Tune in on 11.57 µHz and listen to primary production

Abstract. In this paper we present an elegant approach to reconstruct slowly varying gross primary production (GPP) as a function of time, based on O₂ time series. The approach, called complex demodulation, is based on a direct analogy with amplitude-modulated (AM) radio signals. The O₂ concentrations oscillating at the diel frequency (or 11.57 µHz) can be seen as a carrier wave, while the time variation in the amplitude of this carrier wave is related to the time-varying GPP. The relation follows from an analysis in the frequency domain of the governing equations of O₂ dynamics. After the theoretical derivation, we assess the performance of the approach by applying it to three artificial O₂ time series, generated with models representative of a well-mixed vertical water column, a river and an estuary. These models are forced with hourly observed incident irradiance, resulting in a variability of GPP on scales from hours to months. The dynamic build-up of algal biomass further increases the seasonality. Complex demodulation allows for reconstruction, with great precision, of time-varying GPP of the vertical water column and the river model. Surprisingly, it is possible to derive daily averaged GPP – complex demodulation thus reconstructs the amplitude of every single diel cycle. Also, in estuaries time-varying GPP can be reconstructed to a great extent. But there, the influence of the tides prevent achieving the same temporal resolution. In particular, the combination of horizontal O₂ gradients with quasi-diurnal harmonics in the tides interferes with the complex demodulation procedure and introduces spurious amplitude variation that can not be attributed to GPP. We demonstrate that these spurious effects also occur in real-world time series (Hörnum Tief, Germany). The spurious effects due to K1 and P1 quasi-diurnals can not be distinguished from GPP. However, the spurious fluctuations introduced by O1 and Q1 can be removed to a large extent by increasing the averaging time to 15 days. As such, we demonstrate that a good estimate of the running 15-day average of GPP can be obtained in tidal systems. Apart from the direct merits of estimating GPP from O₂ time series, the analysis in the frequency domain enhances our insights into O₂ dynamics in tidal systems in general, and into the performance of O₂ methods to estimate GPP in particular.