Tune in on 11.57 µHz and listen to primary production

Abstract

Abstract. In this paper we present an elegant approach to reconstruct slowly varying gross primary production (GPP) as a function of time, based on O 2 time series. The approach, called complex demodulation, is based on a direct analogy with amplitude-modulated (AM) radio signals. The O 2 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 timevarying GPP. The relation follows from an analysis in the frequency domain of the governing equations of O 2 dynamics. After the theoretical derivation, we assess the performance of the approach by applying it to three artificial O 2 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 O 2 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 O 2 time series, the analysis in the frequency domain enhances our insights into O 2 dynamics in tidal systems in general, and into the performance of O 2 methods to estimate GPP in particular.

Seasonal Dynamics of Primary Production in the Southeastern Bering Sea Assessed Using Continuous Temporal and Vertical Dissolved Oxygen and Chlorophyll‐a Measurements

“…For a full explanation of the method see Cox et al (2015). Implementation was done using the r-package "GPPfourier" (Cox, 2017) on the hourly O 2 data, and using a complex demodulation smoothing technique which lowers the influence of short-term physical processes on the O 2 concentration time series (Cox et al, 2017). Uncertainties of the GPP Fourier estimates were calculated using a Monte Carlo simulation approach that included independent random noise terms for O 2 vertical gradients and within-day variation of community respiration, sensor correction, air-sea flux, and turbulence (Figure S2 in Supporting Information S1); see Supporting Information S1 for full details.…”