Universal multifractal analysis as a tool to characterize multiscale intermittent patterns: example of phytoplankton distribution in turbulent coastal waters

A multifractal method of analysis, initially developed in the framework of turbulence and having had developments and applications in various geophysical domains (meteorology, hydrology, climate, remote sensing, environmental monitoring, seismicity, volcanology), has previously been demonstrated to be an efficient tool to analyse the intermittent fluctuations of physical or biological oceanographic data (Seuront et al., Geophys. Res. Lett., 23, 3591-3594, 1996 and Nonlin. Processes Geophys., 3, 236-246, 1996). Thus, the aim of this paper is, first, to present the conceptual bases of multifractals and more precisely a stochastic multifractal framework which among different advantages lead in a rather straightforward manner to universal multifractals. We emphasize that contrary to basic analysis techniques such as power spectral analysis, universal multifractals allow the description of the whole statistics of a given field with only three basic parameters. Second, we provide a comprehensive detailed description of the analysis techniques applied in such a framework to marine ecologists and oceanographers; and third, we illustrate their applicability to an original time series of biological and related physical parameters. Our illustrative analyses were based on a 48 h high-frequency time series of in vivo fluorescence (i.e. estimate of phytoplankton biomass), simultaneously recorded with temper- ature and salinity in the tidally mixed coastal waters of the Eastern English Channel. Phytoplankton biomass, which surprisingly exhibits three distinct scaling regimes (i.e. a physical-biological-physical transition), was demonstrated to exhibit a very specific heterogeneous distribution, in the framework of universal multifractals, over smaller (<10 m) and larger (>500 m) scales dominated by different turbulent processes as over intermediate scales (10-500 m) obviously dominated by biological processes.