Relation between deep bioluminescence and oceanographic variables: A statistical analysis using time–frequency decompositions
Introduction
The sampling and the understanding of complex environmental systems aims to detect potential disturbances as a shift from the intrinsic variability of these systems. Marine systems are variable at all time and space scales (Hewitt et al., 2007), and their variability is still poorly understood because of sampling strategy, instrumentation and spatio-temporal heterogeneity challenges. In response to this lack of knowledge, there is a global effort to capitalize oceanographic data and costs for autonomous Eulerian or mobile infrastructures that enable detection of long-term environmental trends as well as special events or perturbations (Favali and Beranzoli, 2006). As an example, OceanSITES, and more generally the Global Ocean Observing System (GOOS), are the major science teams integrating a global network of more than 60 in situ observatories acquiring long-term and high-frequency time series over the world (Send and Lankhorst, 2011).
The ANTARES collaboration (Astronomy with a Neutrino Telescope and Abyss environmental RESearch) developed such an infrastructure, in the North-Western Mediterranean Sea (Fig. 1), at the end of 2007. This deep-sea-cabled observatory is part of global data networks, such as EMSO, KM3NeT, ESONET and EuroSITES. Initially, the ANTARES observatory was dedicated to the search for high-energy particles, such as neutrinos (Amram et al., 2000, Aguilar et al., 2007, Ageron et al., 2011). About 885 photomultiplier tubes (PMTs) are installed between 2000 and 2475 m depth for the purpose of particle physics. All the 12 ANTARES mooring lines are connected, via an electro-optical cable, to a shore station providing real-time acquisition. With the installation of a specific line, namely IL07 (Tamburini et al., 2013), this deep observatory gives the opportunity to record simultaneously high-frequency oceanographic data such as current speed, salinity and temperature (Fig. 2). The IL07 is also equipped with PMTs devoted to the recording of bioluminescence activity. These datasets provide an exceptional way to study the dynamics of the deep ecosystem in real-time and at high-frequency (Craig et al., 2009).
Recently, Tamburini et al. (2013) proposed a descriptive analysis of the ANTARES oceanographic time series gathering both physical and biological variables, with synchronous hydrological records from a surrounding station located in the Gulf of Lion. They highlighted a link between high bioluminescence activity and changes in the properties of deep water temperature and salinity. Such changes attributed to an open-sea convection event renew the deep waters (so-called newly formed deep water) by the fall of upper ocean layer through the water column (Tamburini et al., 2013, Marshall and Schott, 1999, Stabholz et al., 2013, Béthoux et al., 2002). Open-sea convections represent a major vector in fueling the deep-sea ecosystem with nutrients, carbon, oxygen and, potentially, organisms. This might induce higher bioluminescence emission. Indeed, the input of organic matter into the deep water has the potential to fuel the deepsea biological activity. Within this biological stimulation context, bioluminescent bacteria, which are not affected by mechanical stimulation and are able to glow continuously under specific conditions, might be affected by changes in environmental growth conditions. These organisms are potential contributors to high bioluminescence intensity. Moreover, bioluminescent organisms could also be advected from the surface to the deep-sea.
The present study attempts to understand the mechanisms inducing deep-sea bioluminescence activity using temperature, salinity, current speed and bioluminescence time series from the same ANTARES dataset of Tamburini et al. (2013). The search for characteristic scales in time and frequency in this high-frequency sampled dataset is achieved by using statistical methods from signal processing. Whereas most environmental data are non-stationary (Cazelles et al., 2008, Rao and Hsu, 2008, Ghorbani, 2013), most methods used in time-series analyses are based on stationarity assumptions, such as those used in the Fourier decomposition (Frazier, 1999). First, we propose the use of two complementary mathematical methods (Wavelet and Hilbert–Huang transformation) to deal with non-stationarity and to decompose each time series within time and frequency space. Second, we propose some tools to quantify and to illustrate links between bioluminescence time–frequency decomposition and other environmental variable time–frequency decompositions.
Section snippets
Dataset for the deep bioluminescence study
The ANTARES site is located 40 km off the French Mediterranean coast (42°48′N, 6°10′E) at a 2475 m depth (see Fig. 1). This work focuses on multivariate time series sampled from the beginning of 2009 until October 2010 for oceanographic variables such as salinity, potential temperature and current speed (cm ) (Fig. 2). Moreover, bioluminescence emission (kHz) was recorded in 2009 and 2010 from the IL07 instrumented line of the ANTARES telescope. The unit of bioluminescence activity (kHz)
Methods dealing with non-stationary time series
Most methods in time series analysis consist of an expansion of the studied signal into a linear combination of known basis functions. For the Fourier decomposition, the signal is expressed as a linear combination of trigonometric functions:This decomposition provides an analytical expression of the function with amplitude coefficients giving weight to angular frequencies . Both coefficients and are independent of time, providing a global decomposition of
Wavelet coherence
One of the key issue for the analysis of the ANTARES time series is to compare time–frequency decomposition spectra between variables. This point is well developed for the wavelet method using the cross-wavelet representation, which includes both coherence between coefficients of two different variables and phase delays (Torrence and Compo, 1998, Addison, 2010). We consider two time series X(t) and Y(t) and their wavelet transforms and , respectively. The coherence is a measure
Results and discussion for non-stationary time series
Fourier analysis relies on a global expansion of the signal, which can induce spurious harmonic components that cause energy spreading. This misinterpretation especially occurs when dealing with non-linear and non-stationary datasets as shown in Fig. 4A (see introduction of Huang et al. (1998) for more details) compared with the stationary signal decomposed in Fig. 4B. Unlike Fourier decomposition, the continuous wavelet transform and the HHT possess the ability to construct a time–frequency
Bioluminescence mechanically stimulated by current speed
The effects of current speed on bioluminescence activity have been well investigated in the literature (Cussatlegras and Le Gal, 2007, Cussatlegras and Le Gal, 2005, Fritz et al., 1990). This mechanical stimulation triggers a greater bioluminescent response, enhancing cell membrane excitation in fluid motion (Cussatlegras and Le Gal, 2007, Blaser et al., 2002). However, these studies are all based on dinoflagellates, organisms mainly living in the surface waters. As far as we know, few studies
Conclusion
There is a clear interest in recording long time series to understand intrinsic variations in an ecosystem. High-frequency sampling helps to detect characteristic scales within a signal. Few time–frequency decomposition methods are adapted to the analysis of non-stationary and non-linear signals and, consequently, to the detection of frequencies excited during unusual events. Both Huang–Hilbert and wavelet decomposition discriminate events due to newly formed deep water spreading and events
Acknowledgements
SM was granted a MERNT fellowship (Ministry of Education, Research and Technology, France). The authors thank the Collaboration of the ANTARES deep-sea observatory for providing time series data. The authors especially thank S. Escoffier, M. Garel and C. Curtil for their comments and their inputs to this work. The cross wavelet and wavelet coherence software were provided by A. Grinsted. This work was funded by the EC2CO BIOLUX program (CNRS).
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