Exact evaluation of gross photosynthetic production from the oxygen triple-isotope composition of O₂: Implications for the net-to-gross primary production ratios

The oxygen triple-isotope composition of dissolved O₂ provides an integrative method to estimate the rates of Gross Photosynthetic Production (GPP) in the upper ocean, and combined with estimates of Net Community Production (NCP) yields an estimate of the net-to-gross (NCP/GPP) production ratios. However, derivations of GPP from oxygen triple-isotope measurements have involved some mathematical approximations. We derive an exact expression for calculating GPP, and show that small errors associated with approximations result in a relative error of up to ∼38% in GPP, and up to ∼50% in N/G. In open ocean regimes with low primary production, the observed magnitude of the error is comparable to the combined methodological uncertainties. In highly productive ecosystems, the error arising from approximations becomes significant. Using data collected on the Bering Sea shelf, we illustrate the differences in GPP estimates in both high and low productivity regimes that arise from exact and approximated formulations.