Relation between deep bioluminescence and oceanographic variables: A statistical analysis using time–frequency decompositions

We consider the statistical analysis of a 1.7-year high-frequency sampled time series, between 2009 and 2010, recorded at the ANTARES observatory in the deep NW Mediterranean Sea (2475 m depth). The objective was to estimate relationships between bioluminescence and environmental time series (temperature, salinity and current speed). As this entire dataset is characterized by non-linearity and non-stationarity, two time–frequency decomposition methods (wavelet and Hilbert–Huang) were used. These mathematical methods are dedicated to the analysis of a signal at various time and frequencies scales. This work propose some statistical tools dedicated to the study of relationships between two time series. Our study highlights three events of high bioluminescence activity in March 2009, December 2009 and March 2010. We demonstrate that the two events occurring in March 2009 and 2010 are correlated to the arrival of newly formed deep water masses at frequencies of approximately 4.8 × 10 - 7 (period of 24.1 days). In contrast, the event in December 2009 is only correlated with current speed at frequencies of approximately 1.9 × 10 - 6 (period of 6.0 days). The use of both wavelet and Hilbert–Huang transformations has proven to be successful for the analysis of multivariate time series. These methods are well-suited in a context of the increasing number of long time series recorded in oceanography.