Estimating primary production from oxygen time series: A novel approach in the frequency domain

Based on an analysis in the frequency domain of the governing equation of oxygen dynamics in aquatic systems, we derive a new method for estimating gross primary production (GPP) from oxygen time series. The central result of this article is a relation between time averaged GPP and the amplitude of the diel harmonic in an oxygen time series. We call this relation the Fourier method for estimating GPP. To assess the performance and accuracy of the method, we generate synthetic oxygen time series with a series of gradually more complex models, and compare the result with simulated GPP. We demonstrate that the method is applicable in systems with a range of rates of mixing, air–water exchange and primary production. We also apply the new method to oxygen time series from the Scheldt estuary (Belgium) and compare it with 14C-based GPP measurements. We demonstrate the Fourier method is particularly suited for estimating GPP in estuarine and coastal systems where tidal advection has a large imprint in observed oxygen concentrations. As such it enlarges the number of systems where GPP can be estimated from in situ oxygen concentrations. By shifting the focus to the frequency domain, we also gain some useful insights on the effect of observational error and of stochastic drivers of oxygen dynamics on metabolic estimates derived from oxygen time series