-O2 (abbreviated 17δP and 18δP for 17O/16O and 18O/16O, respectively). The comment claims that this leads to an overestimate of the discrepancy between previous studies and that the resulting gross production rates are "30% too high". Nicholson recognises the improved accuracy of Kaiser's direct calculation ("dual-delta") method compared to previous approximate approaches based on 17O excess (17Δ) and its simplicity compared to previous iterative calculation methods. Although he correctly points out that differences in the normalised gross production rate (g) are largely due to different input parameters used in Kaiser's "base case" and previous studies, he does not acknowledge Kaiser's observation that iterative and dual-delta calculation methods give exactly the same g for the same input parameters (disregarding kinetic isotope fractionation during air-sea exchange). The comment is based on misunderstandings with respect to the "base case" 17δP and 18δP values. Since direct measurements of 17δP and 18δPdo not exist or have been lost, Kaiser constructed the "base case" in a way that was consistent and compatible with literature data. Nicholson showed that an alternative reconstruction of 17δP gives g values closer to previous studies. However, unlike Nicholson, we refrain from interpreting either reconstruction as a benchmark for the accuracy of g. A number of publications over the last 12 months have tried to establish which of these two reconstructions is more accurate. Nicholson draws on recently revised measurements of the relative 17O/16O difference between VSMOW and Air-O2 (17δVSMOW; Barkan and Luz, 2011), together with new measurements of photosynthetic isotope fractionation, to support his comment. However, our own measurements disagree with these revised 17δVSMOW values. If scaled for differences in 18δVSMOW, they are actually in good agreement with the original data (Barkan and Luz, 2005) and support Kaiser's "base case" g values. The statement that Kaiser's g values are "30% too high" can therefore not be accepted, pending future work to reconcile different 17δVSMOW measurements. Nicholson also suggests that approximated calculations of gross production should be performed with a triple isotope excess defined as 17Δ#≡ ln (1+17δ)–λ ln(1+18δ), with λ = θR = ln(1+17vR ) / ln(1+18vR). However, this only improves the approximation for certain 17δP and 18δP values, for certain net to gross production ratios (f) and for certain ratios of gross production to gross Air-O2 invasion (g). In other cases, the approximated calculation based on 17Δ† ≡17δ – κ 18δ with κ = γR = 17vR/18vR (Kaiser, 2011a) gives more accurate results.

Abstract.The comment by Nicholson (2011a) questions the "consistency" of the "definition" of the "biological endmember" used by Kaiser (2011a) in the calculation of oxygen gross production."Biological end-member" refers to the relative oxygen isotope ratio difference between photosynthetic oxygen and Air-O 2 (abbreviated 17 δ P and 18 δ P for 17 O / 16 O and 18 O / 16 O, respectively).The comment claims that this leads to an overestimate of the discrepancy between previous studies and that the resulting gross production rates are "30 % too high".
Nicholson recognises the improved accuracy of Kaiser's direct calculation ("dual-delta") method compared to previous approximate approaches based on 17 O excess ( 17 ∆) and its simplicity compared to previous iterative calculation methods.Although he correctly points out that differences in the normalised gross production rate (g) are largely due to different input parameters used in Kaiser's "base case" and previous studies, he does not acknowledge Kaiser's observation that iterative and dual-delta calculation methods give exactly the same g for the same input parameters (disregarding kinetic isotope fractionation during air-sea exchange).The comment is based on misunderstandings with respect to the "base case" 17 δ P and 18 δ P values.Since direct measurements of 17 δ P and 18 δ P do not exist or have been lost, Kaiser constructed the "base case" in a way that was consistent and compatible with literature data.Nicholson showed that an alternative reconstruction of 17 δ P gives g values closer to previous studies.However, unlike Nicholson, we refrain from interpreting either reconstruction as a benchmark for the accuracy of g.
A number of publications over the last 12 months have tried to establish which of these two reconstructions is more accurate.Nicholson draws on recently revised measurements of the relative 17 O / 16 O difference between VSMOW and Air-O 2 ( 17 δ VSMOW ; Barkan and Luz, 2011), together with new measurements of photosynthetic isotope fractionation, to support his comment.However, our own measurements disagree with these revised 17 δ VSMOW values.If scaled for differences in 18 δ VSMOW , they are actually in good agreement with the original data (Barkan and Luz, 2005) and support Kaiser's "base case" g values.The statement that Kaiser's g values are "30 % too high" can therefore not be accepted, pending future work to reconcile different 17 δ VSMOW measurements.
1 Introduction Kaiser (2011a) introduced an improved method to calculate aquatic gross production from oxygen triple isotope measurements, dubbed the "dual-delta method".This method uses 17 δ and 18 δ measurements of dissolved O 2 relative to Air-O 2 directly, rather than the 17 O excess ( 17 ∆) and using an approximation (Luz and Barkan, 2000).The calculation uses the following equation: Equation ( 1) is based on Eq. ( 48) in Kaiser (2011a), but takes into account that previous measurements of the kinetic isotope fractionation during O 2 gas exchange refer to evasion from solution to gas phase (Kaiser, 2011b;Knox et al., 1992).The symbols have the following meaning: g = P / (kc sat ): ratio of gross oxygen production to gross Air-O 2 invasion. 17 Prokopenko et al. (2011) developed virtually the same method, but did not include kinetic isotope fractionation during O 2 gas transfer.This resulted in the simplified solution The comment by Nicholson (2011a) does not question the validity of the dual-delta method.Unlike the approximated calculation of Luz and Barkan (2000), it does not assume steady state for O 2 concentrations and can, therefore, be expected to be more universally applicable.Only the assumption of isotopic steady state is needed.In contrast to the claim that the dual-delta method requires 17 ε R and 18 ε R (Nicholson, 2011b), the above equations clearly show that only γ R is required, which is better constrained than 17 ε R and 18 ε R (Luz and Barkan, 2005).
The comment paper and the reviews it has received (Luz, 2011;Prokopenko, 2011) demonstrate that the definition and use of triple isotope excess values can be very confusing, even for experts in the field.The use of different 17 ∆ definitions with different coefficients causes delays and misunderstandings during scientific communication, which can be avoided with the dual-delta method.In this paper, 17 ∆ values are reported in conjunction with the underlying 17 δ and 18 δ values and the definition of 17 ∆ is indicated by the indices introduced in Kaiser (2011a), to avoid any further confusion.
In Sect.2, we discuss the merits of Nicholson's comment in view of different reconstructions of the isotopic composition of photosynthetic O 2 .In Sect.3, we evaluate his suggested approximated solution to the calculation of g from oxygen triple isotope measurements.

Isotopic composition of photosynthetic O (δ P )
In his comment, Nicholson (2011a) questions the "consistency" of the "definition" of the isotopic composition of the "biological end-member" (i.e., photosynthetic O 2 ) in Kaiser 2011a).Specifically, he remarks that the triple isotope excess ( 17 ∆) adopted for the base case is "too low" and, therefore, also 17 δ P .He does not question the value of −22.835 ‰ assumed for 18 δ P .
The "definition" of the base case 17 δ P or 18 δ P values in Sect. 5 of Kaiser (2011a) followed the approach of previous studies that used the measured 17 O excess of O 2 evolved in flask studies of 17 ∆ † (0.521) = (249 ± 15) ppm (Luz and Barkan, 2000) and combined its numerical value with the inferred 18 δ P value and an entirely different 17 O excess definition, in this case 17 ∆ # (γ R ), where γ R = 0.5179.Even though the reconstructed 17 δ P value of −11.646 ‰ must be considered hypothetical, it is consistent with 17 δ P values derived from actual literature data following two different approaches: one based on the measured isotopic composition of VSMOW and oceanic waters with respect to Air-O 2 (Barkan and Luz, 2005;Luz and Barkan, 2010), combined with the measured photosynthetic isotope fractionation by the cyanobacterium strain Synechocystis sp.PCC 6803 (Helman et al., 2005); the other based on dark-light incubations of the coral Acropora (with its symbiotic algae) in airtight flasks (Luz and Barkan, 2000).The first approach was also used to derive 18 δ P = −22.835‰ .
To dispel any confusion about how the isotopic composition of photosynthetic O 2 (including the triple isotope excess) was calculated, we show the corresponding equations and results in the following subsections and include data that were previously omitted or not yet published.The resulting 17 δ P and 18 δ P values are shown in Table 3.We also update any values in Kaiser (2011a) and Nicholson (2011a) to reflect recent publications by Luz and Barkan displaying them with more decimals than previously; however, this does not significantly change any results or conclusions.

Calculation of δ P based on the isotopic composition
of source water (δ W ) and the photosynthetic isotope fractionation (ε P ) The relative isotope ratio difference of photosynthetic O 2 to Air-O 2 (δ P ) can be calculated via where δ W is the relative isotope ratio difference of source water to Air-O 2 and ε P is the photosynthetic isotope fractionation.The corresponding triple isotope excess is where γ P = 17 ε P / 18 ε P and where θ P = ln(1+ 17 ε P )/ ln(1 + 18 ε P ).

Calculation of δ P based on flask cultures in steady state between photosynthesis and respiration
Following Sect.3.4 in Kaiser (2011a), the isotopic composition of oxygen in concentration steady state (net to gross production ratio f = 0) is given by To derive δ P , Eq. ( 6) is rearranged to In addition to δ S0 , this calculation also requires ε R .Luz and Barkan (2000) performed incubations of a Nannochloropsis species and the hermatypic coral Acropora in airtight flasks.These incubations are supposed to correspond to steady state.No values were reported for δ S0 , only 17 ∆ † S0 (0.521) = (244 ± 20) ppm for Nannochloropsis and (252 ± 5) ppm for Acropora; anecdotal evidence suggests that δ S0 was close to 0 (Barkan and Luz, 2011).
In Sect.4, Nicholson (2011a) comments that 17 ∆ # P (θ R ) = 231 ppm for the Nannochloropsis flask experiments is very close to 17 ∆ # P (θ R ) = 234 ppm for the Acropora flask experiments.Notwithstanding that our own calculations give identical results of 17 ∆ # P (θ R ) = 229 ppm for both cases (Table 3, row 4a and footnote to row 3a), this is not a fair comparison because θ R = 0.5173 for Acropora and θ R = 0.5154 for Nannochloropsis.Clearly, the 17 δ P values differ in both cases (for the same 18 δ P value) and calculations of gross production using the accurate dual-delta method would lead to different results.This illustrates the perils associated with using 17 ∆ values in isolation. 18δ VSMOW and 17 δ VSMOW Four days after publication of Kaiser (2011a) and three days before publication of Nicholson (2011a), new measurements of 18 δ VSMOW and 17 δ VSMOW were published (Barkan and Luz, 2011).The authors of this paper found that they could not reproduce their earlier results for 17 δ VSMOW (Barkan and Luz, 2005).Their new results gave 17 δ VSMOW = (−11.883± 0.012) ‰ (Table 1, row 5), which is 0.048 ‰ or five standard deviations higher than the original value of (−11.931 ± 0.01) ‰ (Barkan and Luz, 2005).The new 18 δ VSMOW value of (−23.324 ± 0.017) ‰ was virtually unchanged compared to the original value of (−23.320 ± 0.02) ‰.In terms of 17 ∆ † VSMOW (0.5179), this amounts to a change from (146 ± 4) ppm to (196 ± 4) ppm.The authors do not give an explanation for this change, other than that "experimental system and measurement procedures were somewhat improved" (Barkan and Luz, 2011).
Our 17 ∆ † W (0.5179) value is in good agreement with the original measurements of Barkan and Luz (2005), but disagrees with their revised results (Barkan and Luz, 2011).Just as the results of Barkan and Luz, our data have been obtained using CoF 3 fluorination on a Finnigan MAT Delta Plus isotope ratio mass spectrometer (University of Nagoya).However, our results have been corrected for a 0.8 % scale contraction, based on gravimetrically calibrated mixtures of 99.7 % pure H 18 2 O with tap water.The scale correction affected 17 ∆ † W (0.5179) by a 2 ppm increase only.It actually brings 18 δ VSMOW into closer agreement with independent estimates of (−23.771 ± 0.06) ‰ (Table 1, row 4), based on isotope measurements in CO 2 (Kaiser and Röckmann, 2008).Barkan andLuz (2005, 2011) did not perform a scale correction, even though their measured SLAP-VSMOW difference of (−55.11± 0.05) ‰ (Barkan and Luz, 2005) differs from the internationally accepted value of −55.5 ‰ (Gonfiantini, 1977(Gonfiantini, , 1978)).If the value of −55.5 ‰ were accurate, the corresponding scale contraction would amount to 0.7 %.A scale contraction of 0.7 to 0.8 % may be typical for this particular type of mass spectrometer.
The varying results for the relative isotope ratio differences between VSMOW and Air-O 2 within a single laboratory and between laboratories warrant further measurements of this important parameter and perhaps inter-laboratory comparisons.
For comparison purposes, we construct mean parameter sets from the species-dependent δ P values (Table 3, rows 5m, 6m and 7m).For the photosynthetic isotope fractionation, we adopt the arithmetic average of the corresponding values based on Eisenstadt et al. (2010), i.e., 18 ε P = (4.119± 2.6) ‰ and 17 ε P = (2.153± 1.3) ‰ (Table 2).This 18 ε P value is in good agreement with the global average 18 ε P of 4 ‰ derived by Luz and Barkan (2011a).A similar approach was taken by Luz and Barkan (2011b), but they excluded C. reinhardtii from their mean δ P values.It would not be appropriate to take the arithmetic average of θ P reported for various organisms to derive 17 ε P because 17 ε P is essentially linearly related to 17 δ P whereas θ P is not.
The good agreement between our own measurements of the isotopic composition of VSMOW relative to Air-O 2 and those of Barkan and Luz (2005) is also reflected by the closely matching species-dependent 17 ∆ P (0.5179) values (Table 3, rows 5a-5e and 7a-7e).In the next section, we will illustrate the systematic impact of different δ P values on g.
3 Dependence of g on the isotopic composition of photosynthetic O 2

Accurate calculation of g using the dual-delta method
Since the interaction between the parameters 17 δ P , 18 δ P and γ R is not straightforward to predict based on Eq. ( 1), their impact on g is best illustrated through example calculations (Kaiser, 2011a).Results for g based on 17 δ P and 18 δ P derived in Sects.2.1-2.3,including the parameters suggested by Nicholson (2011a) and Kaiser (2011a) are compared with those using the mean δ P values based on Barkan and Luz (2005;Table 3, row 5m; Fig. 1a and b) and based on Barkan and Luz (2011;Table 3, row 6m; Fig. 1c and d).The same scenarios as in Kaiser (2011a) were used, i.e., g = 0.4 with −1.0 ≤ f ≤ +1.0 (Fig. 1a   and c) and f = 0.1 with 0.01 ≤ g ≤ 10 (Fig. 1b and d).
For g based on "Table 3, row 6m" (using VSMOW measurements reported by Barkan and Luz, 2011), the speciesspecific parameters for N. oculata, C. reinhardtii and P. tricornutum again agree well with the mean δ P set (Fig. 1c  and d).There is also relative good agreement with "Nicholson (2011a)", "Luz and Barkan (2011b)", "Acropora (flask, 5.814 ‰)" and "Nannochloroposis (flask, 2.85 ‰)".However, the relative deviations are ≥ 35 % for "Kaiser (2011a)", "Table 3, row 5m" and "Table 3, row 7m" and ≤-12 % for "E.huxleyi".Again, for f < 0.1 or g > 0.1, these deviations tend to be even higher (Fig. 1c and d).The relative deviations of g for the Synechocystis parameters are ≥ +18 % from the base case, which means the g values based on E. huxleyi parameters deviate ≤-26 % from the g values based on Synechocystis parameters.The span between these two species is slightly smaller than for "Table 3, row 5m" because the different base case parameters lead to different 17 δ and 18 δ scenarios for the same two cohorts.Nevertheless, there is still a significant uncertainty in g related to which species is assumed to have produced the O 2 and, therefore, which set of parameters 17 δ P , 18 δ P and γ R is adopted for the calculation.
a claim and rather used the disagreement between different estimates of the isotopic composition of photosynthetic O 2 to highlight the need for additional measurements of the required parameters, especially 17 δ P .The claim by Nicholson (2011a) that the g values calculated using the base case of Kaiser (2011a) were 30 % too high is not justified.Nicholson (2011a) also commented that Kaiser (2011a) overestimates the discrepancy of g based on different calculation methods/parameters, as seen in Fig. 3 of Kaiser (2011a) compared to Fig. 1 in Nicholson (2011a).However, this is largely due to how the results are presented (as relative deviations), and as we argue above, Kaiser's "base case" just provides a reference for comparison, not a benchmark for other studies.

Approximate calculation of g
Even though the development of the accurate dual-delta method makes use of approximations in the calculation of g unnecessary, we will revisit the different approximations used in the past to address Nicholson's comment that 17 ∆ should be defined as 17 ∆ # (θ R ) ≡ ln(1+ 17 δ)−θ R ln(1+ 18 δ).
The same authors later revised this method and stated that the triple isotope excess should be defined using the natural logarithm (ln) as 17 ∆ # (γ R ) ≡ ln(1 + 17 δ)γ R ln(1+ 18 δ) with γ R = 0.5179 (Luz and Barkan, 2005), but that this definition shall not apply to 17 ∆ P .Instead, the photosynthetic end-member should be set equal to 17 ∆ # P (θ R ), with θ R = 0.5154 for γ R = 0.5179 and 18 ε R = −20 ‰ (Sect.2.3).As evidenced by its use in Luz and Barkan (2009), a coefficient of γ R is also meant to apply to 17 ∆ # sat .The use of different coefficients for the triple isotope excess is confusing, especially for the non-expert reader.Moreover, θ R can only be computed if 18 ε R is also known.Even though the influence of the uncertainty in 18 ε R is not as severe as when 18 δ were used for the calculation directly (Quay et al., 1993), this goes against the rationale behind the triple oxygen isotope technique (i.e., the absence of the need to know 18 ε R ).Finally, the suggested approximations are mathematically inconsistent with Eqs.(1) and (2).
Instead, Kaiser (2011a) suggested that Eq. ( 10) is used with the triple isotope excess defined as 17 ∆ † (γ R ) ≡ 17 δ − γ R 18 δ.This definition is consistent with the asymptotic behaviour of Eq. ( 2) for 17 δ, 18 δ → 0. However, it was shown that this approximated calculation can lead to systematic biases from the accurate solution calculated using the dual-delta method and the use of this approximation was not recommended.Nicholson (2011a) comments that the approximations of Kaiser (2011a) and, by implication, Luz and Barkan 2005) can be improved if a definition of the triple isotope excess as 17 ∆ # (θ R ) is adopted.The corresponding 17 ∆ # P (θ R ) value is named 17 ∆ BSS for "biological steady state" because it is identical to the 17 ∆ # S0 (θ R ) value under concentration steady state (f = 0).However, as shown in Sect.3.4 and the uncorrected Fig. 1 of Kaiser (2011a), isotopic steady state can also be achieved for f = 0 and in this case, 17 ∆ # S (θ R ) = 17 ∆ # P (θ R ).It is, therefore, not clear a priori whether the approximation suggested by Nicholson (2011a) performs better than the other approximations.
None of the approximations deliver unbiased results for g > 1.Of course, such conditions rarely occur in the environment (except for intense blooms or very low wind speeds).However, even for g < 1 significant biases can occur in all cases under certain conditions.
For all scenarios, method (c) performs worst.However, 17 ∆ # (γ R ) on its own has actually never been used together with Eq. ( 10), as far as we know, so this has no consequence for already published data.
For the base case adopted by Kaiser (2011a) (Table 3, row 1; Fig. 2), method (a) returns nearly unbiased results for f = 0 and g < 0.1.For g < 1 and −0.4 ≤ f ≤ 0.2, the relative deviation from the accurate solution does not exceed ± 22 % (Fig. 2a).g values based on Nicholson's method (d) are biased 10 % low for f = 0, but the relative deviation from the base case is at most −21 % for g ≤ 0.4 (Fig. 2d).Luz and Barkan's method (b) is biased only 7 % low for f = 0 (Fig. 2b), but otherwise the derived g values have larger deviations from the accurate solution than those for method (d), more similar to method (a).
For the scenario using the mean δ P value based on the VS-MOW measurements of Barkan and Luz (2011)   For the scenario based on the Acropora flask experiments ( 18 ε P = 0.5 ‰; Table 3, row 3a; Fig. 4), method (a) gives the least bias for f = 0.In this case, methods (b) and (d) are biased low by 19 % and 12 %, respectively.Interestingly, method (d) does not show any significant variation in this bias for g < 0.1 and the entire range in f .In summary, none of the calculation methods is free from bias under all conditions and scenarios.The value Nicholson (2011a) attributed to method (d) may be due to the particular hypothetical scenario he has chosen, which is very similar to that defined by "Table 3, row 6m" (Fig. 1c and  d).However, if other 17 δ P and 18 δ P parameters were adopted such as those of the Acropora flask experiments (assuming 18 ε P = 0.5 ‰), then significant deviations from the accurate solution would occur.

Conclusions
It is important to make the distinction between different calculation methods (e.g., iterative versus dual-delta method; approximate based on a" b" c" d" Fig. 3. Relative deviation of the approximated solution for g (Eq.10) from the accurate solution (Eq. 1) for the parameters in Table 3, row 6m (δ W based on Barkan and Luz, 2011).and 18 δ pairs) and different calculation parameters.With the development of the dual-delta method (Kaiser, 2011a;Prokopenko et al., 2011), it is time to abandon approximated solutions based on the triple isotope excess ( 17 ∆).The end of the discussion about what the appropriate definition is for 17 ∆, which is the right coefficient and whether it should be defined in terms of δ or ln(1+δ), will also help alleviate the confusion that newcomers and students feel when they first enter this field of research.Even though the methodological bias due to the use of Eq. (10) may often be smaller than the uncertainty due to wind speed-gas exchange parameterisations, there is no reason for such bias to exist at all if the dual-delta method is adopted.
We agree with Nicholson (2011a) that different parameters are key to explaining the differences between Kaiser's base case and previous studies (e.g., Hendricks et al., 2004;Reuer et al., 2007;Juranek and Quay, 2010).However, considerable systematic uncertainty remains in the calculation of g due to the uncertainty in the isotopic composition of photosynthetic O 2 , 17 δ P and 18 δ P .Part of this uncertainty is due to conflicting results for the 17 O / 16 O isotope ratio of seawater relative to Air-O 2 (Sect.2.4).Moreover, the experiments by Eisenstadt et al. (2010) and the results in Fig. 1  a" b" c" d" Fig. 4. Relative deviation of the approximated solution for g (Eq.10) from the accurate solution (Eq. 1) for the parameters in Table 1, row 3a (Acropora (flask), 18 ε P = 0.5 ‰ ).isotope fractionation and the inferred gross production g, depending on what species is assumed to have produced the oxygen.Independent measurements and perhaps laboratory comparison exercises should be performed to establish the reproducibility of 17 O / 16 O isotope ratio measurements in water.Further experiments with cultures under steady-state conditions would help to verify the calculations based on the isotopic composition of water and the photosynthetic isotope fractionation.
The comment by Nicholson (2011a) on "Consistent calculation of aquatic gross production from oxygen triple isotope measurements" by Kaiser (2011a) centred on the appropriate choice of 17 δ P and 18 δ P .At the moment, however, it seems to be more important to emphasise the differences that result from different parameters and calculation methods.The demand for the "correct" choice is premature and besides the main topic of Kaiser's original paper.
6m; Fig.3), methods (a), (b) and (d) give nearly unbiased results for f = 0 and the entire range of g values explored.Method (d) has the least bias for g < 1, whereas methods (a) and (b) perform similarly.

Table 1 .
Historic and new measurements of the relative oxygen isotope ratio differences between Vienna Standard Mean Ocean Water (VS-MOW) and Air-O 2 ( 17 δ VSMOW , 18 δ VSMOW , 17 ∆ VSMOW ).For clarity, all values are shown with the same number of decimals, irrespective of their uncertainty.
a Minimum error based on the uncertainty of the corresponding 17 δ value.b No error estimate was given.
18ε P ) values.It is useful for error propagation purposes.The resultant y-axis intercept of (0.012 ± 0.013) ‰ is statistically indistinguishable from zero.For clarity, θ P and 17 ε P values are shown with the same number of decimals, irrespective of their uncertainty.

Table 3 .
Isotopic composition of photosynthetic O For clarity, all values are shown with the same number of decimals, irrespective of their uncertainty.Directly measured values are in bold.
(Luz and Barkan, 2010), row(Barkan and Luz, 2005); rows to 6m are based on Table1, row(Barkan and Luz, 2011); rows to 7m are based on Table1, row (this paper); all account for the 5 ppm lower O / O ratio of ocean water compared to VSMOW(Luz and Barkan, 2010)and the photosynthetic isotope fractionations in Table2.