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

Abstract

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.

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“…In Cox et al (2015), we demonstrated that the time-averaged GPP can be estimated from high-frequency in situ O 2 series as…”

“…Finally, the evolution of GPP over a day is approximated by a truncated sinusoid. In Cox et al (2015) we assessed these assumptions and concluded that they are valid in a wide range of systems. In tidal systems the performance of the Fourier method was lowest, although Eq.…”

“…The second describes a typical riverine or estuarine situation, characterized by substantial horizontal gradients in the O 2 concentration. A full description of these models is found in Cox et al (2015).…”

“…This results in the so-called diel oxygen method, or the Odum method: GPP is estimated from the observed rate of change of oxygen during daylight hours, while adding the rate of community respiration determined at night (Howarth and Michaels, 2000). Recently we proposed a different approach, based on a description of O 2 dynamics in the frequency domain (Cox et al, 2015). Our analysis resulted in the Fourier method, which estimates time-averaged GPP directly from the diel amplitude of O 2 time series.…”

“…By focussing specifically on the diel harmonic in O 2 time series, frequency domain methods partly circumvent this challenge. As such the Fourier method extends the applicability of in situ oxygen methods to aquatic systems with a strong imprint of transport processes (Cox et al, 2015). The central idea behind the analysis is that primary production is the dominant process that induces a 24 h periodicity in the oxygen concentration, while other processes have their imprint at other frequencies.…”