Biogeosciences Comment on : “ Technical note : Consistent calculation of aquatic gross production from oxygen triple isotope measurements ” by Kaiser ( 2011 )

Kaiser (2011) has introduced an improved method for calculating gross productivity from the triple isotopic composition of dissolved oxygen in aquatic systems. His equation avoids approximations of previous methodologies, and also accounts for additional physical processes such as kinetic fractionation during invasion and evasion at the airsea interface. However, when comparing his new approach to previous methods, Kaiser inconsistently defines the biological end-member with the result of overestimating the degree to which the various approaches of previous studies diverge. In particular, for his base case, Kaiser assigns a 17O excess to the product of photosynthesis ( δP) that is too low, resulting in his result being∼30 % too high when compared to previous equations. When this is corrected, I find that Kaiser’s equations are consistent with all previous study methodologies within about ±20 % for realistic conditions of metabolic balance ( f ) and gross productivity ( g). A methodological bias of±20 % is of similar magnitude to current uncertainty in the wind-speed dependence of the air-sea gas transfer velocity, k, which directly impacts calculated gross productivity rates as well. While previous results could and should be revisited and corrected using the proposed improved equations, the magnitude of such corrections may be much less than implied by Kaiser.


Introduction
In the manuscript "Consistent calculation of aquatic gross production from oxygen triple isotope measurements" Kaiser derives exact equations for calculating gross oxygen pro-Correspondence to: D. P. Nicholson (dnicholson@whoi.edu)duction (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 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 † 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 endmember 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 D. P. Nicholson: Comment on Kaiser (2011) 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). 17S0 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 17 S0 and not 17 P because the original experiment measured dissolved oxygen in an aquarium 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 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" 17 value would have been 58 ppm higher (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) is essential to the following discussion.Photosynthetic oxygen is produced from seawater with only a small fractionation (Eisenstadt et al., 2010) and thus has a 18 δ P much closer to that of VSMOW, than to air (Kaiser's base case is 18 δ P = −22.835‰, where air is the standard).Biological steady-state refers to the composition of dissolved 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 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), * 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 (Luz and 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 (see Appendix for derivation of Eqs. 4 and 5): The slope (λ BSS ) that satisfies the criteria that 17 BSS P = 17 BSS S0 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 well constrained (γ R − λ BSS = 2.5 × 10 −3 ± 2.5 × 10 −4 ).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 descriptive definition of the original approximate equation for calculating g (Luz and Barkan, 2000) can then be written It is important to note that 17 BSS is the appropriate photosynthetic end-member term, not 17 # P .

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) 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 17 O 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. .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 within ±20 %.The following abbreviations are used to refer to previous studies: Using Eqs. ( 4) and ( 5) instead with values of 17 BSS = 249 ppm, 18 δ P = −22.835‰, γ R = 0.5179 and 18 ε R = −20 ‰, I calculate 17 δ P = −11.588‰.Using 17 δ P = −11.588‰ in Eq. (1) yields 17 † (κ = 0.5179) = 238 ppm rather than 180 ppm as reported by Kaiser.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 Eq. ( 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 Fig. 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 −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, although not detailed in the publication, the relationship 17 α R = ( 18 α R ) λ was used (L.W. Juranek, personal communication, 2011), similarly to Hendricks et al. (2004) and Reuer 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).