Technical note: Consistent calculation of aquatic gross production from oxygen triple isotope measurements

Abstract. Oxygen triple isotope measurements can be used to calculate aquatic gross oxygen production rates. Past studies have emphasised the appropriate definition of the ¹⁷O excess and often used an approximation to derive production rates from the ¹⁷O excess. Here, I show that the calculation can be phrased more consistently and without any approximations using the relative ¹⁷O/¹⁶O and ¹⁸O/¹⁶O isotope ratio differences (delta values) directly. I call this the "dual delta method". The ¹⁷O excess is merely a mathematical construct and the derived production rate is independent of its definition, provided all calculations are performed with a consistent definition. I focus on the mixed layer, but also show how time series of triple isotope measurements below the mixed layer can be used to derive gross production.

In the calculation of mixed layer productivity, I explicitly include isotopic fractionation during gas invasion and evasion, which requires the oxygen supersaturation s to be measured as well. I also suggest how bubble injection could be considered in the same mathematical framework. I distinguish between concentration steady state and isotopic steady state and show that only the latter needs to be assumed in the calculation. It is even possible to derive an estimate of the net production rate in the mixed layer that is independent of the assumption of concentration steady state.

I review measurements of the parameters required for the calculation of gross production rates and show how their systematic uncertainties as well as the use of different published calculation methods can cause large variations in the production rates for the same underlying isotope ratios. In particular, the ¹⁷O excess of dissolved O₂ in equilibrium with atmospheric O₂ and the ¹⁷O excess of photosynthetic O₂ need to be re-measured. Because of these uncertainties, all calculation parameters should always be fully documented and the measured relative isotope ratio differences as well as the oxygen supersaturation should be permanently archived, so that improved measurements of the calculation parameters can be used to retrospectively improve production rates.