Biogeosciences Corrigendum to “ Technical note : Consistent calculation of aquatic gross production from oxygen triple isotope measurements ” published in Biogeosciences , 8 , 1793 – 1811 , 2011

In Fig. 1, 1S was calculated with λ = ln(1 + eR)/ ln(1 + eR) = 0.5154 instead of λ = γR = 0.5179, as intended. A correct version of Fig. 1 is shown below. The sentence “In particular, 1S is only equal to 1P for f = 1.” does not apply for this choice of λ value. On p. 1801, the steady-state δS value of oxygen produced by Acropora was stated as −9.66 ‰, but should be −9.16 ‰. The stated 1S and 1P values of 224 ppm and 175 ppm, respectively, are correct. The kinetic isotope fractionation during gas exchange was assumed to be eI=−2.8 ‰ for O2 invasion. However, this value actually applies to kinetic isotope fractionation during O2 evasion (eE) as per Eq. (8) in Knox et al. (1992). The same error appears in Luz et al. (2002). Consequently, eE=−2.8 ‰ and eI= (1 + eE) (1 + δsat)−1=−2.1 ‰ for the base case. eE and eE are calculated as before. Updated values are show in italics in Tables 2 and 3 below. This correction changes the calculated g values by 1.4 ‰ or less and is therefore not noticeable in the updated versions of Figs. 2 and 3 below. In Table 2 of Juranek and Quay (2010) the 17O/16O fractionation factor for respiration is listed as 0.9896, which is equivalent to eR=−10.4 ‰. I previously assumed that this was calculated as eR= 0.518 eR= 0.518 (−20 ‰)=−10.370 ‰. However, it was actually calculated as eR= (1 + eR)−1=−10.410 ‰ (L. Juranek, personal communication, 2011). Both values are indistinguishable from −10.4 ‰ if rounded to 0.1 ‰. The 18O/16O fractionation factor listed as 0.979 in Table 2 of Juranek and Quay (2010) is incorrect because their calculations actually used a value of 0.980, which is identical to the value of

The kinetic isotope fractionation during gas exchange was assumed to be 18 ε I = −2.8‰ for O 2 invasion.However, this value actually applies to kinetic isotope fractionation during O 2 evasion ( 18 ε E ) as per Eq. ( 8) in Knox et al. (1992).
The same error appears in Luz et al. (2002).Consequently, 18 ε E = −2.8‰ and 18 ε I = (1 + 18 ε E ) (1 + 18 δ sat ) −1 = −2.1 ‰ for the base case. 17ε E and 17 ε E are calculated as before.Updated values are show in italics in Tables 2 and 3 below.This correction changes the calculated g values by 1.4 ‰ or less and is therefore not noticeable in the updated versions of Figs. 2 and 3 below.
In Table 2 of 2010) is incorrect because their calculations actually used a value of 0.980, which is identical to the value of Correspondence to: J. Kaiser (j.kaiser@uea.ac.uk) 18 ε R = −20 ‰ I attributed to the paper.The corrected 17 ε R value and the resulting γ R value of 0.5205 are show in italics in Table 3 below.The resulting changes in g are reflected by the updated version of Fig. 3 below.The second half of the sentence "A better agreement with the base case is found for the iterative calculations "Hendricks et al. ( 2004)", "Reuer et al. ( 2007)" and "Juranek and Quay (2010)", with the latter calculation method giving the best agreement, mainly because the chosen γ R and λ values of 0.518 are closest to the base case value 0.5179" on p. 1807 no longer applies.

Fig. 2 .
Fig. 2.Relative deviation of g from the base case (see Table2) for different parameters in Eq. (7).Panel (a) corresponds to g = 0.4 and a range of f from −1.0 to +1.0 (negative values correspond to net heterotrophy, positive value to net autotrophy).Panel (b) corresponds to f = 0.1 and range of g from 0.01 to 10 (logarithmic axis).

Fig. 3 .
Fig. 3. Relative deviation of g for different calculation methods (Table3).Panel (a) corresponds to g = 0.4 and a range of f from −1.0 to +1.0 (negative values correspond to net heterotrophy, positive value to net autotrophy).Panel (b) corresponds to f = 0.1 and range of g from 0.01 to 10 (logarithmic axis).Black curves correspond to calculation methods based on Eq. (1).Red curves correspond to iterative methods.

Table 2 of
Juranek and  Quay (

Table 2 .
Input parameters used as base case in the calculation of g (Sect.6.1) and their uncertainties (Sect.5).All δ values are relative to Air-O 2 .The 17 values are defined as17= 17 δ − 0.5179 18 δ (cf.Eq.8) and expressed relative to Air-O 2 .However, they are not needed for the calculation according to Eq. (48) and are listed for reference only.All values have been adjusted to the same decimal for clarity, irrespective of their actual uncertainty.

Table 3 .
Comparison between different calculation methods for g.A dash (-) or values in brackets mean that the corresponding parameters are not used in the calculation.The "used" 17 O excess values are used by the different calculation methods.The "implied" 17 O excess values are calculated using the definitions adopted by the different calculation methods, based on the listed 17 δ P , 18 δ P , 17 δ sat and 18 δ sat values.Where the calculation method does not require these δ values, the values for the "best case" in Table2have been used for the "implied" 17 O excess.