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 ¹⁷&delta;_P and ¹⁸&delta;_P 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 (¹⁷&Delta;) and its simplicity compared to previous iterative calculation methods. Although he correctly points out that differences in the normalised gross production rate (<i>g</i>) 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 <i>g</i> 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&delta;_P and ¹⁸&delta;_P values. Since direct measurements of ¹⁷&delta;_P and ¹⁸&delta;_Pdo 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&delta;_P gives <i>g</i> values closer to previous studies. However, unlike Nicholson, we refrain from interpreting either reconstruction as a benchmark for the accuracy of <i>g</i>. 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 (¹⁷&delta;_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&delta;_VSMOW values. If scaled for differences in ¹⁸&delta;_VSMOW, they are actually in good agreement with the original data (Barkan and Luz, 2005) and support Kaiser's "base case" <i>g</i> values. The statement that Kaiser's <i>g</i> values are "30% too high" can therefore not be accepted, pending future work to reconcile different ¹⁷&delta;_VSMOW measurements. Nicholson also suggests that approximated calculations of gross production should be performed with a triple isotope excess defined as ¹⁷&Delta;^#&equiv; ln (1+¹⁷&delta;)–&lambda; ln(1+¹⁸&delta;), with &lambda; = &theta;_R = ln(1+¹⁷&varepsilon;_R ) / ln(1+¹⁸&varepsilon;_R). However, this only improves the approximation for certain ¹⁷&delta;_P and ¹⁸&delta;_P values, for certain net to gross production ratios (<i>f</i>) and for certain ratios of gross production to gross Air-O₂ invasion (<i>g</i>). In other cases, the approximated calculation based on ¹⁷&Delta;^&dagger; &equiv;¹⁷&delta; – &kappa; ¹⁸&delta; with &kappa; = &gamma;_R = ¹⁷&varepsilon;_R/¹⁸&varepsilon;_R (Kaiser, 2011a) gives more accurate results.