Multiscaling statistical procedures for the exploration of biophysical couplings in intermittent turbulence. Part I. Theory

Intermittency, a fundamental property of high Reynolds number turbulence, has seldom been described in ocean sciences. As a consequence, and despite several recent studies describing the intermittent distributions of temperature, salinity, nutrient concentrations, phytoplankton biomass and zooplankton abundance, the implications of intermittency on (i) the distribution of purely passive and biologically active scalars (e.g., phytoplankton cells) and (ii) biophysical couplings in the ocean are still poorly understood. We thus present both terminological and phenomenological clarification of the intermittency concept in turbulence studies. Next, univariate multifractal procedures investigating the properties of intermittent stochastic processes are presented. They characterize the statistics of intermittent variables using a set of three basic parameters in the multifractal framework, whatever the scales and the intensity. The multifractal formalism is then extended to more than one variable to investigate the degree of dependence among random fields by investigating the nature of their joint distribution. The main advantages of these unusual formalisms are that they make no assumptions about the spectrum or the distribution of data sets, fully take into account the intrinsic multiscaling properties of the data, and more generally explore qualitatively and quantitatively the correlations of large and small fluctuations of processes.