Statistical properties and time-frequency analysis of temperature, salinity and turbidity measured by the MAREL Carnot station in the coastal waters of Boulogne-sur-Mer (France)

Abstract

In marine sciences, many fields display high variability over a large range of spatial and temporal scales, from seconds to thousands of years. The longer recorded time series, with an increasing sampling frequency, in this field are often nonlinear, nonstationary, multiscale and noisy. Their analysis faces new challenges and thus requires the implementation of adequate and specific methods. The objective of this paper is to highlight time series analysis methods already applied in econometrics, signal processing, health, etc. to the environmental marine domain, assess advantages and inconvenients and compare classical techniques with more recent ones. Temperature, turbidity and salinity are important quantities for ecosystem studies. The authors here consider the fluctuations of sea level, salinity, turbidity and temperature recorded from the MAREL Carnot system of Boulogne-sur-Mer (France), which is a moored buoy equipped with physico-chemical measuring devices, working in continuous and autonomous conditions. In order to perform adequate statistical and spectral analyses, it is necessary to know the nature of the considered time series. For this purpose, the stationarity of the series and the occurrence of unit-root are addressed with the Augmented-Dickey Fuller tests. As an example, the harmonic analysis is not relevant for temperature, turbidity and salinity due to the nonstationary condition, except for the nearly stationary sea level datasets. In order to consider the dominant frequencies associated to the dynamics, the large number of data provided by the sensors should enable the estimation of Fourier spectral analysis. Different power spectra show a complex variability and reveal an influence of environmental factors such as tides. However, the previous classical spectral analysis, namely the Blackman-Tukey method, requires not only linear and stationary data but also evenly-spaced data. Interpolating the time series introduces numerous artifacts to the data. The Lomb-Scargle algorithm is adapted to unevenly-spaced data and is used as an alternative. The limits of the method are also set out. It was found that beyond 50% of missing measures, few significant frequencies are detected, several seasonalities are no more visible, and even a whole range of high frequency disappears progressively. Furthermore, two time-frequency decomposition methods, namely wavelets and Hilbert-Huang Transformation (HHT), are applied for the analysis of the entire dataset. Using the Continuous Wavelet Transform (CWT), some properties of the time series are determined. Then, the inertial wave and several low-frequency tidal waves are identified by the application of the Empirical Mode Decomposition (EMD). Finally, EMD based Time Dependent Intrinsic Correlation (TDIC) analysis is applied to consider the correlation between two nonstationary time series.

Multi-Scale Correlation between Soil Loss and Natural Rainfall on Sloping Farmland Using the Hilbert–Huang Transform in Southwestern China

“…The global correlation considers the average over time as defined in an integral sense based on the complete dataset [29]. However, in fact, correlations may show rich dynamics, and strong correlations can be quite local in the time domain [32]. Therefore, the classical cross-correlation, as applied to nonlinear and nonstationary time series, may ignore local correlations and distort the true correlation information between time series, consequently providing misleading interpretations [29,30,46].…”

“…TDIC was proposed by Chen et al (2010) [30] and can track the temporal evolution of the local correlation between two modes using adaptive sliding windows based on the EMD. Owing to these advantages, TDIC has been applied in many fields, such as marine science [13,31,32], hydrometeorology [6,18], and air pollution [29,33]. To the best of our knowledge, however, few studies have employed TDIC to investigate the correlations between soil loss, rainfall, and runoff.…”

Toward a European Coastal Observing Network to Provide Better Answers to Science and to Societal Challenges; The JERICO Research Infrastructure

“…JERICO-RI currently provides a network of multiplatform coastal observations (Charria et al, 2016;Berta et al, 2018;Heslop et al, 2019), which are being integrated into a System of Systems. Basic elements of the System are nationally funded observing platforms, e.g., FerryBoxes, fixed platforms e.g., moorings, pilings (Kbaier Ben Ismail et al, 2016), underwater gliders (Cotroneo et al, 2019), HF radars (Rubio et al, 2011(Rubio et al, , 2017Sciascia et al, 2018), profilers and vessels of opportunitye.g., fishing-boats (Aydogdu et al, 2016). Common scientifically sound best practices are adopted, as far as possible, including technologies used, deployment, maintenance, quality control and assessment of data, and delivery to European databases.…”

Progress in marine science supported by European joint coastal observation systems: The JERICO-RI research infrastructure

“…With benefit of technology developments and real-time data, scientists have to handle an increasing data flow, which is not appropriately addressed by the existing marine data systems. In order to step over this challenge, a specific data set was used for testing several methods of time series analysis (Kbaier et al, 2016).…”