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Describing Intermittent Processes in the Ocean: Univariate and Bivariate Multiscaling Procedures

Abstract : Univariate and bivariate procedures for investigating the properties of single and joint intermittent stochastic processes are presented. They allow the characterization of all 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 examining the nature of their joint distribution. These formalisms, which do not require any assumption about the spectrum or the probability distribution of the data sets under consideration, are finally illustrated, first, by studying the properties of turbulent velocity fluctuations recorded in a laboratory grid-generated turbulence experiment and in the ocean using a high-frequency free-fall profiler. Second, we investigate the distributions of temperature, salinity and in vivo fluorescence (a proxy of phytoplankton biomass) time series recorded in the coastal waters of the Southern Bight of the North Sea, as well as their potential correlation.