Interactive comment on “ Consistent calculation of aquatic gross production from oxygen triple isotope measurements

The author provides a detailed description of the methods used to calculate gross production from measurements of oxygen triple isotopes. The manuscript provides a comparison of the different equations that have been used for estimating 17O excess and a thorough analysis of the uncertainty associated with parameters used in these calculations. The author clearly identifies discrepancies in calculations using the triple isotope system and a need for consistency within the field. He also derives an equation for gross oxygen production that is based on 17δ, 18δ, and O2 supersaturation and avoids the need for a steady state assumption or the poorly constrained respiratory isotope effect.


Introduction
In the manuscript "Consistent calculation of aquatic gross production from oxygen triple isotope measurements" Kaiser derives exact equations for calculating gross oxygen production (GOP) from the triple oxygen isotopic composition of dissolved oxygen ( 17 ∆).The derived equations improve upon previous methods of calculating GOP in that they avoid approximations and account for additional processes such as kinetic fractionation during air-sea evasion and invasion of oxygen.These new equations and similar results of Prokopenko et al. (2011), provide improved methodology that should Introduction

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Full be applied to future studies that interpret triple oxygen isotopic composition of dissolved oxygen in seawater.However, in comparing the results of these new equations to previous methods of calculating GOP, I believe Kaiser has misinterpreted previous results with the consequence of overstating the difference between various previous methods of calculating GOP (e.g.Kaiser's Fig. 3).Since differing definitions of 17 O excess are used, I repeat here definitions 4 and 7 from Kaiser (2011).
17 ∆ † = 17 δ − κ 18 δ (1) where κ and λ are mass dependent fractionation slopes.For Kaiser's "base case", both are assigned the observed slope for a ln(1+ 18 δ) vs. ln (1+ 17 δ) plot for dark respiration of γ R = 0.5179 (Luz and Barkan, 2005).The crux of the discrepancy is in the assumptions Kaiser uses to calculated the relation between 17 δ P and 18 δ P , where the subscript "P " refers to dissolved oxygen produced by photosynthesis.In his "base case" used for comparison of methods, Kaiser uses Eq. ( 2) by assuming a 17 ∆ # P (λ = 0.518) = 249 ppm where 249 ppm is the biological end-member value reported by Luz and Barkan (2000).I will argue that the 249 must be applied instead to oxygen in biological steady state with seawater ( 17 ∆ S0 ) which is influenced by photosynthesis and respiration, rather than 17 ∆ P in order for consistent comparison between calculation methods.I introduce the notation 17 ∆ S0 to refer specifically to the biological steady-state condition in which P = R (and thus f = 0, where f is the net to gross production ratio). 17∆ S0 is distinctly different than 17 ∆ P as noted by Kaiser, because 17 ∆ P is the pure photosynthetic product, while 17 ∆ S0 is a balance of P and R. The 249 ppm value published by Luz and Barkan (2000) was a measure of and not 17 ∆ P because the original experiment measured dissolved oxygen in a terrarium experiment which was in biological steady state (P ≈ R).For a system in biological steady state, it has been demonstrated that the appropriate slope (λ BSS ) for relating Introduction

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Full the composition of 17 ∆ S0 and 17 ∆ P is systematically less than γ R (Angert et al., 2003).
In the following sections I will describe how 17 δ P and 18 δ P should have been defined using a slope of λ BSS = 0.5154 instead of γ R .With this correction, Kaiser's "base case" value can be corrected from 17 ∆ † P = 180 to 17 ∆ † P = 238 ppm (see Sect. 3) and the discrepancy between the calculation methods of earlier studies and the new method proposed by Kaiser becomes much smaller.
I will focus my comments on this aspect of the manuscript and stress that I am not questioning the validity of the equations derived by Kaiser, but rather how he has interpreted previous results and measurements in order to fairly compare GOP from previous calculation methods to the proposed new equations.To communicate the difference between previous methodology and the proposed method, it is important to clarify the relative roles of (1) measured physical parameters used in calculations, such as 17 δ and 18 δ and fractionation factors 18 ε R and (2) the accuracy of various equations under varying conditions of metabolic balance (f ) and productivity (g) when the same physical parameters are used.

Biological steady state
Understanding the distinction between composition of photosynthetic oxygen (P) and oxygen in biological steady-state (S) and is essential to the following discussion.Photosynthetic oxygen is produced from seawater with only a very small fractionation (∼0.5 ‰) and thus has a 18 δ P near that of VSMOW (Kaiser's base case is 18 δ P = −22.835‰) (Eisenstadt et al., 2010).Biological steady-state refers to the composition of oxygen reached with a constant rate of photosynthesis and respiration (see Kaiser Sect.3.4).For the special case where P = R, I use the subscript "S0".Angert et al. (2003) described the relationship between * δ P and * δ S0 using the mass balance equation Tables Figures

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Full where " * " indicates 17 or 18 and α R is the fractionation factor for respiration.Since average ocean α R is 0.980 ( 18 α R = 1+ 18 ε R = −20 ‰) (Kiddon et al., 1993) The slope (λ BSS ) that satisfies the criteria that 17 depends on the magnitude of fractionation during respiration such that Thus, for 18 ε R = −20 ‰ and γ R = 0.5179 I calculate λ BSS = 0.5154.Additionally, assuming an error in 18 ε R of ±2 ‰ the difference between γ R and λ BSS is very well For the above definition, the same 17 ∆ BSS should be acquired whether measuring the direct product of photosynthesis or a system in biological steady-state ( 17 ∆ BSS S0 = 17 ∆ BSS P ).The experimental determination of the biological end-member by Luz and Barkan (2000), ( 17∆ bio = = 249 ± 15 ppm) was a measurement of dissolved oxygen in biological steady-state with seawater (P ≈ R) and thus its composition relative to seawater should be governed by Eq. ( 4) (Angert et al., 2003;Luz and Barkan, 2000).A more precise definition of the original approximate equation for calculating g (Luz and Introduction

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Full Barkan, 2000) should then be 3 Consistent comparison of equations used to calculate g Equation ( 6) for calculating g uses 17 ∆ BSS as the biological end member, while both the iterative equation .(Hendricks et al., 2004)  Thus if the value of 249 ppm is used for 17 ∆ BSS in Eq. ( 5), then the comparable 17 δ P for an equivalent calculation using Kaiser's Eqn.48 should be −11.588‰ not −11.646‰.This correction has a significant impact when comparing various equations (Hendricks et al., 2004;Luz andBarkan, 2000, 2005;Miller, 2002) that have previously been used to calculated g and 17 ∆ to the equation derived by Kaiser.
Based on the changes I describe, I illustrate the importance of the suggested correction by recalculating Figs.3a and b from Kaiser (2011).In addition to the results presented by Kaiser, I have added two green lines to the plot that show the error induced by the choice of equation form alone (Fig. 1).For these two cases, 17 O excess is calculated using the "base case" values from Kaiser except with 17 δ P = −11.588‰ as described above.Using the approximate Eq. ( 6) results in an error no greater than about Introduction

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Full −25 % at the extremely heterotrophic conditions (Fig. 1a) and 40 % at very high production rates (Fig. 1b).Under more typical conditions (−0.1 < f < 0.4 and 0.01 < g < 1) the error is less than ∼10 %.Using the iterative method of Hendricks et al. (2004), the bias is much less still, overestimating g by less than 5 % under all conditions.The ∼5 % overestimate is caused primarily by the kinetic fractionating effects during gas exchange (i.e.ε I and ε E ) which are accounted for by Kaiser but not by earlier equations.The red and black lines are calculated from Kaiser Table 3 data except for one correction: in column 6 showing results of Juranek and Quay (2010) the γ R value should be 0.5205 (not 0.518) because the relationship 17g α R = ( 18 α R ) λ was used, similarly to Hendricks et al. (2004) andReuer et. al. (2007).In Kaiser's Fig. 3, relative error for many of the methods clusters around −30 % for f ∼0 (Kaiser Fig. 3a) and g ∼ 0.5.Although notation varied, each study using an iterative approach defined the composition of 17 δ P using a λ BSS slope ≈ 2.5 × 10 −3 less than the implied respiratory fractionation slope (γ R ) as described by Eq. ( 4).Thus, despite taking various approaches, each previous study has calculated g in a manner that is accurate to within about 20 % for the relevant environmental conditions.The more precise equation introduced by Kaiser and Prokopenko is superior to previous methods and should be applied to future studies, however much care should be taken in any attempt to "reinterpret" previous results.
Effectively, Kaiser has compared previous equations with a 17 ∆ BSS = 249 ppm to his equation using 17 ∆ BSS = 191 ppm (the 17 ∆ BSS value for Kaiser's "base case" values).
This difference is responsible for the majority of the apparent discrepancy between methods.The significantly lower 17 ∆ BSS of 191 ppm is why Kaiser's calculations yield g ∼30 % higher than most other calculation methods (Kaiser Fig. 3).After correcting Kaiser's "base case" with 17 δ P = −11.588‰ (and thus 17 ∆ BSS = 249 ppm), the remaining differences have clear explanations.Variations in the slope λ from the base case cause an error dependent on f where slopes greater than the base case causing an overestimate under strongly autotrophic conditions (f > 0) and underestimate for heterotrophic conditions (f < 0) (Fig. 1a).If a lower gas exchange end-member ( 17 ∆ sat ) is used, g is overestimated, particularly for low values of g (Fig. 1b).Neglecting kinetic Introduction

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Full fractionation during gas exchange causes iterative methods to be slightly too high.
When regressing the results of Reuer et al. (2007), Kaiser arrives at a result ∼40 % higher than Reuer (Kaiser Fig. 4).I find that about 30 % of the discrepancy is due to the difference in implied 17 ∆ BSS while the remaining difference is due to how the gas exchange end member was parameterized.

Inconsistent estimates of the biological end member
In the above section, I argue that 17 ∆ BSS = 249 ppm is consistent with 17 δ P = −11.588and 18 δ P = −22.835.However, as noted by Kaiser, previous studies provide results that often imply conflicting values for the biological end member of photosynthetically produced dissolved oxygen.Both the biological end member and atmospheric equilibrium end member should be redetermined.An important point is that a new value for 17 ∆ BSS would effect all equations almost equally without changing the relative error between equations or significantly altering the results shown in Fig. 1.While the 18 δ and 17 δ associated with 249 ± 15 ppm were not reported by Luz and Barkan (2000), it is possible to reinterpret these results using some reasonable guesses.The commonly used vale of 249 ±15 ppm (Luz and Barkan, 2000) was determined by measuring dissolved oxygen in biological steady state with seawater for Nannochloropsis (244 ± 20 ppm) and the coral Acropa with its symbiotic algae (252 ± 5 ppm).However as Kaiser points out, these values were calculated using an outdated definition of 17 O excess ( 17 ∆ † (κ = 0.521)).I recalculate the 17 O excess assuming the values of 18 ε R = −20 ‰ and λ R = 0.5179 for Nannochloropsis and 18 ε R = −13.8‰ and λ R = 0.519 for Acropa (Luz and Barkan, 2005).Values for Acropa were measured, while we assign the "base case" values for Nannochloropsis.The biosteady state 18 δ S0 for each case is estimated from Eq. somewhat lower than the commonly used value of 249 ppm but significantly higher than the 17 ∆ BSS = 191 ppm implied by Kaiser's base case values.

Conclusions
Since the introduction of the triple isotopic composition of dissolved oxygen was introduced as a tracer of gross oxygen production by Luz and Barkan (2000), the methodology for calculating g from measured isotopic ratios has evolved and improved.While improved equations will better estimates of g, perhaps the greater cause of error is in analytically determining what the accurate and appropriate photosynthetic and gas exchange end members should be ( 17 δ P , 18 δ P , 17 δ sat and 18 δ sat ).
When applying an equation to calculate g that requires 17 δ P in the calculation, it is essential to set 17 δ P using the slope λ BSS and Eq. ( 4).If when remeasured 249 ppm turns out to be the correct value for 17 ∆ BSS then the g calculated by Kaiser for the "base case" scenario is ∼30 % too high.If, as suggested in Sect.4, the true 17 ∆ BSS falls somewhere between 191 ppm (as implied by Kaiser's base case) and 249 ppm (as used by previous studies), the estimates of g provided by Kaiser would need to be revised downward by somewhat less than 30 % while g from previous studies would need to be revised slightly upwards.

Appendix A Derivation for biological steady-state
The following derivation is adapted from Angert et al. (2003) and shows the relationship between λ BSS and γ R for a P = R steady-state system.Introduction

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Full ) .The solid green line 9 'iter' shows error due to using the corrected 'base case' values ( 17 δ P = -11.588‰ , 18ε R = - 10 20‰ and λ = 0.5179 ) with the iterative method from Hendricks et al. (2004).Red and black 11 lines show deviation from base case using the parameters and approaches employed in 12 previous studies (see Table 3 in Kaiser, 2011 for details).They are calculated from the same 13 values as used by Kaiser, except now compared against the 'corrected base case' Within 14 typical oceanic conditions ( -0.1 < f < 0.4 and 0.01 < g < 1), the methods generally agree with 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (3).When recalculated using Eq.(4) these values are equivalent to 17 ∆ BSS = 231 ppm and 17 ∆ BSS = 234 ppm for Nannochloropsis and Acropa, respectively.The true 17 ∆ BSS therefore is likely Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 :
Figure 1: Relative deviation of g from the 'corrected base case' as calculated using the 5 equation proposed by Kaiser.All values are the same as Kaiser's base case except 17 δ P = - 6 11.588‰ instead of 17 δ P = -11.646‰as described in Section 3. The dashed green line 7 'approx' shows error when 'modified base case' values are used with the approximate 8 equation from Luz and Barkan (2000) (Eqn.5) and 17 Δ # λ = 0.5179() .The solid green line

Fig. 1 .
Fig. 1.Relative deviation of g from the "corrected base case" as calculated using the equation proposed by Kaiser.All values are the same as Kaiser's base case except 17 δ P = −11.588‰ instead of 17 δ P = −11.646‰ as described in Sect.3. The dashed green line "approx" shows error when "modified base case" values are used with the approximate equation from Luz and Barkan (2000) (Eq.5) and 17 ∆ # (λ = 0.5179).The solid green line 'iter' shows error due to using the corrected "base case" values ( 17 δ P = −11.588‰ , 18 ε R = −20 ‰ and λ = 0.5179) with the iterative method from Hendricks et al. (2004).Red and black lines show deviation from base case using the parameters and approaches employed in previous studies (see Table 3 in Kaiser, 2011 for details).They are calculated from the same values as used by Kaiser, except now compared against the "corrected base case" Within typical oceanic conditions ( −0.1 < f < 0.4 and 0.01 < g < 1), the methods generally agree with ±20 %.The following abbreviations are used to refer to previous studies: (H04 = Hendricks et al., 2004; JQ05, JQ10 = Juranek and Quay, 2005, 2010; LB00 = Luz and Barkan, 2005; R07 = Reuer et al., 2007; S05 = Sarma et al., 2005).
, * δ S0 is much closer to 0 ‰ (with air as the standard) than to * δ VSMOW .Inferring 17 ∆ P from an observed 17 ∆ S0 involves extrapolating across a large difference in 18 δ and thus large error can be introduced if an incorrect mass dependent slope is used .(Luzand Barkan, 2005) causing 17 ∆ P and 17 ∆ S0 to differ significantly unless an appropriate "tuned" definition is used.Angert et al. (2003) demonstrated that 17 ∆ P equals 17 ∆ S0 when the following definition is used 17 and Kaiser's equation use 17 δ P and 18 δ P .To consistently compare the skill of such equations relative to each other, Eq. (4) and λ BSS must be used to relate 17 δ P to 17 ∆ BSS .However for the default case, Kaiser calculates values for 17 δ P = −11.646‰ and 18 δ P = −22.835‰ (Kaiser Table 2) by applying the equation for 17 ∆ # (Eq.2) rather than 17 ∆ BSS (Eq.4), effectively underestimating the 17O excess of photosynthetically produced oxygen.The implied 17 ∆ BSS from Kaiser's "base case" scenario using Eq.(4) is 191 ppm rather than 249 ppm.† (κ = 0.5179) = 238 ppm rather than 180 ppm as reported byKaiser.