[1] Recently, the method for estimation of marine gross production from measurements of ^{17}O/^{16}O and ^{18}O/^{16}O of dissolved O_{2} has been improved by obtaining a rigorous equation for evaluation of gross production, and it has been suggested that small errors associated with approximations resulted in significant underestimation of gross production rates. The new equation requires accurate knowledge of the isotopic composition of photosynthetic and atmospheric oxygen. While the values for the latter have been determined very precisely, those of the former have never been measured. Here we present the first experimentally derived values of δ^{17}O_{p} and δ^{18}O_{p} of marine photosynthetic O_{2} (−10.126 and −20.014 ‰). Based on these, we show that the suggested underestimation was not the result of approximation errors, rather it was caused by inaccurate estimated values of δ^{17}O_{p} and δ^{18}O_{p}.

The quantity ^{17}Δ denotes an excess of ^{17}O for a given δ^{18}O. It has been defined in several ways [e.g., Kaiser, 2011], but in most studies the logarithmic form has been used:

The main reason for this choice was that in this form, as noted by Miller [2002], the value of λ is independent of the choice of isotopic reference. This facilitates direct comparison of fractionation data and results of different laboratories. In contrast, it is clear from equation (2) that the magnitude of ^{17}Δ depends on the isotopic composition of the standards (e.g., atmospheric O_{2} or VSMOW – Vienna Standard Mean Ocean Water) and also on the reference slope λ. Therefore, both should be chosen such that they optimally fit the system under consideration. The background theory of three isotope fractionations of O_{2} for kinetic processes and under steady state conditions and derivation of equation (1) for these cases are discussed by Luz and Barkan [2005, Appendix A].

[3]Prokopenko et al. [2011] have recently published a new, elegantly derived, rigorous equation by which gross production can be calculated directly from measured δ^{17}O and δ^{18}O of dissolved O_{2}. Furthermore, their paper suggests that calculations with equation (1), which is an approximation, leads to underestimation of the ratio of net to gross O_{2} production (N/G) by up to 50%. Whereas we agree that equation (1) is an approximation, we disagree with their conclusion that the 50% discrepancy results from approximation errors.

2. Proper Choice of δ^{17}O and δ^{18}O of Photosynthetic O_{2} for Calculating G

[4] All the parameters in equation (1), with the exception of ^{17}Δ_{bio}, are as defined by Luz and Barkan [2000]. The parameter ^{17}Δ_{bio} (previously denoted by the less intuitive symbol ^{17}Δ_{max}) stands for pure biological O_{2} having maximum value of ^{17}Δ (vs. atmospheric O_{2}) that is affected by both photosynthesis and respiration in steady state, but not gas exchange.

[5] The biogeochemical concepts underlying the triple isotope method of Luz and Barkan [2000] and its application using equation (1) remain the same in the rigorous equation of Prokopenko et al. [2011]. Their equation can be written as follows:

where δ*O = *R_{s}/*R_{ref} − 1. The factor 0.518 in equation (3) is a value of parameter λ in Equation 7 of Prokopenko et al. that equals (1 − α^{17})/(1 − α^{18}). This ratio for respiration, the most relevant process, was accurately determined in direct measurements of Luz and Barkan [2005] and is not based on any assumptions. Importantly, δ^{17}O_{p} and δ^{18}O_{p} stand for photosynthetic O_{2} that is not affected by respiration at all. In contrast, ^{17}Δ_{bio} in equation (1) is derived from δ^{17}O_{bio} and δ^{18}O_{bio} at biological steady state where rates of photosynthesis and respiration are equal. Correct value of ^{17}Δ_{bio} can be derived from δ^{17}O_{p} and δ^{18}O_{p} only with proper choice of λ.

[6] A major advantage of the new equation is that it makes it possible, for the first time, to calculate G/(kO_{eq}) directly from measured δ^{17}O and δ^{18}O of dissolved oxygen and corresponding values of O_{2} produced by photosynthesis (δ^{17}O_{p} and δ^{18}O_{p}) and in equilibrium with atmospheric O_{2} (δ^{17}O_{eq} and δ^{18}O_{eq}).

[7] While the values of δ^{17}O_{eq} and δ^{18}O_{eq} are known over a wide range of temperatures [Benson and Krause, 1984; Luz and Barkan, 2009], the situation with δ^{17}O_{p} and δ^{18}O_{p} is more complicated. Until recently, it has been generally accepted that δ^{18}O_{p} equals that of substrate water, and δ^{17}O_{p} was calculated from equation (2) assuming ^{17}Δ_{bio} = 249 (the value experimental determined by Luz and Barkan [2000]). A major drawback of this approach is that it is necessary to select a value for parameter λ in equation (2). Despite attempts [Angert et al., 2003; Luz and Barkan, 2005] to explain the proper choice of λ for calculations of δ^{17}O_{p}, this, evidently, has remained a confusing subject [e.g., Kaiser, 2011; Nicholson, 2011].

[8] Prokopenko et al. present results based on two values of λ: 0.518 and 0.516. In the first case the differences from calculations with the approximate equation were ∼38% and ∼50% in G and N/G, respectively, but in the second case the differences were much smaller. Evidently, the authors chose to emphasize the first case by giving it strong presence both in their abstract and Table 1. Furthermore, they made a strong statement in the abstract that small errors associated with approximations resulted in large relative errors in G and N/G. We do not agree with this statement because a different choice of λ leads to reasonable agreement between values obtained with the new and old equations. In fact, the authors themselves demonstrated this point.

Table 1. Comparison of G/(kO_{eq}) and N/G Calculated Using Equations (1) and (3)

[9] We emphasize that a properly chosen value of λ for calculating δ^{17}O_{p} must be smaller than 0.518. Indeed, for steady state between photosynthesis and respiration for which Prokopenko et al. derived their equation, λ should be obtained from equation 17 of Angert et al. [2003]. This equation was obtained with the specific aim to explaining photosynthesis-respiration steady-state. Depending on the known sizes of respiratory fractionations (about −30 to −14 ‰), λ can be calculated to range between 0.5142 and 0.5162. This point is discussed in considerable detail by Nicholson [2011]. Yet, realizing the confusion associated with proper choice of λ, we present here direct determination of δ^{17}O_{p} and δ^{18}O_{p} from experimental data of Helman et al. [2005], Eisenstadt et al. [2010] and Barkan and Luz [2011].

[10] In Figure 1 we show δ^{17}O_{p} and δ^{18}O_{p} values calculated from data in the above studies. As can be seen, they are always larger than the corresponding values of VSMOW. Furthermore, in the ln(δ^{18}O_{p} + 1) vs. ln(δ^{17}O_{p} + 1) plot there is very tight correlation (R^{2} = 0.99999) with regression slope of 0.5237. This slope is significantly larger than the 0.518 ratio of ordinary respiration or cyanide resistant respiration [Helman et al., 2005; Luz and Barkan, 2005]. Because the experiments were run at zero O_{2} in the medium, we can rule out respiration due to lack of substrate. It was suggested that the ^{17}O and ^{18}O enrichments were caused by rapid recycling of O_{2} by chlororespiration or PTOX in very close proximity to the production site in photosystem-2 [Eisenstadt et al., 2010].

[11] The new values of δ^{17}O_{p} and δ^{18}O_{p} are given in Table 1 along with corresponding G/(kO_{eq}) and N/G calculated with equation (3), and relative deviations calculated with respect to G/(kO_{eq}) and N/G obtained with equation (1). In addition, similar deviations were calculated for δ^{17}O_{p} and δ^{18}O_{p} from Prokopenko et al. As can be seen, the deviations for all marine organisms, except coccolithophores are less than ∼13% in both G/(kO_{eq}) and N/G, and are within the range of estimation errors with either equation (1) or equation (3). We also present results of calculations made by Prokopenko et al. for λ = 0.518 and λ = 0.516. Clearly, while in the first case the differences are large, in the second case they are only ∼5%, the same order as for the studied phytoplankton. This independently confirms our point of view that for proper calculation of G/(kO_{eq}), λ = 0.516 is a better choice.

[12] The obtained average phytoplankton values of δ^{17}O_{p} and δ^{18}O_{p} are at present the most accurate ones, and thus, we recommend using them for calculations of marine gross O_{2} production. We note that for the purpose of improving G/(kO_{eq}) accuracy, it will be worthwhile studying more marine organisms and also the potential gross production rate of each group of phytoplankton.

[13] From the discussion above, it is begging asking the question of whether calculations with the new rigorous equation of Prokopenko et al. [2011] and direct measurements of δ^{17}O_{p} and δ^{18}O_{p} is an improvement over the previous approach of Luz and Barkan [2000] with ^{17}Δ_{bio}. The answer is clearly positive. Mainly so because as done by Luz and Barkan [2000] the value of ^{17}Δ_{bio} = 249 per meg was derived with relatively low precision (±15 per meg) from difficult experiments with corals and green algae, one of these does not represent open ocean phytoplankton. In contrast, the current average values of δ^{17}O_{p} and δ^{18}O_{p} are based on four groups of phytoplankton, three of which (cyanobacteria, diatoms and coccolithophores) are very important primary producers in the world's oceans.

[14] Finally, Prokopenko et al. [2011] pointed out that the N/G ratios obtained with the approximate equation were erroneously high and exceeded biologically feasible value of 0.4 to 0.5. We strongly disagree with this statement and point out that there is no basis for the claim that N/G values larger than 0.5 are not biologically feasible. For example, in the seminal paper on gross and net O_{2} production of Bender et al. [1987], the authors conducted careful laboratory experiments and determined N/G values in the range of 0.79 to 0.96 [see Bender et al., 1987, Tables 5 and 7]. Yet, such high N/G ratios are exceptional as are the 0.4 and 0.55 values of Halsey et al. [2010] and Bender et al. [1999]. Much smaller ratios (0 to 0.3) are more common over wide oceanic areas [e.g., Reuer et al., 2007].

[15] In conclusion, the new rigorous equation of Prokopenko et al. [2011] is a very welcome addition to studies of gross O_{2} production in the ocean surface and, in our opinion, should be adopted and used from now on by marine biogeochemists. However, we emphasize that estimates done previously with the approximate equation yielded results that are close to those that can now be calculated with the rigorous one.

Acknowledgments

[16] This research has been supported by grants from the Israel Science Foundation.

[17] The Editor thanks Maria Prokopenko and an anonymous reviewer for their assistance in evaluating this paper.